MAYBE 0.08/0.19 MAYBE 0.08/0.19 0.08/0.19 Problem: 0.08/0.19 app(nil(),k) -> k 0.08/0.19 app(l,nil()) -> l 0.08/0.19 app(cons(x,l),k) -> cons(x,app(l,k)) 0.08/0.19 sum(cons(x,nil())) -> cons(x,nil()) 0.08/0.19 sum(cons(x,cons(y,l))) -> sum(cons(plus(x,y),l)) 0.08/0.19 sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k))))) 0.08/0.19 plus(s(x),s(y)) -> s(s(plus(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y))))) 0.08/0.19 plus(s(x),x) -> plus(if(gt(x,x),id(x),id(x)),s(x)) 0.08/0.19 plus(zero(),y) -> y 0.08/0.19 plus(id(x),s(y)) -> s(plus(x,if(gt(s(y),y),y,s(y)))) 0.08/0.19 id(x) -> x 0.08/0.19 if(true(),x,y) -> x 0.08/0.19 if(false(),x,y) -> y 0.08/0.19 not(x) -> if(x,false(),true()) 0.08/0.19 gt(s(x),zero()) -> true() 0.08/0.19 gt(zero(),y) -> false() 0.08/0.19 gt(s(x),s(y)) -> gt(x,y) 0.08/0.19 0.08/0.19 Proof: 0.08/0.19 Open 0.08/0.19 EOF