Termination proof of /tmp/aprove_benchmark_example

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)) → 2nd(cons1(X, X1))
2nd(cons1(X, cons(Y))) → Y
from(X) → cons(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)) → 2nd(cons1(X, X1))
2nd(cons1(X, cons(Y))) → Y
from(X) → cons(X)

The rule 2nd(cons(X)) → 2nd(cons1(X, X1)) contains free variables in its right-hand side. Hence the TRS is not-terminating.