(VAR X X1 X2 X3 Y )
(RULES 
        a__fact(X) -> a__if(a__zero(mark(X)), s(0), prod(X, fact(p(X))))
        a__add(0, X) -> mark(X)
        a__add(s(X), Y) -> s(a__add(mark(X), mark(Y)))
        a__prod(0, X) -> 0
        a__prod(s(X), Y) -> a__add(mark(Y), a__prod(mark(X), mark(Y)))
        a__if(true, X, Y) -> mark(X)
        a__if(false, X, Y) -> mark(Y)
        a__zero(0) -> true
        a__zero(s(X)) -> false
        a__p(s(X)) -> mark(X)
        mark(fact(X)) -> a__fact(mark(X))
        mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3)
        mark(zero(X)) -> a__zero(mark(X))
        mark(prod(X1, X2)) -> a__prod(mark(X1), mark(X2))
        mark(p(X)) -> a__p(mark(X))
        mark(add(X1, X2)) -> a__add(mark(X1), mark(X2))
        mark(s(X)) -> s(mark(X))
        mark(0) -> 0
        mark(true) -> true
        mark(false) -> false
        a__fact(X) -> fact(X)
        a__if(X1, X2, X3) -> if(X1, X2, X3)
        a__zero(X) -> zero(X)
        a__prod(X1, X2) -> prod(X1, X2)
        a__p(X) -> p(X)
        a__add(X1, X2) -> add(X1, X2)
        
)