(VAR X X1 X2 X3 Y )
(RULES 
        active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X)))))
        active(add(0, X)) -> mark(X)
        active(add(s(X), Y)) -> mark(s(add(X, Y)))
        active(prod(0, X)) -> mark(0)
        active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y)))
        active(if(true, X, Y)) -> mark(X)
        active(if(false, X, Y)) -> mark(Y)
        active(zero(0)) -> mark(true)
        active(zero(s(X))) -> mark(false)
        active(p(s(X))) -> mark(X)
        mark(fact(X)) -> active(fact(mark(X)))
        mark(if(X1, X2, X3)) -> active(if(mark(X1), X2, X3))
        mark(zero(X)) -> active(zero(mark(X)))
        mark(s(X)) -> active(s(mark(X)))
        mark(0) -> active(0)
        mark(prod(X1, X2)) -> active(prod(mark(X1), mark(X2)))
        mark(p(X)) -> active(p(mark(X)))
        mark(add(X1, X2)) -> active(add(mark(X1), mark(X2)))
        mark(true) -> active(true)
        mark(false) -> active(false)
        fact(mark(X)) -> fact(X)
        fact(active(X)) -> fact(X)
        if(mark(X1), X2, X3) -> if(X1, X2, X3)
        if(X1, mark(X2), X3) -> if(X1, X2, X3)
        if(X1, X2, mark(X3)) -> if(X1, X2, X3)
        if(active(X1), X2, X3) -> if(X1, X2, X3)
        if(X1, active(X2), X3) -> if(X1, X2, X3)
        if(X1, X2, active(X3)) -> if(X1, X2, X3)
        zero(mark(X)) -> zero(X)
        zero(active(X)) -> zero(X)
        s(mark(X)) -> s(X)
        s(active(X)) -> s(X)
        prod(mark(X1), X2) -> prod(X1, X2)
        prod(X1, mark(X2)) -> prod(X1, X2)
        prod(active(X1), X2) -> prod(X1, X2)
        prod(X1, active(X2)) -> prod(X1, X2)
        p(mark(X)) -> p(X)
        p(active(X)) -> p(X)
        add(mark(X1), X2) -> add(X1, X2)
        add(X1, mark(X2)) -> add(X1, X2)
        add(active(X1), X2) -> add(X1, X2)
        add(X1, active(X2)) -> add(X1, X2)
        
)