Termination proof of /tmp/tmpUv1XUz/PEANO_complete

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
U41(tt) → s(plus(N, M))
and(tt) → X
U11(tt) → U12(isNat)
U12(tt) → U13(isNat)
U13(tt) → tt
U21(tt) → U22(isNat)
U22(tt) → tt
isNat → tt
isNat → U11(and(isNatKind))
isNat → U21(isNatKind)
isNatKind → tt
isNatKind → and(isNatKind)
isNatKind → isNatKind
plus(N, 0) → U31(and(isNat))
plus(N, s(M)) → U41(and(and(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
U41(tt) → s(plus(N, M))
and(tt) → X
U11(tt) → U12(isNat)
U12(tt) → U13(isNat)
U13(tt) → tt
U21(tt) → U22(isNat)
U22(tt) → tt
isNat → tt
isNat → U11(and(isNatKind))
isNat → U21(isNatKind)
isNatKind → tt
isNatKind → and(isNatKind)
isNatKind → isNatKind
plus(N, 0) → U31(and(isNat))
plus(N, s(M)) → U41(and(and(isNat)))

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