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:

U12(tt) → s(plus(N, M))
U22(tt) → plus(x(N, M), N)
U11(tt) → U12(tt)
U21(tt) → U22(tt)
plus(N, 0) → N
plus(N, s(M)) → U11(tt)
x(N, 0) → 0
x(N, s(M)) → U21(tt)

Innermost Strategy.


↳ 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))
U22(tt) → plus(x(N, M), N)
U11(tt) → U12(tt)
U21(tt) → U22(tt)
plus(N, 0) → N
plus(N, s(M)) → U11(tt)
x(N, 0) → 0
x(N, s(M)) → U21(tt)

Innermost Strategy.

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