MAYBE

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

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