Innermost 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)
from(X) → cons(X)
first(0, Z) → nil
first(s(X), cons(Y)) → cons(Y)
sel(0, cons(X)) → X

Innermost Strategy.


↳ 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)
from(X) → cons(X)
first(0, Z) → nil
first(s(X), cons(Y)) → cons(Y)
sel(0, cons(X)) → X

Innermost Strategy.

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