Termination proof of /tmp/tmpw72Bq2/MYNAT_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:

U41(tt) → N
U52(tt) → s(plus(N, M))
U72(tt) → plus(x(N, M), N)
U11(tt) → U12(isNat)
U12(tt) → tt
U21(tt) → tt
U31(tt) → U32(isNat)
U32(tt) → tt
U51(tt) → U52(isNat)
U61(tt) → 0
U71(tt) → U72(isNat)
isNat → tt
isNat → U11(isNat)
isNat → U21(isNat)
isNat → U31(isNat)
plus(N, 0) → U41(isNat)
plus(N, s(M)) → U51(isNat)
x(N, 0) → U61(isNat)
x(N, s(M)) → U71(isNat)

↳ GTRS

  ↳ CritRuleProof

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

U41(tt) → N
U52(tt) → s(plus(N, M))
U72(tt) → plus(x(N, M), N)
U11(tt) → U12(isNat)
U12(tt) → tt
U21(tt) → tt
U31(tt) → U32(isNat)
U32(tt) → tt
U51(tt) → U52(isNat)
U61(tt) → 0
U71(tt) → U72(isNat)
isNat → tt
isNat → U11(isNat)
isNat → U21(isNat)
isNat → U31(isNat)
plus(N, 0) → U41(isNat)
plus(N, s(M)) → U51(isNat)
x(N, 0) → U61(isNat)
x(N, s(M)) → U71(isNat)

The rule U41(tt) → N contains free variables in its right-hand side. Hence the TRS is not-terminating.