(VAR X X1 X2 Y )
(RULES 
        fact(X) -> if(zero(X), n__s(n__0), n__prod(X, n__fact(n__p(X))))
        add(0, X) -> X
        add(s(X), Y) -> s(add(X, Y))
        prod(0, X) -> 0
        prod(s(X), Y) -> add(Y, prod(X, Y))
        if(true, X, Y) -> activate(X)
        if(false, X, Y) -> activate(Y)
        zero(0) -> true
        zero(s(X)) -> false
        p(s(X)) -> X
        s(X) -> n__s(X)
        0 -> n__0
        prod(X1, X2) -> n__prod(X1, X2)
        fact(X) -> n__fact(X)
        p(X) -> n__p(X)
        activate(n__s(X)) -> s(activate(X))
        activate(n__0) -> 0
        activate(n__prod(X1, X2)) -> prod(activate(X1), activate(X2))
        activate(n__fact(X)) -> fact(activate(X))
        activate(n__p(X)) -> p(activate(X))
        activate(X) -> X
        
)