Termination proof of /tmp/tmpxVnEsO/PEANO_complete-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:

U52(tt) → N
U64(tt) → s(plus(N, M))
U11(tt) → U12(isNatKind)
U12(tt) → U13(isNatKind)
U13(tt) → U14(isNatKind)
U14(tt) → U15(isNat)
U15(tt) → U16(isNat)
U16(tt) → tt
U21(tt) → U22(isNatKind)
U22(tt) → U23(isNat)
U23(tt) → tt
U31(tt) → U32(isNatKind)
U32(tt) → tt
U41(tt) → tt
U51(tt) → U52(isNatKind)
U61(tt) → U62(isNatKind)
U62(tt) → U63(isNat)
U63(tt) → U64(isNatKind)
isNat → tt
isNat → U11(isNatKind)
isNat → U21(isNatKind)
isNatKind → tt
isNatKind → U31(isNatKind)
isNatKind → U41(isNatKind)
plus(N, 0) → U51(isNat)
plus(N, s(M)) → U61(isNat)

↳ GTRS

  ↳ CritRuleProof

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

U52(tt) → N
U64(tt) → s(plus(N, M))
U11(tt) → U12(isNatKind)
U12(tt) → U13(isNatKind)
U13(tt) → U14(isNatKind)
U14(tt) → U15(isNat)
U15(tt) → U16(isNat)
U16(tt) → tt
U21(tt) → U22(isNatKind)
U22(tt) → U23(isNat)
U23(tt) → tt
U31(tt) → U32(isNatKind)
U32(tt) → tt
U41(tt) → tt
U51(tt) → U52(isNatKind)
U61(tt) → U62(isNatKind)
U62(tt) → U63(isNat)
U63(tt) → U64(isNatKind)
isNat → tt
isNat → U11(isNatKind)
isNat → U21(isNatKind)
isNatKind → tt
isNatKind → U31(isNatKind)
isNatKind → U41(isNatKind)
plus(N, 0) → U51(isNat)
plus(N, s(M)) → U61(isNat)

The rule U52(tt) → N contains free variables in its right-hand side. Hence the TRS is not-terminating.