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())
  TDG 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())
   graph:
    if#(true(),x,c) -> help#(x,s(c)) ->
    help#(x,c) -> if#(lt(c,x),x,c)
    if#(true(),x,c) -> help#(x,s(c)) -> help#(x,c) -> lt#(c,x)
    help#(x,c) -> if#(lt(c,x),x,c) -> if#(true(),x,c) -> help#(x,s(c))
    help#(x,c) -> lt#(c,x) -> lt#(s(x),s(y)) -> lt#(x,y)
    fac#(x) -> help#(x,0()) -> help#(x,c) -> if#(lt(c,x),x,c)
    fac#(x) -> help#(x,0()) -> help#(x,c) -> lt#(c,x)
    lt#(s(x),s(y)) -> lt#(x,y) -> lt#(s(x),s(y)) -> lt#(x,y)
   SCC Processor:
    #sccs: 2
    #rules: 3
    #arcs: 7/25
    DPs:
     if#(true(),x,c) -> help#(x,s(c))
     help#(x,c) -> if#(lt(c,x),x,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())
    Open
    
    DPs:
     lt#(s(x),s(y)) -> lt#(x,y)
    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())
    Subterm Criterion Processor:
     simple projection:
      pi(lt#) = 1
     problem:
      DPs:
       
      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())
     Qed