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:
2nd(cons(X)) → head(XS)
sel(s(N), cons(X)) → sel(N, XS)
from(X) → cons(X)
head(cons(X)) → X
take(0, XS) → nil
take(s(N), cons(X)) → cons(X)
sel(0, cons(X)) → X
↳ GTRS
↳ CritRuleProof
Generalized rewrite system (where rules with free variables on rhs are allowed):
The TRS R consists of the following rules:
2nd(cons(X)) → head(XS)
sel(s(N), cons(X)) → sel(N, XS)
from(X) → cons(X)
head(cons(X)) → X
take(0, XS) → nil
take(s(N), cons(X)) → cons(X)
sel(0, cons(X)) → X
The rule 2nd(cons(X)) → head(XS) contains free variables in its right-hand side. Hence the TRS is not-terminating.