MAYBE

Problem:
 U11(tt(),V2) -> U12(isNat(activate(V2)))
 U12(tt()) -> tt()
 U21(tt()) -> tt()
 U31(tt(),V2) -> U32(isNat(activate(V2)))
 U32(tt()) -> tt()
 U41(tt(),N) -> activate(N)
 U51(tt(),M,N) -> U52(isNat(activate(N)),activate(M),activate(N))
 U52(tt(),M,N) -> s(plus(activate(N),activate(M)))
 U61(tt()) -> 0()
 U71(tt(),M,N) -> U72(isNat(activate(N)),activate(M),activate(N))
 U72(tt(),M,N) -> plus(x(activate(N),activate(M)),activate(N))
 isNat(n__0()) -> tt()
 isNat(n__plus(V1,V2)) -> U11(isNat(activate(V1)),activate(V2))
 isNat(n__s(V1)) -> U21(isNat(activate(V1)))
 isNat(n__x(V1,V2)) -> U31(isNat(activate(V1)),activate(V2))
 plus(N,0()) -> U41(isNat(N),N)
 plus(N,s(M)) -> U51(isNat(M),M,N)
 x(N,0()) -> U61(isNat(N))
 x(N,s(M)) -> U71(isNat(M),M,N)
 0() -> n__0()
 plus(X1,X2) -> n__plus(X1,X2)
 s(X) -> n__s(X)
 x(X1,X2) -> n__x(X1,X2)
 activate(n__0()) -> 0()
 activate(n__plus(X1,X2)) -> plus(activate(X1),activate(X2))
 activate(n__s(X)) -> s(activate(X))
 activate(n__x(X1,X2)) -> x(activate(X1),activate(X2))
 activate(X) -> X

Proof:
 Open