MAYBE
0.08/0.20	MAYBE
0.17/0.20	
0.17/0.20	Problem:
0.17/0.20	 p(0()) -> 0()
0.17/0.20	 p(s(x)) -> x
0.17/0.20	 plus(x,0()) -> x
0.17/0.20	 plus(0(),y) -> y
0.17/0.20	 plus(s(x),y) -> s(plus(x,y))
0.17/0.20	 plus(s(x),y) -> s(plus(p(s(x)),y))
0.17/0.20	 plus(x,s(y)) -> s(plus(x,p(s(y))))
0.17/0.20	 times(0(),y) -> 0()
0.17/0.20	 times(s(0()),y) -> y
0.17/0.20	 times(s(x),y) -> plus(y,times(x,y))
0.17/0.20	 div(0(),y) -> 0()
0.17/0.20	 div(x,y) -> quot(x,y,y)
0.17/0.20	 quot(zero(y),s(y),z) -> 0()
0.17/0.20	 quot(s(x),s(y),z) -> quot(x,y,z)
0.17/0.20	 quot(x,0(),s(z)) -> s(div(x,s(z)))
0.17/0.20	 div(div(x,y),z) -> div(x,times(zero(y),z))
0.17/0.20	 eq(0(),0()) -> true()
0.17/0.20	 eq(s(x),0()) -> false()
0.17/0.20	 eq(0(),s(y)) -> false()
0.17/0.20	 eq(s(x),s(y)) -> eq(x,y)
0.17/0.20	 divides(y,x) -> eq(x,times(div(x,y),y))
0.17/0.20	 prime(s(s(x))) -> pr(s(s(x)),s(x))
0.17/0.20	 pr(x,s(0())) -> true()
0.17/0.20	 pr(x,s(s(y))) -> if(divides(s(s(y)),x),x,s(y))
0.17/0.20	 if(true(),x,y) -> false()
0.17/0.20	 if(false(),x,y) -> pr(x,y)
0.17/0.20	 zero(div(x,x)) -> x
0.17/0.20	 zero(divides(x,x)) -> x
0.17/0.20	 zero(times(x,x)) -> x
0.17/0.20	 zero(quot(x,x,x)) -> x
0.17/0.20	 zero(s(x)) -> if(eq(x,s(0())),plus(zero(0()),0()),s(plus(0(),zero(0()))))
0.17/0.20	
0.17/0.20	Proof:
0.17/0.20	 Open
0.17/0.20	EOF