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:

tail(cons(X)) → XS
pairNs → cons(0)
oddNs → incr(pairNs)
incr(cons(X)) → cons(s(X))
take(0, XS) → nil
take(s(N), cons(X)) → cons(X)
zip(nil, XS) → nil
zip(X, nil) → nil
zip(cons(X), cons(Y)) → cons(pair(X, Y))
repItems(nil) → nil
repItems(cons(X)) → cons(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:

tail(cons(X)) → XS
pairNs → cons(0)
oddNs → incr(pairNs)
incr(cons(X)) → cons(s(X))
take(0, XS) → nil
take(s(N), cons(X)) → cons(X)
zip(nil, XS) → nil
zip(X, nil) → nil
zip(cons(X), cons(Y)) → cons(pair(X, Y))
repItems(nil) → nil
repItems(cons(X)) → cons(X)

Innermost Strategy.

The rule tail(cons(X)) → XS contains free variables in its right-hand side. Hence the TRS is not-terminating.