Termination proof of /tmp/tmp4Fy5ar/LengthOfFiniteLists_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:

U62(tt) → s(length(L))
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(isNat)
isNat → tt
isNat → U11(isNatList)
isNat → U21(isNat)
isNatIList → U31(isNatList)
isNatIList → tt
isNatIList → U41(isNat)
isNatList → tt
isNatList → U51(isNat)
length(nil) → 0
length(cons(N)) → U61(isNatList)

↳ GTRS

  ↳ CritRuleProof

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

U62(tt) → s(length(L))
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(isNat)
isNat → tt
isNat → U11(isNatList)
isNat → U21(isNat)
isNatIList → U31(isNatList)
isNatIList → tt
isNatIList → U41(isNat)
isNatList → tt
isNatList → U51(isNat)
length(nil) → 0
length(cons(N)) → U61(isNatList)

The rule U62(tt) → s(length(L)) contains free variables in its right-hand side. Hence the TRS is not-terminating.