Termination proof of /tmp/tmp9OMHqK/PEANO_nosorts-noand

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:

U12(tt) → s(plus(N, M))
U11(tt) → U12(tt)
plus(N, 0) → N
plus(N, s(M)) → U11(tt)

↳ GTRS

  ↳ CritRuleProof

Generalized rewrite system (where rules with free variables on rhs are allowed):
The TRS R consists of the following rules:

U12(tt) → s(plus(N, M))
U11(tt) → U12(tt)
plus(N, 0) → N
plus(N, s(M)) → U11(tt)

The rule U12(tt) → s(plus(N, M)) contains free variables in its right-hand side. Hence the TRS is not-terminating.