MAYBE

Problem:
 times(x,y) -> help(x,y,0())
 help(x,y,c) -> if(lt(c,y),x,y,c)
 if(true(),x,y,c) -> plus(x,help(x,y,s(c)))
 if(false(),x,y,c) -> 0()
 lt(0(),s(x)) -> true()
 lt(s(x),0()) -> false()
 lt(s(x),s(y)) -> lt(x,y)
 plus(x,0()) -> x
 plus(0(),x) -> x
 plus(x,s(y)) -> s(plus(x,y))
 plus(s(x),y) -> s(plus(x,y))

Proof:
 DP Processor:
  DPs:
   times#(x,y) -> help#(x,y,0())
   help#(x,y,c) -> lt#(c,y)
   help#(x,y,c) -> if#(lt(c,y),x,y,c)
   if#(true(),x,y,c) -> help#(x,y,s(c))
   if#(true(),x,y,c) -> plus#(x,help(x,y,s(c)))
   lt#(s(x),s(y)) -> lt#(x,y)
   plus#(x,s(y)) -> plus#(x,y)
   plus#(s(x),y) -> plus#(x,y)
  TRS:
   times(x,y) -> help(x,y,0())
   help(x,y,c) -> if(lt(c,y),x,y,c)
   if(true(),x,y,c) -> plus(x,help(x,y,s(c)))
   if(false(),x,y,c) -> 0()
   lt(0(),s(x)) -> true()
   lt(s(x),0()) -> false()
   lt(s(x),s(y)) -> lt(x,y)
   plus(x,0()) -> x
   plus(0(),x) -> x
   plus(x,s(y)) -> s(plus(x,y))
   plus(s(x),y) -> s(plus(x,y))
  Usable Rule Processor:
   DPs:
    times#(x,y) -> help#(x,y,0())
    help#(x,y,c) -> lt#(c,y)
    help#(x,y,c) -> if#(lt(c,y),x,y,c)
    if#(true(),x,y,c) -> help#(x,y,s(c))
    if#(true(),x,y,c) -> plus#(x,help(x,y,s(c)))
    lt#(s(x),s(y)) -> lt#(x,y)
    plus#(x,s(y)) -> plus#(x,y)
    plus#(s(x),y) -> plus#(x,y)
   TRS:
    lt(0(),s(x)) -> true()
    lt(s(x),0()) -> false()
    lt(s(x),s(y)) -> lt(x,y)
    help(x,y,c) -> if(lt(c,y),x,y,c)
    if(true(),x,y,c) -> plus(x,help(x,y,s(c)))
    if(false(),x,y,c) -> 0()
    plus(x,0()) -> x
    plus(0(),x) -> x
    plus(x,s(y)) -> s(plus(x,y))
    plus(s(x),y) -> s(plus(x,y))
   Open