MAYBE

Problem:
 a__U11(tt(),N) -> mark(N)
 a__U21(tt(),M,N) -> s(a__plus(mark(N),mark(M)))
 a__U31(tt()) -> 0()
 a__U41(tt(),M,N) -> a__plus(a__x(mark(N),mark(M)),mark(N))
 a__and(tt(),X) -> mark(X)
 a__isNat(0()) -> tt()
 a__isNat(plus(V1,V2)) -> a__and(a__isNat(V1),isNat(V2))
 a__isNat(s(V1)) -> a__isNat(V1)
 a__isNat(x(V1,V2)) -> a__and(a__isNat(V1),isNat(V2))
 a__plus(N,0()) -> a__U11(a__isNat(N),N)
 a__plus(N,s(M)) -> a__U21(a__and(a__isNat(M),isNat(N)),M,N)
 a__x(N,0()) -> a__U31(a__isNat(N))
 a__x(N,s(M)) -> a__U41(a__and(a__isNat(M),isNat(N)),M,N)
 mark(U11(X1,X2)) -> a__U11(mark(X1),X2)
 mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3)
 mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
 mark(U31(X)) -> a__U31(mark(X))
 mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3)
 mark(x(X1,X2)) -> a__x(mark(X1),mark(X2))
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(isNat(X)) -> a__isNat(X)
 mark(tt()) -> tt()
 mark(s(X)) -> s(mark(X))
 mark(0()) -> 0()
 a__U11(X1,X2) -> U11(X1,X2)
 a__U21(X1,X2,X3) -> U21(X1,X2,X3)
 a__plus(X1,X2) -> plus(X1,X2)
 a__U31(X) -> U31(X)
 a__U41(X1,X2,X3) -> U41(X1,X2,X3)
 a__x(X1,X2) -> x(X1,X2)
 a__and(X1,X2) -> and(X1,X2)
 a__isNat(X) -> isNat(X)

Proof:
 Open