Termination of the following Term Rewriting System could be disproven:
Generalized rewrite system (where rules with free variables on rhs are allowed):
The TRS R consists of the following rules:
after(s(N), cons(X)) → after(N, XS)
from(X) → cons(X)
after(0, XS) → XS
↳ GTRS
↳ CritRuleProof
Generalized rewrite system (where rules with free variables on rhs are allowed):
The TRS R consists of the following rules:
after(s(N), cons(X)) → after(N, XS)
from(X) → cons(X)
after(0, XS) → XS
The rule after(s(N), cons(X)) → after(N, XS) contains free variables in its right-hand side. Hence the TRS is not-terminating.