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(s(X), X) → f(X, a(X))
f(X, c(X)) → f(s(X), X)
f(X, X) → c(X)
Q is empty.
↳ QTRS
↳ DirectTerminationProof
Q restricted rewrite system:
The TRS R consists of the following rules:
f(s(X), X) → f(X, a(X))
f(X, c(X)) → f(s(X), X)
f(X, X) → c(X)
Q is empty.
We use [23] with the following order to prove termination.
Recursive path order with status [2].
Precedence:
f2 > c1 > s1 > a1
Status:
a1: multiset
f2: multiset
c1: multiset
s1: multiset