MAYBE 0.10/0.18 MAYBE 0.10/0.18 0.10/0.18 Problem: 0.10/0.18 minus(x,0()) -> x 0.10/0.18 minus(s(x),s(y)) -> minus(x,y) 0.10/0.18 quot(0(),s(y)) -> 0() 0.10/0.18 quot(s(x),s(y)) -> s(quot(minus(x,y),s(y))) 0.10/0.18 plus(s(x),s(y)) -> s(s(plus(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y))))) 0.10/0.18 plus(s(x),x) -> plus(if(gt(x,x),id(x),id(x)),s(x)) 0.10/0.18 plus(zero(),y) -> y 0.10/0.18 plus(id(x),s(y)) -> s(plus(x,if(gt(s(y),y),y,s(y)))) 0.10/0.18 id(x) -> x 0.10/0.18 if(true(),x,y) -> x 0.10/0.18 if(false(),x,y) -> y 0.10/0.18 not(x) -> if(x,false(),true()) 0.10/0.18 gt(s(x),zero()) -> true() 0.10/0.18 gt(zero(),y) -> false() 0.10/0.18 gt(s(x),s(y)) -> gt(x,y) 0.10/0.18 0.10/0.18 Proof: 0.10/0.18 Open 0.10/0.18 EOF