MAYBE 0.08/0.19 MAYBE 0.08/0.19 0.08/0.19 Problem: 0.08/0.19 minus(minus(x,y),z) -> minus(x,plus(y,z)) 0.08/0.19 minus(0(),y) -> 0() 0.08/0.19 minus(x,0()) -> x 0.08/0.19 minus(s(x),s(y)) -> minus(x,y) 0.08/0.19 plus(0(),y) -> y 0.08/0.19 plus(s(x),y) -> plus(x,s(y)) 0.08/0.19 plus(s(x),y) -> s(plus(y,x)) 0.08/0.19 zero(s(x)) -> false() 0.08/0.19 zero(0()) -> true() 0.08/0.19 p(s(x)) -> x 0.08/0.19 p(0()) -> 0() 0.08/0.19 div(x,y) -> quot(x,y,0()) 0.08/0.19 quot(s(x),s(y),z) -> quot(minus(p(ack(0(),x)),y),s(y),s(z)) 0.08/0.19 quot(0(),s(y),z) -> z 0.08/0.19 ack(0(),x) -> s(x) 0.08/0.19 ack(0(),x) -> plus(x,s(0())) 0.08/0.19 ack(s(x),0()) -> ack(x,s(0())) 0.08/0.19 ack(s(x),s(y)) -> ack(x,ack(s(x),y)) 0.08/0.19 0.08/0.19 Proof: 0.08/0.19 Open 0.08/0.19 EOF