(0) Obligation:
Generalized rewrite system (where rules with free variables on rhs are allowed):
The TRS R consists of the following rules:
U72(tt) → s(length(L))
U93(tt) → cons(N)
zeros → cons(0)
U11(tt) → tt
U21(tt) → tt
U31(tt) → tt
U41(tt) → U42(isNatIList)
U42(tt) → tt
U51(tt) → U52(isNatList)
U52(tt) → tt
U61(tt) → U62(isNatIList)
U62(tt) → tt
U71(tt) → U72(isNat)
U81(tt) → nil
U91(tt) → U92(isNat)
U92(tt) → U93(isNat)
isNat → tt
isNat → U11(isNatList)
isNat → U21(isNat)
isNatIList → U31(isNatList)
isNatIList → tt
isNatIList → U41(isNat)
isNatList → tt
isNatList → U51(isNat)
isNatList → U61(isNat)
length(nil) → 0
length(cons(N)) → U71(isNatList)
take(0, IL) → U81(isNatIList)
take(s(M), cons(N)) → U91(isNatIList)
(1) CritRuleProof (EQUIVALENT transformation)
The rule U72(tt) → s(length(L)) contains free variables in its right-hand side. Hence the TRS is not-terminating.
(2) NO