MAYBE

Problem:
 minus(x,0()) -> x
 minus(s(x),s(y)) -> minus(x,y)
 quot(0(),s(y)) -> 0()
 quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))

Proof:
 DP Processor:
  DPs:
   minus#(s(x),s(y)) -> minus#(x,y)
   quot#(s(x),s(y)) -> minus#(x,y)
   quot#(s(x),s(y)) -> quot#(minus(x,y),s(y))
  TRS:
   minus(x,0()) -> x
   minus(s(x),s(y)) -> minus(x,y)
   quot(0(),s(y)) -> 0()
   quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
  Usable Rule Processor:
   DPs:
    minus#(s(x),s(y)) -> minus#(x,y)
    quot#(s(x),s(y)) -> minus#(x,y)
    quot#(s(x),s(y)) -> quot#(minus(x,y),s(y))
   TRS:
    f6(x,y) -> x
    f6(x,y) -> y
    minus(x,0()) -> x
    minus(s(x),s(y)) -> minus(x,y)
   TDG Processor:
    DPs:
     minus#(s(x),s(y)) -> minus#(x,y)
     quot#(s(x),s(y)) -> minus#(x,y)
     quot#(s(x),s(y)) -> quot#(minus(x,y),s(y))
    TRS:
     f6(x,y) -> x
     f6(x,y) -> y
     minus(x,0()) -> x
     minus(s(x),s(y)) -> minus(x,y)
    graph:
     quot#(s(x),s(y)) -> quot#(minus(x,y),s(y)) ->
     quot#(s(x),s(y)) -> quot#(minus(x,y),s(y))
     quot#(s(x),s(y)) -> quot#(minus(x,y),s(y)) ->
     quot#(s(x),s(y)) -> minus#(x,y)
     quot#(s(x),s(y)) -> minus#(x,y) ->
     minus#(s(x),s(y)) -> minus#(x,y)
     minus#(s(x),s(y)) -> minus#(x,y) -> minus#(s(x),s(y)) -> minus#(x,y)
    Restore Modifier:
     DPs:
      minus#(s(x),s(y)) -> minus#(x,y)
      quot#(s(x),s(y)) -> minus#(x,y)
      quot#(s(x),s(y)) -> quot#(minus(x,y),s(y))
     TRS:
      minus(x,0()) -> x
      minus(s(x),s(y)) -> minus(x,y)
      quot(0(),s(y)) -> 0()
      quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
     SCC Processor:
      #sccs: 2
      #rules: 2
      #arcs: 4/9
      DPs:
       quot#(s(x),s(y)) -> quot#(minus(x,y),s(y))
      TRS:
       minus(x,0()) -> x
       minus(s(x),s(y)) -> minus(x,y)
       quot(0(),s(y)) -> 0()
       quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
      Open
      
      DPs:
       minus#(s(x),s(y)) -> minus#(x,y)
      TRS:
       minus(x,0()) -> x
       minus(s(x),s(y)) -> minus(x,y)
       quot(0(),s(y)) -> 0()
       quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
      Open