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:
 DP Processor:
  DPs:
   app#(x,y) -> length#(y)
   app#(x,y) -> length#(x)
   app#(x,y) -> plus#(length(x),length(y))
   app#(x,y) -> helpa#(0(),plus(length(x),length(y)),x,y)
   plus#(x,s(y)) -> plus#(x,y)
   length#(cons(x,y)) -> length#(y)
   helpa#(c,l,ys,zs) -> ge#(c,l)
   helpa#(c,l,ys,zs) -> if#(ge(c,l),c,l,ys,zs)
   ge#(s(x),s(y)) -> ge#(x,y)
   if#(false(),c,l,ys,zs) -> helpb#(c,l,ys,zs)
   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) -> helpa#(s(c),l,ys,zs)
   helpb#(c,l,ys,zs) -> take#(c,ys,zs)
  TRS:
   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))
  Open