Termination proof of /tmp/tmp0rSqzq/Ex4_Zan97

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:

sel(s(X), cons(Y)) → sel(X, Z)
f(X) → cons(X)
g(0) → s(0)
g(s(X)) → s(s(g(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:

sel(s(X), cons(Y)) → sel(X, Z)
f(X) → cons(X)
g(0) → s(0)
g(s(X)) → s(s(g(X)))
sel(0, cons(X)) → X

The rule sel(s(X), cons(Y)) → sel(X, Z) contains free variables in its right-hand side. Hence the TRS is not-terminating.