(0) Obligation:
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))
U41(tt) → plus(x(N, M), N)
and(tt) → X
U31(tt) → 0
isNat → tt
isNat → and(isNat)
isNat → isNat
plus(N, 0) → U11(isNat)
plus(N, s(M)) → U21(and(isNat))
x(N, 0) → U31(isNat)
x(N, s(M)) → U41(and(isNat))
(1) CritRuleProof (EQUIVALENT transformation)
The rule U11(tt) → N contains free variables in its right-hand side. Hence the TRS is not-terminating.
(2) NO