MAYBE
Time: 0.025829
TRS:
 {  minus(x, 0()) -> x,
  minus(s x, s y) -> minus(x, y),
       le(0(), y) -> true(),
     le(s x, 0()) -> false(),
     le(s x, s y) -> le(x, y),
   quot(0(), s y) -> 0(),
   quot(s x, s y) -> s quot(minus(s x, s y), s y)}
 DP:
  DP:
   {minus#(s x, s y) -> minus#(x, y),
       le#(s x, s y) -> le#(x, y),
     quot#(s x, s y) -> minus#(s x, s y),
     quot#(s x, s y) -> quot#(minus(s x, s y), s y)}
  TRS:
  {  minus(x, 0()) -> x,
   minus(s x, s y) -> minus(x, y),
        le(0(), y) -> true(),
      le(s x, 0()) -> false(),
      le(s x, s y) -> le(x, y),
    quot(0(), s y) -> 0(),
    quot(s x, s y) -> s quot(minus(s x, s y), s y)}
  UR:
   {  minus(x, 0()) -> x,
    minus(s x, s y) -> minus(x, y)}
   EDG:
    {(quot#(s x, s y) -> quot#(minus(s x, s y), s y), quot#(s x, s y) -> quot#(minus(s x, s y), s y))
     (quot#(s x, s y) -> quot#(minus(s x, s y), s y), quot#(s x, s y) -> minus#(s x, s y))
     (le#(s x, s y) -> le#(x, y), le#(s x, s y) -> le#(x, y))
     (minus#(s x, s y) -> minus#(x, y), minus#(s x, s y) -> minus#(x, y))
     (quot#(s x, s y) -> minus#(s x, s y), minus#(s x, s y) -> minus#(x, y))}
    STATUS:
     arrows: 0.687500
     SCCS (3):
      Scc:
       {le#(s x, s y) -> le#(x, y)}
      Scc:
       {quot#(s x, s y) -> quot#(minus(s x, s y), s y)}
      Scc:
       {minus#(s x, s y) -> minus#(x, y)}
      
      SCC (1):
       Strict:
        {le#(s x, s y) -> le#(x, y)}
       Weak:
       {  minus(x, 0()) -> x,
        minus(s x, s y) -> minus(x, y),
             le(0(), y) -> true(),
           le(s x, 0()) -> false(),
           le(s x, s y) -> le(x, y),
         quot(0(), s y) -> 0(),
         quot(s x, s y) -> s quot(minus(s x, s y), s y)}
       POLY:
        Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
        Interpretation:
         [minus](x0, x1) = x0 + 1,
         
         [le](x0, x1) = x0 + 1,
         
         [quot](x0, x1) = x0,
         
         [s](x0) = x0 + 1,
         
         [0] = 1,
         
         [true] = 0,
         
         [false] = 0,
         
         [le#](x0, x1) = x0
        Strict:
         le#(s x, s y) -> le#(x, y)
         1 + 0x + 1y >= 0 + 0x + 1y
        Weak:
         quot(s x, s y) -> s quot(minus(s x, s y), s y)
         1 + 0x + 1y >= 2 + 0x + 1y
         quot(0(), s y) -> 0()
         1 + 1y >= 1
         le(s x, s y) -> le(x, y)
         2 + 1x + 0y >= 1 + 1x + 0y
         le(s x, 0()) -> false()
         2 + 1x >= 0
         le(0(), y) -> true()
         2 + 0y >= 0
         minus(s x, s y) -> minus(x, y)
         2 + 0x + 1y >= 1 + 0x + 1y
         minus(x, 0()) -> x
         2 + 0x >= 1x
       Qed
     SCC (1):
      Strict:
       {quot#(s x, s y) -> quot#(minus(s x, s y), s y)}
      Weak:
      {  minus(x, 0()) -> x,
       minus(s x, s y) -> minus(x, y),
            le(0(), y) -> true(),
          le(s x, 0()) -> false(),
          le(s x, s y) -> le(x, y),
        quot(0(), s y) -> 0(),
        quot(s x, s y) -> s quot(minus(s x, s y), s y)}
      Fail
     
     SCC (1):
      Strict:
       {minus#(s x, s y) -> minus#(x, y)}
      Weak:
      {  minus(x, 0()) -> x,
       minus(s x, s y) -> minus(x, y),
            le(0(), y) -> true(),
          le(s x, 0()) -> false(),
          le(s x, s y) -> le(x, y),
        quot(0(), s y) -> 0(),
        quot(s x, s y) -> s quot(minus(s x, s y), s y)}
      POLY:
       Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
       Interpretation:
        [minus](x0, x1) = x0 + 1,
        
        [le](x0, x1) = x0 + 1,
        
        [quot](x0, x1) = x0,
        
        [s](x0) = x0 + 1,
        
        [0] = 1,
        
        [true] = 0,
        
        [false] = 0,
        
        [minus#](x0, x1) = x0
       Strict:
        minus#(s x, s y) -> minus#(x, y)
        1 + 0x + 1y >= 0 + 0x + 1y
       Weak:
        quot(s x, s y) -> s quot(minus(s x, s y), s y)
        1 + 0x + 1y >= 2 + 0x + 1y
        quot(0(), s y) -> 0()
        1 + 1y >= 1
        le(s x, s y) -> le(x, y)
        2 + 1x + 0y >= 1 + 1x + 0y
        le(s x, 0()) -> false()
        2 + 1x >= 0
        le(0(), y) -> true()
        2 + 0y >= 0
        minus(s x, s y) -> minus(x, y)
        2 + 0x + 1y >= 1 + 0x + 1y
        minus(x, 0()) -> x
        2 + 0x >= 1x
      Qed