YES (VAR V1 V2 N M X1 X2 X) (RULES U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X ) Proving termination of rewriting for PEANO_complete_noand_Z: -> Dependency pairs: nF_U11(tt,V1,V2) -> nF_U12(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_U11(tt,V1,V2) -> nF_isNatKind(activate(V1)) nF_U11(tt,V1,V2) -> nF_activate(V1) nF_U11(tt,V1,V2) -> nF_activate(V2) nF_U12(tt,V1,V2) -> nF_U13(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U12(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U12(tt,V1,V2) -> nF_activate(V2) nF_U12(tt,V1,V2) -> nF_activate(V1) nF_U13(tt,V1,V2) -> nF_U14(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U13(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U13(tt,V1,V2) -> nF_activate(V2) nF_U13(tt,V1,V2) -> nF_activate(V1) nF_U14(tt,V1,V2) -> nF_U15(isNat(activate(V1)),activate(V2)) nF_U14(tt,V1,V2) -> nF_isNat(activate(V1)) nF_U14(tt,V1,V2) -> nF_activate(V1) nF_U14(tt,V1,V2) -> nF_activate(V2) nF_U15(tt,V2) -> nF_U16(isNat(activate(V2))) nF_U15(tt,V2) -> nF_isNat(activate(V2)) nF_U15(tt,V2) -> nF_activate(V2) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_U21(tt,V1) -> nF_isNatKind(activate(V1)) nF_U21(tt,V1) -> nF_activate(V1) nF_U22(tt,V1) -> nF_U23(isNat(activate(V1))) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U22(tt,V1) -> nF_activate(V1) nF_U31(tt,V2) -> nF_U32(isNatKind(activate(V2))) nF_U31(tt,V2) -> nF_isNatKind(activate(V2)) nF_U31(tt,V2) -> nF_activate(V2) nF_U51(tt,N) -> nF_U52(isNatKind(activate(N)),activate(N)) nF_U51(tt,N) -> nF_isNatKind(activate(N)) nF_U51(tt,N) -> nF_activate(N) nF_U52(tt,N) -> nF_activate(N) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_U61(tt,M,N) -> nF_isNatKind(activate(M)) nF_U61(tt,M,N) -> nF_activate(M) nF_U61(tt,M,N) -> nF_activate(N) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_isNat(activate(N)) nF_U62(tt,M,N) -> nF_activate(N) nF_U62(tt,M,N) -> nF_activate(M) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U63(tt,M,N) -> nF_isNatKind(activate(N)) nF_U63(tt,M,N) -> nF_activate(N) nF_U63(tt,M,N) -> nF_activate(M) nF_U64(tt,M,N) -> nF_s(plus(activate(N),activate(M))) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U64(tt,M,N) -> nF_activate(N) nF_U64(tt,M,N) -> nF_activate(M) nF_isNat(n__plus(V1,V2)) -> nF_U11(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_isNat(n__plus(V1,V2)) -> nF_activate(V1) nF_isNat(n__plus(V1,V2)) -> nF_activate(V2) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_isNat(n__s(V1)) -> nF_activate(V1) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_isNatKind(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__plus(V1,V2)) -> nF_activate(V1) nF_isNatKind(n__plus(V1,V2)) -> nF_activate(V2) nF_isNatKind(n__s(V1)) -> nF_U41(isNatKind(activate(V1))) nF_isNatKind(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__s(V1)) -> nF_activate(V1) nF_plus(N,0) -> nF_U51(isNat(N),N) nF_plus(N,0) -> nF_isNat(N) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_plus(N,s(M)) -> nF_isNat(M) nF_activate(n__0) -> nF_0 nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_activate(n__s(X)) -> nF_s(X) -> Proof of termination for PEANO_complete_noand_Z_1: -> -> Dependency pairs in cycle: nF_U11(tt,V1,V2) -> nF_U12(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_U11(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_plus(N,s(M)) -> nF_isNat(M) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_isNatKind(n__s(V1)) -> nF_activate(V1) nF_isNatKind(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_isNat(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_plus(N,0) -> nF_isNat(N) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_U62(tt,M,N) -> nF_isNat(activate(N)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U15(tt,V2) -> nF_isNat(activate(V2)) nF_U14(tt,V1,V2) -> nF_U15(isNat(activate(V1)),activate(V2)) nF_U13(tt,V1,V2) -> nF_U14(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U12(tt,V1,V2) -> nF_U13(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U14(tt,V1,V2) -> nF_isNat(activate(V1)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_U63(tt,M,N) -> nF_isNatKind(activate(N)) nF_U61(tt,M,N) -> nF_isNatKind(activate(M)) nF_U51(tt,N) -> nF_isNatKind(activate(N)) nF_plus(N,0) -> nF_U51(isNat(N),N) nF_U31(tt,V2) -> nF_isNatKind(activate(V2)) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_U21(tt,V1) -> nF_isNatKind(activate(V1)) nF_U13(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U12(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U11(tt,V1,V2) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__plus(V1,V2)) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_activate(V1) nF_isNat(n__s(V1)) -> nF_activate(V1) nF_isNat(n__plus(V1,V2)) -> nF_activate(V2) nF_isNat(n__plus(V1,V2)) -> nF_activate(V1) nF_U64(tt,M,N) -> nF_activate(M) nF_U64(tt,M,N) -> nF_activate(N) nF_U63(tt,M,N) -> nF_activate(M) nF_U63(tt,M,N) -> nF_activate(N) nF_U62(tt,M,N) -> nF_activate(M) nF_U62(tt,M,N) -> nF_activate(N) nF_U61(tt,M,N) -> nF_activate(N) nF_U61(tt,M,N) -> nF_activate(M) nF_U52(tt,N) -> nF_activate(N) nF_U51(tt,N) -> nF_U52(isNatKind(activate(N)),activate(N)) nF_U51(tt,N) -> nF_activate(N) nF_U31(tt,V2) -> nF_activate(V2) nF_U22(tt,V1) -> nF_activate(V1) nF_U21(tt,V1) -> nF_activate(V1) nF_U15(tt,V2) -> nF_activate(V2) nF_U14(tt,V1,V2) -> nF_activate(V2) nF_U14(tt,V1,V2) -> nF_activate(V1) nF_U13(tt,V1,V2) -> nF_activate(V1) nF_U13(tt,V1,V2) -> nF_activate(V2) nF_U12(tt,V1,V2) -> nF_activate(V1) nF_U12(tt,V1,V2) -> nF_activate(V2) nF_U11(tt,V1,V2) -> nF_activate(V2) nF_U11(tt,V1,V2) -> nF_activate(V1) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = X1 [tt] = 1 [U12](X1,X2,X3) = X1 [isNatKind](X) = 1 [activate](X) = X [U13](X1,X2,X3) = 1 [U14](X1,X2,X3) = X1 [U15](X1,X2) = X1 [isNat](X) = 1 [U16](X) = 1 [U21](X1,X2) = 1 [U22](X1,X2) = X1 [U23](X) = 1 [U31](X1,X2) = X1 [U32](X) = 1 [U41](X) = 1 [U51](X1,X2) = X2 + 1 [U52](X1,X2) = X1 + X2 [U61](X1,X2,X3) = X2 + X3 + 1 [U62](X1,X2,X3) = X1 + X2 + X3 [U63](X1,X2,X3) = X1 + X2 + X3 [U64](X1,X2,X3) = X1 + X2 + X3 [s](X) = X + 1 [plus](X1,X2) = X1 + X2 [n__0] = 1 [n__plus](X1,X2) = X1 + X2 [n__s](X) = X + 1 [0] = 1 [nF_U11](X1,X2,X3) = X1 + X2 + X3 [nF_isNat](X) = X + 1 [nF_plus](X1,X2) = X1 + X2 [nF_activate](X) = X [nF_isNatKind](X) = X [nF_U64](X1,X2,X3) = X1 + X2 + X3 [nF_U63](X1,X2,X3) = X2 + X3 + 1 [nF_U62](X1,X2,X3) = X1 + X2 + X3 [nF_U61](X1,X2,X3) = X2 + X3 + 1 [nF_U22](X1,X2) = X1 + X2 [nF_U21](X1,X2) = X1 + X2 [nF_U15](X1,X2) = X1 + X2 [nF_U14](X1,X2,X3) = X2 + X3 + 1 [nF_U13](X1,X2,X3) = X1 + X2 + X3 [nF_U12](X1,X2,X3) = X1 + X2 + X3 [nF_U51](X1,X2) = X1 + X2 [nF_U31](X1,X2) = X2 [nF_U52](X1,X2) = X1 + X2 TIME: 0.206707 -> -> Dependency pairs in cycle: nF_U11(tt,V1,V2) -> nF_U12(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_U11(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_U14(tt,V1,V2) -> nF_isNat(activate(V1)) nF_U13(tt,V1,V2) -> nF_U14(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U12(tt,V1,V2) -> nF_U13(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U15(tt,V2) -> nF_isNat(activate(V2)) nF_U14(tt,V1,V2) -> nF_U15(isNat(activate(V1)),activate(V2)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U62(tt,M,N) -> nF_isNat(activate(N)) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_U11(tt,V1,V2) -> nF_activate(V2) nF_U12(tt,V1,V2) -> nF_activate(V2) nF_U12(tt,V1,V2) -> nF_activate(V1) nF_U13(tt,V1,V2) -> nF_activate(V2) nF_U13(tt,V1,V2) -> nF_activate(V1) nF_U14(tt,V1,V2) -> nF_activate(V1) nF_U14(tt,V1,V2) -> nF_activate(V2) nF_U15(tt,V2) -> nF_activate(V2) nF_U21(tt,V1) -> nF_activate(V1) nF_U22(tt,V1) -> nF_activate(V1) nF_U31(tt,V2) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_U11(tt,V1,V2) -> nF_isNatKind(activate(V1)) nF_U12(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U13(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U21(tt,V1) -> nF_isNatKind(activate(V1)) nF_U31(tt,V2) -> nF_isNatKind(activate(V2)) nF_U51(tt,N) -> nF_isNatKind(activate(N)) nF_plus(N,0) -> nF_U51(isNat(N),N) nF_U61(tt,M,N) -> nF_isNatKind(activate(M)) nF_U63(tt,M,N) -> nF_isNatKind(activate(N)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_plus(N,0) -> nF_isNat(N) nF_plus(N,s(M)) -> nF_isNat(M) nF_isNat(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_U51(tt,N) -> nF_activate(N) nF_U52(tt,N) -> nF_activate(N) nF_U51(tt,N) -> nF_U52(isNatKind(activate(N)),activate(N)) nF_U61(tt,M,N) -> nF_activate(M) nF_U61(tt,M,N) -> nF_activate(N) nF_U62(tt,M,N) -> nF_activate(N) nF_U62(tt,M,N) -> nF_activate(M) nF_U63(tt,M,N) -> nF_activate(N) nF_U63(tt,M,N) -> nF_activate(M) nF_U64(tt,M,N) -> nF_activate(N) nF_U64(tt,M,N) -> nF_activate(M) nF_isNat(n__plus(V1,V2)) -> nF_activate(V1) nF_isNat(n__plus(V1,V2)) -> nF_activate(V2) nF_isNat(n__s(V1)) -> nF_activate(V1) nF_isNatKind(n__plus(V1,V2)) -> nF_activate(V1) nF_isNatKind(n__plus(V1,V2)) -> nF_activate(V2) nF_isNatKind(n__s(V1)) -> nF_activate(V1) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = X1 [tt] = 1 [U12](X1,X2,X3) = 1 [isNatKind](X) = 1 [activate](X) = X [U13](X1,X2,X3) = X1 [U14](X1,X2,X3) = X1 [U15](X1,X2) = X1 [isNat](X) = 1 [U16](X) = 1 [U21](X1,X2) = 1 [U22](X1,X2) = X1 [U23](X) = 1 [U31](X1,X2) = X1 [U32](X) = 1 [U41](X) = 1 [U51](X1,X2) = X2 + 1 [U52](X1,X2) = X1 + X2 [U61](X1,X2,X3) = X1 + X2 + X3 + 1 [U62](X1,X2,X3) = X1 + X2 + X3 + 1 [U63](X1,X2,X3) = X1 + X2 + X3 + 1 [U64](X1,X2,X3) = X1 + X2 + X3 + 1 [s](X) = X + 1 [plus](X1,X2) = X1 + X2 + 1 [n__0] = 0 [n__plus](X1,X2) = X1 + X2 + 1 [n__s](X) = X + 1 [0] = 0 [nF_U11](X1,X2,X3) = X2 + X3 + 1 [nF_isNat](X) = X [nF_U14](X1,X2,X3) = X1 + X2 + X3 [nF_U13](X1,X2,X3) = X2 + X3 + 1 [nF_U12](X1,X2,X3) = X1 + X2 + X3 [nF_U15](X1,X2) = X1 + X2 [nF_U22](X1,X2) = X1 + X2 [nF_U21](X1,X2) = X2 + 1 [nF_U62](X1,X2,X3) = X1 + X2 + X3 [nF_U61](X1,X2,X3) = X2 + X3 + 1 [nF_plus](X1,X2) = X1 + X2 [nF_U64](X1,X2,X3) = X1 + X2 + X3 [nF_U63](X1,X2,X3) = X2 + X3 + 1 [nF_activate](X) = X [nF_U31](X1,X2) = X1 + X2 [nF_isNatKind](X) = X [nF_U51](X1,X2) = X2 [nF_U52](X1,X2) = X2 TIME: 0.21935099999999996 -> -> Dependency pairs in cycle: nF_U11(tt,V1,V2) -> nF_U12(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_U11(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_plus(N,s(M)) -> nF_isNat(M) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_isNatKind(n__plus(V1,V2)) -> nF_activate(V2) nF_isNatKind(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_isNat(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_plus(N,0) -> nF_isNat(N) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_U62(tt,M,N) -> nF_isNat(activate(N)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U15(tt,V2) -> nF_isNat(activate(V2)) nF_U14(tt,V1,V2) -> nF_U15(isNat(activate(V1)),activate(V2)) nF_U13(tt,V1,V2) -> nF_U14(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U12(tt,V1,V2) -> nF_U13(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U14(tt,V1,V2) -> nF_isNat(activate(V1)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_U63(tt,M,N) -> nF_isNatKind(activate(N)) nF_U61(tt,M,N) -> nF_isNatKind(activate(M)) nF_U51(tt,N) -> nF_isNatKind(activate(N)) nF_plus(N,0) -> nF_U51(isNat(N),N) nF_U31(tt,V2) -> nF_isNatKind(activate(V2)) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_U21(tt,V1) -> nF_isNatKind(activate(V1)) nF_U13(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U12(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U11(tt,V1,V2) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__plus(V1,V2)) -> nF_activate(V1) nF_isNat(n__s(V1)) -> nF_activate(V1) nF_isNat(n__plus(V1,V2)) -> nF_activate(V2) nF_isNat(n__plus(V1,V2)) -> nF_activate(V1) nF_U64(tt,M,N) -> nF_activate(M) nF_U64(tt,M,N) -> nF_activate(N) nF_U63(tt,M,N) -> nF_activate(M) nF_U63(tt,M,N) -> nF_activate(N) nF_U62(tt,M,N) -> nF_activate(M) nF_U62(tt,M,N) -> nF_activate(N) nF_U61(tt,M,N) -> nF_activate(N) nF_U61(tt,M,N) -> nF_activate(M) nF_U52(tt,N) -> nF_activate(N) nF_U51(tt,N) -> nF_U52(isNatKind(activate(N)),activate(N)) nF_U51(tt,N) -> nF_activate(N) nF_U31(tt,V2) -> nF_activate(V2) nF_U22(tt,V1) -> nF_activate(V1) nF_U21(tt,V1) -> nF_activate(V1) nF_U15(tt,V2) -> nF_activate(V2) nF_U14(tt,V1,V2) -> nF_activate(V2) nF_U14(tt,V1,V2) -> nF_activate(V1) nF_U13(tt,V1,V2) -> nF_activate(V1) nF_U13(tt,V1,V2) -> nF_activate(V2) nF_U12(tt,V1,V2) -> nF_activate(V1) nF_U12(tt,V1,V2) -> nF_activate(V2) nF_U11(tt,V1,V2) -> nF_activate(V2) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = X1 [tt] = 1 [U12](X1,X2,X3) = 1 [isNatKind](X) = 1 [activate](X) = X [U13](X1,X2,X3) = X1 [U14](X1,X2,X3) = X1 [U15](X1,X2) = X1 [isNat](X) = 1 [U16](X) = 1 [U21](X1,X2) = 1 [U22](X1,X2) = X1 [U23](X) = 1 [U31](X1,X2) = X1 [U32](X) = 1 [U41](X) = 1 [U51](X1,X2) = X2 + 1 [U52](X1,X2) = X1 + X2 [U61](X1,X2,X3) = X2 + X3 + 1 [U62](X1,X2,X3) = X1 + X2 + X3 [U63](X1,X2,X3) = X1 + X2 + X3 [U64](X1,X2,X3) = X1 + X2 + X3 [s](X) = X + 1 [plus](X1,X2) = X1 + X2 [n__0] = 1 [n__plus](X1,X2) = X1 + X2 [n__s](X) = X + 1 [0] = 1 [nF_U11](X1,X2,X3) = X1 + X2 + X3 [nF_isNat](X) = X + 1 [nF_plus](X1,X2) = X1 + X2 [nF_activate](X) = X [nF_isNatKind](X) = X [nF_U64](X1,X2,X3) = X1 + X2 + X3 [nF_U63](X1,X2,X3) = X2 + X3 + 1 [nF_U62](X1,X2,X3) = X1 + X2 + X3 [nF_U61](X1,X2,X3) = X2 + X3 + 1 [nF_U22](X1,X2) = X1 + X2 [nF_U21](X1,X2) = X1 + X2 [nF_U15](X1,X2) = X1 + X2 [nF_U14](X1,X2,X3) = X2 + X3 + 1 [nF_U13](X1,X2,X3) = X2 + X3 + 1 [nF_U12](X1,X2,X3) = X1 + X2 + X3 [nF_U51](X1,X2) = X1 + X2 [nF_U31](X1,X2) = X2 [nF_U52](X1,X2) = X1 + X2 TIME: 0.217563 -> -> Dependency pairs in cycle: