YES
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))}
 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)}
  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))}
  EDG:
   {(quot#(s(x), s(y)) -> minus#(x, y), minus#(s(x), s(y)) -> minus#(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#(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()))))
    (quot#(s(x), s(y)) -> quot#(minus(x, y), s(y)), quot#(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)))
    (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))
    (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)}
    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)}
     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))}
     POLY:
      Argument Filtering:
       pi(plus#) = [0,1], pi(plus) = [], pi(quot) = [], pi(s) = [0], pi(0) = [], pi(minus) = 0
      Usable Rules:
       {}
      Interpretation:
       [plus#](x0, x1) = x0 + x1,
       [s](x0) = x0 + 1
      Strict:
       {plus#(minus(x, s(0())), minus(y, s(s(z)))) -> plus#(minus(y, s(s(z))), minus(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))}
      EDG:
       {(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()))))}
       SCCS:
        Scc:
         {plus#(minus(x, s(0())), minus(y, s(s(z)))) -> plus#(minus(y, s(s(z))), minus(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())))}
         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))}
         UR:
          {    minus(x, 0()) -> x,
           minus(s(x), s(y)) -> minus(x, y)}
          BOUND:
           Bound: match(-raise)-bounded by 1
           Automaton:
            {plus#_1(4, 7) -> 1*
             plus#_0(1, 1) -> 1*
                    s_1(5) -> 6*
                    s_1(2) -> 3*
                    s_1(1) -> 2*
                    s_0(1) -> 1*
                     0_1() -> 5*
                     0_0() -> 1*
             minus_1(1, 6) -> 7*
             minus_1(1, 5) -> 7*
             minus_1(1, 3) -> 4*
             minus_1(1, 2) -> 4*
             minus_1(1, 1) -> 4 | 1
             minus_0(1, 1) -> 1*
                         1 -> 7 | 4}
           Strict:
            {}
           Qed
    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))}
     POLY:
      Argument Filtering:
       pi(plus) = [], pi(quot#) = [0,1], pi(quot) = [], pi(s) = [0], pi(0) = [], pi(minus) = 0
      Usable Rules:
       {}
      Interpretation:
       [quot#](x0, x1) = x0 + x1,
       [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))}
      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))}
     SPSC:
      Simple Projection:
       pi(minus#) = 0
      Strict:
       {}
      Qed