Termination proof of /tmp/tmp5ESsMY/PEANO_nokinds-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:

U31(tt) → N
U42(tt) → s(plus(N, M))
U11(tt) → U12(isNat)
U12(tt) → tt
U21(tt) → tt
U41(tt) → U42(isNat)
isNat → tt
isNat → U11(isNat)
isNat → U21(isNat)
plus(N, 0) → U31(isNat)
plus(N, s(M)) → U41(isNat)

↳ GTRS

  ↳ CritRuleProof

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

U31(tt) → N
U42(tt) → s(plus(N, M))
U11(tt) → U12(isNat)
U12(tt) → tt
U21(tt) → tt
U41(tt) → U42(isNat)
isNat → tt
isNat → U11(isNat)
isNat → U21(isNat)
plus(N, 0) → U31(isNat)
plus(N, s(M)) → U41(isNat)

The rule U31(tt) → N contains free variables in its right-hand side. Hence the TRS is not-terminating.