(VAR M N X X1 X2 X3 )
(RULES 
        active(U11(tt, M, N)) -> mark(U12(tt, M, N))
        active(U12(tt, M, N)) -> mark(s(plus(N, M)))
        active(U21(tt, M, N)) -> mark(U22(tt, M, N))
        active(U22(tt, M, N)) -> mark(plus(x(N, M), N))
        active(plus(N, 0)) -> mark(N)
        active(plus(N, s(M))) -> mark(U11(tt, M, N))
        active(x(N, 0)) -> mark(0)
        active(x(N, s(M))) -> mark(U21(tt, M, N))
        active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3)
        active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3)
        active(s(X)) -> s(active(X))
        active(plus(X1, X2)) -> plus(active(X1), X2)
        active(plus(X1, X2)) -> plus(X1, active(X2))
        active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3)
        active(U22(X1, X2, X3)) -> U22(active(X1), X2, X3)
        active(x(X1, X2)) -> x(active(X1), X2)
        active(x(X1, X2)) -> x(X1, active(X2))
        U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3))
        U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3))
        s(mark(X)) -> mark(s(X))
        plus(mark(X1), X2) -> mark(plus(X1, X2))
        plus(X1, mark(X2)) -> mark(plus(X1, X2))
        U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3))
        U22(mark(X1), X2, X3) -> mark(U22(X1, X2, X3))
        x(mark(X1), X2) -> mark(x(X1, X2))
        x(X1, mark(X2)) -> mark(x(X1, X2))
        proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3))
        proper(tt) -> ok(tt)
        proper(U12(X1, X2, X3)) -> U12(proper(X1), proper(X2), proper(X3))
        proper(s(X)) -> s(proper(X))
        proper(plus(X1, X2)) -> plus(proper(X1), proper(X2))
        proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3))
        proper(U22(X1, X2, X3)) -> U22(proper(X1), proper(X2), proper(X3))
        proper(x(X1, X2)) -> x(proper(X1), proper(X2))
        proper(0) -> ok(0)
        U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3))
        U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3))
        s(ok(X)) -> ok(s(X))
        plus(ok(X1), ok(X2)) -> ok(plus(X1, X2))
        U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3))
        U22(ok(X1), ok(X2), ok(X3)) -> ok(U22(X1, X2, X3))
        x(ok(X1), ok(X2)) -> ok(x(X1, X2))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
        
)