DONT KNOW
Welcome to CiME version 2.02 - Built on 14/04/2004 13:29:51

- : unit = ()
- : unit = ()
X : variable_set = <variable set>

F : signature = <signature>
R : HTRS = { zeros -> cons(0,zeros),
             U11(tt,V1) -> U12(isNatList(V1)),
             U12(tt) -> tt,
             U21(tt,V1) -> U22(isNat(V1)),
             U22(tt) -> tt,
             U31(tt,V) -> U32(isNatList(V)),
             U32(tt) -> tt,
             U41(tt,V1,V2) -> U42(isNat(V1),V2),
             U42(tt,V2) -> U43(isNatIList(V2)),
             U43(tt) -> tt,
             U51(tt,V1,V2) -> U52(isNat(V1),V2),
             U52(tt,V2) -> U53(isNatList(V2)),
             U53(tt) -> tt,
             U61(tt,V1,V2) -> U62(isNat(V1),V2),
             U62(tt,V2) -> U63(isNatIList(V2)),
             U63(tt) -> tt,
             U71(tt,L) -> s(length(L)),
             U81(tt) -> nil,
             U91(tt,IL,M,N) -> cons(N,take(M,IL)),
             and(tt,X) -> X,
             isNat(0) -> tt,
             isNat(length(V1)) -> U11(isNatIListKind(V1),V1),
             isNat(s(V1)) -> U21(isNatKind(V1),V1),
             isNatIList(V) -> U31(isNatIListKind(V),V),
             isNatIList(zeros) -> tt,
             isNatIList(cons(V1,V2)) ->
             U41(and(isNatKind(V1),isNatIListKind(V2)),V1,V2),
             isNatIListKind(nil) -> tt,
             isNatIListKind(zeros) -> tt,
             isNatIListKind(cons(V1,V2)) ->
             and(isNatKind(V1),isNatIListKind(V2)),
             isNatIListKind(take(V1,V2)) ->
             and(isNatKind(V1),isNatIListKind(V2)),
             isNatKind(0) -> tt,
             isNatKind(length(V1)) -> isNatIListKind(V1),
             isNatKind(s(V1)) -> isNatKind(V1),
             isNatList(nil) -> tt,
             isNatList(cons(V1,V2)) ->
             U51(and(isNatKind(V1),isNatIListKind(V2)),V1,V2),
             isNatList(take(V1,V2)) ->
             U61(and(isNatKind(V1),isNatIListKind(V2)),V1,V2),
             length(nil) -> 0,
             length(cons(N,L)) ->
             U71(and(and(isNatList(L),isNatIListKind(L)),and(isNat(N),
                                                         isNatKind(N))),L),
             take(0,IL) -> U81(and(isNatIList(IL),isNatIListKind(IL))),
             take(s(M),cons(N,IL)) ->
             U91(and(and(isNatIList(IL),isNatIListKind(IL)),and(and(isNat(M),
                                                                isNatKind(M)),
                                                            and(isNat(N),
                                                            isNatKind(N)))),IL,M,N) }
             (40 rules)
Termination now uses minimal decomposition
- : unit = ()
Entering the termination expert for modules. Verbose level = 0
Checking module:
{}

The dependency graph is
(0 nodes)
Checking each of the 0 strongly connected components :

Checking module:
{ and(tt,V_7) -> V_7 } (1 rules)

The dependency graph is
(0 nodes)
Checking each of the 0 strongly connected components :

Checking module:
{}

The dependency graph is
(0 nodes)
Checking each of the 0 strongly connected components :

Checking module:
{}

The dependency graph is
(0 nodes)
Checking each of the 0 strongly connected components :

Checking module:
{ U81(tt) -> nil } (1 rules)

The dependency graph is
(0 nodes)
Checking each of the 0 strongly connected components :

Checking module:
{}

The dependency graph is
(0 nodes)
Checking each of the 0 strongly connected components :

Checking module:
{ U43(tt) -> tt } (1 rules)

The dependency graph is
(0 nodes)
Checking each of the 0 strongly connected components :

Checking module:
{ U63(tt) -> tt } (1 rules)

The dependency graph is
(0 nodes)
Checking each of the 0 strongly connected components :

Checking module:
{ U53(tt) -> tt } (1 rules)

The dependency graph is
(0 nodes)
Checking each of the 0 strongly connected components :

Checking module:
{}

The dependency graph is
(0 nodes)
Checking each of the 0 strongly connected components :

Checking module:
{ U22(tt) -> tt } (1 rules)

The dependency graph is
(0 nodes)
Checking each of the 0 strongly connected components :

Checking module:
{ U12(tt) -> tt } (1 rules)

The dependency graph is
(0 nodes)
Checking each of the 0 strongly connected components :

Checking module:
{ U32(tt) -> tt } (1 rules)

The dependency graph is
(0 nodes)
Checking each of the 0 strongly connected components :

Checking module:
{ zeros -> cons(0,zeros) } (1 rules)

The dependency graph is
(1 nodes)
Checking each of the 1 strongly connected components :
Checking component 1
Trying simple graph criterion.
Trying to solve the following constraints:
(2 termination constraints)
Search parameters: linear polynomials, coefficient bound is 2.
No solution found for these parameters.
Search parameters: simple polynomials, coefficient bound is 3.
No solution found for these parameters.
No solution found for these constraints.
Trying strongly connected part criterion.
Trying to solve the following constraints:
(2 termination constraints)
Search parameters: linear polynomials, coefficient bound is 2.
No solution found for these parameters.
Search parameters: simple polynomials, coefficient bound is 3.
No solution found for these parameters.
No solution found for these constraints.
No modular termination proof found.
- : unit = ()
The last proof attempt failed.
- : unit = ()

Quitting.
Standard error: