MAYBE

Problem:
 lt(0(),s(x)) -> true()
 lt(x,0()) -> false()
 lt(s(x),s(y)) -> lt(x,y)
 minus(x,y) -> help(lt(y,x),x,y)
 help(true(),x,y) -> s(minus(x,s(y)))
 help(false(),x,y) -> 0()

Proof:
 DP Processor:
  DPs:
   lt#(s(x),s(y)) -> lt#(x,y)
   minus#(x,y) -> lt#(y,x)
   minus#(x,y) -> help#(lt(y,x),x,y)
   help#(true(),x,y) -> minus#(x,s(y))
  TRS:
   lt(0(),s(x)) -> true()
   lt(x,0()) -> false()
   lt(s(x),s(y)) -> lt(x,y)
   minus(x,y) -> help(lt(y,x),x,y)
   help(true(),x,y) -> s(minus(x,s(y)))
   help(false(),x,y) -> 0()
  TDG Processor:
   DPs:
    lt#(s(x),s(y)) -> lt#(x,y)
    minus#(x,y) -> lt#(y,x)
    minus#(x,y) -> help#(lt(y,x),x,y)
    help#(true(),x,y) -> minus#(x,s(y))
   TRS:
    lt(0(),s(x)) -> true()
    lt(x,0()) -> false()
    lt(s(x),s(y)) -> lt(x,y)
    minus(x,y) -> help(lt(y,x),x,y)
    help(true(),x,y) -> s(minus(x,s(y)))
    help(false(),x,y) -> 0()
   graph:
    help#(true(),x,y) -> minus#(x,s(y)) ->
    minus#(x,y) -> help#(lt(y,x),x,y)
    help#(true(),x,y) -> minus#(x,s(y)) -> minus#(x,y) -> lt#(y,x)
    minus#(x,y) -> help#(lt(y,x),x,y) -> help#(true(),x,y) -> minus#(x,s(y))
    minus#(x,y) -> lt#(y,x) -> lt#(s(x),s(y)) -> lt#(x,y)
    lt#(s(x),s(y)) -> lt#(x,y) -> lt#(s(x),s(y)) -> lt#(x,y)
   SCC Processor:
    #sccs: 2
    #rules: 3
    #arcs: 5/16
    DPs:
     help#(true(),x,y) -> minus#(x,s(y))
     minus#(x,y) -> help#(lt(y,x),x,y)
    TRS:
     lt(0(),s(x)) -> true()
     lt(x,0()) -> false()
     lt(s(x),s(y)) -> lt(x,y)
     minus(x,y) -> help(lt(y,x),x,y)
     help(true(),x,y) -> s(minus(x,s(y)))
     help(false(),x,y) -> 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)
     minus(x,y) -> help(lt(y,x),x,y)
     help(true(),x,y) -> s(minus(x,s(y)))
     help(false(),x,y) -> 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)
       minus(x,y) -> help(lt(y,x),x,y)
       help(true(),x,y) -> s(minus(x,s(y)))
       help(false(),x,y) -> 0()
     Qed