(0) Obligation:
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)
(1) CritRuleProof (EQUIVALENT transformation)
The rule U12(tt) → s(plus(N, M)) contains free variables in its right-hand side. Hence the TRS is not-terminating.
(2) FALSE