MAYBE 0.08/0.19 MAYBE 0.08/0.19 0.08/0.19 Problem: 0.08/0.19 app(x,y) -> helpa(0(),plus(length(x),length(y)),x,y) 0.08/0.19 plus(x,0()) -> x 0.08/0.19 plus(x,s(y)) -> s(plus(x,y)) 0.08/0.19 length(nil()) -> 0() 0.08/0.19 length(cons(x,y)) -> s(length(y)) 0.08/0.19 helpa(c,l,ys,zs) -> if(ge(c,l),c,l,ys,zs) 0.08/0.19 ge(x,0()) -> true() 0.08/0.19 ge(0(),s(x)) -> false() 0.08/0.19 ge(s(x),s(y)) -> ge(x,y) 0.08/0.19 if(true(),c,l,ys,zs) -> nil() 0.08/0.19 if(false(),c,l,ys,zs) -> helpb(c,l,ys,zs) 0.08/0.19 take(0(),cons(x,xs()),ys) -> x 0.08/0.19 take(0(),nil(),cons(y,ys)) -> y 0.08/0.19 take(s(c),cons(x,xs()),ys) -> take(c,xs(),ys) 0.08/0.19 take(s(c),nil(),cons(y,ys)) -> take(c,nil(),ys) 0.08/0.19 helpb(c,l,ys,zs) -> cons(take(c,ys,zs),helpa(s(c),l,ys,zs)) 0.08/0.19 0.08/0.19 Proof: 0.08/0.19 Open 0.08/0.19 EOF