Termination proof of /tmp/tmpFXT5x7/PEANO_nokinds

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:

U11(tt) → N
U21(tt) → s(plus(N, M))
and(tt) → X
isNat → tt
isNat → and(isNat)
isNat → isNat
plus(N, 0) → U11(isNat)
plus(N, s(M)) → U21(and(isNat))

↳ GTRS

  ↳ CritRuleProof

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

U11(tt) → N
U21(tt) → s(plus(N, M))
and(tt) → X
isNat → tt
isNat → and(isNat)
isNat → isNat
plus(N, 0) → U11(isNat)
plus(N, s(M)) → U21(and(isNat))

The rule U11(tt) → N contains free variables in its right-hand side. Hence the TRS is not-terminating.