YES
Time: 0.024075
TRS:
 {  quot(x, 0(), s z) -> s quot(x, plus(z, s 0()), s z),
  quot(0(), s y, s z) -> 0(),
    quot(s x, s y, z) -> quot(x, y, z),
         plus(0(), y) -> y,
         plus(s x, y) -> s plus(x, y)}
 DP:
  DP:
   {quot#(x, 0(), s z) -> quot#(x, plus(z, s 0()), s z),
    quot#(x, 0(), s z) -> plus#(z, s 0()),
    quot#(s x, s y, z) -> quot#(x, y, z),
         plus#(s x, y) -> plus#(x, y)}
  TRS:
  {  quot(x, 0(), s z) -> s quot(x, plus(z, s 0()), s z),
   quot(0(), s y, s z) -> 0(),
     quot(s x, s y, z) -> quot(x, y, z),
          plus(0(), y) -> y,
          plus(s x, y) -> s plus(x, y)}
  EDG:
   {(quot#(s x, s y, z) -> quot#(x, y, z), quot#(s x, s y, z) -> quot#(x, y, z))
    (quot#(s x, s y, z) -> quot#(x, y, z), quot#(x, 0(), s z) -> plus#(z, s 0()))
    (quot#(s x, s y, z) -> quot#(x, y, z), quot#(x, 0(), s z) -> quot#(x, plus(z, s 0()), s z))
    (plus#(s x, y) -> plus#(x, y), plus#(s x, y) -> plus#(x, y))
    (quot#(x, 0(), s z) -> quot#(x, plus(z, s 0()), s z), quot#(x, 0(), s z) -> quot#(x, plus(z, s 0()), s z))
    (quot#(x, 0(), s z) -> quot#(x, plus(z, s 0()), s z), quot#(x, 0(), s z) -> plus#(z, s 0()))
    (quot#(x, 0(), s z) -> quot#(x, plus(z, s 0()), s z), quot#(s x, s y, z) -> quot#(x, y, z))
    (quot#(x, 0(), s z) -> plus#(z, s 0()), plus#(s x, y) -> plus#(x, y))}
   STATUS:
    arrows: 0.500000
    SCCS (2):
     Scc:
      {quot#(x, 0(), s z) -> quot#(x, plus(z, s 0()), s z),
       quot#(s x, s y, z) -> quot#(x, y, z)}
     Scc:
      {plus#(s x, y) -> plus#(x, y)}
     
     SCC (2):
      Strict:
       {quot#(x, 0(), s z) -> quot#(x, plus(z, s 0()), s z),
        quot#(s x, s y, z) -> quot#(x, y, z)}
      Weak:
      {  quot(x, 0(), s z) -> s quot(x, plus(z, s 0()), s z),
       quot(0(), s y, s z) -> 0(),
         quot(s x, s y, z) -> quot(x, y, z),
              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:
        [quot](x0, x1, x2) = x0 + x1 + 1,
        
        [plus](x0, x1) = x0,
        
        [s](x0) = x0 + 1,
        
        [0] = 0,
        
        [quot#](x0, x1, x2) = x0 + x1
       Strict:
        quot#(s x, s y, z) -> quot#(x, y, z)
        1 + 0y + 1z + 1x >= 0 + 0y + 1z + 1x
        quot#(x, 0(), s z) -> quot#(x, plus(z, s 0()), s z)
        1 + 1z + 1x >= 1 + 1z + 1x
       Weak:
        plus(s x, y) -> s plus(x, y)
        1 + 0y + 1x >= 1 + 0y + 1x
        plus(0(), y) -> y
        0 + 0y >= 1y
        quot(s x, s y, z) -> quot(x, y, z)
        2 + 0y + 1z + 1x >= 1 + 0y + 1z + 1x
        quot(0(), s y, s z) -> 0()
        2 + 0y + 1z >= 0
        quot(x, 0(), s z) -> s quot(x, plus(z, s 0()), s z)
        2 + 1z + 1x >= 3 + 1z + 1x
      SCCS (1):
       Scc:
        {quot#(x, 0(), s z) -> quot#(x, plus(z, s 0()), s z)}
       
       SCC (1):
        Strict:
         {quot#(x, 0(), s z) -> quot#(x, plus(z, s 0()), s z)}
        Weak:
        {  quot(x, 0(), s z) -> s quot(x, plus(z, s 0()), s z),
         quot(0(), s y, s z) -> 0(),
           quot(s x, s y, z) -> quot(x, y, z),
                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:
          [quot](x0, x1, x2) = x0 + x1 + 1,
          
          [plus](x0, x1) = x0,
          
          [s](x0) = 0,
          
          [0] = 1,
          
          [quot#](x0, x1, x2) = x0
         Strict:
          quot#(x, 0(), s z) -> quot#(x, plus(z, s 0()), s z)
          1 + 0z + 0x >= 0 + 0z + 0x
         Weak:
          plus(s x, y) -> s plus(x, y)
          0 + 1y + 0x >= 0 + 0y + 0x
          plus(0(), y) -> y
          0 + 1y >= 1y
          quot(s x, s y, z) -> quot(x, y, z)
          1 + 0y + 0z + 0x >= 1 + 1y + 0z + 1x
          quot(0(), s y, s z) -> 0()
          2 + 0y + 0z >= 1
          quot(x, 0(), s z) -> s quot(x, plus(z, s 0()), s z)
          2 + 0z + 1x >= 0 + 0z + 0x
        Qed
    
    SCC (1):
     Strict:
      {plus#(s x, y) -> plus#(x, y)}
     Weak:
     {  quot(x, 0(), s z) -> s quot(x, plus(z, s 0()), s z),
      quot(0(), s y, s z) -> 0(),
        quot(s x, s y, z) -> quot(x, y, z),
             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:
       [quot](x0, x1, x2) = 0,
       
       [plus](x0, x1) = 0,
       
       [s](x0) = x0 + 1,
       
       [0] = 0,
       
       [plus#](x0, x1) = x0
      Strict:
       plus#(s x, y) -> plus#(x, y)
       1 + 0y + 1x >= 0 + 0y + 1x
      Weak:
       plus(s x, y) -> s plus(x, y)
       0 + 0y + 0x >= 1 + 0y + 0x
       plus(0(), y) -> y
       0 + 0y >= 1y
       quot(s x, s y, z) -> quot(x, y, z)
       0 + 0y + 0z + 0x >= 0 + 0y + 0z + 0x
       quot(0(), s y, s z) -> 0()
       0 + 0y + 0z >= 0
       quot(x, 0(), s z) -> s quot(x, plus(z, s 0()), s z)
       0 + 0z + 0x >= 1 + 0z + 0x
     Qed