(VAR X Y X1 X2 X3)
(RULES 
active(p(0)) -> mark(0)
active(p(s(X))) -> mark(X)
active(leq(0,Y)) -> mark(true)
active(leq(s(X),0)) -> mark(false)
active(leq(s(X),s(Y))) -> mark(leq(X,Y))
active(if(true,X,Y)) -> mark(X)
active(if(false,X,Y)) -> mark(Y)
active(diff(X,Y)) -> mark(if(leq(X,Y),0,s(diff(p(X),Y))))
active(p(X)) -> p(active(X))
active(s(X)) -> s(active(X))
active(leq(X1,X2)) -> leq(active(X1),X2)
active(leq(X1,X2)) -> leq(X1,active(X2))
active(if(X1,X2,X3)) -> if(active(X1),X2,X3)
active(diff(X1,X2)) -> diff(active(X1),X2)
active(diff(X1,X2)) -> diff(X1,active(X2))
p(mark(X)) -> mark(p(X))
s(mark(X)) -> mark(s(X))
leq(mark(X1),X2) -> mark(leq(X1,X2))
leq(X1,mark(X2)) -> mark(leq(X1,X2))
if(mark(X1),X2,X3) -> mark(if(X1,X2,X3))
diff(mark(X1),X2) -> mark(diff(X1,X2))
diff(X1,mark(X2)) -> mark(diff(X1,X2))
proper(p(X)) -> p(proper(X))
proper(0) -> ok(0)
proper(s(X)) -> s(proper(X))
proper(leq(X1,X2)) -> leq(proper(X1),proper(X2))
proper(true) -> ok(true)
proper(false) -> ok(false)
proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3))
proper(diff(X1,X2)) -> diff(proper(X1),proper(X2))
p(ok(X)) -> ok(p(X))
s(ok(X)) -> ok(s(X))
leq(ok(X1),ok(X2)) -> ok(leq(X1,X2))
if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3))
diff(ok(X1),ok(X2)) -> ok(diff(X1,X2))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
)