MAYBE 0.08/0.19 MAYBE 0.08/0.19 0.08/0.19 Problem: 0.08/0.19 isEmpty(cons(x,xs)) -> false() 0.08/0.19 isEmpty(nil()) -> true() 0.08/0.19 isZero(0()) -> true() 0.08/0.19 isZero(s(x)) -> false() 0.08/0.19 head(cons(x,xs)) -> x 0.08/0.19 tail(cons(x,xs)) -> xs 0.08/0.19 tail(nil()) -> nil() 0.08/0.19 p(s(s(x))) -> s(p(s(x))) 0.08/0.19 p(s(0())) -> 0() 0.08/0.19 p(0()) -> 0() 0.08/0.19 inc(s(x)) -> s(inc(x)) 0.08/0.19 inc(0()) -> s(0()) 0.08/0.19 sumList(xs,y) -> if(isEmpty(xs),isZero(head(xs)),y,tail(xs),cons(p(head(xs)),tail(xs)),inc(y)) 0.08/0.19 if(true(),b,y,xs,ys,x) -> y 0.08/0.19 if(false(),true(),y,xs,ys,x) -> sumList(xs,y) 0.08/0.19 if(false(),false(),y,xs,ys,x) -> sumList(ys,x) 0.08/0.19 sum(xs) -> sumList(xs,0()) 0.08/0.19 0.08/0.19 Proof: 0.08/0.19 Open 0.08/0.19 EOF