(VAR X X1 X2 X3 Y )
(RULES 
        a__p(0) -> 0
        a__p(s(X)) -> mark(X)
        a__leq(0, Y) -> true
        a__leq(s(X), 0) -> false
        a__leq(s(X), s(Y)) -> a__leq(mark(X), mark(Y))
        a__if(true, X, Y) -> mark(X)
        a__if(false, X, Y) -> mark(Y)
        a__diff(X, Y) -> a__if(a__leq(mark(X), mark(Y)), 0, s(diff(p(X), Y)))
        mark(p(X)) -> a__p(mark(X))
        mark(leq(X1, X2)) -> a__leq(mark(X1), mark(X2))
        mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3)
        mark(diff(X1, X2)) -> a__diff(mark(X1), mark(X2))
        mark(0) -> 0
        mark(s(X)) -> s(mark(X))
        mark(true) -> true
        mark(false) -> false
        a__p(X) -> p(X)
        a__leq(X1, X2) -> leq(X1, X2)
        a__if(X1, X2, X3) -> if(X1, X2, X3)
        a__diff(X1, X2) -> diff(X1, X2)
        
)