YES
Time: 0.008745
TRS:
 {        minus(x, 0()) -> x,
  minus(minus(x, y), z) -> minus(x, plus(y, z)),
        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(0(), y) -> y,
           plus(s x, y) -> s plus(x, y)}
 DP:
  DP:
   {minus#(minus(x, y), z) -> minus#(x, plus(y, z)),
    minus#(minus(x, y), z) -> plus#(y, z),
          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#(s x, y) -> plus#(x, y)}
  TRS:
  {        minus(x, 0()) -> x,
   minus(minus(x, y), z) -> minus(x, plus(y, z)),
         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(0(), y) -> y,
            plus(s x, y) -> s plus(x, y)}
  EDG:
   {(minus#(minus(x, y), z) -> plus#(y, z), plus#(s x, y) -> plus#(x, y))
    (quot#(s x, s y) -> minus#(x, y), minus#(s x, s y) -> minus#(x, y))
    (quot#(s x, s y) -> minus#(x, y), minus#(minus(x, y), z) -> plus#(y, z))
    (quot#(s x, s y) -> minus#(x, y), minus#(minus(x, y), z) -> minus#(x, plus(y, z)))
    (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#(s x, y) -> plus#(x, y), plus#(s x, y) -> plus#(x, y))
    (minus#(s x, s y) -> minus#(x, y), minus#(minus(x, y), z) -> minus#(x, plus(y, z)))
    (minus#(s x, s y) -> minus#(x, y), minus#(minus(x, y), z) -> plus#(y, z))
    (minus#(s x, s y) -> minus#(x, y), minus#(s x, s y) -> minus#(x, y))
    (minus#(minus(x, y), z) -> minus#(x, plus(y, z)), minus#(minus(x, y), z) -> minus#(x, plus(y, z)))
    (minus#(minus(x, y), z) -> minus#(x, plus(y, z)), minus#(minus(x, y), z) -> plus#(y, z))
    (minus#(minus(x, y), z) -> minus#(x, plus(y, z)), minus#(s x, s y) -> minus#(x, y))}
   SCCS (3):
    Scc:
     {plus#(s x, y) -> plus#(x, y)}
    Scc:
     {quot#(s x, s y) -> quot#(minus(x, y), s y)}
    Scc:
     {minus#(minus(x, y), z) -> minus#(x, plus(y, z)),
            minus#(s x, s y) -> minus#(x, y)}
    SCC (1):
     Strict:
      {plus#(s x, y) -> plus#(x, y)}
     Weak:
     {        minus(x, 0()) -> x,
      minus(minus(x, y), z) -> minus(x, plus(y, z)),
            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(0(), y) -> y,
               plus(s x, y) -> s plus(x, y)}
     SPSC:
      Simple Projection:
       pi(plus#) = 0
      Strict:
       {}
      Qed
    SCC (1):
     Strict:
      {quot#(s x, s y) -> quot#(minus(x, y), s y)}
     Weak:
     {        minus(x, 0()) -> x,
      minus(minus(x, y), z) -> minus(x, plus(y, z)),
            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(0(), y) -> y,
               plus(s x, y) -> s plus(x, y)}
     POLY:
      Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
      Interpretation:
       [minus](x0, x1) = x0,
       
       [quot](x0, x1) = x0 + 1,
       
       [plus](x0, x1) = 0,
       
       [s](x0) = x0 + 1,
       
       [0] = 0,
       
       [quot#](x0, x1) = x0 + 1
      Strict:
       quot#(s x, s y) -> quot#(minus(x, y), s y)
       2 + 1x + 0y >= 1 + 1x + 0y
      Weak:
       
     Qed
   SCC (2):
    Strict:
     {minus#(minus(x, y), z) -> minus#(x, plus(y, z)),
            minus#(s x, s y) -> minus#(x, y)}
    Weak:
    {        minus(x, 0()) -> x,
     minus(minus(x, y), z) -> minus(x, plus(y, z)),
           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(0(), y) -> y,
              plus(s x, y) -> s plus(x, y)}
    SPSC:
     Simple Projection:
      pi(minus#) = 0
     Strict:
      {minus#(s x, s y) -> minus#(x, y)}
     EDG:
      {(minus#(s x, s y) -> minus#(x, y), minus#(s x, s y) -> minus#(x, y))}
      SCCS (1):
       Scc:
        {minus#(s x, s y) -> minus#(x, y)}
       SCC (1):
        Strict:
         {minus#(s x, s y) -> minus#(x, y)}
        Weak:
        {        minus(x, 0()) -> x,
         minus(minus(x, y), z) -> minus(x, plus(y, z)),
               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(0(), y) -> y,
                  plus(s x, y) -> s plus(x, y)}
        SPSC:
         Simple Projection:
          pi(minus#) = 1
         Strict:
          {}
         Qed