MAYBE

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

Proof:
 DP Processor:
  DPs:
   minus#(s(x),s(y)) -> minus#(x,y)
   le#(s(x),s(y)) -> le#(x,y)
   quot#(s(x),s(y)) -> minus#(s(x),s(y))
   quot#(s(x),s(y)) -> quot#(minus(s(x),s(y)),s(y))
  TRS:
   minus(x,0()) -> x
   minus(s(x),s(y)) -> minus(x,y)
   le(0(),y) -> true()
   le(s(x),0()) -> false()
   le(s(x),s(y)) -> le(x,y)
   quot(0(),s(y)) -> 0()
   quot(s(x),s(y)) -> s(quot(minus(s(x),s(y)),s(y)))
  EDG Processor:
   DPs:
    minus#(s(x),s(y)) -> minus#(x,y)
    le#(s(x),s(y)) -> le#(x,y)
    quot#(s(x),s(y)) -> minus#(s(x),s(y))
    quot#(s(x),s(y)) -> quot#(minus(s(x),s(y)),s(y))
   TRS:
    minus(x,0()) -> x
    minus(s(x),s(y)) -> minus(x,y)
    le(0(),y) -> true()
    le(s(x),0()) -> false()
    le(s(x),s(y)) -> le(x,y)
    quot(0(),s(y)) -> 0()
    quot(s(x),s(y)) -> s(quot(minus(s(x),s(y)),s(y)))
   graph:
    quot#(s(x),s(y)) -> quot#(minus(s(x),s(y)),s(y)) ->
    quot#(s(x),s(y)) -> minus#(s(x),s(y))
    quot#(s(x),s(y)) -> quot#(minus(s(x),s(y)),s(y)) ->
    quot#(s(x),s(y)) -> quot#(minus(s(x),s(y)),s(y))
    quot#(s(x),s(y)) -> minus#(s(x),s(y)) ->
    minus#(s(x),s(y)) -> minus#(x,y)
    le#(s(x),s(y)) -> le#(x,y) -> le#(s(x),s(y)) -> le#(x,y)
    minus#(s(x),s(y)) -> minus#(x,y) -> minus#(s(x),s(y)) -> minus#(x,y)
   SCC Processor:
    #sccs: 3
    #rules: 3
    #arcs: 5/16
    DPs:
     le#(s(x),s(y)) -> le#(x,y)
    TRS:
     minus(x,0()) -> x
     minus(s(x),s(y)) -> minus(x,y)
     le(0(),y) -> true()
     le(s(x),0()) -> false()
     le(s(x),s(y)) -> le(x,y)
     quot(0(),s(y)) -> 0()
     quot(s(x),s(y)) -> s(quot(minus(s(x),s(y)),s(y)))
    Open
    
    DPs:
     quot#(s(x),s(y)) -> quot#(minus(s(x),s(y)),s(y))
    TRS:
     minus(x,0()) -> x
     minus(s(x),s(y)) -> minus(x,y)
     le(0(),y) -> true()
     le(s(x),0()) -> false()
     le(s(x),s(y)) -> le(x,y)
     quot(0(),s(y)) -> 0()
     quot(s(x),s(y)) -> s(quot(minus(s(x),s(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)
     le(0(),y) -> true()
     le(s(x),0()) -> false()
     le(s(x),s(y)) -> le(x,y)
     quot(0(),s(y)) -> 0()
     quot(s(x),s(y)) -> s(quot(minus(s(x),s(y)),s(y)))
    Open