YES
Termination w.r.t. Q proof of ../tpdb/TRS/TRCSR/Ex25_Luc06_L.trs
Termination w.r.t. Q of the following Term Rewriting System could be proven:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(f(X)) → c
c → d
h(X) → c
Q is empty.
↳ QTRS
↳ RRRPoloQTRSProof
Q restricted rewrite system:
The TRS R consists of the following rules:
f(f(X)) → c
c → d
h(X) → c
Q is empty.
The following Q TRS is given: Q restricted rewrite system:
The TRS R consists of the following rules:
f(f(X)) → c
c → d
h(X) → c
Q is empty.
The following rules can be removed by the rule removal processor [15] because they are oriented strictly by a polynomial ordering:
f(f(X)) → c
c → d
h(X) → c
Used ordering:
Polynomial interpretation [25]:
POL(c) = 1
POL(d) = 0
POL(f(x1)) = 2 + 2·x1
POL(h(x1)) = 2 + x1
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RisEmptyProof
Q restricted rewrite system:
R is empty.
Q is empty.
The TRS R is empty. Hence, termination is trivially proven.