MAYBE
0.18/0.22	MAYBE
0.18/0.23	
0.18/0.23	Problem:
0.18/0.23	 active(primes()) -> mark(sieve(from(s(s(0())))))
0.18/0.23	 active(from(X)) -> mark(cons(X,from(s(X))))
0.18/0.23	 active(head(cons(X,Y))) -> mark(X)
0.18/0.23	 active(tail(cons(X,Y))) -> mark(Y)
0.18/0.23	 active(if(true(),X,Y)) -> mark(X)
0.18/0.23	 active(if(false(),X,Y)) -> mark(Y)
0.18/0.23	 active(filter(s(s(X)),cons(Y,Z))) ->
0.18/0.23	 mark(if(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y)))))
0.18/0.23	 active(sieve(cons(X,Y))) -> mark(cons(X,filter(X,sieve(Y))))
0.18/0.23	 active(sieve(X)) -> sieve(active(X))
0.18/0.23	 active(from(X)) -> from(active(X))
0.18/0.23	 active(s(X)) -> s(active(X))
0.18/0.23	 active(cons(X1,X2)) -> cons(active(X1),X2)
0.18/0.23	 active(head(X)) -> head(active(X))
0.18/0.23	 active(tail(X)) -> tail(active(X))
0.18/0.23	 active(if(X1,X2,X3)) -> if(active(X1),X2,X3)
0.18/0.23	 active(filter(X1,X2)) -> filter(active(X1),X2)
0.18/0.23	 active(filter(X1,X2)) -> filter(X1,active(X2))
0.18/0.23	 active(divides(X1,X2)) -> divides(active(X1),X2)
0.18/0.23	 active(divides(X1,X2)) -> divides(X1,active(X2))
0.18/0.23	 sieve(mark(X)) -> mark(sieve(X))
0.18/0.23	 from(mark(X)) -> mark(from(X))
0.18/0.23	 s(mark(X)) -> mark(s(X))
0.18/0.23	 cons(mark(X1),X2) -> mark(cons(X1,X2))
0.18/0.23	 head(mark(X)) -> mark(head(X))
0.18/0.23	 tail(mark(X)) -> mark(tail(X))
0.18/0.23	 if(mark(X1),X2,X3) -> mark(if(X1,X2,X3))
0.18/0.23	 filter(mark(X1),X2) -> mark(filter(X1,X2))
0.18/0.23	 filter(X1,mark(X2)) -> mark(filter(X1,X2))
0.18/0.23	 divides(mark(X1),X2) -> mark(divides(X1,X2))
0.18/0.23	 divides(X1,mark(X2)) -> mark(divides(X1,X2))
0.18/0.23	 proper(primes()) -> ok(primes())
0.18/0.23	 proper(sieve(X)) -> sieve(proper(X))
0.18/0.23	 proper(from(X)) -> from(proper(X))
0.18/0.23	 proper(s(X)) -> s(proper(X))
0.18/0.23	 proper(0()) -> ok(0())
0.18/0.23	 proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
0.18/0.23	 proper(head(X)) -> head(proper(X))
0.18/0.23	 proper(tail(X)) -> tail(proper(X))
0.18/0.23	 proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3))
0.18/0.23	 proper(true()) -> ok(true())
0.18/0.23	 proper(false()) -> ok(false())
0.18/0.23	 proper(filter(X1,X2)) -> filter(proper(X1),proper(X2))
0.18/0.23	 proper(divides(X1,X2)) -> divides(proper(X1),proper(X2))
0.18/0.23	 sieve(ok(X)) -> ok(sieve(X))
0.18/0.23	 from(ok(X)) -> ok(from(X))
0.18/0.23	 s(ok(X)) -> ok(s(X))
0.18/0.23	 cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
0.18/0.23	 head(ok(X)) -> ok(head(X))
0.18/0.23	 tail(ok(X)) -> ok(tail(X))
0.18/0.23	 if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3))
0.18/0.23	 filter(ok(X1),ok(X2)) -> ok(filter(X1,X2))
0.18/0.23	 divides(ok(X1),ok(X2)) -> ok(divides(X1,X2))
0.18/0.23	 top(mark(X)) -> top(proper(X))
0.18/0.23	 top(ok(X)) -> top(active(X))
0.18/0.23	
0.18/0.23	Proof:
0.18/0.23	 Open
0.18/0.23	EOF