MAYBE

Problem:
 U11(tt(),V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2))
 U12(tt(),V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2))
 U13(tt(),V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2))
 U14(tt(),V1,V2) -> U15(isNat(activate(V1)),activate(V2))
 U15(tt(),V2) -> U16(isNat(activate(V2)))
 U16(tt()) -> tt()
 U21(tt(),V1) -> U22(isNatKind(activate(V1)),activate(V1))
 U22(tt(),V1) -> U23(isNat(activate(V1)))
 U23(tt()) -> tt()
 U31(tt(),V2) -> U32(isNatKind(activate(V2)))
 U32(tt()) -> tt()
 U41(tt()) -> tt()
 U51(tt(),N) -> U52(isNatKind(activate(N)),activate(N))
 U52(tt(),N) -> activate(N)
 U61(tt(),M,N) -> U62(isNatKind(activate(M)),activate(M),activate(N))
 U62(tt(),M,N) -> U63(isNat(activate(N)),activate(M),activate(N))
 U63(tt(),M,N) -> U64(isNatKind(activate(N)),activate(M),activate(N))
 U64(tt(),M,N) -> s(plus(activate(N),activate(M)))
 isNat(n__0()) -> tt()
 isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2))
 isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1))
 isNatKind(n__0()) -> tt()
 isNatKind(n__plus(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V2))
 isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1)))
 plus(N,0()) -> U51(isNat(N),N)
 plus(N,s(M)) -> U61(isNat(M),M,N)
 0() -> n__0()
 plus(X1,X2) -> n__plus(X1,X2)
 s(X) -> n__s(X)
 activate(n__0()) -> 0()
 activate(n__plus(X1,X2)) -> plus(activate(X1),activate(X2))
 activate(n__s(X)) -> s(activate(X))
 activate(X) -> X

Proof:
 Open