MAYBE 0.08/0.19 MAYBE 0.08/0.19 0.08/0.19 Problem: 0.08/0.19 minus(x,0()) -> x 0.08/0.19 minus(s(x),s(y)) -> minus(x,y) 0.08/0.19 quot(0(),s(y)) -> 0() 0.08/0.19 quot(s(x),s(y)) -> s(quot(minus(x,y),s(y))) 0.08/0.19 le(0(),y) -> true() 0.08/0.19 le(s(x),0()) -> false() 0.08/0.19 le(s(x),s(y)) -> le(x,y) 0.08/0.19 app(nil(),y) -> y 0.08/0.19 app(add(n,x),y) -> add(n,app(x,y)) 0.08/0.19 low(n,nil()) -> nil() 0.08/0.19 low(n,add(m,x)) -> if_low(le(m,n),n,add(m,x)) 0.08/0.19 if_low(true(),n,add(m,x)) -> add(m,low(n,x)) 0.08/0.19 if_low(false(),n,add(m,x)) -> low(n,x) 0.08/0.19 high(n,nil()) -> nil() 0.08/0.19 high(n,add(m,x)) -> if_high(le(m,n),n,add(m,x)) 0.08/0.19 if_high(true(),n,add(m,x)) -> high(n,x) 0.08/0.19 if_high(false(),n,add(m,x)) -> add(m,high(n,x)) 0.08/0.19 quicksort(nil()) -> nil() 0.08/0.19 quicksort(add(n,x)) -> app(quicksort(low(n,x)),add(n,quicksort(high(n,x)))) 0.08/0.19 0.08/0.19 Proof: 0.08/0.19 Open 0.08/0.19 EOF