Termination proof of /tmp/aprove_benchmark_example

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:

U11(tt) → s(length(L))
U31(tt) → cons(N)
and(tt) → X
zeros → cons(0)
U21(tt) → nil
isNat → tt
isNat → isNatList
isNat → isNat
isNatIList → isNatList
isNatIList → tt
isNatIList → and(isNat)
isNatList → tt
isNatList → and(isNat)
length(nil) → 0
length(cons(N)) → U11(and(isNatList))
take(0, IL) → U21(isNatIList)
take(s(M), cons(N)) → U31(and(isNatIList))

↳ GTRS

  ↳ CritRuleProof

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

U11(tt) → s(length(L))
U31(tt) → cons(N)
and(tt) → X
zeros → cons(0)
U21(tt) → nil
isNat → tt
isNat → isNatList
isNat → isNat
isNatIList → isNatList
isNatIList → tt
isNatIList → and(isNat)
isNatList → tt
isNatList → and(isNat)
length(nil) → 0
length(cons(N)) → U11(and(isNatList))
take(0, IL) → U21(isNatIList)
take(s(M), cons(N)) → U31(and(isNatIList))

The rule U11(tt) → s(length(L)) contains free variables in its right-hand side. Hence the TRS is not-terminating.