MAYBE

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

Proof:
 DP Processor:
  DPs:
   minus#(s(x),s(y)) -> minus#(x,y)
   f#(s(x)) -> f#(x)
   f#(s(x)) -> g#(f(x))
   f#(s(x)) -> minus#(s(x),g(f(x)))
   g#(s(x)) -> g#(x)
   g#(s(x)) -> f#(g(x))
   g#(s(x)) -> minus#(s(x),f(g(x)))
  TRS:
   minus(x,0()) -> x
   minus(s(x),s(y)) -> minus(x,y)
   f(0()) -> s(0())
   f(s(x)) -> minus(s(x),g(f(x)))
   g(0()) -> 0()
   g(s(x)) -> minus(s(x),f(g(x)))
  TDG Processor:
   DPs:
    minus#(s(x),s(y)) -> minus#(x,y)
    f#(s(x)) -> f#(x)
    f#(s(x)) -> g#(f(x))
    f#(s(x)) -> minus#(s(x),g(f(x)))
    g#(s(x)) -> g#(x)
    g#(s(x)) -> f#(g(x))
    g#(s(x)) -> minus#(s(x),f(g(x)))
   TRS:
    minus(x,0()) -> x
    minus(s(x),s(y)) -> minus(x,y)
    f(0()) -> s(0())
    f(s(x)) -> minus(s(x),g(f(x)))
    g(0()) -> 0()
    g(s(x)) -> minus(s(x),f(g(x)))
   graph:
    g#(s(x)) -> g#(x) -> g#(s(x)) -> minus#(s(x),f(g(x)))
    g#(s(x)) -> g#(x) -> g#(s(x)) -> f#(g(x))
    g#(s(x)) -> g#(x) -> g#(s(x)) -> g#(x)
    g#(s(x)) -> f#(g(x)) -> f#(s(x)) -> minus#(s(x),g(f(x)))
    g#(s(x)) -> f#(g(x)) -> f#(s(x)) -> g#(f(x))
    g#(s(x)) -> f#(g(x)) -> f#(s(x)) -> f#(x)
    g#(s(x)) -> minus#(s(x),f(g(x))) -> minus#(s(x),s(y)) -> minus#(x,y)
    f#(s(x)) -> g#(f(x)) -> g#(s(x)) -> minus#(s(x),f(g(x)))
    f#(s(x)) -> g#(f(x)) -> g#(s(x)) -> f#(g(x))
    f#(s(x)) -> g#(f(x)) -> g#(s(x)) -> g#(x)
    f#(s(x)) -> f#(x) -> f#(s(x)) -> minus#(s(x),g(f(x)))
    f#(s(x)) -> f#(x) -> f#(s(x)) -> g#(f(x))
    f#(s(x)) -> f#(x) -> f#(s(x)) -> f#(x)
    f#(s(x)) -> minus#(s(x),g(f(x))) ->
    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)
     f#(s(x)) -> f#(x)
     f#(s(x)) -> g#(f(x))
     f#(s(x)) -> minus#(s(x),g(f(x)))
     g#(s(x)) -> g#(x)
     g#(s(x)) -> f#(g(x))
     g#(s(x)) -> minus#(s(x),f(g(x)))
    TRS:
     minus(x,0()) -> x
     minus(s(x),s(y)) -> minus(x,y)
     f(0()) -> s(0())
     f(s(x)) -> minus(s(x),g(f(x)))
     g(0()) -> 0()
     g(s(x)) -> minus(s(x),f(g(x)))
    SCC Processor:
     #sccs: 2
     #rules: 5
     #arcs: 15/49
     DPs:
      g#(s(x)) -> g#(x)
      g#(s(x)) -> f#(g(x))
      f#(s(x)) -> f#(x)
      f#(s(x)) -> g#(f(x))
     TRS:
      minus(x,0()) -> x
      minus(s(x),s(y)) -> minus(x,y)
      f(0()) -> s(0())
      f(s(x)) -> minus(s(x),g(f(x)))
      g(0()) -> 0()
      g(s(x)) -> minus(s(x),f(g(x)))
     Open
     
     DPs:
      minus#(s(x),s(y)) -> minus#(x,y)
     TRS:
      minus(x,0()) -> x
      minus(s(x),s(y)) -> minus(x,y)
      f(0()) -> s(0())
      f(s(x)) -> minus(s(x),g(f(x)))
      g(0()) -> 0()
      g(s(x)) -> minus(s(x),f(g(x)))
     Open