MAYBE

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

Proof:
 Open