(VAR X X1 X2 X3 Y )
(RULES 
        active(f(X)) -> mark(if(X, c, f(true)))
        active(if(true, X, Y)) -> mark(X)
        active(if(false, X, Y)) -> mark(Y)
        active(f(X)) -> f(active(X))
        active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
        active(if(X1, X2, X3)) -> if(X1, active(X2), X3)
        f(mark(X)) -> mark(f(X))
        if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
        if(X1, mark(X2), X3) -> mark(if(X1, X2, X3))
        proper(f(X)) -> f(proper(X))
        proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
        proper(c) -> ok(c)
        proper(true) -> ok(true)
        proper(false) -> ok(false)
        f(ok(X)) -> ok(f(X))
        if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
        
)