(0) Obligation:
Generalized rewrite system (where rules with free variables on rhs are allowed):
The TRS R consists of the following rules:
U104(tt) → plus(x(N, M), N)
U72(tt) → N
U84(tt) → s(plus(N, M))
U101(tt) → U102(isNatKind)
U102(tt) → U103(isNat)
U103(tt) → U104(isNatKind)
U11(tt) → U12(isNatKind)
U12(tt) → U13(isNatKind)
U13(tt) → U14(isNatKind)
U14(tt) → U15(isNat)
U15(tt) → U16(isNat)
U16(tt) → tt
U21(tt) → U22(isNatKind)
U22(tt) → U23(isNat)
U23(tt) → tt
U31(tt) → U32(isNatKind)
U32(tt) → U33(isNatKind)
U33(tt) → U34(isNatKind)
U34(tt) → U35(isNat)
U35(tt) → U36(isNat)
U36(tt) → tt
U41(tt) → U42(isNatKind)
U42(tt) → tt
U51(tt) → tt
U61(tt) → U62(isNatKind)
U62(tt) → tt
U71(tt) → U72(isNatKind)
U81(tt) → U82(isNatKind)
U82(tt) → U83(isNat)
U83(tt) → U84(isNatKind)
U91(tt) → U92(isNatKind)
U92(tt) → 0
isNat → tt
isNat → U11(isNatKind)
isNat → U21(isNatKind)
isNat → U31(isNatKind)
isNatKind → tt
isNatKind → U41(isNatKind)
isNatKind → U51(isNatKind)
isNatKind → U61(isNatKind)
plus(N, 0) → U71(isNat)
plus(N, s(M)) → U81(isNat)
x(N, 0) → U91(isNat)
x(N, s(M)) → U101(isNat)