MAYBE
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))),
  plus(minus(x, s(0())), minus(y, s(s(z)))) -> plus(minus(y, s(s(z))), minus(x, s(0()))),
                               plus(0(), y) -> y,
                              plus(s(x), y) -> s(plus(x, y)),
    plus(plus(x, s(0())), plus(y, s(s(z)))) -> plus(plus(y, s(s(z))), plus(x, s(0())))}
 DP:
  Strict:
   {                        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)),
    plus#(minus(x, s(0())), minus(y, s(s(z)))) -> plus#(minus(y, s(s(z))), minus(x, s(0()))),
                                plus#(s(x), y) -> plus#(x, y),
      plus#(plus(x, s(0())), plus(y, s(s(z)))) -> plus#(plus(y, s(s(z))), plus(x, s(0())))}
  Weak:
  {                            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))),
   plus(minus(x, s(0())), minus(y, s(s(z)))) -> plus(minus(y, s(s(z))), minus(x, s(0()))),
                                plus(0(), y) -> y,
                               plus(s(x), y) -> s(plus(x, y)),
     plus(plus(x, s(0())), plus(y, s(s(z)))) -> plus(plus(y, s(s(z))), plus(x, s(0())))}
  EDG:
   {(quot#(s(x), s(y)) -> minus#(x, y), minus#(s(x), s(y)) -> minus#(x, 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)) -> quot#(minus(x, y), s(y)), quot#(s(x), s(y)) -> minus#(x, y))
    (plus#(plus(x, s(0())), plus(y, s(s(z)))) -> plus#(plus(y, s(s(z))), plus(x, s(0()))), plus#(plus(x, s(0())), plus(y, s(s(z)))) -> plus#(plus(y, s(s(z))), plus(x, s(0()))))
    (plus#(plus(x, s(0())), plus(y, s(s(z)))) -> plus#(plus(y, s(s(z))), plus(x, s(0()))), plus#(s(x), y) -> plus#(x, y))
    (plus#(plus(x, s(0())), plus(y, s(s(z)))) -> plus#(plus(y, s(s(z))), plus(x, s(0()))), plus#(minus(x, s(0())), minus(y, s(s(z)))) -> plus#(minus(y, s(s(z))), minus(x, s(0()))))
    (plus#(minus(x, s(0())), minus(y, s(s(z)))) -> plus#(minus(y, s(s(z))), minus(x, s(0()))), plus#(minus(x, s(0())), minus(y, s(s(z)))) -> plus#(minus(y, s(s(z))), minus(x, s(0()))))
    (plus#(minus(x, s(0())), minus(y, s(s(z)))) -> plus#(minus(y, s(s(z))), minus(x, s(0()))), plus#(s(x), y) -> plus#(x, y))
    (plus#(minus(x, s(0())), minus(y, s(s(z)))) -> plus#(minus(y, s(s(z))), minus(x, s(0()))), plus#(plus(x, s(0())), plus(y, s(s(z)))) -> plus#(plus(y, s(s(z))), plus(x, s(0()))))
    (plus#(s(x), y) -> plus#(x, y), plus#(minus(x, s(0())), minus(y, s(s(z)))) -> plus#(minus(y, s(s(z))), minus(x, s(0()))))
    (plus#(s(x), y) -> plus#(x, y), plus#(s(x), y) -> plus#(x, y))
    (plus#(s(x), y) -> plus#(x, y), plus#(plus(x, s(0())), plus(y, s(s(z)))) -> plus#(plus(y, s(s(z))), plus(x, s(0()))))
    (minus#(s(x), s(y)) -> minus#(x, y), minus#(s(x), s(y)) -> minus#(x, y))}
   SCCS:
    Scc:
     {plus#(minus(x, s(0())), minus(y, s(s(z)))) -> plus#(minus(y, s(s(z))), minus(x, s(0()))),
                                  plus#(s(x), y) -> plus#(x, y),
        plus#(plus(x, s(0())), plus(y, s(s(z)))) -> plus#(plus(y, s(s(z))), plus(x, s(0())))}
    Scc:
     {quot#(s(x), s(y)) -> quot#(minus(x, y), s(y))}
    Scc:
     {minus#(s(x), s(y)) -> minus#(x, y)}
    SCC:
     Strict:
      {plus#(minus(x, s(0())), minus(y, s(s(z)))) -> plus#(minus(y, s(s(z))), minus(x, s(0()))),
                                   plus#(s(x), y) -> plus#(x, y),
         plus#(plus(x, s(0())), plus(y, s(s(z)))) -> plus#(plus(y, s(s(z))), plus(x, s(0())))}
     Weak:
     {                            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))),
      plus(minus(x, s(0())), minus(y, s(s(z)))) -> plus(minus(y, s(s(z))), minus(x, s(0()))),
                                   plus(0(), y) -> y,
                                  plus(s(x), y) -> s(plus(x, y)),
        plus(plus(x, s(0())), plus(y, s(s(z)))) -> plus(plus(y, s(s(z))), plus(x, s(0())))}
     POLY:
      Argument Filtering:
       pi(plus#) = [0,1], pi(plus) = [0,1], pi(quot) = [], pi(s) = [0], pi(0) = [], pi(minus) = 0
      Usable Rules:
       {}
      Interpretation:
       [plus#](x0, x1) = x0 + x1,
       [plus](x0, x1) = x0 + x1,
       [s](x0) = x0 + 1,