nF_U11(tt,V1,V2) -> nF_U12(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_U11(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_U14(tt,V1,V2) -> nF_isNat(activate(V1)) nF_U13(tt,V1,V2) -> nF_U14(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U12(tt,V1,V2) -> nF_U13(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U15(tt,V2) -> nF_isNat(activate(V2)) nF_U14(tt,V1,V2) -> nF_U15(isNat(activate(V1)),activate(V2)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U62(tt,M,N) -> nF_isNat(activate(N)) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_U12(tt,V1,V2) -> nF_activate(V2) nF_U12(tt,V1,V2) -> nF_activate(V1) nF_U13(tt,V1,V2) -> nF_activate(V2) nF_U13(tt,V1,V2) -> nF_activate(V1) nF_U14(tt,V1,V2) -> nF_activate(V1) nF_U14(tt,V1,V2) -> nF_activate(V2) nF_U15(tt,V2) -> nF_activate(V2) nF_U21(tt,V1) -> nF_activate(V1) nF_U22(tt,V1) -> nF_activate(V1) nF_U31(tt,V2) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_U11(tt,V1,V2) -> nF_isNatKind(activate(V1)) nF_U12(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U13(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U21(tt,V1) -> nF_isNatKind(activate(V1)) nF_U31(tt,V2) -> nF_isNatKind(activate(V2)) nF_U51(tt,N) -> nF_isNatKind(activate(N)) nF_plus(N,0) -> nF_U51(isNat(N),N) nF_U61(tt,M,N) -> nF_isNatKind(activate(M)) nF_U63(tt,M,N) -> nF_isNatKind(activate(N)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_plus(N,0) -> nF_isNat(N) nF_plus(N,s(M)) -> nF_isNat(M) nF_isNat(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_U51(tt,N) -> nF_activate(N) nF_U52(tt,N) -> nF_activate(N) nF_U51(tt,N) -> nF_U52(isNatKind(activate(N)),activate(N)) nF_U61(tt,M,N) -> nF_activate(M) nF_U61(tt,M,N) -> nF_activate(N) nF_U62(tt,M,N) -> nF_activate(N) nF_U62(tt,M,N) -> nF_activate(M) nF_U63(tt,M,N) -> nF_activate(N) nF_U63(tt,M,N) -> nF_activate(M) nF_U64(tt,M,N) -> nF_activate(N) nF_U64(tt,M,N) -> nF_activate(M) nF_isNat(n__plus(V1,V2)) -> nF_activate(V1) nF_isNat(n__plus(V1,V2)) -> nF_activate(V2) nF_isNat(n__s(V1)) -> nF_activate(V1) nF_isNatKind(n__plus(V1,V2)) -> nF_activate(V1) nF_isNatKind(n__plus(V1,V2)) -> nF_activate(V2) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = X1 [tt] = 1 [U12](X1,X2,X3) = 1 [isNatKind](X) = 1 [activate](X) = X [U13](X1,X2,X3) = X1 [U14](X1,X2,X3) = X1 [U15](X1,X2) = X1 [isNat](X) = 1 [U16](X) = 1 [U21](X1,X2) = 1 [U22](X1,X2) = X1 [U23](X) = 1 [U31](X1,X2) = X1 [U32](X) = 1 [U41](X) = 1 [U51](X1,X2) = X2 + 1 [U52](X1,X2) = X1 + X2 [U61](X1,X2,X3) = X2 + X3 + 1 [U62](X1,X2,X3) = X1 + X2 + X3 [U63](X1,X2,X3) = X1 + X2 + X3 [U64](X1,X2,X3) = X1 + X2 + X3 [s](X) = X [plus](X1,X2) = X1 + X2 + 1 [n__0] = 0 [n__plus](X1,X2) = X1 + X2 + 1 [n__s](X) = X [0] = 0 [nF_U11](X1,X2,X3) = X2 + X3 + 1 [nF_isNat](X) = X [nF_U14](X1,X2,X3) = X1 + X2 + X3 [nF_U13](X1,X2,X3) = X2 + X3 + 1 [nF_U12](X1,X2,X3) = X1 + X2 + X3 [nF_U15](X1,X2) = X1 + X2 [nF_U22](X1,X2) = X2 [nF_U21](X1,X2) = X2 [nF_U62](X1,X2,X3) = X2 + X3 [nF_U61](X1,X2,X3) = X2 + X3 [nF_plus](X1,X2) = X1 + X2 [nF_U64](X1,X2,X3) = X2 + X3 [nF_U63](X1,X2,X3) = X2 + X3 [nF_activate](X) = X [nF_U31](X1,X2) = X1 + X2 [nF_isNatKind](X) = X [nF_U51](X1,X2) = X2 [nF_U52](X1,X2) = X2 TIME: 0.217795 -> -> Dependency pairs in cycle: nF_U11(tt,V1,V2) -> nF_U12(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_U11(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_plus(N,s(M)) -> nF_isNat(M) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_isNatKind(n__plus(V1,V2)) -> nF_activate(V1) nF_isNatKind(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_isNat(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_plus(N,0) -> nF_isNat(N) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_U62(tt,M,N) -> nF_isNat(activate(N)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U15(tt,V2) -> nF_isNat(activate(V2)) nF_U14(tt,V1,V2) -> nF_U15(isNat(activate(V1)),activate(V2)) nF_U13(tt,V1,V2) -> nF_U14(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U12(tt,V1,V2) -> nF_U13(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U14(tt,V1,V2) -> nF_isNat(activate(V1)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_U63(tt,M,N) -> nF_isNatKind(activate(N)) nF_U61(tt,M,N) -> nF_isNatKind(activate(M)) nF_U51(tt,N) -> nF_isNatKind(activate(N)) nF_plus(N,0) -> nF_U51(isNat(N),N) nF_U31(tt,V2) -> nF_isNatKind(activate(V2)) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_U21(tt,V1) -> nF_isNatKind(activate(V1)) nF_U13(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U12(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U11(tt,V1,V2) -> nF_isNatKind(activate(V1)) nF_isNat(n__s(V1)) -> nF_activate(V1) nF_isNat(n__plus(V1,V2)) -> nF_activate(V2) nF_isNat(n__plus(V1,V2)) -> nF_activate(V1) nF_U64(tt,M,N) -> nF_activate(M) nF_U64(tt,M,N) -> nF_activate(N) nF_U63(tt,M,N) -> nF_activate(M) nF_U63(tt,M,N) -> nF_activate(N) nF_U62(tt,M,N) -> nF_activate(M) nF_U62(tt,M,N) -> nF_activate(N) nF_U61(tt,M,N) -> nF_activate(N) nF_U61(tt,M,N) -> nF_activate(M) nF_U52(tt,N) -> nF_activate(N) nF_U51(tt,N) -> nF_U52(isNatKind(activate(N)),activate(N)) nF_U51(tt,N) -> nF_activate(N) nF_U31(tt,V2) -> nF_activate(V2) nF_U22(tt,V1) -> nF_activate(V1) nF_U21(tt,V1) -> nF_activate(V1) nF_U15(tt,V2) -> nF_activate(V2) nF_U14(tt,V1,V2) -> nF_activate(V2) nF_U14(tt,V1,V2) -> nF_activate(V1) nF_U13(tt,V1,V2) -> nF_activate(V1) nF_U13(tt,V1,V2) -> nF_activate(V2) nF_U12(tt,V1,V2) -> nF_activate(V1) nF_U12(tt,V1,V2) -> nF_activate(V2) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = X1 + 1 [tt] = 0 [U12](X1,X2,X3) = 1 [isNatKind](X) = 1 [activate](X) = X [U13](X1,X2,X3) = 1 [U14](X1,X2,X3) = X1 [U15](X1,X2) = 0 [isNat](X) = X + 1 [U16](X) = 0 [U21](X1,X2) = 1 [U22](X1,X2) = X1 [U23](X) = 0 [U31](X1,X2) = 0 [U32](X) = 0 [U41](X) = 0 [U51](X1,X2) = X2 + 1 [U52](X1,X2) = X1 + X2 [U61](X1,X2,X3) = X2 + X3 + 1 [U62](X1,X2,X3) = X2 + X3 + 1 [U63](X1,X2,X3) = X2 + X3 + 1 [U64](X1,X2,X3) = X2 + X3 + 1 [s](X) = X [plus](X1,X2) = X1 + X2 + 1 [n__0] = 0 [n__plus](X1,X2) = X1 + X2 + 1 [n__s](X) = X [0] = 0 [nF_U11](X1,X2,X3) = X1 + X2 + X3 + 1 [nF_isNat](X) = X + 1 [nF_plus](X1,X2) = X1 + X2 + 1 [nF_activate](X) = X [nF_isNatKind](X) = X [nF_U64](X1,X2,X3) = X2 + X3 + 1 [nF_U63](X1,X2,X3) = X2 + X3 + 1 [nF_U62](X1,X2,X3) = X2 + X3 + 1 [nF_U61](X1,X2,X3) = X2 + X3 + 1 [nF_U22](X1,X2) = X2 + 1 [nF_U21](X1,X2) = X2 + 1 [nF_U15](X1,X2) = X2 + 1 [nF_U14](X1,X2,X3) = X2 + X3 + 1 [nF_U13](X1,X2,X3) = X2 + X3 + 1 [nF_U12](X1,X2,X3) = X2 + X3 + 1 [nF_U51](X1,X2) = X2 + 1 [nF_U31](X1,X2) = X1 + X2 [nF_U52](X1,X2) = X1 + X2 TIME: 0.213454 -> -> Dependency pairs in cycle: nF_U11(tt,V1,V2) -> nF_U12(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_U11(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_U14(tt,V1,V2) -> nF_isNat(activate(V1)) nF_U13(tt,V1,V2) -> nF_U14(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U12(tt,V1,V2) -> nF_U13(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U15(tt,V2) -> nF_isNat(activate(V2)) nF_U14(tt,V1,V2) -> nF_U15(isNat(activate(V1)),activate(V2)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U62(tt,M,N) -> nF_isNat(activate(N)) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_U12(tt,V1,V2) -> nF_activate(V1) nF_U13(tt,V1,V2) -> nF_activate(V2) nF_U13(tt,V1,V2) -> nF_activate(V1) nF_U14(tt,V1,V2) -> nF_activate(V1) nF_U14(tt,V1,V2) -> nF_activate(V2) nF_U15(tt,V2) -> nF_activate(V2) nF_U21(tt,V1) -> nF_activate(V1) nF_U22(tt,V1) -> nF_activate(V1) nF_U31(tt,V2) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_U11(tt,V1,V2) -> nF_isNatKind(activate(V1)) nF_U12(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U13(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U21(tt,V1) -> nF_isNatKind(activate(V1)) nF_U31(tt,V2) -> nF_isNatKind(activate(V2)) nF_U51(tt,N) -> nF_isNatKind(activate(N)) nF_plus(N,0) -> nF_U51(isNat(N),N) nF_U61(tt,M,N) -> nF_isNatKind(activate(M)) nF_U63(tt,M,N) -> nF_isNatKind(activate(N)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_plus(N,0) -> nF_isNat(N) nF_plus(N,s(M)) -> nF_isNat(M) nF_isNat(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_U51(tt,N) -> nF_activate(N) nF_U52(tt,N) -> nF_activate(N) nF_U51(tt,N) -> nF_U52(isNatKind(activate(N)),activate(N)) nF_U61(tt,M,N) -> nF_activate(M) nF_U61(tt,M,N) -> nF_activate(N) nF_U62(tt,M,N) -> nF_activate(N) nF_U62(tt,M,N) -> nF_activate(M) nF_U63(tt,M,N) -> nF_activate(N) nF_U63(tt,M,N) -> nF_activate(M) nF_U64(tt,M,N) -> nF_activate(N) nF_U64(tt,M,N) -> nF_activate(M) nF_isNat(n__plus(V1,V2)) -> nF_activate(V1) nF_isNat(n__plus(V1,V2)) -> nF_activate(V2) nF_isNat(n__s(V1)) -> nF_activate(V1) nF_isNatKind(n__plus(V1,V2)) -> nF_activate(V1) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = 1 [tt] = 1 [U12](X1,X2,X3) = X1 [isNatKind](X) = 1 [activate](X) = X [U13](X1,X2,X3) = 1 [U14](X1,X2,X3) = 1 [U15](X1,X2) = 1 [isNat](X) = 1 [U16](X) = X [U21](X1,X2) = 1 [U22](X1,X2) = 1 [U23](X) = X [U31](X1,X2) = 1 [U32](X) = X [U41](X) = 1 [U51](X1,X2) = X2 + 1 [U52](X1,X2) = X1 + X2 [U61](X1,X2,X3) = X2 + X3 + 1 [U62](X1,X2,X3) = X2 + X3 + 1 [U63](X1,X2,X3) = X2 + X3 + 1 [U64](X1,X2,X3) = X1 + X2 + X3 [s](X) = X [plus](X1,X2) = X1 + X2 + 1 [n__0] = 0 [n__plus](X1,X2) = X1 + X2 + 1 [n__s](X) = X [0] = 0 [nF_U11](X1,X2,X3) = X2 + X3 + 1 [nF_isNat](X) = X [nF_U14](X1,X2,X3) = X1 + X2 + X3 [nF_U13](X1,X2,X3) = X2 + X3 + 1 [nF_U12](X1,X2,X3) = X1 + X2 + X3 [nF_U15](X1,X2) = X1 + X2 [nF_U22](X1,X2) = X2 [nF_U21](X1,X2) = X2 [nF_U62](X1,X2,X3) = X2 + X3 [nF_U61](X1,X2,X3) = X2 + X3 [nF_plus](X1,X2) = X1 + X2 [nF_U64](X1,X2,X3) = X2 + X3 [nF_U63](X1,X2,X3) = X2 + X3 [nF_activate](X) = X [nF_U31](X1,X2) = X1 + X2 [nF_isNatKind](X) = X [nF_U51](X1,X2) = X2 [nF_U52](X1,X2) = X2 TIME: 0.22267899999999996 -> -> Dependency pairs in cycle: nF_U11(tt,V1,V2) -> nF_U12(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_U11(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_plus(N,s(M)) -> nF_isNat(M) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_isNat(n__s(V1)) -> nF_activate(V1) nF_plus(N,0) -> nF_isNat(N) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_U62(tt,M,N) -> nF_isNat(activate(N)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U15(tt,V2) -> nF_isNat(activate(V2)) nF_U14(tt,V1,V2) -> nF_U15(isNat(activate(V1)),activate(V2)) nF_U13(tt,V1,V2) -> nF_U14(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U12(tt,V1,V2) -> nF_U13(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U14(tt,V1,V2) -> nF_isNat(activate(V1)) nF_isNat(n__plus(V1,V2)) -> nF_activate(V2) nF_isNat(n__plus(V1,V2)) -> nF_activate(V1) nF_U64(tt,M,N) -> nF_activate(M) nF_U64(tt,M,N) -> nF_activate(N) nF_U63(tt,M,N) -> nF_activate(M) nF_U63(tt,M,N) -> nF_activate(N) nF_U62(tt,M,N) -> nF_activate(M) nF_U62(tt,M,N) -> nF_activate(N) nF_U61(tt,M,N) -> nF_activate(N) nF_U61(tt,M,N) -> nF_activate(M) nF_U52(tt,N) -> nF_activate(N) nF_U51(tt,N) -> nF_U52(isNatKind(activate(N)),activate(N)) nF_plus(N,0) -> nF_U51(isNat(N),N) nF_U51(tt,N) -> nF_activate(N) nF_U31(tt,V2) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_isNatKind(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_isNat(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_U63(tt,M,N) -> nF_isNatKind(activate(N)) nF_U61(tt,M,N) -> nF_isNatKind(activate(M)) nF_U51(tt,N) -> nF_isNatKind(activate(N)) nF_U31(tt,V2) -> nF_isNatKind(activate(V2)) nF_U21(tt,V1) -> nF_isNatKind(activate(V1)) nF_U13(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U12(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U11(tt,V1,V2) -> nF_isNatKind(activate(V1)) nF_U22(tt,V1) -> nF_activate(V1) nF_U21(tt,V1) -> nF_activate(V1) nF_U15(tt,V2) -> nF_activate(V2) nF_U14(tt,V1,V2) -> nF_activate(V2) nF_U14(tt,V1,V2) -> nF_activate(V1) nF_U13(tt,V1,V2) -> nF_activate(V1) nF_U13(tt,V1,V2) -> nF_activate(V2) nF_U12(tt,V1,V2) -> nF_activate(V1) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = X1 + 1 [tt] = 0 [U12](X1,X2,X3) = 1 [isNatKind](X) = 1 [activate](X) = X [U13](X1,X2,X3) = 1 [U14](X1,X2,X3) = X1 [U15](X1,X2) = 0 [isNat](X) = X + 1 [U16](X) = 0 [U21](X1,X2) = 1 [U22](X1,X2) = X1 [U23](X) = 0 [U31](X1,X2) = 0 [U32](X) = 0 [U41](X) = 0 [U51](X1,X2) = X2 + 1 [U52](X1,X2) = X1 + X2 [U61](X1,X2,X3) = X2 + X3 + 1 [U62](X1,X2,X3) = X2 + X3 + 1 [U63](X1,X2,X3) = X2 + X3 + 1 [U64](X1,X2,X3) = X2 + X3 + 1 [s](X) = X [plus](X1,X2) = X1 + X2 + 1 [n__0] = 0 [n__plus](X1,X2) = X1 + X2 + 1 [n__s](X) = X [0] = 0 [nF_U11](X1,X2,X3) = X1 + X2 + X3 + 1 [nF_isNat](X) = X + 1 [nF_plus](X1,X2) = X1 + X2 + 1 [nF_activate](X) = X [nF_U64](X1,X2,X3) = X2 + X3 + 1 [nF_U63](X1,X2,X3) = X2 + X3 + 1 [nF_U62](X1,X2,X3) = X2 + X3 + 1 [nF_U61](X1,X2,X3) = X2 + X3 + 1 [nF_U22](X1,X2) = X2 + 1 [nF_U21](X1,X2) = X2 + 1 [nF_U15](X1,X2) = X2 + 1 [nF_U14](X1,X2,X3) = X2 + X3 + 1 [nF_U13](X1,X2,X3) = X2 + X3 + 1 [nF_U12](X1,X2,X3) = X2 + X3 + 1 [nF_U52](X1,X2) = X1 + X2 [nF_U51](X1,X2) = X2 + 1 [nF_U31](X1,X2) = X2 [nF_isNatKind](X) = X TIME: 0.212678 -> -> Dependency pairs in cycle: nF_U11(tt,V1,V2) -> nF_U12(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_U11(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_U14(tt,V1,V2) -> nF_isNat(activate(V1)) nF_U13(tt,V1,V2) -> nF_U14(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U12(tt,V1,V2) -> nF_U13(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U15(tt,V2) -> nF_isNat(activate(V2)) nF_U14(tt,V1,V2) -> nF_U15(isNat(activate(V1)),activate(V2)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U62(tt,M,N) -> nF_isNat(activate(N)) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_U13(tt,V1,V2) -> nF_activate(V2) nF_U13(tt,V1,V2) -> nF_activate(V1) nF_U14(tt,V1,V2) -> nF_activate(V1) nF_U14(tt,V1,V2) -> nF_activate(V2) nF_U15(tt,V2) -> nF_activate(V2) nF_U21(tt,V1) -> nF_activate(V1) nF_U22(tt,V1) -> nF_activate(V1) nF_U31(tt,V2) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_U11(tt,V1,V2) -> nF_isNatKind(activate(V1)) nF_U12(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U13(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U21(tt,V1) -> nF_isNatKind(activate(V1)) nF_U31(tt,V2) -> nF_isNatKind(activate(V2)) nF_U51(tt,N) -> nF_isNatKind(activate(N)) nF_plus(N,0) -> nF_U51(isNat(N),N) nF_U61(tt,M,N) -> nF_isNatKind(activate(M)) nF_U63(tt,M,N) -> nF_isNatKind(activate(N)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_plus(N,0) -> nF_isNat(N) nF_plus(N,s(M)) -> nF_isNat(M) nF_isNat(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_U51(tt,N) -> nF_activate(N) nF_U52(tt,N) -> nF_activate(N) nF_U51(tt,N) -> nF_U52(isNatKind(activate(N)),activate(N)) nF_U61(tt,M,N) -> nF_activate(M) nF_U61(tt,M,N) -> nF_activate(N) nF_U62(tt,M,N) -> nF_activate(N) nF_U62(tt,M,N) -> nF_activate(M) nF_U63(tt,M,N) -> nF_activate(N) nF_U63(tt,M,N) -> nF_activate(M) nF_U64(tt,M,N) -> nF_activate(N) nF_U64(tt,M,N) -> nF_activate(M) nF_isNat(n__plus(V1,V2)) -> nF_activate(V1) nF_isNat(n__plus(V1,V2)) -> nF_activate(V2) nF_isNat(n__s(V1)) -> nF_activate(V1) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = X1 [tt] = 1 [U12](X1,X2,X3) = 1 [isNatKind](X) = 1 [activate](X) = X [U13](X1,X2,X3) = X1 [U14](X1,X2,X3) = X1 [U15](X1,X2) = X1 [isNat](X) = 1 [U16](X) = 1 [U21](X1,X2) = 1 [U22](X1,X2) = X1 [U23](X) = 1 [U31](X1,X2) = X1 [U32](X) = 1 [U41](X) = 1 [U51](X1,X2) = X2 + 1 [U52](X1,X2) = X1 + X2 [U61](X1,X2,X3) = X1 + X2 + X3 + 1 [U62](X1,X2,X3) = X1 + X2 + X3 + 1 [U63](X1,X2,X3) = X1 + X2 + X3 + 1 [U64](X1,X2,X3) = X1 + X2 + X3 + 1 [s](X) = X + 1 [plus](X1,X2) = X1 + X2 + 1 [n__0] = 0 [n__plus](X1,X2) = X1 + X2 + 1 [n__s](X) = X + 1 [0] = 0 [nF_U11](X1,X2,X3) = X2 + X3 + 1 [nF_isNat](X) = X [nF_U14](X1,X2,X3) = X1 + X2 + X3 [nF_U13](X1,X2,X3) = X2 + X3 + 1 [nF_U12](X1,X2,X3) = X1 + X2 + X3 [nF_U15](X1,X2) = X1 + X2 [nF_U22](X1,X2) = X1 + X2 [nF_U21](X1,X2) = X2 + 1 [nF_U62](X1,X2,X3) = X1 + X2 + X3 [nF_U61](X1,X2,X3) = X2 + X3 + 1 [nF_plus](X1,X2) = X1 + X2 [nF_U64](X1,X2,X3) = X1 + X2 + X3 [nF_U63](X1,X2,X3) = X2 + X3 + 1 [nF_activate](X) = X [nF_U31](X1,X2) = X1 + X2 [nF_isNatKind](X) = X [nF_U51](X1,X2) = X2 [nF_U52](X1,X2) = X2 TIME: 0.220632 -> -> Dependency pairs in cycle: nF_U11(tt,V1,V2) -> nF_U12(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_U11(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_plus(N,s(M)) -> nF_isNat(M) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_isNat(n__plus(V1,V2)) -> nF_activate(V2) nF_plus(N,0) -> nF_isNat(N) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_U62(tt,M,N) -> nF_isNat(activate(N)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U15(tt,V2) -> nF_isNat(activate(V2)) nF_U14(tt,V1,V2) -> nF_U15(isNat(activate(V1)),activate(V2)) nF_U13(tt,V1,V2) -> nF_U14(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U12(tt,V1,V2) -> nF_U13(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U14(tt,V1,V2) -> nF_isNat(activate(V1)) nF_isNat(n__plus(V1,V2)) -> nF_activate(V1) nF_U64(tt,M,N) -> nF_activate(M) nF_U64(tt,M,N) -> nF_activate(N) nF_U63(tt,M,N) -> nF_activate(M) nF_U63(tt,M,N) -> nF_activate(N) nF_U62(tt,M,N) -> nF_activate(M) nF_U62(tt,M,N) -> nF_activate(N) nF_U61(tt,M,N) -> nF_activate(N) nF_U61(tt,M,N) -> nF_activate(M) nF_U52(tt,N) -> nF_activate(N) nF_U51(tt,N) -> nF_U52(isNatKind(activate(N)),activate(N)) nF_plus(N,0) -> nF_U51(isNat(N),N) nF_U51(tt,N) -> nF_activate(N) nF_U31(tt,V2) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_isNatKind(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_isNat(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_U63(tt,M,N) -> nF_isNatKind(activate(N)) nF_U61(tt,M,N) -> nF_isNatKind(activate(M)) nF_U51(tt,N) -> nF_isNatKind(activate(N)) nF_U31(tt,V2) -> nF_isNatKind(activate(V2)) nF_U21(tt,V1) -> nF_isNatKind(activate(V1)) nF_U13(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U12(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U11(tt,V1,V2) -> nF_isNatKind(activate(V1)) nF_U22(tt,V1) -> nF_activate(V1) nF_U21(tt,V1) -> nF_activate(V1) nF_U15(tt,V2) -> nF_activate(V2) nF_U14(tt,V1,V2) -> nF_activate(V2) nF_U14(tt,V1,V2) -> nF_activate(V1) nF_U13(tt,V1,V2) -> nF_activate(V1) nF_U13(tt,V1,V2) -> nF_activate(V2) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = X1 + X2 + 1 [tt] = 0 [U12](X1,X2,X3) = X2 + 1 [isNatKind](X) = 1 [activate](X) = X [U13](X1,X2,X3) = X2 + 1 [U14](X1,X2,X3) = X2 + 1 [U15](X1,X2) = X1 [isNat](X) = X + 1 [U16](X) = 0 [U21](X1,X2) = 1 [U22](X1,X2) = X1 [U23](X) = 0 [U31](X1,X2) = 0 [U32](X) = 0 [U41](X) = 0 [U51](X1,X2) = X2 + 1 [U52](X1,X2) = X1 + X2 [U61](X1,X2,X3) = X2 + X3 + 1 [U62](X1,X2,X3) = X2 + X3 + 1 [U63](X1,X2,X3) = X2 + X3 + 1 [U64](X1,X2,X3) = X2 + X3 + 1 [s](X) = X [plus](X1,X2) = X1 + X2 + 1 [n__0] = 0 [n__plus](X1,X2) = X1 + X2 + 1 [n__s](X) = X [0] = 0 [nF_U11](X1,X2,X3) = X1 + X2 + X3 + 1 [nF_isNat](X) = X + 1 [nF_plus](X1,X2) = X1 + X2 + 1 [nF_activate](X) = X [nF_U64](X1,X2,X3) = X2 + X3 + 1 [nF_U63](X1,X2,X3) = X2 + X3 + 1 [nF_U62](X1,X2,X3) = X2 + X3 + 1 [nF_U61](X1,X2,X3) = X2 + X3 + 1 [nF_U22](X1,X2) = X2 + 1 [nF_U21](X1,X2) = X2 + 1 [nF_U15](X1,X2) = X2 + 1 [nF_U14](X1,X2,X3) = X2 + X3 + 1 [nF_U13](X1,X2,X3) = X2 + X3 + 1 [nF_U12](X1,X2,X3) = X2 + X3 + 1 [nF_U52](X1,X2) = X1 + X2 [nF_U51](X1,X2) = X2 + 1 [nF_U31](X1,X2) = X1 + X2 [nF_isNatKind](X) = X TIME: 0.225728 -> -> Dependency pairs in cycle: nF_U11(tt,V1,V2) -> nF_U12(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_U11(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_U14(tt,V1,V2) -> nF_isNat(activate(V1)) nF_U13(tt,V1,V2) -> nF_U14(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U12(tt,V1,V2) -> nF_U13(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U15(tt,V2) -> nF_isNat(activate(V2)) nF_U14(tt,V1,V2) -> nF_U15(isNat(activate(V1)),activate(V2)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U62(tt,M,N) -> nF_isNat(activate(N)) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_U13(tt,V1,V2) -> nF_activate(V1) nF_U14(tt,V1,V2) -> nF_activate(V1) nF_U14(tt,V1,V2) -> nF_activate(V2) nF_U15(tt,V2) -> nF_activate(V2) nF_U21(tt,V1) -> nF_activate(V1) nF_U22(tt,V1) -> nF_activate(V1) nF_U31(tt,V2) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_U11(tt,V1,V2) -> nF_isNatKind(activate(V1)) nF_U12(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U13(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U21(tt,V1) -> nF_isNatKind(activate(V1)) nF_U31(tt,V2) -> nF_isNatKind(activate(V2)) nF_U51(tt,N) -> nF_isNatKind(activate(N)) nF_plus(N,0) -> nF_U51(isNat(N),N) nF_U61(tt,M,N) -> nF_isNatKind(activate(M)) nF_U63(tt,M,N) -> nF_isNatKind(activate(N)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_plus(N,0) -> nF_isNat(N) nF_plus(N,s(M)) -> nF_isNat(M) nF_isNat(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_U51(tt,N) -> nF_activate(N) nF_U52(tt,N) -> nF_activate(N) nF_U51(tt,N) -> nF_U52(isNatKind(activate(N)),activate(N)) nF_U61(tt,M,N) -> nF_activate(M) nF_U61(tt,M,N) -> nF_activate(N) nF_U62(tt,M,N) -> nF_activate(N) nF_U62(tt,M,N) -> nF_activate(M) nF_U63(tt,M,N) -> nF_activate(N) nF_U63(tt,M,N) -> nF_activate(M) nF_U64(tt,M,N) -> nF_activate(N) nF_U64(tt,M,N) -> nF_activate(M) nF_isNat(n__plus(V1,V2)) -> nF_activate(V1) nF_isNat(n__plus(V1,V2)) -> nF_activate(V2) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = X1 [tt] = 1 [U12](X1,X2,X3) = 1 [isNatKind](X) = 1 [activate](X) = X [U13](X1,X2,X3) = X1 [U14](X1,X2,X3) = X1 [U15](X1,X2) = X1 [isNat](X) = 1 [U16](X) = 1 [U21](X1,X2) = 1 [U22](X1,X2) = X1 [U23](X) = 1 [U31](X1,X2) = X1 [U32](X) = 1 [U41](X) = 1 [U51](X1,X2) = X2 + 1 [U52](X1,X2) = X1 + X2 [U61](X1,X2,X3) = X1 + X2 + X3 [U62](X1,X2,X3) = X1 + X2 + X3 [U63](X1,X2,X3) = X1 + X2 + X3 [U64](X1,X2,X3) = X1 + X2 + X3 [s](X) = X [plus](X1,X2) = X1 + X2 + 1 [n__0] = 0 [n__plus](X1,X2) = X1 + X2 + 1 [n__s](X) = X [0] = 0 [nF_U11](X1,X2,X3) = X2 + X3 + 1 [nF_isNat](X) = X [nF_U14](X1,X2,X3) = X1 + X2 + X3 [nF_U13](X1,X2,X3) = X2 + X3 + 1 [nF_U12](X1,X2,X3) = X1 + X2 + X3 [nF_U15](X1,X2) = X1 + X2 [nF_U22](X1,X2) = X2 [nF_U21](X1,X2) = X2 [nF_U62](X1,X2,X3) = X2 + X3 [nF_U61](X1,X2,X3) = X2 + X3 [nF_plus](X1,X2) = X1 + X2 [nF_U64](X1,X2,X3) = X2 + X3 [nF_U63](X1,X2,X3) = X2 + X3 [nF_activate](X) = X [nF_U31](X1,X2) = X1 + X2 [nF_isNatKind](X) = X [nF_U51](X1,X2) = X2 [nF_U52](X1,X2) = X2 TIME: 0.24462399999999995 -> -> Dependency pairs in cycle: nF_U11(tt,V1,V2) -> nF_U12(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_U11(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_plus(N,s(M)) -> nF_isNat(M) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_isNat(n__plus(V1,V2)) -> nF_activate(V1) nF_plus(N,0) -> nF_isNat(N) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_U62(tt,M,N) -> nF_isNat(activate(N)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U15(tt,V2) -> nF_isNat(activate(V2)) nF_U14(tt,V1,V2) -> nF_U15(isNat(activate(V1)),activate(V2)) nF_U13(tt,V1,V2) -> nF_U14(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U12(tt,V1,V2) -> nF_U13(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U14(tt,V1,V2) -> nF_isNat(activate(V1)) nF_U64(tt,M,N) -> nF_activate(M) nF_U64(tt,M,N) -> nF_activate(N) nF_U63(tt,M,N) -> nF_activate(M) nF_U63(tt,M,N) -> nF_activate(N) nF_U62(tt,M,N) -> nF_activate(M) nF_U62(tt,M,N) -> nF_activate(N) nF_U61(tt,M,N) -> nF_activate(N) nF_U61(tt,M,N) -> nF_activate(M) nF_U52(tt,N) -> nF_activate(N) nF_U51(tt,N) -> nF_U52(isNatKind(activate(N)),activate(N)) nF_plus(N,0) -> nF_U51(isNat(N),N) nF_U51(tt,N) -> nF_activate(N) nF_U31(tt,V2) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_isNatKind(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_isNat(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_U63(tt,M,N) -> nF_isNatKind(activate(N)) nF_U61(tt,M,N) -> nF_isNatKind(activate(M)) nF_U51(tt,N) -> nF_isNatKind(activate(N)) nF_U31(tt,V2) -> nF_isNatKind(activate(V2)) nF_U21(tt,V1) -> nF_isNatKind(activate(V1)) nF_U13(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U12(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U11(tt,V1,V2) -> nF_isNatKind(activate(V1)) nF_U22(tt,V1) -> nF_activate(V1) nF_U21(tt,V1) -> nF_activate(V1) nF_U15(tt,V2) -> nF_activate(V2) nF_U14(tt,V1,V2) -> nF_activate(V2) nF_U14(tt,V1,V2) -> nF_activate(V1) nF_U13(tt,V1,V2) -> nF_activate(V1) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = X2 + 1 [tt] = 0 [U12](X1,X2,X3) = X2 + 1 [isNatKind](X) = X [activate](X) = X [U13](X1,X2,X3) = X2 + 1 [U14](X1,X2,X3) = X2 + 1 [U15](X1,X2) = X1 [isNat](X) = X + 1 [U16](X) = 0 [U21](X1,X2) = 0 [U22](X1,X2) = 0 [U23](X) = 0 [U31](X1,X2) = 0 [U32](X) = 0 [U41](X) = 0 [U51](X1,X2) = X2 [U52](X1,X2) = X2 [U61](X1,X2,X3) = X2 + X3 + 1 [U62](X1,X2,X3) = X2 + X3 + 1 [U63](X1,X2,X3) = X2 + X3 + 1 [U64](X1,X2,X3) = X2 + X3 + 1 [s](X) = X [plus](X1,X2) = X1 + X2 + 1 [n__0] = 1 [n__plus](X1,X2) = X1 + X2 + 1 [n__s](X) = X [0] = 1 [nF_U11](X1,X2,X3) = X2 + X3 + 1 [nF_isNat](X) = X [nF_plus](X1,X2) = X1 + X2 [nF_activate](X) = X [nF_U64](X1,X2,X3) = X2 + X3 [nF_U63](X1,X2,X3) = X2 + X3 [nF_U62](X1,X2,X3) = X2 + X3 [nF_U61](X1,X2,X3) = X2 + X3 [nF_U22](X1,X2) = X2 [nF_U21](X1,X2) = X2 [nF_U15](X1,X2) = X1 + X2 [nF_U14](X1,X2,X3) = X2 + X3 + 1 [nF_U13](X1,X2,X3) = X2 + X3 + 1 [nF_U12](X1,X2,X3) = X2 + X3 + 1 [nF_U52](X1,X2) = X2 [nF_U51](X1,X2) = X2 [nF_U31](X1,X2) = X2 [nF_isNatKind](X) = X TIME: 0.227952 -> -> Dependency pairs in cycle: nF_U11(tt,V1,V2) -> nF_U12(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_U11(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_U14(tt,V1,V2) -> nF_isNat(activate(V1)) nF_U13(tt,V1,V2) -> nF_U14(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U12(tt,V1,V2) -> nF_U13(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U15(tt,V2) -> nF_isNat(activate(V2)) nF_U14(tt,V1,V2) -> nF_U15(isNat(activate(V1)),activate(V2)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U62(tt,M,N) -> nF_isNat(activate(N)) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_U14(tt,V1,V2) -> nF_activate(V1) nF_U14(tt,V1,V2) -> nF_activate(V2) nF_U15(tt,V2) -> nF_activate(V2) nF_U21(tt,V1) -> nF_activate(V1) nF_U22(tt,V1) -> nF_activate(V1) nF_U31(tt,V2) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_U11(tt,V1,V2) -> nF_isNatKind(activate(V1)) nF_U12(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U13(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U21(tt,V1) -> nF_isNatKind(activate(V1)) nF_U31(tt,V2) -> nF_isNatKind(activate(V2)) nF_U51(tt,N) -> nF_isNatKind(activate(N)) nF_plus(N,0) -> nF_U51(isNat(N),N) nF_U61(tt,M,N) -> nF_isNatKind(activate(M)) nF_U63(tt,M,N) -> nF_isNatKind(activate(N)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_plus(N,0) -> nF_isNat(N) nF_plus(N,s(M)) -> nF_isNat(M) nF_isNat(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_U51(tt,N) -> nF_activate(N) nF_U52(tt,N) -> nF_activate(N) nF_U51(tt,N) -> nF_U52(isNatKind(activate(N)),activate(N)) nF_U61(tt,M,N) -> nF_activate(M) nF_U61(tt,M,N) -> nF_activate(N) nF_U62(tt,M,N) -> nF_activate(N) nF_U62(tt,M,N) -> nF_activate(M) nF_U63(tt,M,N) -> nF_activate(N) nF_U63(tt,M,N) -> nF_activate(M) nF_U64(tt,M,N) -> nF_activate(N) nF_U64(tt,M,N) -> nF_activate(M) nF_isNat(n__plus(V1,V2)) -> nF_activate(V1) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = 1 [tt] = 1 [U12](X1,X2,X3) = X1 [isNatKind](X) = 1 [activate](X) = X [U13](X1,X2,X3) = 1 [U14](X1,X2,X3) = 1 [U15](X1,X2) = 1 [isNat](X) = 1 [U16](X) = X [U21](X1,X2) = 1 [U22](X1,X2) = 1 [U23](X) = X [U31](X1,X2) = 1 [U32](X) = X [U41](X) = 1 [U51](X1,X2) = X2 + 1 [U52](X1,X2) = X1 + X2 [U61](X1,X2,X3) = X2 + X3 + 1 [U62](X1,X2,X3) = X2 + X3 + 1 [U63](X1,X2,X3) = X2 + X3 + 1 [U64](X1,X2,X3) = X2 + X3 + 1 [s](X) = X [plus](X1,X2) = X1 + X2 + 1 [n__0] = 0 [n__plus](X1,X2) = X1 + X2 + 1 [n__s](X) = X [0] = 0 [nF_U11](X1,X2,X3) = X2 + X3 + 1 [nF_isNat](X) = X [nF_U14](X1,X2,X3) = X1 + X2 + X3 [nF_U13](X1,X2,X3) = X2 + X3 + 1 [nF_U12](X1,X2,X3) = X1 + X2 + X3 [nF_U15](X1,X2) = X1 + X2 [nF_U22](X1,X2) = X2 [nF_U21](X1,X2) = X2 [nF_U62](X1,X2,X3) = X2 + X3 [nF_U61](X1,X2,X3) = X2 + X3 [nF_plus](X1,X2) = X1 + X2 [nF_U64](X1,X2,X3) = X2 + X3 [nF_U63](X1,X2,X3) = X2 + X3 [nF_activate](X) = X [nF_U31](X1,X2) = X1 + X2 [nF_isNatKind](X) = X [nF_U51](X1,X2) = X2 [nF_U52](X1,X2) = X2 TIME: 0.558003 -> -> Dependency pairs in cycle: nF_U11(tt,V1,V2) -> nF_U12(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_U11(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_plus(N,s(M)) -> nF_isNat(M) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_U64(tt,M,N) -> nF_activate(M) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U64(tt,M,N) -> nF_activate(N) nF_U63(tt,M,N) -> nF_activate(M) nF_U63(tt,M,N) -> nF_activate(N) nF_U62(tt,M,N) -> nF_activate(M) nF_U62(tt,M,N) -> nF_activate(N) nF_U61(tt,M,N) -> nF_activate(N) nF_U61(tt,M,N) -> nF_activate(M) nF_U52(tt,N) -> nF_activate(N) nF_U51(tt,N) -> nF_U52(isNatKind(activate(N)),activate(N)) nF_plus(N,0) -> nF_U51(isNat(N),N) nF_U51(tt,N) -> nF_activate(N) nF_U31(tt,V2) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_isNatKind(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_isNat(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_plus(N,0) -> nF_isNat(N) nF_U62(tt,M,N) -> nF_isNat(activate(N)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U15(tt,V2) -> nF_isNat(activate(V2)) nF_U14(tt,V1,V2) -> nF_U15(isNat(activate(V1)),activate(V2)) nF_U13(tt,V1,V2) -> nF_U14(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U12(tt,V1,V2) -> nF_U13(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U14(tt,V1,V2) -> nF_isNat(activate(V1)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_U63(tt,M,N) -> nF_isNatKind(activate(N)) nF_U61(tt,M,N) -> nF_isNatKind(activate(M)) nF_U51(tt,N) -> nF_isNatKind(activate(N)) nF_U31(tt,V2) -> nF_isNatKind(activate(V2)) nF_U21(tt,V1) -> nF_isNatKind(activate(V1)) nF_U13(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U12(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U11(tt,V1,V2) -> nF_isNatKind(activate(V1)) nF_U22(tt,V1) -> nF_activate(V1) nF_U21(tt,V1) -> nF_activate(V1) nF_U15(tt,V2) -> nF_activate(V2) nF_U14(tt,V1,V2) -> nF_activate(V2) nF_U14(tt,V1,V2) -> nF_activate(V1) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = X1 [tt] = 0 [U12](X1,X2,X3) = 0 [isNatKind](X) = 1 [activate](X) = X [U13](X1,X2,X3) = 0 [U14](X1,X2,X3) = 0 [U15](X1,X2) = 0 [isNat](X) = 1 [U16](X) = 0 [U21](X1,X2) = 1 [U22](X1,X2) = X1 [U23](X) = 0 [U31](X1,X2) = 0 [U32](X) = 0 [U41](X) = 0 [U51](X1,X2) = X2 + 1 [U52](X1,X2) = X1 + X2 [U61](X1,X2,X3) = X2 + X3 + 1 [U62](X1,X2,X3) = X2 + X3 + 1 [U63](X1,X2,X3) = X2 + X3 + 1 [U64](X1,X2,X3) = X2 + X3 + 1 [s](X) = X [plus](X1,X2) = X1 + X2 + 1 [n__0] = 0 [n__plus](X1,X2) = X1 + X2 + 1 [n__s](X) = X [0] = 0 [nF_U11](X1,X2,X3) = X1 + X2 + X3 + 1 [nF_isNat](X) = X + 1 [nF_plus](X1,X2) = X1 + X2 + 1 [nF_activate](X) = X [nF_U64](X1,X2,X3) = X2 + X3 + 1 [nF_U63](X1,X2,X3) = X2 + X3 + 1 [nF_U62](X1,X2,X3) = X2 + X3 + 1 [nF_U61](X1,X2,X3) = X2 + X3 + 1 [nF_U52](X1,X2) = X1 + X2 [nF_U51](X1,X2) = X2 + 1 [nF_U31](X1,X2) = X1 + X2 [nF_isNatKind](X) = X [nF_U22](X1,X2) = X2 + 1 [nF_U21](X1,X2) = X2 + 1 [nF_U15](X1,X2) = X2 + 1 [nF_U14](X1,X2,X3) = X2 + X3 + 1 [nF_U13](X1,X2,X3) = X2 + X3 + 1 [nF_U12](X1,X2,X3) = X2 + X3 + 1 TIME: 0.407467 -> -> Dependency pairs in cycle: nF_U11(tt,V1,V2) -> nF_U12(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_U11(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_U14(tt,V1,V2) -> nF_isNat(activate(V1)) nF_U13(tt,V1,V2) -> nF_U14(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U12(tt,V1,V2) -> nF_U13(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U15(tt,V2) -> nF_isNat(activate(V2)) nF_U14(tt,V1,V2) -> nF_U15(isNat(activate(V1)),activate(V2)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U62(tt,M,N) -> nF_isNat(activate(N)) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_U14(tt,V1,V2) -> nF_activate(V2) nF_U15(tt,V2) -> nF_activate(V2) nF_U21(tt,V1) -> nF_activate(V1) nF_U22(tt,V1) -> nF_activate(V1) nF_U31(tt,V2) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_U11(tt,V1,V2) -> nF_isNatKind(activate(V1)) nF_U12(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U13(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U21(tt,V1) -> nF_isNatKind(activate(V1)) nF_U31(tt,V2) -> nF_isNatKind(activate(V2)) nF_U51(tt,N) -> nF_isNatKind(activate(N)) nF_plus(N,0) -> nF_U51(isNat(N),N) nF_U61(tt,M,N) -> nF_isNatKind(activate(M)) nF_U63(tt,M,N) -> nF_isNatKind(activate(N)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_plus(N,0) -> nF_isNat(N) nF_plus(N,s(M)) -> nF_isNat(M) nF_isNat(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_U51(tt,N) -> nF_activate(N) nF_U52(tt,N) -> nF_activate(N) nF_U51(tt,N) -> nF_U52(isNatKind(activate(N)),activate(N)) nF_U61(tt,M,N) -> nF_activate(M) nF_U61(tt,M,N) -> nF_activate(N) nF_U62(tt,M,N) -> nF_activate(N) nF_U62(tt,M,N) -> nF_activate(M) nF_U63(tt,M,N) -> nF_activate(N) nF_U63(tt,M,N) -> nF_activate(M) nF_U64(tt,M,N) -> nF_activate(N) nF_U64(tt,M,N) -> nF_activate(M) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = 0 [tt] = 0 [U12](X1,X2,X3) = 0 [isNatKind](X) = X [activate](X) = X [U13](X1,X2,X3) = 0 [U14](X1,X2,X3) = 0 [U15](X1,X2) = 0 [isNat](X) = X [U16](X) = 0 [U21](X1,X2) = 0 [U22](X1,X2) = 0 [U23](X) = 0 [U31](X1,X2) = 0 [U32](X) = 0 [U41](X) = 0 [U51](X1,X2) = X2 [U52](X1,X2) = X2 [U61](X1,X2,X3) = X2 + X3 + 1 [U62](X1,X2,X3) = X2 + X3 + 1 [U63](X1,X2,X3) = X2 + X3 + 1 [U64](X1,X2,X3) = X2 + X3 + 1 [s](X) = X + 1 [plus](X1,X2) = X1 + X2 [n__0] = 1 [n__plus](X1,X2) = X1 + X2 [n__s](X) = X + 1 [0] = 1 [nF_U11](X1,X2,X3) = X2 + X3 [nF_isNat](X) = X [nF_U14](X1,X2,X3) = X2 + X3 [nF_U13](X1,X2,X3) = X2 + X3 [nF_U12](X1,X2,X3) = X2 + X3 [nF_U15](X1,X2) = X2 [nF_U22](X1,X2) = X2 [nF_U21](X1,X2) = X2 [nF_U62](X1,X2,X3) = X2 + X3 + 1 [nF_U61](X1,X2,X3) = X2 + X3 + 1 [nF_plus](X1,X2) = X1 + X2 [nF_U64](X1,X2,X3) = X2 + X3 + 1 [nF_U63](X1,X2,X3) = X2 + X3 + 1 [nF_activate](X) = X [nF_U31](X1,X2) = X2 [nF_isNatKind](X) = X [nF_U51](X1,X2) = X2 [nF_U52](X1,X2) = X2 TIME: 0.220455 -> -> Dependency pairs in cycle: nF_U11(tt,V1,V2) -> nF_U12(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_U11(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_plus(N,s(M)) -> nF_isNat(M) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_U64(tt,M,N) -> nF_activate(N) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U63(tt,M,N) -> nF_activate(M) nF_U63(tt,M,N) -> nF_activate(N) nF_U62(tt,M,N) -> nF_activate(M) nF_U62(tt,M,N) -> nF_activate(N) nF_U61(tt,M,N) -> nF_activate(N) nF_U61(tt,M,N) -> nF_activate(M) nF_U52(tt,N) -> nF_activate(N) nF_U51(tt,N) -> nF_U52(isNatKind(activate(N)),activate(N)) nF_plus(N,0) -> nF_U51(isNat(N),N) nF_U51(tt,N) -> nF_activate(N) nF_U31(tt,V2) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_isNatKind(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_isNat(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_plus(N,0) -> nF_isNat(N) nF_U62(tt,M,N) -> nF_isNat(activate(N)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U15(tt,V2) -> nF_isNat(activate(V2)) nF_U14(tt,V1,V2) -> nF_U15(isNat(activate(V1)),activate(V2)) nF_U13(tt,V1,V2) -> nF_U14(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U12(tt,V1,V2) -> nF_U13(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U14(tt,V1,V2) -> nF_isNat(activate(V1)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_U63(tt,M,N) -> nF_isNatKind(activate(N)) nF_U61(tt,M,N) -> nF_isNatKind(activate(M)) nF_U51(tt,N) -> nF_isNatKind(activate(N)) nF_U31(tt,V2) -> nF_isNatKind(activate(V2)) nF_U21(tt,V1) -> nF_isNatKind(activate(V1)) nF_U13(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U12(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U11(tt,V1,V2) -> nF_isNatKind(activate(V1)) nF_U22(tt,V1) -> nF_activate(V1) nF_U21(tt,V1) -> nF_activate(V1) nF_U15(tt,V2) -> nF_activate(V2) nF_U14(tt,V1,V2) -> nF_activate(V2) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = X2 + 1 [tt] = 0 [U12](X1,X2,X3) = X2 + 1 [isNatKind](X) = X [activate](X) = X [U13](X1,X2,X3) = X2 + 1 [U14](X1,X2,X3) = X2 + 1 [U15](X1,X2) = X1 [isNat](X) = X + 1 [U16](X) = 0 [U21](X1,X2) = 0 [U22](X1,X2) = 0 [U23](X) = 0 [U31](X1,X2) = 0 [U32](X) = 0 [U41](X) = 0 [U51](X1,X2) = X2 [U52](X1,X2) = X2 [U61](X1,X2,X3) = X2 + X3 + 1 [U62](X1,X2,X3) = X2 + X3 + 1 [U63](X1,X2,X3) = X2 + X3 + 1 [U64](X1,X2,X3) = X2 + X3 + 1 [s](X) = X [plus](X1,X2) = X1 + X2 + 1 [n__0] = 1 [n__plus](X1,X2) = X1 + X2 + 1 [n__s](X) = X [0] = 1 [nF_U11](X1,X2,X3) = X2 + X3 + 1 [nF_isNat](X) = X [nF_plus](X1,X2) = X1 + X2 [nF_activate](X) = X [nF_U64](X1,X2,X3) = X2 + X3 [nF_U63](X1,X2,X3) = X2 + X3 [nF_U62](X1,X2,X3) = X2 + X3 [nF_U61](X1,X2,X3) = X2 + X3 [nF_U52](X1,X2) = X2 [nF_U51](X1,X2) = X2 [nF_U31](X1,X2) = X2 [nF_isNatKind](X) = X [nF_U22](X1,X2) = X2 [nF_U21](X1,X2) = X2 [nF_U15](X1,X2) = X1 + X2 [nF_U14](X1,X2,X3) = X2 + X3 + 1 [nF_U13](X1,X2,X3) = X2 + X3 + 1 [nF_U12](X1,X2,X3) = X2 + X3 + 1 TIME: 0.213691 -> -> Dependency pairs in cycle: nF_U11(tt,V1,V2) -> nF_U12(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_U11(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_U14(tt,V1,V2) -> nF_isNat(activate(V1)) nF_U13(tt,V1,V2) -> nF_U14(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U12(tt,V1,V2) -> nF_U13(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U15(tt,V2) -> nF_isNat(activate(V2)) nF_U14(tt,V1,V2) -> nF_U15(isNat(activate(V1)),activate(V2)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U62(tt,M,N) -> nF_isNat(activate(N)) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_U15(tt,V2) -> nF_activate(V2) nF_U21(tt,V1) -> nF_activate(V1) nF_U22(tt,V1) -> nF_activate(V1) nF_U31(tt,V2) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_U11(tt,V1,V2) -> nF_isNatKind(activate(V1)) nF_U12(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U13(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U21(tt,V1) -> nF_isNatKind(activate(V1)) nF_U31(tt,V2) -> nF_isNatKind(activate(V2)) nF_U51(tt,N) -> nF_isNatKind(activate(N)) nF_plus(N,0) -> nF_U51(isNat(N),N) nF_U61(tt,M,N) -> nF_isNatKind(activate(M)) nF_U63(tt,M,N) -> nF_isNatKind(activate(N)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_plus(N,0) -> nF_isNat(N) nF_plus(N,s(M)) -> nF_isNat(M) nF_isNat(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_U51(tt,N) -> nF_activate(N) nF_U52(tt,N) -> nF_activate(N) nF_U51(tt,N) -> nF_U52(isNatKind(activate(N)),activate(N)) nF_U61(tt,M,N) -> nF_activate(M) nF_U61(tt,M,N) -> nF_activate(N) nF_U62(tt,M,N) -> nF_activate(N) nF_U62(tt,M,N) -> nF_activate(M) nF_U63(tt,M,N) -> nF_activate(N) nF_U63(tt,M,N) -> nF_activate(M) nF_U64(tt,M,N) -> nF_activate(N) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = 0 [tt] = 0 [U12](X1,X2,X3) = 0 [isNatKind](X) = X [activate](X) = X [U13](X1,X2,X3) = 0 [U14](X1,X2,X3) = 0 [U15](X1,X2) = 0 [isNat](X) = 0 [U16](X) = 0 [U21](X1,X2) = 0 [U22](X1,X2) = 0 [U23](X) = 0 [U31](X1,X2) = 0 [U32](X) = 0 [U41](X) = 0 [U51](X1,X2) = X2 [U52](X1,X2) = X2 [U61](X1,X2,X3) = X2 + X3 + 1 [U62](X1,X2,X3) = X2 + X3 + 1 [U63](X1,X2,X3) = X2 + X3 + 1 [U64](X1,X2,X3) = X2 + X3 + 1 [s](X) = X [plus](X1,X2) = X1 + X2 + 1 [n__0] = 1 [n__plus](X1,X2) = X1 + X2 + 1 [n__s](X) = X [0] = 1 [nF_U11](X1,X2,X3) = X2 + X3 [nF_isNat](X) = X [nF_U14](X1,X2,X3) = X2 + X3 [nF_U13](X1,X2,X3) = X2 + X3 [nF_U12](X1,X2,X3) = X2 + X3 [nF_U15](X1,X2) = X2 [nF_U22](X1,X2) = X2 [nF_U21](X1,X2) = X2 [nF_U62](X1,X2,X3) = X2 + X3 + 1 [nF_U61](X1,X2,X3) = X2 + X3 + 1 [nF_plus](X1,X2) = X1 + X2 + 1 [nF_U64](X1,X2,X3) = X2 + X3 + 1 [nF_U63](X1,X2,X3) = X2 + X3 + 1 [nF_activate](X) = X [nF_U31](X1,X2) = X2 [nF_isNatKind](X) = X [nF_U51](X1,X2) = X2 [nF_U52](X1,X2) = X2 TIME: 0.215856 -> -> Dependency pairs in cycle: nF_U11(tt,V1,V2) -> nF_U12(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_U11(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_plus(N,s(M)) -> nF_isNat(M) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_U63(tt,M,N) -> nF_activate(M) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U63(tt,M,N) -> nF_activate(N) nF_U62(tt,M,N) -> nF_activate(M) nF_U62(tt,M,N) -> nF_activate(N) nF_U61(tt,M,N) -> nF_activate(N) nF_U61(tt,M,N) -> nF_activate(M) nF_U52(tt,N) -> nF_activate(N) nF_U51(tt,N) -> nF_U52(isNatKind(activate(N)),activate(N)) nF_plus(N,0) -> nF_U51(isNat(N),N) nF_U51(tt,N) -> nF_activate(N) nF_U31(tt,V2) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_isNatKind(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_isNat(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_plus(N,0) -> nF_isNat(N) nF_U62(tt,M,N) -> nF_isNat(activate(N)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U15(tt,V2) -> nF_isNat(activate(V2)) nF_U14(tt,V1,V2) -> nF_U15(isNat(activate(V1)),activate(V2)) nF_U13(tt,V1,V2) -> nF_U14(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U12(tt,V1,V2) -> nF_U13(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U14(tt,V1,V2) -> nF_isNat(activate(V1)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_U63(tt,M,N) -> nF_isNatKind(activate(N)) nF_U61(tt,M,N) -> nF_isNatKind(activate(M)) nF_U51(tt,N) -> nF_isNatKind(activate(N)) nF_U31(tt,V2) -> nF_isNatKind(activate(V2)) nF_U21(tt,V1) -> nF_isNatKind(activate(V1)) nF_U13(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U12(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U11(tt,V1,V2) -> nF_isNatKind(activate(V1)) nF_U22(tt,V1) -> nF_activate(V1) nF_U21(tt,V1) -> nF_activate(V1) nF_U15(tt,V2) -> nF_activate(V2) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = X1 [tt] = 1 [U12](X1,X2,X3) = 1 [isNatKind](X) = 1 [activate](X) = X [U13](X1,X2,X3) = X1 [U14](X1,X2,X3) = X1 [U15](X1,X2) = 1 [isNat](X) = 1 [U16](X) = X [U21](X1,X2) = X1 [U22](X1,X2) = 1 [U23](X) = 1 [U31](X1,X2) = X1 [U32](X) = 1 [U41](X) = 1 [U51](X1,X2) = X2 + 1 [U52](X1,X2) = X1 + X2 [U61](X1,X2,X3) = X2 + X3 + 1 [U62](X1,X2,X3) = X1 + X2 + X3 [U63](X1,X2,X3) = X1 + X2 + X3 [U64](X1,X2,X3) = X1 + X2 + X3 [s](X) = X [plus](X1,X2) = X1 + X2 + 1 [n__0] = 0 [n__plus](X1,X2) = X1 + X2 + 1 [n__s](X) = X [0] = 0 [nF_U11](X1,X2,X3) = X1 + X2 + X3 [nF_isNat](X) = X [nF_plus](X1,X2) = X1 + X2 [nF_activate](X) = X [nF_U63](X1,X2,X3) = X2 + X3 [nF_U62](X1,X2,X3) = X2 + X3 [nF_U61](X1,X2,X3) = X2 + X3 [nF_U64](X1,X2,X3) = X2 + X3 [nF_U52](X1,X2) = X2 [nF_U51](X1,X2) = X2 [nF_U31](X1,X2) = X2 [nF_isNatKind](X) = X [nF_U22](X1,X2) = X2 [nF_U21](X1,X2) = X2 [nF_U15](X1,X2) = X1 + X2 [nF_U14](X1,X2,X3) = X2 + X3 + 1 [nF_U13](X1,X2,X3) = X1 + X2 + X3 [nF_U12](X1,X2,X3) = X2 + X3 + 1 TIME: 0.23883500000000002 -> -> Dependency pairs in cycle: nF_U11(tt,V1,V2) -> nF_U12(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_U11(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_U14(tt,V1,V2) -> nF_isNat(activate(V1)) nF_U13(tt,V1,V2) -> nF_U14(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U12(tt,V1,V2) -> nF_U13(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U15(tt,V2) -> nF_isNat(activate(V2)) nF_U14(tt,V1,V2) -> nF_U15(isNat(activate(V1)),activate(V2)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U62(tt,M,N) -> nF_isNat(activate(N)) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_U21(tt,V1) -> nF_activate(V1) nF_U22(tt,V1) -> nF_activate(V1) nF_U31(tt,V2) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_U11(tt,V1,V2) -> nF_isNatKind(activate(V1)) nF_U12(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U13(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U21(tt,V1) -> nF_isNatKind(activate(V1)) nF_U31(tt,V2) -> nF_isNatKind(activate(V2)) nF_U51(tt,N) -> nF_isNatKind(activate(N)) nF_plus(N,0) -> nF_U51(isNat(N),N) nF_U61(tt,M,N) -> nF_isNatKind(activate(M)) nF_U63(tt,M,N) -> nF_isNatKind(activate(N)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_plus(N,0) -> nF_isNat(N) nF_plus(N,s(M)) -> nF_isNat(M) nF_isNat(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_U51(tt,N) -> nF_activate(N) nF_U52(tt,N) -> nF_activate(N) nF_U51(tt,N) -> nF_U52(isNatKind(activate(N)),activate(N)) nF_U61(tt,M,N) -> nF_activate(M) nF_U61(tt,M,N) -> nF_activate(N) nF_U62(tt,M,N) -> nF_activate(N) nF_U62(tt,M,N) -> nF_activate(M) nF_U63(tt,M,N) -> nF_activate(N) nF_U63(tt,M,N) -> nF_activate(M) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = X1 + X2 [tt] = 1 [U12](X1,X2,X3) = X1 + X2 [isNatKind](X) = 1 [activate](X) = X [U13](X1,X2,X3) = X1 + X2 [U14](X1,X2,X3) = X2 [U15](X1,X2) = X1 [isNat](X) = X [U16](X) = 1 [U21](X1,X2) = X2 [U22](X1,X2) = X2 [U23](X) = X [U31](X1,X2) = X1 [U32](X) = 1 [U41](X) = 1 [U51](X1,X2) = X2 + 1 [U52](X1,X2) = X1 + X2 [U61](X1,X2,X3) = X2 + X3 + 1 [U62](X1,X2,X3) = X1 + X2 + X3 [U63](X1,X2,X3) = X2 + X3 + 1 [U64](X1,X2,X3) = X1 + X2 + X3 [s](X) = X [plus](X1,X2) = X1 + X2 + 1 [n__0] = 1 [n__plus](X1,X2) = X1 + X2 + 1 [n__s](X) = X [0] = 1 [nF_U11](X1,X2,X3) = X2 + X3 + 1 [nF_isNat](X) = X + 1 [nF_U14](X1,X2,X3) = X1 + X2 + X3 [nF_U13](X1,X2,X3) = X2 + X3 + 1 [nF_U12](X1,X2,X3) = X1 + X2 + X3 [nF_U15](X1,X2) = X1 + X2 [nF_U22](X1,X2) = X1 + X2 [nF_U21](X1,X2) = X2 + 1 [nF_U62](X1,X2,X3) = X1 + X2 + X3 [nF_U61](X1,X2,X3) = X2 + X3 + 1 [nF_plus](X1,X2) = X1 + X2 + 1 [nF_U64](X1,X2,X3) = X1 + X2 + X3 [nF_U63](X1,X2,X3) = X2 + X3 + 1 [nF_activate](X) = X [nF_U31](X1,X2) = X1 + X2 [nF_isNatKind](X) = X [nF_U51](X1,X2) = X2 + 1 [nF_U52](X1,X2) = X1 + X2 TIME: 0.238928 -> -> Dependency pairs in cycle: nF_U11(tt,V1,V2) -> nF_U12(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_U11(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_plus(N,s(M)) -> nF_isNat(M) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_U63(tt,M,N) -> nF_activate(N) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_activate(M) nF_U62(tt,M,N) -> nF_activate(N) nF_U61(tt,M,N) -> nF_activate(N) nF_U61(tt,M,N) -> nF_activate(M) nF_U52(tt,N) -> nF_activate(N) nF_U51(tt,N) -> nF_U52(isNatKind(activate(N)),activate(N)) nF_plus(N,0) -> nF_U51(isNat(N),N) nF_U51(tt,N) -> nF_activate(N) nF_U31(tt,V2) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_isNatKind(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_isNat(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_plus(N,0) -> nF_isNat(N) nF_U62(tt,M,N) -> nF_isNat(activate(N)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U15(tt,V2) -> nF_isNat(activate(V2)) nF_U14(tt,V1,V2) -> nF_U15(isNat(activate(V1)),activate(V2)) nF_U13(tt,V1,V2) -> nF_U14(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U12(tt,V1,V2) -> nF_U13(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U14(tt,V1,V2) -> nF_isNat(activate(V1)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_U63(tt,M,N) -> nF_isNatKind(activate(N)) nF_U61(tt,M,N) -> nF_isNatKind(activate(M)) nF_U51(tt,N) -> nF_isNatKind(activate(N)) nF_U31(tt,V2) -> nF_isNatKind(activate(V2)) nF_U21(tt,V1) -> nF_isNatKind(activate(V1)) nF_U13(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U12(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U11(tt,V1,V2) -> nF_isNatKind(activate(V1)) nF_U22(tt,V1) -> nF_activate(V1) nF_U21(tt,V1) -> nF_activate(V1) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = 1 [tt] = 0 [U12](X1,X2,X3) = 1 [isNatKind](X) = 1 [activate](X) = X [U13](X1,X2,X3) = X1 [U14](X1,X2,X3) = 0 [U15](X1,X2) = 0 [isNat](X) = X + 1 [U16](X) = 0 [U21](X1,X2) = X1 + 1 [U22](X1,X2) = X1 [U23](X) = 0 [U31](X1,X2) = 0 [U32](X) = 0 [U41](X) = 0 [U51](X1,X2) = X2 + 1 [U52](X1,X2) = X1 + X2 [U61](X1,X2,X3) = X2 + X3 + 1 [U62](X1,X2,X3) = X2 + X3 + 1 [U63](X1,X2,X3) = X2 + X3 + 1 [U64](X1,X2,X3) = X2 + X3 + 1 [s](X) = X + 1 [plus](X1,X2) = X1 + X2 [n__0] = 1 [n__plus](X1,X2) = X1 + X2 [n__s](X) = X + 1 [0] = 1 [nF_U11](X1,X2,X3) = X2 + X3 + 1 [nF_isNat](X) = X + 1 [nF_plus](X1,X2) = X1 + X2 [nF_activate](X) = X [nF_U63](X1,X2,X3) = X2 + X3 + 1 [nF_U62](X1,X2,X3) = X2 + X3 + 1 [nF_U61](X1,X2,X3) = X2 + X3 + 1 [nF_U64](X1,X2,X3) = X1 + X2 + X3 [nF_U52](X1,X2) = X1 + X2 [nF_U51](X1,X2) = X2 + 1 [nF_U31](X1,X2) = X2 [nF_isNatKind](X) = X [nF_U22](X1,X2) = X2 + 1 [nF_U21](X1,X2) = X1 + X2 + 1 [nF_U15](X1,X2) = X2 + 1 [nF_U14](X1,X2,X3) = X2 + X3 + 1 [nF_U13](X1,X2,X3) = X2 + X3 + 1 [nF_U12](X1,X2,X3) = X2 + X3 + 1 TIME: 0.229824 -> -> Dependency pairs in cycle: nF_U11(tt,V1,V2) -> nF_U12(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_U11(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_U14(tt,V1,V2) -> nF_isNat(activate(V1)) nF_U13(tt,V1,V2) -> nF_U14(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U12(tt,V1,V2) -> nF_U13(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U15(tt,V2) -> nF_isNat(activate(V2)) nF_U14(tt,V1,V2) -> nF_U15(isNat(activate(V1)),activate(V2)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U62(tt,M,N) -> nF_isNat(activate(N)) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_U22(tt,V1) -> nF_activate(V1) nF_U31(tt,V2) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_U11(tt,V1,V2) -> nF_isNatKind(activate(V1)) nF_U12(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U13(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U21(tt,V1) -> nF_isNatKind(activate(V1)) nF_U31(tt,V2) -> nF_isNatKind(activate(V2)) nF_U51(tt,N) -> nF_isNatKind(activate(N)) nF_plus(N,0) -> nF_U51(isNat(N),N) nF_U61(tt,M,N) -> nF_isNatKind(activate(M)) nF_U63(tt,M,N) -> nF_isNatKind(activate(N)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_plus(N,0) -> nF_isNat(N) nF_plus(N,s(M)) -> nF_isNat(M) nF_isNat(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_U51(tt,N) -> nF_activate(N) nF_U52(tt,N) -> nF_activate(N) nF_U51(tt,N) -> nF_U52(isNatKind(activate(N)),activate(N)) nF_U61(tt,M,N) -> nF_activate(M) nF_U61(tt,M,N) -> nF_activate(N) nF_U62(tt,M,N) -> nF_activate(N) nF_U62(tt,M,N) -> nF_activate(M) nF_U63(tt,M,N) -> nF_activate(N) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = X1 + X2 [tt] = 1 [U12](X1,X2,X3) = X1 + X2 [isNatKind](X) = 1 [activate](X) = X [U13](X1,X2,X3) = X1 + X2 [U14](X1,X2,X3) = X2 [U15](X1,X2) = X1 [isNat](X) = X [U16](X) = 1 [U21](X1,X2) = X2 [U22](X1,X2) = X2 [U23](X) = X [U31](X1,X2) = X1 [U32](X) = 1 [U41](X) = 1 [U51](X1,X2) = X2 + 1 [U52](X1,X2) = X1 + X2 [U61](X1,X2,X3) = X2 + X3 + 1 [U62](X1,X2,X3) = X1 + X2 + X3 [U63](X1,X2,X3) = X2 + X3 + 1 [U64](X1,X2,X3) = X1 + X2 + X3 [s](X) = X [plus](X1,X2) = X1 + X2 + 1 [n__0] = 1 [n__plus](X1,X2) = X1 + X2 + 1 [n__s](X) = X [0] = 1 [nF_U11](X1,X2,X3) = X2 + X3 + 1 [nF_isNat](X) = X + 1 [nF_U14](X1,X2,X3) = X1 + X2 + X3 [nF_U13](X1,X2,X3) = X2 + X3 + 1 [nF_U12](X1,X2,X3) = X1 + X2 + X3 [nF_U15](X1,X2) = X1 + X2 [nF_U22](X1,X2) = X1 + X2 [nF_U21](X1,X2) = X2 + 1 [nF_U62](X1,X2,X3) = X1 + X2 + X3 [nF_U61](X1,X2,X3) = X2 + X3 + 1 [nF_plus](X1,X2) = X1 + X2 + 1 [nF_U64](X1,X2,X3) = X1 + X2 + X3 [nF_U63](X1,X2,X3) = X2 + X3 + 1 [nF_activate](X) = X [nF_U31](X1,X2) = X1 + X2 [nF_isNatKind](X) = X [nF_U51](X1,X2) = X2 [nF_U52](X1,X2) = X2 TIME: 0.214083 -> -> Dependency pairs in cycle: nF_U11(tt,V1,V2) -> nF_U12(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_U11(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_plus(N,s(M)) -> nF_isNat(M) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_U62(tt,M,N) -> nF_activate(M) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_activate(N) nF_U61(tt,M,N) -> nF_activate(N) nF_U61(tt,M,N) -> nF_activate(M) nF_U52(tt,N) -> nF_activate(N) nF_U51(tt,N) -> nF_U52(isNatKind(activate(N)),activate(N)) nF_plus(N,0) -> nF_U51(isNat(N),N) nF_U51(tt,N) -> nF_activate(N) nF_U31(tt,V2) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_isNatKind(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_isNat(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_plus(N,0) -> nF_isNat(N) nF_U62(tt,M,N) -> nF_isNat(activate(N)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U15(tt,V2) -> nF_isNat(activate(V2)) nF_U14(tt,V1,V2) -> nF_U15(isNat(activate(V1)),activate(V2)) nF_U13(tt,V1,V2) -> nF_U14(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U12(tt,V1,V2) -> nF_U13(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U14(tt,V1,V2) -> nF_isNat(activate(V1)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_U63(tt,M,N) -> nF_isNatKind(activate(N)) nF_U61(tt,M,N) -> nF_isNatKind(activate(M)) nF_U51(tt,N) -> nF_isNatKind(activate(N)) nF_U31(tt,V2) -> nF_isNatKind(activate(V2)) nF_U21(tt,V1) -> nF_isNatKind(activate(V1)) nF_U13(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U12(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U11(tt,V1,V2) -> nF_isNatKind(activate(V1)) nF_U22(tt,V1) -> nF_activate(V1) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = X1 [tt] = 1 [U12](X1,X2,X3) = X1 [isNatKind](X) = 1 [activate](X) = X [U13](X1,X2,X3) = 1 [U14](X1,X2,X3) = X1 [U15](X1,X2) = X1 [isNat](X) = 1 [U16](X) = 1 [U21](X1,X2) = 1 [U22](X1,X2) = X1 [U23](X) = 1 [U31](X1,X2) = X1 [U32](X) = 1 [U41](X) = 1 [U51](X1,X2) = X2 + 1 [U52](X1,X2) = X1 + X2 [U61](X1,X2,X3) = X1 + X2 + X3 + 1 [U62](X1,X2,X3) = X1 + X2 + X3 + 1 [U63](X1,X2,X3) = X1 + X2 + X3 + 1 [U64](X1,X2,X3) = X1 + X2 + X3 + 1 [s](X) = X + 1 [plus](X1,X2) = X1 + X2 + 1 [n__0] = 0 [n__plus](X1,X2) = X1 + X2 + 1 [n__s](X) = X + 1 [0] = 0 [nF_U11](X1,X2,X3) = X2 + X3 + 1 [nF_isNat](X) = X [nF_plus](X1,X2) = X1 + X2 [nF_activate](X) = X [nF_U62](X1,X2,X3) = X1 + X2 + X3 [nF_U61](X1,X2,X3) = X2 + X3 + 1 [nF_U64](X1,X2,X3) = X1 + X2 + X3 [nF_U63](X1,X2,X3) = X2 + X3 + 1 [nF_U52](X1,X2) = X2 [nF_U51](X1,X2) = X2 [nF_U31](X1,X2) = X1 + X2 [nF_isNatKind](X) = X [nF_U22](X1,X2) = X1 + X2 [nF_U21](X1,X2) = X1 + X2 [nF_U15](X1,X2) = X1 + X2 [nF_U14](X1,X2,X3) = X1 + X2 + X3 [nF_U13](X1,X2,X3) = X2 + X3 + 1 [nF_U12](X1,X2,X3) = X1 + X2 + X3 TIME: 0.22106899999999996 -> -> Dependency pairs in cycle: nF_U11(tt,V1,V2) -> nF_U12(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_U11(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_U14(tt,V1,V2) -> nF_isNat(activate(V1)) nF_U13(tt,V1,V2) -> nF_U14(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U12(tt,V1,V2) -> nF_U13(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U15(tt,V2) -> nF_isNat(activate(V2)) nF_U14(tt,V1,V2) -> nF_U15(isNat(activate(V1)),activate(V2)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U62(tt,M,N) -> nF_isNat(activate(N)) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_U31(tt,V2) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_U11(tt,V1,V2) -> nF_isNatKind(activate(V1)) nF_U12(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U13(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U21(tt,V1) -> nF_isNatKind(activate(V1)) nF_U31(tt,V2) -> nF_isNatKind(activate(V2)) nF_U51(tt,N) -> nF_isNatKind(activate(N)) nF_plus(N,0) -> nF_U51(isNat(N),N) nF_U61(tt,M,N) -> nF_isNatKind(activate(M)) nF_U63(tt,M,N) -> nF_isNatKind(activate(N)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_plus(N,0) -> nF_isNat(N) nF_plus(N,s(M)) -> nF_isNat(M) nF_isNat(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_U51(tt,N) -> nF_activate(N) nF_U52(tt,N) -> nF_activate(N) nF_U51(tt,N) -> nF_U52(isNatKind(activate(N)),activate(N)) nF_U61(tt,M,N) -> nF_activate(M) nF_U61(tt,M,N) -> nF_activate(N) nF_U62(tt,M,N) -> nF_activate(N) nF_U62(tt,M,N) -> nF_activate(M) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = X1 [tt] = 1 [U12](X1,X2,X3) = 1 [isNatKind](X) = 1 [activate](X) = X [U13](X1,X2,X3) = 1 [U14](X1,X2,X3) = X1 [U15](X1,X2) = X1 [isNat](X) = 1 [U16](X) = 1 [U21](X1,X2) = 1 [U22](X1,X2) = X1 [U23](X) = 1 [U31](X1,X2) = X1 [U32](X) = 1 [U41](X) = 1 [U51](X1,X2) = X2 + 1 [U52](X1,X2) = X1 + X2 [U61](X1,X2,X3) = X1 + X2 + X3 + 1 [U62](X1,X2,X3) = X1 + X2 + X3 + 1 [U63](X1,X2,X3) = X1 + X2 + X3 + 1 [U64](X1,X2,X3) = X1 + X2 + X3 + 1 [s](X) = X + 1 [plus](X1,X2) = X1 + X2 + 1 [n__0] = 0 [n__plus](X1,X2) = X1 + X2 + 1 [n__s](X) = X + 1 [0] = 0 [nF_U11](X1,X2,X3) = X2 + X3 + 1 [nF_isNat](X) = X [nF_U14](X1,X2,X3) = X1 + X2 + X3 [nF_U13](X1,X2,X3) = X2 + X3 + 1 [nF_U12](X1,X2,X3) = X1 + X2 + X3 [nF_U15](X1,X2) = X1 + X2 [nF_U22](X1,X2) = X1 + X2 [nF_U21](X1,X2) = X2 + 1 [nF_U62](X1,X2,X3) = X1 + X2 + X3 [nF_U61](X1,X2,X3) = X1 + X2 + X3 [nF_plus](X1,X2) = X1 + X2 [nF_U64](X1,X2,X3) = X1 + X2 + X3 [nF_U63](X1,X2,X3) = X2 + X3 + 1 [nF_activate](X) = X [nF_U31](X1,X2) = X1 + X2 [nF_isNatKind](X) = X [nF_U51](X1,X2) = X2 [nF_U52](X1,X2) = X2 TIME: 0.21107 -> -> Dependency pairs in cycle: nF_U11(tt,V1,V2) -> nF_U12(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_U11(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_plus(N,s(M)) -> nF_isNat(M) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_U62(tt,M,N) -> nF_activate(N) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_U61(tt,M,N) -> nF_activate(N) nF_U61(tt,M,N) -> nF_activate(M) nF_U52(tt,N) -> nF_activate(N) nF_U51(tt,N) -> nF_U52(isNatKind(activate(N)),activate(N)) nF_plus(N,0) -> nF_U51(isNat(N),N) nF_U51(tt,N) -> nF_activate(N) nF_U31(tt,V2) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_isNatKind(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_isNat(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_plus(N,0) -> nF_isNat(N) nF_U62(tt,M,N) -> nF_isNat(activate(N)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U15(tt,V2) -> nF_isNat(activate(V2)) nF_U14(tt,V1,V2) -> nF_U15(isNat(activate(V1)),activate(V2)) nF_U13(tt,V1,V2) -> nF_U14(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U12(tt,V1,V2) -> nF_U13(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U14(tt,V1,V2) -> nF_isNat(activate(V1)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_U63(tt,M,N) -> nF_isNatKind(activate(N)) nF_U61(tt,M,N) -> nF_isNatKind(activate(M)) nF_U51(tt,N) -> nF_isNatKind(activate(N)) nF_U31(tt,V2) -> nF_isNatKind(activate(V2)) nF_U21(tt,V1) -> nF_isNatKind(activate(V1)) nF_U13(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U12(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U11(tt,V1,V2) -> nF_isNatKind(activate(V1)) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = 1 [tt] = 0 [U12](X1,X2,X3) = 1 [isNatKind](X) = X [activate](X) = X [U13](X1,X2,X3) = 1 [U14](X1,X2,X3) = 1 [U15](X1,X2) = X1 [isNat](X) = 1 [U16](X) = 0 [U21](X1,X2) = 0 [U22](X1,X2) = 0 [U23](X) = 0 [U31](X1,X2) = 0 [U32](X) = 0 [U41](X) = 0 [U51](X1,X2) = X2 [U52](X1,X2) = X2 [U61](X1,X2,X3) = X2 + X3 + 1 [U62](X1,X2,X3) = X2 + X3 + 1 [U63](X1,X2,X3) = X2 + X3 + 1 [U64](X1,X2,X3) = X2 + X3 + 1 [s](X) = X + 1 [plus](X1,X2) = X1 + X2 [n__0] = 1 [n__plus](X1,X2) = X1 + X2 [n__s](X) = X + 1 [0] = 1 [nF_U11](X1,X2,X3) = X2 + X3 + 1 [nF_isNat](X) = X + 1 [nF_plus](X1,X2) = X1 + X2 [nF_activate](X) = X [nF_U62](X1,X2,X3) = X2 + X3 + 1 [nF_U61](X1,X2,X3) = X2 + X3 + 1 [nF_U64](X1,X2,X3) = X2 + X3 [nF_U63](X1,X2,X3) = X1 + X2 + X3 [nF_U52](X1,X2) = X2 [nF_U51](X1,X2) = X2 [nF_U31](X1,X2) = X2 [nF_isNatKind](X) = X [nF_U22](X1,X2) = X2 + 1 [nF_U21](X1,X2) = X2 + 1 [nF_U15](X1,X2) = X2 + 1 [nF_U14](X1,X2,X3) = X2 + X3 + 1 [nF_U13](X1,X2,X3) = X2 + X3 + 1 [nF_U12](X1,X2,X3) = X2 + X3 + 1 TIME: 0.211307 -> -> Dependency pairs in cycle: nF_U11(tt,V1,V2) -> nF_U12(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_U11(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_U14(tt,V1,V2) -> nF_isNat(activate(V1)) nF_U13(tt,V1,V2) -> nF_U14(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U12(tt,V1,V2) -> nF_U13(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U15(tt,V2) -> nF_isNat(activate(V2)) nF_U14(tt,V1,V2) -> nF_U15(isNat(activate(V1)),activate(V2)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U62(tt,M,N) -> nF_isNat(activate(N)) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_U31(tt,V2) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_U12(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U13(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U21(tt,V1) -> nF_isNatKind(activate(V1)) nF_U31(tt,V2) -> nF_isNatKind(activate(V2)) nF_U51(tt,N) -> nF_isNatKind(activate(N)) nF_plus(N,0) -> nF_U51(isNat(N),N) nF_U61(tt,M,N) -> nF_isNatKind(activate(M)) nF_U63(tt,M,N) -> nF_isNatKind(activate(N)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_plus(N,0) -> nF_isNat(N) nF_plus(N,s(M)) -> nF_isNat(M) nF_isNat(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_U51(tt,N) -> nF_activate(N) nF_U52(tt,N) -> nF_activate(N) nF_U51(tt,N) -> nF_U52(isNatKind(activate(N)),activate(N)) nF_U61(tt,M,N) -> nF_activate(M) nF_U61(tt,M,N) -> nF_activate(N) nF_U62(tt,M,N) -> nF_activate(N) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = 0 [tt] = 0 [U12](X1,X2,X3) = 0 [isNatKind](X) = X [activate](X) = X [U13](X1,X2,X3) = 0 [U14](X1,X2,X3) = 0 [U15](X1,X2) = 0 [isNat](X) = X [U16](X) = 0 [U21](X1,X2) = 0 [U22](X1,X2) = 0 [U23](X) = 0 [U31](X1,X2) = 0 [U32](X) = 0 [U41](X) = 0 [U51](X1,X2) = X2 [U52](X1,X2) = X2 [U61](X1,X2,X3) = X2 + X3 + 1 [U62](X1,X2,X3) = X2 + X3 + 1 [U63](X1,X2,X3) = X2 + X3 + 1 [U64](X1,X2,X3) = X2 + X3 + 1 [s](X) = X + 1 [plus](X1,X2) = X1 + X2 [n__0] = 1 [n__plus](X1,X2) = X1 + X2 [n__s](X) = X + 1 [0] = 1 [nF_U11](X1,X2,X3) = X2 + X3 [nF_isNat](X) = X [nF_U14](X1,X2,X3) = X2 + X3 [nF_U13](X1,X2,X3) = X2 + X3 [nF_U12](X1,X2,X3) = X2 + X3 [nF_U15](X1,X2) = X2 [nF_U22](X1,X2) = X2 [nF_U21](X1,X2) = X2 [nF_U62](X1,X2,X3) = X2 + X3 + 1 [nF_U61](X1,X2,X3) = X2 + X3 + 1 [nF_plus](X1,X2) = X1 + X2 [nF_U64](X1,X2,X3) = X2 + X3 [nF_U63](X1,X2,X3) = X2 + X3 [nF_activate](X) = X [nF_U31](X1,X2) = X2 [nF_isNatKind](X) = X [nF_U51](X1,X2) = X2 [nF_U52](X1,X2) = X2 TIME: 0.216462 -> -> Dependency pairs in cycle: nF_U11(tt,V1,V2) -> nF_U12(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_U11(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_plus(N,s(M)) -> nF_isNat(M) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_U61(tt,M,N) -> nF_activate(N) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_U61(tt,M,N) -> nF_activate(M) nF_U52(tt,N) -> nF_activate(N) nF_U51(tt,N) -> nF_U52(isNatKind(activate(N)),activate(N)) nF_plus(N,0) -> nF_U51(isNat(N),N) nF_U51(tt,N) -> nF_activate(N) nF_U31(tt,V2) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_isNatKind(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_isNat(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_plus(N,0) -> nF_isNat(N) nF_U62(tt,M,N) -> nF_isNat(activate(N)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U15(tt,V2) -> nF_isNat(activate(V2)) nF_U14(tt,V1,V2) -> nF_U15(isNat(activate(V1)),activate(V2)) nF_U13(tt,V1,V2) -> nF_U14(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U12(tt,V1,V2) -> nF_U13(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U14(tt,V1,V2) -> nF_isNat(activate(V1)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_U63(tt,M,N) -> nF_isNatKind(activate(N)) nF_U61(tt,M,N) -> nF_isNatKind(activate(M)) nF_U51(tt,N) -> nF_isNatKind(activate(N)) nF_U31(tt,V2) -> nF_isNatKind(activate(V2)) nF_U21(tt,V1) -> nF_isNatKind(activate(V1)) nF_U13(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U12(tt,V1,V2) -> nF_isNatKind(activate(V2)) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = 1 [tt] = 0 [U12](X1,X2,X3) = 1 [isNatKind](X) = X [activate](X) = X [U13](X1,X2,X3) = 1 [U14](X1,X2,X3) = 1 [U15](X1,X2) = X1 [isNat](X) = 1 [U16](X) = 0 [U21](X1,X2) = 0 [U22](X1,X2) = 0 [U23](X) = 0 [U31](X1,X2) = 0 [U32](X) = 0 [U41](X) = 0 [U51](X1,X2) = X2 [U52](X1,X2) = X2 [U61](X1,X2,X3) = X2 + X3 + 1 [U62](X1,X2,X3) = X2 + X3 + 1 [U63](X1,X2,X3) = X2 + X3 + 1 [U64](X1,X2,X3) = X2 + X3 + 1 [s](X) = X + 1 [plus](X1,X2) = X1 + X2 [n__0] = 1 [n__plus](X1,X2) = X1 + X2 [n__s](X) = X + 1 [0] = 1 [nF_U11](X1,X2,X3) = X2 + X3 + 1 [nF_isNat](X) = X + 1 [nF_plus](X1,X2) = X1 + X2 [nF_activate](X) = X [nF_U61](X1,X2,X3) = X2 + X3 + 1 [nF_U64](X1,X2,X3) = X2 + X3 [nF_U63](X1,X2,X3) = X1 + X2 + X3 [nF_U62](X1,X2,X3) = X2 + X3 + 1 [nF_U52](X1,X2) = X2 [nF_U51](X1,X2) = X2 [nF_U31](X1,X2) = X2 [nF_isNatKind](X) = X [nF_U22](X1,X2) = X2 + 1 [nF_U21](X1,X2) = X2 + 1 [nF_U15](X1,X2) = X2 + 1 [nF_U14](X1,X2,X3) = X2 + X3 + 1 [nF_U13](X1,X2,X3) = X2 + X3 + 1 [nF_U12](X1,X2,X3) = X2 + X3 + 1 TIME: 0.24073 -> -> Dependency pairs in cycle: nF_U11(tt,V1,V2) -> nF_U12(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_U11(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_U14(tt,V1,V2) -> nF_isNat(activate(V1)) nF_U13(tt,V1,V2) -> nF_U14(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U12(tt,V1,V2) -> nF_U13(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U15(tt,V2) -> nF_isNat(activate(V2)) nF_U14(tt,V1,V2) -> nF_U15(isNat(activate(V1)),activate(V2)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U62(tt,M,N) -> nF_isNat(activate(N)) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_U31(tt,V2) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_U13(tt,V1,V2) -> nF_isNatKind(activate(V2)) nF_U21(tt,V1) -> nF_isNatKind(activate(V1)) nF_U31(tt,V2) -> nF_isNatKind(activate(V2)) nF_U51(tt,N) -> nF_isNatKind(activate(N)) nF_plus(N,0) -> nF_U51(isNat(N),N) nF_U61(tt,M,N) -> nF_isNatKind(activate(M)) nF_U63(tt,M,N) -> nF_isNatKind(activate(N)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_plus(N,0) -> nF_isNat(N) nF_plus(N,s(M)) -> nF_isNat(M) nF_isNat(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_U51(tt,N) -> nF_activate(N) nF_U52(tt,N) -> nF_activate(N) nF_U51(tt,N) -> nF_U52(isNatKind(activate(N)),activate(N)) nF_U61(tt,M,N) -> nF_activate(M) nF_U61(tt,M,N) -> nF_activate(N) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = X1 [tt] = 1 [U12](X1,X2,X3) = 1 [isNatKind](X) = 1 [activate](X) = X [U13](X1,X2,X3) = X1 [U14](X1,X2,X3) = X1 [U15](X1,X2) = X1 [isNat](X) = 1 [U16](X) = 1 [U21](X1,X2) = 1 [U22](X1,X2) = X1 [U23](X) = 1 [U31](X1,X2) = X1 [U32](X) = 1 [U41](X) = 1 [U51](X1,X2) = X2 + 1 [U52](X1,X2) = X1 + X2 [U61](X1,X2,X3) = X1 + X2 + X3 + 1 [U62](X1,X2,X3) = X1 + X2 + X3 + 1 [U63](X1,X2,X3) = X1 + X2 + X3 + 1 [U64](X1,X2,X3) = X1 + X2 + X3 + 1 [s](X) = X + 1 [plus](X1,X2) = X1 + X2 + 1 [n__0] = 0 [n__plus](X1,X2) = X1 + X2 + 1 [n__s](X) = X + 1 [0] = 0 [nF_U11](X1,X2,X3) = X2 + X3 + 1 [nF_isNat](X) = X [nF_U14](X1,X2,X3) = X1 + X2 + X3 [nF_U13](X1,X2,X3) = X2 + X3 + 1 [nF_U12](X1,X2,X3) = X1 + X2 + X3 [nF_U15](X1,X2) = X1 + X2 [nF_U22](X1,X2) = X1 + X2 [nF_U21](X1,X2) = X2 + 1 [nF_U62](X1,X2,X3) = X1 + X2 + X3 [nF_U61](X1,X2,X3) = X1 + X2 + X3 [nF_plus](X1,X2) = X1 + X2 [nF_U64](X1,X2,X3) = X1 + X2 + X3 [nF_U63](X1,X2,X3) = X2 + X3 + 1 [nF_activate](X) = X [nF_U31](X1,X2) = X1 + X2 [nF_isNatKind](X) = X [nF_U51](X1,X2) = X2 [nF_U52](X1,X2) = X2 TIME: 0.22269499999999998 -> -> Dependency pairs in cycle: nF_U11(tt,V1,V2) -> nF_U12(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_U11(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_plus(N,s(M)) -> nF_isNat(M) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_U61(tt,M,N) -> nF_activate(M) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_U52(tt,N) -> nF_activate(N) nF_U51(tt,N) -> nF_U52(isNatKind(activate(N)),activate(N)) nF_plus(N,0) -> nF_U51(isNat(N),N) nF_U51(tt,N) -> nF_activate(N) nF_U31(tt,V2) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_isNatKind(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_isNat(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_plus(N,0) -> nF_isNat(N) nF_U62(tt,M,N) -> nF_isNat(activate(N)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U15(tt,V2) -> nF_isNat(activate(V2)) nF_U14(tt,V1,V2) -> nF_U15(isNat(activate(V1)),activate(V2)) nF_U13(tt,V1,V2) -> nF_U14(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U12(tt,V1,V2) -> nF_U13(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U14(tt,V1,V2) -> nF_isNat(activate(V1)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_U63(tt,M,N) -> nF_isNatKind(activate(N)) nF_U61(tt,M,N) -> nF_isNatKind(activate(M)) nF_U51(tt,N) -> nF_isNatKind(activate(N)) nF_U31(tt,V2) -> nF_isNatKind(activate(V2)) nF_U21(tt,V1) -> nF_isNatKind(activate(V1)) nF_U13(tt,V1,V2) -> nF_isNatKind(activate(V2)) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = 0 [tt] = 0 [U12](X1,X2,X3) = 0 [isNatKind](X) = X [activate](X) = X [U13](X1,X2,X3) = 0 [U14](X1,X2,X3) = 0 [U15](X1,X2) = 0 [isNat](X) = X [U16](X) = 0 [U21](X1,X2) = 0 [U22](X1,X2) = 0 [U23](X) = 0 [U31](X1,X2) = 0 [U32](X) = 0 [U41](X) = 0 [U51](X1,X2) = X2 [U52](X1,X2) = X2 [U61](X1,X2,X3) = X2 + X3 + 1 [U62](X1,X2,X3) = X2 + X3 + 1 [U63](X1,X2,X3) = X2 + X3 + 1 [U64](X1,X2,X3) = X2 + X3 + 1 [s](X) = X + 1 [plus](X1,X2) = X1 + X2 [n__0] = 1 [n__plus](X1,X2) = X1 + X2 [n__s](X) = X + 1 [0] = 1 [nF_U11](X1,X2,X3) = X2 + X3 + 1 [nF_isNat](X) = X + 1 [nF_plus](X1,X2) = X1 + X2 [nF_activate](X) = X [nF_U61](X1,X2,X3) = X2 + X3 + 1 [nF_U64](X1,X2,X3) = X2 + X3 [nF_U63](X1,X2,X3) = X2 + X3 [nF_U62](X1,X2,X3) = X2 + X3 + 1 [nF_U52](X1,X2) = X2 [nF_U51](X1,X2) = X2 [nF_U31](X1,X2) = X2 [nF_isNatKind](X) = X [nF_U22](X1,X2) = X2 + 1 [nF_U21](X1,X2) = X2 + 1 [nF_U15](X1,X2) = X2 + 1 [nF_U14](X1,X2,X3) = X2 + X3 + 1 [nF_U13](X1,X2,X3) = X2 + X3 + 1 [nF_U12](X1,X2,X3) = X2 + X3 + 1 TIME: 0.209653 -> -> Dependency pairs in cycle: nF_U11(tt,V1,V2) -> nF_U12(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_U11(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_U14(tt,V1,V2) -> nF_isNat(activate(V1)) nF_U13(tt,V1,V2) -> nF_U14(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U12(tt,V1,V2) -> nF_U13(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U15(tt,V2) -> nF_isNat(activate(V2)) nF_U14(tt,V1,V2) -> nF_U15(isNat(activate(V1)),activate(V2)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U62(tt,M,N) -> nF_isNat(activate(N)) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_U31(tt,V2) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_U21(tt,V1) -> nF_isNatKind(activate(V1)) nF_U31(tt,V2) -> nF_isNatKind(activate(V2)) nF_U51(tt,N) -> nF_isNatKind(activate(N)) nF_plus(N,0) -> nF_U51(isNat(N),N) nF_U61(tt,M,N) -> nF_isNatKind(activate(M)) nF_U63(tt,M,N) -> nF_isNatKind(activate(N)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_plus(N,0) -> nF_isNat(N) nF_plus(N,s(M)) -> nF_isNat(M) nF_isNat(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_U51(tt,N) -> nF_activate(N) nF_U52(tt,N) -> nF_activate(N) nF_U51(tt,N) -> nF_U52(isNatKind(activate(N)),activate(N)) nF_U61(tt,M,N) -> nF_activate(M) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = 0 [tt] = 0 [U12](X1,X2,X3) = 0 [isNatKind](X) = 1 [activate](X) = X [U13](X1,X2,X3) = 0 [U14](X1,X2,X3) = 0 [U15](X1,X2) = 0 [isNat](X) = X [U16](X) = 0 [U21](X1,X2) = 1 [U22](X1,X2) = X1 [U23](X) = 0 [U31](X1,X2) = 0 [U32](X) = 0 [U41](X) = 0 [U51](X1,X2) = X2 + 1 [U52](X1,X2) = X1 + X2 [U61](X1,X2,X3) = X2 + X3 + 1 [U62](X1,X2,X3) = X2 + X3 + 1 [U63](X1,X2,X3) = X2 + X3 + 1 [U64](X1,X2,X3) = X2 + X3 + 1 [s](X) = X + 1 [plus](X1,X2) = X1 + X2 [n__0] = 1 [n__plus](X1,X2) = X1 + X2 [n__s](X) = X + 1 [0] = 1 [nF_U11](X1,X2,X3) = X2 + X3 [nF_isNat](X) = X [nF_U14](X1,X2,X3) = X2 + X3 [nF_U13](X1,X2,X3) = X2 + X3 [nF_U12](X1,X2,X3) = X2 + X3 [nF_U15](X1,X2) = X2 [nF_U22](X1,X2) = X2 [nF_U21](X1,X2) = X2 [nF_U62](X1,X2,X3) = X1 + X2 + X3 [nF_U61](X1,X2,X3) = X2 + X3 + 1 [nF_plus](X1,X2) = X1 + X2 [nF_U64](X1,X2,X3) = X2 + X3 [nF_U63](X1,X2,X3) = X2 + X3 [nF_activate](X) = X [nF_U31](X1,X2) = X2 [nF_isNatKind](X) = X [nF_U51](X1,X2) = X2 + 1 [nF_U52](X1,X2) = X1 + X2 TIME: 0.195074 -> -> Dependency pairs in cycle: nF_U11(tt,V1,V2) -> nF_U12(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_U11(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_plus(N,s(M)) -> nF_isNat(M) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_U52(tt,N) -> nF_activate(N) nF_U51(tt,N) -> nF_U52(isNatKind(activate(N)),activate(N)) nF_plus(N,0) -> nF_U51(isNat(N),N) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_U51(tt,N) -> nF_activate(N) nF_U31(tt,V2) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_isNatKind(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_isNat(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_plus(N,0) -> nF_isNat(N) nF_U62(tt,M,N) -> nF_isNat(activate(N)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U15(tt,V2) -> nF_isNat(activate(V2)) nF_U14(tt,V1,V2) -> nF_U15(isNat(activate(V1)),activate(V2)) nF_U13(tt,V1,V2) -> nF_U14(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U12(tt,V1,V2) -> nF_U13(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U14(tt,V1,V2) -> nF_isNat(activate(V1)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_U63(tt,M,N) -> nF_isNatKind(activate(N)) nF_U61(tt,M,N) -> nF_isNatKind(activate(M)) nF_U51(tt,N) -> nF_isNatKind(activate(N)) nF_U31(tt,V2) -> nF_isNatKind(activate(V2)) nF_U21(tt,V1) -> nF_isNatKind(activate(V1)) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = 1 [tt] = 0 [U12](X1,X2,X3) = 1 [isNatKind](X) = X [activate](X) = X [U13](X1,X2,X3) = 1 [U14](X1,X2,X3) = 1 [U15](X1,X2) = X1 [isNat](X) = 1 [U16](X) = 0 [U21](X1,X2) = 0 [U22](X1,X2) = 0 [U23](X) = 0 [U31](X1,X2) = 0 [U32](X) = 0 [U41](X) = 0 [U51](X1,X2) = X2 [U52](X1,X2) = X2 [U61](X1,X2,X3) = X2 + X3 + 1 [U62](X1,X2,X3) = X2 + X3 + 1 [U63](X1,X2,X3) = X2 + X3 + 1 [U64](X1,X2,X3) = X2 + X3 + 1 [s](X) = X + 1 [plus](X1,X2) = X1 + X2 [n__0] = 1 [n__plus](X1,X2) = X1 + X2 [n__s](X) = X + 1 [0] = 1 [nF_U11](X1,X2,X3) = X2 + X3 [nF_isNat](X) = X [nF_plus](X1,X2) = X1 + X2 [nF_activate](X) = X [nF_U52](X1,X2) = X2 [nF_U51](X1,X2) = X2 [nF_U64](X1,X2,X3) = X2 + X3 [nF_U63](X1,X2,X3) = X1 + X2 + X3 [nF_U62](X1,X2,X3) = X2 + X3 + 1 [nF_U61](X1,X2,X3) = X2 + X3 + 1 [nF_U31](X1,X2) = X2 [nF_isNatKind](X) = X [nF_U22](X1,X2) = X2 [nF_U21](X1,X2) = X2 + 1 [nF_U15](X1,X2) = X2 [nF_U14](X1,X2,X3) = X2 + X3 [nF_U13](X1,X2,X3) = X2 + X3 [nF_U12](X1,X2,X3) = X2 + X3 TIME: 0.212944 -> -> Dependency pairs in cycle: nF_U11(tt,V1,V2) -> nF_U12(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_U11(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_U14(tt,V1,V2) -> nF_isNat(activate(V1)) nF_U13(tt,V1,V2) -> nF_U14(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U12(tt,V1,V2) -> nF_U13(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U15(tt,V2) -> nF_isNat(activate(V2)) nF_U14(tt,V1,V2) -> nF_U15(isNat(activate(V1)),activate(V2)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U62(tt,M,N) -> nF_isNat(activate(N)) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_U31(tt,V2) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_U31(tt,V2) -> nF_isNatKind(activate(V2)) nF_U51(tt,N) -> nF_isNatKind(activate(N)) nF_plus(N,0) -> nF_U51(isNat(N),N) nF_U61(tt,M,N) -> nF_isNatKind(activate(M)) nF_U63(tt,M,N) -> nF_isNatKind(activate(N)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_plus(N,0) -> nF_isNat(N) nF_plus(N,s(M)) -> nF_isNat(M) nF_isNat(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_U51(tt,N) -> nF_activate(N) nF_U52(tt,N) -> nF_activate(N) nF_U51(tt,N) -> nF_U52(isNatKind(activate(N)),activate(N)) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = 0 [tt] = 0 [U12](X1,X2,X3) = 0 [isNatKind](X) = 0 [activate](X) = X [U13](X1,X2,X3) = 0 [U14](X1,X2,X3) = 0 [U15](X1,X2) = 0 [isNat](X) = 0 [U16](X) = 0 [U21](X1,X2) = 0 [U22](X1,X2) = 0 [U23](X) = 0 [U31](X1,X2) = 0 [U32](X) = 0 [U41](X) = 0 [U51](X1,X2) = X2 [U52](X1,X2) = X2 [U61](X1,X2,X3) = X2 + X3 + 1 [U62](X1,X2,X3) = X2 + X3 + 1 [U63](X1,X2,X3) = X2 + X3 + 1 [U64](X1,X2,X3) = X2 + X3 + 1 [s](X) = X [plus](X1,X2) = X1 + X2 + 1 [n__0] = 0 [n__plus](X1,X2) = X1 + X2 + 1 [n__s](X) = X [0] = 0 [nF_U11](X1,X2,X3) = X2 + X3 [nF_isNat](X) = X [nF_U14](X1,X2,X3) = X2 + X3 [nF_U13](X1,X2,X3) = X2 + X3 [nF_U12](X1,X2,X3) = X2 + X3 [nF_U15](X1,X2) = X2 [nF_U22](X1,X2) = X2 [nF_U21](X1,X2) = X2 [nF_U62](X1,X2,X3) = X2 + X3 + 1 [nF_U61](X1,X2,X3) = X2 + X3 + 1 [nF_plus](X1,X2) = X1 + X2 + 1 [nF_U64](X1,X2,X3) = X2 + X3 + 1 [nF_U63](X1,X2,X3) = X2 + X3 + 1 [nF_activate](X) = X [nF_U31](X1,X2) = X2 [nF_isNatKind](X) = X [nF_U51](X1,X2) = X2 + 1 [nF_U52](X1,X2) = X2 TIME: 0.20428100000000005 -> -> Dependency pairs in cycle: nF_U11(tt,V1,V2) -> nF_U12(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_U11(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_plus(N,s(M)) -> nF_isNat(M) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_U51(tt,N) -> nF_activate(N) nF_plus(N,0) -> nF_U51(isNat(N),N) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_U31(tt,V2) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_isNatKind(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_isNat(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_plus(N,0) -> nF_isNat(N) nF_U62(tt,M,N) -> nF_isNat(activate(N)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U15(tt,V2) -> nF_isNat(activate(V2)) nF_U14(tt,V1,V2) -> nF_U15(isNat(activate(V1)),activate(V2)) nF_U13(tt,V1,V2) -> nF_U14(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U12(tt,V1,V2) -> nF_U13(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U14(tt,V1,V2) -> nF_isNat(activate(V1)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_U63(tt,M,N) -> nF_isNatKind(activate(N)) nF_U61(tt,M,N) -> nF_isNatKind(activate(M)) nF_U51(tt,N) -> nF_isNatKind(activate(N)) nF_U31(tt,V2) -> nF_isNatKind(activate(V2)) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = X1 + X3 [tt] = 1 [U12](X1,X2,X3) = X3 + 1 [isNatKind](X) = X + 1 [activate](X) = X [U13](X1,X2,X3) = X1 [U14](X1,X2,X3) = 1 [U15](X1,X2) = 1 [isNat](X) = X + 1 [U16](X) = 1 [U21](X1,X2) = X2 + 1 [U22](X1,X2) = X1 [U23](X) = 1 [U31](X1,X2) = X1 [U32](X) = 1 [U41](X) = 1 [U51](X1,X2) = X2 [U52](X1,X2) = X2 [U61](X1,X2,X3) = X2 + X3 + 1 [U62](X1,X2,X3) = X2 + X3 + 1 [U63](X1,X2,X3) = X2 + X3 + 1 [U64](X1,X2,X3) = X2 + X3 + 1 [s](X) = X [plus](X1,X2) = X1 + X2 + 1 [n__0] = 1 [n__plus](X1,X2) = X1 + X2 + 1 [n__s](X) = X [0] = 1 [nF_U11](X1,X2,X3) = X2 + X3 [nF_isNat](X) = X [nF_plus](X1,X2) = X1 + X2 [nF_activate](X) = X [nF_U51](X1,X2) = X2 [nF_U64](X1,X2,X3) = X2 + X3 [nF_U63](X1,X2,X3) = X2 + X3 [nF_U62](X1,X2,X3) = X2 + X3 [nF_U61](X1,X2,X3) = X2 + X3 [nF_U31](X1,X2) = X1 + X2 [nF_isNatKind](X) = X [nF_U22](X1,X2) = X2 [nF_U21](X1,X2) = X2 [nF_U15](X1,X2) = X2 [nF_U14](X1,X2,X3) = X2 + X3 [nF_U13](X1,X2,X3) = X2 + X3 [nF_U12](X1,X2,X3) = X2 + X3 TIME: 0.202533 -> -> Dependency pairs in cycle: nF_U11(tt,V1,V2) -> nF_U12(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_U11(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_U14(tt,V1,V2) -> nF_isNat(activate(V1)) nF_U13(tt,V1,V2) -> nF_U14(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U12(tt,V1,V2) -> nF_U13(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U15(tt,V2) -> nF_isNat(activate(V2)) nF_U14(tt,V1,V2) -> nF_U15(isNat(activate(V1)),activate(V2)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U62(tt,M,N) -> nF_isNat(activate(N)) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_U31(tt,V2) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_U51(tt,N) -> nF_isNatKind(activate(N)) nF_plus(N,0) -> nF_U51(isNat(N),N) nF_U61(tt,M,N) -> nF_isNatKind(activate(M)) nF_U63(tt,M,N) -> nF_isNatKind(activate(N)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_plus(N,0) -> nF_isNat(N) nF_plus(N,s(M)) -> nF_isNat(M) nF_isNat(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_U51(tt,N) -> nF_activate(N) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = 0 [tt] = 0 [U12](X1,X2,X3) = 0 [isNatKind](X) = 1 [activate](X) = X [U13](X1,X2,X3) = 0 [U14](X1,X2,X3) = 0 [U15](X1,X2) = 0 [isNat](X) = 0 [U16](X) = 0 [U21](X1,X2) = 0 [U22](X1,X2) = 0 [U23](X) = 0 [U31](X1,X2) = 0 [U32](X) = 0 [U41](X) = 0 [U51](X1,X2) = X2 + 1 [U52](X1,X2) = X1 + X2 [U61](X1,X2,X3) = X2 + X3 + 1 [U62](X1,X2,X3) = X2 + X3 + 1 [U63](X1,X2,X3) = X2 + X3 + 1 [U64](X1,X2,X3) = X2 + X3 + 1 [s](X) = X [plus](X1,X2) = X1 + X2 + 1 [n__0] = 0 [n__plus](X1,X2) = X1 + X2 + 1 [n__s](X) = X [0] = 0 [nF_U11](X1,X2,X3) = X2 + X3 + 1 [nF_isNat](X) = X [nF_U14](X1,X2,X3) = X2 + X3 [nF_U13](X1,X2,X3) = X2 + X3 [nF_U12](X1,X2,X3) = X1 + X2 + X3 [nF_U15](X1,X2) = X2 [nF_U22](X1,X2) = X2 [nF_U21](X1,X2) = X2 [nF_U62](X1,X2,X3) = X2 + X3 + 1 [nF_U61](X1,X2,X3) = X2 + X3 + 1 [nF_plus](X1,X2) = X1 + X2 + 1 [nF_U64](X1,X2,X3) = X2 + X3 + 1 [nF_U63](X1,X2,X3) = X2 + X3 + 1 [nF_activate](X) = X [nF_U31](X1,X2) = X1 + X2 [nF_isNatKind](X) = X [nF_U51](X1,X2) = X2 + 1 TIME: 0.258369 -> -> Dependency pairs in cycle: nF_U11(tt,V1,V2) -> nF_U12(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_U11(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_plus(N,s(M)) -> nF_isNat(M) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_U31(tt,V2) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_isNatKind(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_isNat(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_plus(N,0) -> nF_isNat(N) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_U62(tt,M,N) -> nF_isNat(activate(N)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U15(tt,V2) -> nF_isNat(activate(V2)) nF_U14(tt,V1,V2) -> nF_U15(isNat(activate(V1)),activate(V2)) nF_U13(tt,V1,V2) -> nF_U14(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U12(tt,V1,V2) -> nF_U13(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U14(tt,V1,V2) -> nF_isNat(activate(V1)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_U63(tt,M,N) -> nF_isNatKind(activate(N)) nF_U61(tt,M,N) -> nF_isNatKind(activate(M)) nF_U51(tt,N) -> nF_isNatKind(activate(N)) nF_plus(N,0) -> nF_U51(isNat(N),N) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = 0 [tt] = 0 [U12](X1,X2,X3) = 0 [isNatKind](X) = 0 [activate](X) = X [U13](X1,X2,X3) = 0 [U14](X1,X2,X3) = 0 [U15](X1,X2) = 0 [isNat](X) = 0 [U16](X) = 0 [U21](X1,X2) = 0 [U22](X1,X2) = 0 [U23](X) = 0 [U31](X1,X2) = 0 [U32](X) = 0 [U41](X) = 0 [U51](X1,X2) = X2 [U52](X1,X2) = X2 [U61](X1,X2,X3) = X2 + X3 + 1 [U62](X1,X2,X3) = X2 + X3 + 1 [U63](X1,X2,X3) = X2 + X3 + 1 [U64](X1,X2,X3) = X2 + X3 + 1 [s](X) = X [plus](X1,X2) = X1 + X2 + 1 [n__0] = 0 [n__plus](X1,X2) = X1 + X2 + 1 [n__s](X) = X [0] = 0 [nF_U11](X1,X2,X3) = X2 + X3 [nF_isNat](X) = X [nF_plus](X1,X2) = X1 + X2 + 1 [nF_activate](X) = X [nF_U31](X1,X2) = X2 [nF_isNatKind](X) = X [nF_U64](X1,X2,X3) = X2 + X3 + 1 [nF_U63](X1,X2,X3) = X2 + X3 + 1 [nF_U62](X1,X2,X3) = X2 + X3 + 1 [nF_U61](X1,X2,X3) = X2 + X3 + 1 [nF_U22](X1,X2) = X2 [nF_U21](X1,X2) = X2 [nF_U15](X1,X2) = X2 [nF_U14](X1,X2,X3) = X2 + X3 [nF_U13](X1,X2,X3) = X2 + X3 [nF_U12](X1,X2,X3) = X2 + X3 [nF_U51](X1,X2) = X2 TIME: 0.19041 -> -> Dependency pairs in cycle: nF_U11(tt,V1,V2) -> nF_U12(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_U11(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_U14(tt,V1,V2) -> nF_isNat(activate(V1)) nF_U13(tt,V1,V2) -> nF_U14(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U12(tt,V1,V2) -> nF_U13(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U15(tt,V2) -> nF_isNat(activate(V2)) nF_U14(tt,V1,V2) -> nF_U15(isNat(activate(V1)),activate(V2)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U62(tt,M,N) -> nF_isNat(activate(N)) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_U31(tt,V2) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_U61(tt,M,N) -> nF_isNatKind(activate(M)) nF_U63(tt,M,N) -> nF_isNatKind(activate(N)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_plus(N,0) -> nF_isNat(N) nF_plus(N,s(M)) -> nF_isNat(M) nF_isNat(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__s(V1)) -> nF_isNatKind(activate(V1)) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = X2 + X3 + 1 [tt] = 1 [U12](X1,X2,X3) = X1 + X3 [isNatKind](X) = X + 1 [activate](X) = X [U13](X1,X2,X3) = X3 + 1 [U14](X1,X2,X3) = X3 + 1 [U15](X1,X2) = X2 + 1 [isNat](X) = X + 1 [U16](X) = X [U21](X1,X2) = X2 + 1 [U22](X1,X2) = X2 + 1 [U23](X) = X [U31](X1,X2) = X2 + 1 [U32](X) = X [U41](X) = X [U51](X1,X2) = X2 [U52](X1,X2) = X2 [U61](X1,X2,X3) = X2 + X3 + 1 [U62](X1,X2,X3) = X2 + X3 + 1 [U63](X1,X2,X3) = X2 + X3 + 1 [U64](X1,X2,X3) = X2 + X3 + 1 [s](X) = X + 1 [plus](X1,X2) = X1 + X2 [n__0] = 1 [n__plus](X1,X2) = X1 + X2 [n__s](X) = X + 1 [0] = 1 [nF_U11](X1,X2,X3) = X2 + X3 + 1 [nF_isNat](X) = X + 1 [nF_U14](X1,X2,X3) = X2 + X3 + 1 [nF_U13](X1,X2,X3) = X2 + X3 + 1 [nF_U12](X1,X2,X3) = X2 + X3 + 1 [nF_U15](X1,X2) = X1 + X2 [nF_U22](X1,X2) = X2 + 1 [nF_U21](X1,X2) = X2 + 1 [nF_U62](X1,X2,X3) = X2 + X3 + 1 [nF_U61](X1,X2,X3) = X2 + X3 + 1 [nF_plus](X1,X2) = X1 + X2 [nF_U64](X1,X2,X3) = X2 + X3 [nF_U63](X1,X2,X3) = X2 + X3 + 1 [nF_activate](X) = X [nF_U31](X1,X2) = X1 + X2 [nF_isNatKind](X) = X + 1 TIME: 0.181641 -> -> Dependency pairs in cycle: nF_U11(tt,V1,V2) -> nF_U12(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_U11(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_plus(N,s(M)) -> nF_isNat(M) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_U31(tt,V2) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_isNatKind(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_isNat(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_plus(N,0) -> nF_isNat(N) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_U62(tt,M,N) -> nF_isNat(activate(N)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U15(tt,V2) -> nF_isNat(activate(V2)) nF_U14(tt,V1,V2) -> nF_U15(isNat(activate(V1)),activate(V2)) nF_U13(tt,V1,V2) -> nF_U14(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U12(tt,V1,V2) -> nF_U13(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U14(tt,V1,V2) -> nF_isNat(activate(V1)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_U63(tt,M,N) -> nF_isNatKind(activate(N)) nF_U61(tt,M,N) -> nF_isNatKind(activate(M)) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = X3 + 1 [tt] = 0 [U12](X1,X2,X3) = X3 + 1 [isNatKind](X) = X + 1 [activate](X) = X [U13](X1,X2,X3) = X3 + 1 [U14](X1,X2,X3) = X1 [U15](X1,X2) = 0 [isNat](X) = X [U16](X) = 0 [U21](X1,X2) = 0 [U22](X1,X2) = 0 [U23](X) = 0 [U31](X1,X2) = 0 [U32](X) = 0 [U41](X) = 0 [U51](X1,X2) = X2 [U52](X1,X2) = X2 [U61](X1,X2,X3) = X2 + X3 + 1 [U62](X1,X2,X3) = X2 + X3 + 1 [U63](X1,X2,X3) = X2 + X3 + 1 [U64](X1,X2,X3) = X2 + X3 + 1 [s](X) = X [plus](X1,X2) = X1 + X2 + 1 [n__0] = 1 [n__plus](X1,X2) = X1 + X2 + 1 [n__s](X) = X [0] = 1 [nF_U11](X1,X2,X3) = X2 + X3 [nF_isNat](X) = X [nF_plus](X1,X2) = X1 + X2 + 1 [nF_activate](X) = X [nF_U31](X1,X2) = X1 + X2 [nF_isNatKind](X) = X [nF_U64](X1,X2,X3) = X2 + X3 + 1 [nF_U63](X1,X2,X3) = X2 + X3 + 1 [nF_U62](X1,X2,X3) = X2 + X3 + 1 [nF_U61](X1,X2,X3) = X2 + X3 + 1 [nF_U22](X1,X2) = X2 [nF_U21](X1,X2) = X2 [nF_U15](X1,X2) = X2 [nF_U14](X1,X2,X3) = X2 + X3 [nF_U13](X1,X2,X3) = X2 + X3 [nF_U12](X1,X2,X3) = X2 + X3 TIME: 0.19362999999999997 -> -> Dependency pairs in cycle: nF_U11(tt,V1,V2) -> nF_U12(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_U11(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_U14(tt,V1,V2) -> nF_isNat(activate(V1)) nF_U13(tt,V1,V2) -> nF_U14(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U12(tt,V1,V2) -> nF_U13(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U15(tt,V2) -> nF_isNat(activate(V2)) nF_U14(tt,V1,V2) -> nF_U15(isNat(activate(V1)),activate(V2)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U62(tt,M,N) -> nF_isNat(activate(N)) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_U31(tt,V2) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_U63(tt,M,N) -> nF_isNatKind(activate(N)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_plus(N,0) -> nF_isNat(N) nF_plus(N,s(M)) -> nF_isNat(M) nF_isNat(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_isNatKind(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = X2 + X3 + 1 [tt] = 1 [U12](X1,X2,X3) = X1 + X3 [isNatKind](X) = X + 1 [activate](X) = X [U13](X1,X2,X3) = X3 [U14](X1,X2,X3) = X3 [U15](X1,X2) = X2 [isNat](X) = X [U16](X) = X [U21](X1,X2) = X2 [U22](X1,X2) = X2 [U23](X) = X [U31](X1,X2) = X2 + 1 [U32](X) = X [U41](X) = X [U51](X1,X2) = X2 [U52](X1,X2) = X2 [U61](X1,X2,X3) = X2 + X3 + 1 [U62](X1,X2,X3) = X2 + X3 + 1 [U63](X1,X2,X3) = X2 + X3 + 1 [U64](X1,X2,X3) = X2 + X3 + 1 [s](X) = X [plus](X1,X2) = X1 + X2 + 1 [n__0] = 1 [n__plus](X1,X2) = X1 + X2 + 1 [n__s](X) = X [0] = 1 [nF_U11](X1,X2,X3) = X2 + X3 [nF_isNat](X) = X [nF_U14](X1,X2,X3) = X2 + X3 [nF_U13](X1,X2,X3) = X2 + X3 [nF_U12](X1,X2,X3) = X2 + X3 [nF_U15](X1,X2) = X1 + X2 [nF_U22](X1,X2) = X2 [nF_U21](X1,X2) = X2 [nF_U62](X1,X2,X3) = X2 + X3 [nF_U61](X1,X2,X3) = X2 + X3 [nF_plus](X1,X2) = X1 + X2 [nF_U64](X1,X2,X3) = X2 + X3 [nF_U63](X1,X2,X3) = X2 + X3 [nF_activate](X) = X [nF_U31](X1,X2) = X1 + X2 [nF_isNatKind](X) = X TIME: 0.204012 -> -> Dependency pairs in cycle: nF_U11(tt,V1,V2) -> nF_U12(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_U11(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_plus(N,s(M)) -> nF_isNat(M) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_U31(tt,V2) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_isNat(n__s(V1)) -> nF_isNatKind(activate(V1)) nF_plus(N,0) -> nF_isNat(N) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_U62(tt,M,N) -> nF_isNat(activate(N)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U15(tt,V2) -> nF_isNat(activate(V2)) nF_U14(tt,V1,V2) -> nF_U15(isNat(activate(V1)),activate(V2)) nF_U13(tt,V1,V2) -> nF_U14(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U12(tt,V1,V2) -> nF_U13(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U14(tt,V1,V2) -> nF_isNat(activate(V1)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_U63(tt,M,N) -> nF_isNatKind(activate(N)) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = 0 [tt] = 0 [U12](X1,X2,X3) = 0 [isNatKind](X) = X [activate](X) = X [U13](X1,X2,X3) = 0 [U14](X1,X2,X3) = 0 [U15](X1,X2) = 0 [isNat](X) = X [U16](X) = 0 [U21](X1,X2) = 0 [U22](X1,X2) = 0 [U23](X) = 0 [U31](X1,X2) = 0 [U32](X) = 0 [U41](X) = 0 [U51](X1,X2) = X2 [U52](X1,X2) = X2 [U61](X1,X2,X3) = X2 + X3 + 1 [U62](X1,X2,X3) = X2 + X3 + 1 [U63](X1,X2,X3) = X2 + X3 + 1 [U64](X1,X2,X3) = X2 + X3 + 1 [s](X) = X [plus](X1,X2) = X1 + X2 + 1 [n__0] = 1 [n__plus](X1,X2) = X1 + X2 + 1 [n__s](X) = X [0] = 1 [nF_U11](X1,X2,X3) = X2 + X3 [nF_isNat](X) = X [nF_plus](X1,X2) = X1 + X2 + 1 [nF_activate](X) = X [nF_U31](X1,X2) = X2 [nF_isNatKind](X) = X [nF_U64](X1,X2,X3) = X2 + X3 + 1 [nF_U63](X1,X2,X3) = X2 + X3 + 1 [nF_U62](X1,X2,X3) = X2 + X3 + 1 [nF_U61](X1,X2,X3) = X2 + X3 + 1 [nF_U22](X1,X2) = X2 [nF_U21](X1,X2) = X2 [nF_U15](X1,X2) = X2 [nF_U14](X1,X2,X3) = X2 + X3 [nF_U13](X1,X2,X3) = X2 + X3 [nF_U12](X1,X2,X3) = X2 + X3 TIME: 0.191094 -> -> Dependency pairs in cycle: nF_U11(tt,V1,V2) -> nF_U12(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_U11(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_U14(tt,V1,V2) -> nF_isNat(activate(V1)) nF_U13(tt,V1,V2) -> nF_U14(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U12(tt,V1,V2) -> nF_U13(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U15(tt,V2) -> nF_isNat(activate(V2)) nF_U14(tt,V1,V2) -> nF_U15(isNat(activate(V1)),activate(V2)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U62(tt,M,N) -> nF_isNat(activate(N)) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_U31(tt,V2) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_plus(N,0) -> nF_isNat(N) nF_plus(N,s(M)) -> nF_isNat(M) nF_isNat(n__s(V1)) -> nF_isNatKind(activate(V1)) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = 1 [tt] = 0 [U12](X1,X2,X3) = 1 [isNatKind](X) = X [activate](X) = X [U13](X1,X2,X3) = 1 [U14](X1,X2,X3) = 1 [U15](X1,X2) = X1 [isNat](X) = 1 [U16](X) = 0 [U21](X1,X2) = 0 [U22](X1,X2) = 0 [U23](X) = 0 [U31](X1,X2) = 0 [U32](X) = 0 [U41](X) = 0 [U51](X1,X2) = X2 [U52](X1,X2) = X2 [U61](X1,X2,X3) = X2 + X3 + 1 [U62](X1,X2,X3) = X2 + X3 + 1 [U63](X1,X2,X3) = X2 + X3 + 1 [U64](X1,X2,X3) = X2 + X3 + 1 [s](X) = X + 1 [plus](X1,X2) = X1 + X2 [n__0] = 1 [n__plus](X1,X2) = X1 + X2 [n__s](X) = X + 1 [0] = 1 [nF_U11](X1,X2,X3) = X2 + X3 [nF_isNat](X) = X [nF_U14](X1,X2,X3) = X2 + X3 [nF_U13](X1,X2,X3) = X2 + X3 [nF_U12](X1,X2,X3) = X2 + X3 [nF_U15](X1,X2) = X2 [nF_U22](X1,X2) = X2 [nF_U21](X1,X2) = X2 [nF_U62](X1,X2,X3) = X2 + X3 + 1 [nF_U61](X1,X2,X3) = X2 + X3 + 1 [nF_plus](X1,X2) = X1 + X2 [nF_U64](X1,X2,X3) = X2 + X3 [nF_U63](X1,X2,X3) = X1 + X2 + X3 [nF_activate](X) = X [nF_U31](X1,X2) = X2 [nF_isNatKind](X) = X TIME: 0.200986 -> -> Dependency pairs in cycle: nF_U11(tt,V1,V2) -> nF_U12(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_U11(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_plus(N,s(M)) -> nF_isNat(M) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_U31(tt,V2) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_plus(N,0) -> nF_isNat(N) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_U62(tt,M,N) -> nF_isNat(activate(N)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U15(tt,V2) -> nF_isNat(activate(V2)) nF_U14(tt,V1,V2) -> nF_U15(isNat(activate(V1)),activate(V2)) nF_U13(tt,V1,V2) -> nF_U14(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U12(tt,V1,V2) -> nF_U13(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U14(tt,V1,V2) -> nF_isNat(activate(V1)) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = X1 + X2 [tt] = 1 [U12](X1,X2,X3) = X1 + X2 [isNatKind](X) = 1 [activate](X) = X [U13](X1,X2,X3) = X2 + 1 [U14](X1,X2,X3) = X1 + X2 [U15](X1,X2) = X1 [isNat](X) = X [U16](X) = 1 [U21](X1,X2) = X2 [U22](X1,X2) = X2 [U23](X) = X [U31](X1,X2) = X1 [U32](X) = 1 [U41](X) = 1 [U51](X1,X2) = X2 + 1 [U52](X1,X2) = X1 + X2 [U61](X1,X2,X3) = X2 + X3 + 1 [U62](X1,X2,X3) = X1 + X2 + X3 [U63](X1,X2,X3) = X2 + X3 + 1 [U64](X1,X2,X3) = X2 + X3 + 1 [s](X) = X [plus](X1,X2) = X1 + X2 + 1 [n__0] = 1 [n__plus](X1,X2) = X1 + X2 + 1 [n__s](X) = X [0] = 1 [nF_U11](X1,X2,X3) = X1 + X2 + X3 [nF_isNat](X) = X [nF_plus](X1,X2) = X1 + X2 [nF_activate](X) = X [nF_U31](X1,X2) = X1 + X2 [nF_isNatKind](X) = X [nF_U64](X1,X2,X3) = X2 + X3 [nF_U63](X1,X2,X3) = X2 + X3 [nF_U62](X1,X2,X3) = X2 + X3 [nF_U61](X1,X2,X3) = X2 + X3 [nF_U22](X1,X2) = X2 [nF_U21](X1,X2) = X2 [nF_U15](X1,X2) = X2 [nF_U14](X1,X2,X3) = X2 + X3 + 1 [nF_U13](X1,X2,X3) = X2 + X3 + 1 [nF_U12](X1,X2,X3) = X1 + X2 + X3 TIME: 0.193136 -> -> Dependency pairs in cycle: nF_U11(tt,V1,V2) -> nF_U12(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_U11(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_U15(tt,V2) -> nF_isNat(activate(V2)) nF_U14(tt,V1,V2) -> nF_U15(isNat(activate(V1)),activate(V2)) nF_U13(tt,V1,V2) -> nF_U14(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U12(tt,V1,V2) -> nF_U13(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U62(tt,M,N) -> nF_isNat(activate(N)) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_U31(tt,V2) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_plus(N,0) -> nF_isNat(N) nF_plus(N,s(M)) -> nF_isNat(M) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = 1 [tt] = 0 [U12](X1,X2,X3) = 1 [isNatKind](X) = X [activate](X) = X [U13](X1,X2,X3) = 1 [U14](X1,X2,X3) = 1 [U15](X1,X2) = X1 [isNat](X) = 1 [U16](X) = 0 [U21](X1,X2) = 0 [U22](X1,X2) = 0 [U23](X) = 0 [U31](X1,X2) = 0 [U32](X) = 0 [U41](X) = 0 [U51](X1,X2) = X2 [U52](X1,X2) = X2 [U61](X1,X2,X3) = X2 + X3 + 1 [U62](X1,X2,X3) = X2 + X3 + 1 [U63](X1,X2,X3) = X2 + X3 + 1 [U64](X1,X2,X3) = X2 + X3 + 1 [s](X) = X + 1 [plus](X1,X2) = X1 + X2 [n__0] = 1 [n__plus](X1,X2) = X1 + X2 [n__s](X) = X + 1 [0] = 1 [nF_U11](X1,X2,X3) = X3 [nF_isNat](X) = X [nF_U15](X1,X2) = X2 [nF_U14](X1,X2,X3) = X3 [nF_U13](X1,X2,X3) = X3 [nF_U12](X1,X2,X3) = X3 [nF_U22](X1,X2) = X2 [nF_U21](X1,X2) = X2 [nF_U62](X1,X2,X3) = X2 + X3 + 1 [nF_U61](X1,X2,X3) = X2 + X3 + 1 [nF_plus](X1,X2) = X1 + X2 [nF_U64](X1,X2,X3) = X2 + X3 [nF_U63](X1,X2,X3) = X1 + X2 + X3 [nF_activate](X) = X [nF_U31](X1,X2) = X2 [nF_isNatKind](X) = X TIME: 0.18071400000000004 -> -> Dependency pairs in cycle: nF_U11(tt,V1,V2) -> nF_U12(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_U11(isNatKind(activate(V1)),activate(V1),activate(V2)) nF_plus(N,0) -> nF_isNat(N) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_U31(tt,V2) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_U62(tt,M,N) -> nF_isNat(activate(N)) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U15(tt,V2) -> nF_isNat(activate(V2)) nF_U14(tt,V1,V2) -> nF_U15(isNat(activate(V1)),activate(V2)) nF_U13(tt,V1,V2) -> nF_U14(isNatKind(activate(V2)),activate(V1),activate(V2)) nF_U12(tt,V1,V2) -> nF_U13(isNatKind(activate(V2)),activate(V1),activate(V2)) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = 0 [tt] = 0 [U12](X1,X2,X3) = 0 [isNatKind](X) = X [activate](X) = X [U13](X1,X2,X3) = 0 [U14](X1,X2,X3) = 0 [U15](X1,X2) = 0 [isNat](X) = X [U16](X) = 0 [U21](X1,X2) = 0 [U22](X1,X2) = 0 [U23](X) = 0 [U31](X1,X2) = 0 [U32](X) = 0 [U41](X) = 0 [U51](X1,X2) = X2 [U52](X1,X2) = X2 [U61](X1,X2,X3) = X2 + X3 + 1 [U62](X1,X2,X3) = X2 + X3 + 1 [U63](X1,X2,X3) = X2 + X3 + 1 [U64](X1,X2,X3) = X2 + X3 + 1 [s](X) = X [plus](X1,X2) = X1 + X2 + 1 [n__0] = 1 [n__plus](X1,X2) = X1 + X2 + 1 [n__s](X) = X [0] = 1 [nF_U11](X1,X2,X3) = X3 + 1 [nF_isNat](X) = X [nF_plus](X1,X2) = X1 [nF_activate](X) = X [nF_U31](X1,X2) = X2 [nF_isNatKind](X) = X [nF_U62](X1,X2,X3) = X3 [nF_U61](X1,X2,X3) = X3 [nF_U64](X1,X2,X3) = X3 [nF_U63](X1,X2,X3) = X3 [nF_U22](X1,X2) = X2 [nF_U21](X1,X2) = X2 [nF_U15](X1,X2) = X2 [nF_U14](X1,X2,X3) = X3 [nF_U13](X1,X2,X3) = X3 [nF_U12](X1,X2,X3) = X3 + 1 TIME: 0.186572 -> -> Dependency pairs in cycle: nF_plus(N,0) -> nF_isNat(N) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_U31(tt,V2) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U62(tt,M,N) -> nF_isNat(activate(N)) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = 0 [tt] = 0 [U12](X1,X2,X3) = 0 [isNatKind](X) = X [activate](X) = X [U13](X1,X2,X3) = 0 [U14](X1,X2,X3) = 0 [U15](X1,X2) = 0 [isNat](X) = 0 [U16](X) = 0 [U21](X1,X2) = 0 [U22](X1,X2) = 0 [U23](X) = 0 [U31](X1,X2) = 0 [U32](X) = 0 [U41](X) = 0 [U51](X1,X2) = X2 [U52](X1,X2) = X2 [U61](X1,X2,X3) = X2 + X3 + 1 [U62](X1,X2,X3) = X2 + X3 + 1 [U63](X1,X2,X3) = X2 + X3 + 1 [U64](X1,X2,X3) = X2 + X3 + 1 [s](X) = X + 1 [plus](X1,X2) = X1 + X2 [n__0] = 1 [n__plus](X1,X2) = X1 + X2 [n__s](X) = X + 1 [0] = 1 [nF_plus](X1,X2) = X1 + X2 [nF_U64](X1,X2,X3) = X2 + X3 [nF_U63](X1,X2,X3) = X2 + X3 [nF_U62](X1,X2,X3) = X2 + X3 + 1 [nF_U61](X1,X2,X3) = X2 + X3 + 1 [nF_activate](X) = X [nF_U31](X1,X2) = X2 [nF_isNatKind](X) = X [nF_isNat](X) = X [nF_U22](X1,X2) = X2 [nF_U21](X1,X2) = X2 TIME: 0.167076 -> -> Dependency pairs in cycle: nF_plus(N,0) -> nF_isNat(N) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_U31(tt,V2) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) nF_U64(tt,M,N) -> nF_plus(activate(N),activate(M)) nF_U63(tt,M,N) -> nF_U64(isNatKind(activate(N)),activate(M),activate(N)) nF_U62(tt,M,N) -> nF_U63(isNat(activate(N)),activate(M),activate(N)) nF_U61(tt,M,N) -> nF_U62(isNatKind(activate(M)),activate(M),activate(N)) nF_plus(N,s(M)) -> nF_U61(isNat(M),M,N) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = 0 [tt] = 0 [U12](X1,X2,X3) = 0 [isNatKind](X) = X [activate](X) = X [U13](X1,X2,X3) = 0 [U14](X1,X2,X3) = 0 [U15](X1,X2) = 0 [isNat](X) = 0 [U16](X) = 0 [U21](X1,X2) = 0 [U22](X1,X2) = 0 [U23](X) = 0 [U31](X1,X2) = 0 [U32](X) = 0 [U41](X) = 0 [U51](X1,X2) = X2 [U52](X1,X2) = X2 [U61](X1,X2,X3) = X2 + X3 + 1 [U62](X1,X2,X3) = X2 + X3 + 1 [U63](X1,X2,X3) = X2 + X3 + 1 [U64](X1,X2,X3) = X2 + X3 + 1 [s](X) = X + 1 [plus](X1,X2) = X1 + X2 [n__0] = 1 [n__plus](X1,X2) = X1 + X2 [n__s](X) = X + 1 [0] = 1 [nF_plus](X1,X2) = X1 + X2 [nF_activate](X) = X [nF_U31](X1,X2) = X2 [nF_isNatKind](X) = X [nF_isNat](X) = X [nF_U22](X1,X2) = X2 [nF_U21](X1,X2) = X2 [nF_U64](X1,X2,X3) = X2 + X3 [nF_U63](X1,X2,X3) = X2 + X3 [nF_U62](X1,X2,X3) = X2 + X3 [nF_U61](X1,X2,X3) = X2 + X3 TIME: 0.146323 -> -> Dependency pairs in cycle: nF_plus(N,0) -> nF_isNat(N) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_U31(tt,V2) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) nF_U22(tt,V1) -> nF_isNat(activate(V1)) nF_U21(tt,V1) -> nF_U22(isNatKind(activate(V1)),activate(V1)) nF_isNat(n__s(V1)) -> nF_U21(isNatKind(activate(V1)),activate(V1)) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = X1 [tt] = 1 [U12](X1,X2,X3) = X1 [isNatKind](X) = 1 [activate](X) = X [U13](X1,X2,X3) = 1 [U14](X1,X2,X3) = X1 [U15](X1,X2) = X1 [isNat](X) = 1 [U16](X) = 1 [U21](X1,X2) = 1 [U22](X1,X2) = X1 [U23](X) = 1 [U31](X1,X2) = X1 [U32](X) = 1 [U41](X) = 1 [U51](X1,X2) = X2 + 1 [U52](X1,X2) = X1 + X2 [U61](X1,X2,X3) = X2 + X3 + 1 [U62](X1,X2,X3) = X1 + X2 + X3 [U63](X1,X2,X3) = X1 + X2 + X3 [U64](X1,X2,X3) = X1 + X2 + X3 [s](X) = X + 1 [plus](X1,X2) = X1 + X2 [n__0] = 1 [n__plus](X1,X2) = X1 + X2 [n__s](X) = X + 1 [0] = 1 [nF_plus](X1,X2) = X1 + X2 [nF_activate](X) = X [nF_U31](X1,X2) = X1 + X2 [nF_isNatKind](X) = X + 1 [nF_isNat](X) = X + 1 [nF_U22](X1,X2) = X1 + X2 [nF_U21](X1,X2) = X2 + 1 TIME: 0.128595 -> -> Dependency pairs in cycle: nF_plus(N,0) -> nF_isNat(N) nF_activate(n__plus(X1,X2)) -> nF_plus(X1,X2) nF_U31(tt,V2) -> nF_activate(V2) nF_isNatKind(n__plus(V1,V2)) -> nF_U31(isNatKind(activate(V1)),activate(V2)) nF_isNat(n__plus(V1,V2)) -> nF_isNatKind(activate(V1)) UsableRules: U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V2) -> U32(isNatKind(activate(V2))) U32(tt) -> tt U41(tt) -> tt U51(tt,N) -> U52(isNatKind(activate(N)),activate(N)) U52(tt,N) -> activate(N) U61(tt,M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N)) U62(tt,M,N) -> U63(isNat(activate(N)),activate(M),activate(N)) U63(tt,M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N)) U64(tt,M,N) -> s(plus(activate(N),activate(M))) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1))) plus(N,0) -> U51(isNat(N),N) plus(N,s(M)) -> U61(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(X) -> X Polynomial Interpretation: [U11](X1,X2,X3) = X2 + X3 + 1 [tt] = 1 [U12](X1,X2,X3) = X1 + X3 [isNatKind](X) = X + 1 [activate](X) = X [U13](X1,X2,X3) = X3 [U14](X1,X2,X3) = X3 [U15](X1,X2) = X2 [isNat](X) = X [U16](X) = X [U21](X1,X2) = X2 [U22](X1,X2) = X2 [U23](X) = X [U31](X1,X2) = X2 + 1 [U32](X) = X [U41](X) = X [U51](X1,X2) = X2 [U52](X1,X2) = X2 [U61](X1,X2,X3) = X2 + X3 + 1 [U62](X1,X2,X3) = X2 + X3 + 1 [U63](X1,X2,X3) = X2 + X3 + 1 [U64](X1,X2,X3) = X2 + X3 + 1 [s](X) = X [plus](X1,X2) = X1 + X2 + 1 [n__0] = 1 [n__plus](X1,X2) = X1 + X2 + 1 [n__s](X) = X [0] = 1 [nF_plus](X1,X2) = X1 + X2 [nF_activate](X) = X [nF_U31](X1,X2) = X1 + X2 [nF_isNatKind](X) = X [nF_isNat](X) = X TIME: 0.13276 SETTINGS: Base ordering: Polynomial ordering Proof mode: SCCs in DG + base ordering Upper bound for coeffs: 1 Rationals below 1 for all non-replacing args: No Polynomial interpretation: Linear Coeffs in polynomials: No rationals Delta: automatic Termination was proved succesfully.