(VAR M N V1 V2 X X1 X2 X3 )
(RULES 
        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)
        
)