MAYBE

Problem:
 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))

Proof:
 Open