MAYBE

Problem:
 lt(0(),s(x)) -> true()
 lt(x,0()) -> false()
 lt(s(x),s(y)) -> lt(x,y)
 times(0(),y) -> 0()
 times(s(x),y) -> plus(y,times(x,y))
 plus(0(),y) -> y
 plus(s(x),y) -> s(plus(x,y))
 fac(x) -> loop(x,s(0()),s(0()))
 loop(x,c,y) -> if(lt(x,c),x,c,y)
 if(false(),x,c,y) -> loop(x,s(c),times(y,s(c)))
 if(true(),x,c,y) -> y

Proof:
 Open