(VAR X Y X1 X2 X3)
(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))
)