       [0] = 1
      Strict:
       {plus#(minus(x, s(0())), minus(y, s(s(z)))) -> plus#(minus(y, s(s(z))), minus(x, s(0()))),
          plus#(plus(x, s(0())), plus(y, s(s(z)))) -> plus#(plus(y, s(s(z))), plus(x, s(0())))}
      Weak:
       {                            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))),
        plus(minus(x, s(0())), minus(y, s(s(z)))) -> plus(minus(y, s(s(z))), minus(x, s(0()))),
                                     plus(0(), y) -> y,
                                    plus(s(x), y) -> s(plus(x, y)),
          plus(plus(x, s(0())), plus(y, s(s(z)))) -> plus(plus(y, s(s(z))), plus(x, s(0())))}
      EDG:
       {(plus#(plus(x, s(0())), plus(y, s(s(z)))) -> plus#(plus(y, s(s(z))), plus(x, s(0()))), plus#(plus(x, s(0())), plus(y, s(s(z)))) -> plus#(plus(y, s(s(z))), plus(x, s(0()))))
        (plus#(plus(x, s(0())), plus(y, s(s(z)))) -> plus#(plus(y, s(s(z))), plus(x, s(0()))), plus#(minus(x, s(0())), minus(y, s(s(z)))) -> plus#(minus(y, s(s(z))), minus(x, s(0()))))
        (plus#(minus(x, s(0())), minus(y, s(s(z)))) -> plus#(minus(y, s(s(z))), minus(x, s(0()))), plus#(minus(x, s(0())), minus(y, s(s(z)))) -> plus#(minus(y, s(s(z))), minus(x, s(0()))))
        (plus#(minus(x, s(0())), minus(y, s(s(z)))) -> plus#(minus(y, s(s(z))), minus(x, s(0()))), plus#(plus(x, s(0())), plus(y, s(s(z)))) -> plus#(plus(y, s(s(z))), plus(x, s(0()))))}
       SCCS:
        Scc:
         {plus#(minus(x, s(0())), minus(y, s(s(z)))) -> plus#(minus(y, s(s(z))), minus(x, s(0()))),
            plus#(plus(x, s(0())), plus(y, s(s(z)))) -> plus#(plus(y, s(s(z))), plus(x, s(0())))}
        SCC:
         Strict:
          {plus#(minus(x, s(0())), minus(y, s(s(z)))) -> plus#(minus(y, s(s(z))), minus(x, s(0()))),
             plus#(plus(x, s(0())), plus(y, s(s(z)))) -> plus#(plus(y, s(s(z))), plus(x, s(0())))}
         Weak:
         {                            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))),
          plus(minus(x, s(0())), minus(y, s(s(z)))) -> plus(minus(y, s(s(z))), minus(x, s(0()))),
                                       plus(0(), y) -> y,
                                      plus(s(x), y) -> s(plus(x, y)),
            plus(plus(x, s(0())), plus(y, s(s(z)))) -> plus(plus(y, s(s(z))), plus(x, s(0())))}
         Fail
    SCC:
     Strict:
      {quot#(s(x), s(y)) -> quot#(minus(x, y), s(y))}
     Weak:
     {                            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))),
      plus(minus(x, s(0())), minus(y, s(s(z)))) -> plus(minus(y, s(s(z))), minus(x, s(0()))),
                                   plus(0(), y) -> y,
                                  plus(s(x), y) -> s(plus(x, y)),
        plus(plus(x, s(0())), plus(y, s(s(z)))) -> plus(plus(y, s(s(z))), plus(x, s(0())))}
     POLY:
      Argument Filtering:
       pi(plus) = [], pi(quot#) = 0, pi(quot) = [], pi(s) = [0], pi(0) = [], pi(minus) = 0
      Usable Rules:
       {}
      Interpretation:
       [s](x0) = x0 + 1
      Strict:
       {}
      Weak:
       {                            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))),
        plus(minus(x, s(0())), minus(y, s(s(z)))) -> plus(minus(y, s(s(z))), minus(x, s(0()))),
                                     plus(0(), y) -> y,
                                    plus(s(x), y) -> s(plus(x, y)),
          plus(plus(x, s(0())), plus(y, s(s(z)))) -> plus(plus(y, s(s(z))), plus(x, s(0())))}
      Qed
    SCC:
     Strict:
      {minus#(s(x), s(y)) -> minus#(x, y)}
     Weak:
     {                            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))),
      plus(minus(x, s(0())), minus(y, s(s(z)))) -> plus(minus(y, s(s(z))), minus(x, s(0()))),
                                   plus(0(), y) -> y,
                                  plus(s(x), y) -> s(plus(x, y)),
        plus(plus(x, s(0())), plus(y, s(s(z)))) -> plus(plus(y, s(s(z))), plus(x, s(0())))}
     SPSC:
      Simple Projection:
       pi(minus#) = 0
      Strict:
       {}
      Qed