(0) Obligation:
Generalized rewrite system (where rules with free variables on rhs are allowed):
The TRS R consists of the following rules:
U94(tt) → s(length(L))
zeros → cons(0)
U11(tt) → U12(isNatIListKind)
U12(tt) → U13(isNatList)
U13(tt) → tt
U21(tt) → U22(isNatKind)
U22(tt) → U23(isNat)
U23(tt) → tt
U31(tt) → U32(isNatIListKind)
U32(tt) → U33(isNatList)
U33(tt) → tt
U41(tt) → U42(isNatKind)
U42(tt) → U43(isNatIListKind)
U43(tt) → U44(isNatIListKind)
U44(tt) → U45(isNat)
U45(tt) → U46(isNatIList)
U46(tt) → tt
U51(tt) → U52(isNatIListKind)
U52(tt) → tt
U61(tt) → tt
U71(tt) → tt
U81(tt) → U82(isNatKind)
U82(tt) → U83(isNatIListKind)
U83(tt) → U84(isNatIListKind)
U84(tt) → U85(isNat)
U85(tt) → U86(isNatList)
U86(tt) → tt
U91(tt) → U92(isNatIListKind)
U92(tt) → U93(isNat)
U93(tt) → U94(isNatKind)
isNat → tt
isNat → U11(isNatIListKind)
isNat → U21(isNatKind)
isNatIList → U31(isNatIListKind)
isNatIList → tt
isNatIList → U41(isNatKind)
isNatIListKind → tt
isNatIListKind → U51(isNatKind)
isNatKind → tt
isNatKind → U61(isNatIListKind)
isNatKind → U71(isNatKind)
isNatList → tt
isNatList → U81(isNatKind)
length(nil) → 0
length(cons(N)) → U91(isNatList)