MAYBE
Time: 0.028275
TRS:
 {               le(0(), y) -> true(),
               le(s x, 0()) -> false(),
               le(s x, s y) -> le(x, y),
              minus(x, 0()) -> x,
            minus(s x, s y) -> minus(x, y),
                mod(0(), y) -> 0(),
              mod(s x, 0()) -> 0(),
              mod(s x, s y) -> if_mod(le(y, x), s x, s y),
       if_mod(true(), x, y) -> mod(minus(x, y), y),
  if_mod(false(), s x, s y) -> s x}
 DP:
  DP:
   {        le#(s x, s y) -> le#(x, y),
         minus#(s x, s y) -> minus#(x, y),
           mod#(s x, s y) -> le#(y, x),
           mod#(s x, s y) -> if_mod#(le(y, x), s x, s y),
    if_mod#(true(), x, y) -> minus#(x, y),
    if_mod#(true(), x, y) -> mod#(minus(x, y), y)}
  TRS:
  {               le(0(), y) -> true(),
                le(s x, 0()) -> false(),
                le(s x, s y) -> le(x, y),
               minus(x, 0()) -> x,
             minus(s x, s y) -> minus(x, y),
                 mod(0(), y) -> 0(),
               mod(s x, 0()) -> 0(),
               mod(s x, s y) -> if_mod(le(y, x), s x, s y),
        if_mod(true(), x, y) -> mod(minus(x, y), y),
   if_mod(false(), s x, s y) -> s x}
  EDG:
   {(le#(s x, s y) -> le#(x, y), le#(s x, s y) -> le#(x, y))
    (mod#(s x, s y) -> if_mod#(le(y, x), s x, s y), if_mod#(true(), x, y) -> mod#(minus(x, y), y))
    (mod#(s x, s y) -> if_mod#(le(y, x), s x, s y), if_mod#(true(), x, y) -> minus#(x, y))
    (if_mod#(true(), x, y) -> mod#(minus(x, y), y), mod#(s x, s y) -> if_mod#(le(y, x), s x, s y))
    (if_mod#(true(), x, y) -> mod#(minus(x, y), y), mod#(s x, s y) -> le#(y, x))
    (if_mod#(true(), x, y) -> minus#(x, y), minus#(s x, s y) -> minus#(x, y))
    (minus#(s x, s y) -> minus#(x, y), minus#(s x, s y) -> minus#(x, y))
    (mod#(s x, s y) -> le#(y, x), le#(s x, s y) -> le#(x, y))}
   STATUS:
    arrows: 0.777778
    SCCS (3):
     Scc:
      {       mod#(s x, s y) -> if_mod#(le(y, x), s x, s y),
       if_mod#(true(), x, y) -> mod#(minus(x, y), y)}
     Scc:
      {minus#(s x, s y) -> minus#(x, y)}
     Scc:
      {le#(s x, s y) -> le#(x, y)}
     
     SCC (2):
      Strict:
       {       mod#(s x, s y) -> if_mod#(le(y, x), s x, s y),
        if_mod#(true(), x, y) -> mod#(minus(x, y), y)}
      Weak:
      {               le(0(), y) -> true(),
                    le(s x, 0()) -> false(),
                    le(s x, s y) -> le(x, y),
                   minus(x, 0()) -> x,
                 minus(s x, s y) -> minus(x, y),
                     mod(0(), y) -> 0(),
                   mod(s x, 0()) -> 0(),
                   mod(s x, s y) -> if_mod(le(y, x), s x, s y),
            if_mod(true(), x, y) -> mod(minus(x, y), y),
       if_mod(false(), s x, s y) -> s x}
      Fail
     
     SCC (1):
      Strict:
       {minus#(s x, s y) -> minus#(x, y)}
      Weak:
      {               le(0(), y) -> true(),
                    le(s x, 0()) -> false(),
                    le(s x, s y) -> le(x, y),
                   minus(x, 0()) -> x,
                 minus(s x, s y) -> minus(x, y),
                     mod(0(), y) -> 0(),
                   mod(s x, 0()) -> 0(),
                   mod(s x, s y) -> if_mod(le(y, x), s x, s y),
            if_mod(true(), x, y) -> mod(minus(x, y), y),
       if_mod(false(), s x, s y) -> s x}
      POLY:
       Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
       Interpretation:
        [if_mod](x0, x1, x2) = x0 + x1,
        
        [le](x0, x1) = x0 + 1,
        
        [minus](x0, x1) = x0 + 1,
        
        [mod](x0, x1) = x0 + 1,
        
        [s](x0) = x0 + 1,
        
        [true] = 0,
        
        [0] = 1,
        
        [false] = 1,
        
        [minus#](x0, x1) = x0 + 1
       Strict:
        minus#(s x, s y) -> minus#(x, y)
        2 + 0y + 1x >= 1 + 0y + 1x
       Weak:
        if_mod(false(), s x, s y) -> s x
        2 + 0y + 1x >= 1 + 1x
        if_mod(true(), x, y) -> mod(minus(x, y), y)
        0 + 0y + 1x >= 2 + 1y + 0x
        mod(s x, s y) -> if_mod(le(y, x), s x, s y)
        2 + 0y + 1x >= 2 + 1y + 1x
        mod(s x, 0()) -> 0()
        2 + 1x >= 1
        mod(0(), y) -> 0()
        2 + 0y >= 1
        minus(s x, s y) -> minus(x, y)
        2 + 1y + 0x >= 1 + 1y + 0x
        minus(x, 0()) -> x
        2 + 0x >= 1x
        le(s x, s y) -> le(x, y)
        2 + 0y + 1x >= 1 + 0y + 1x
        le(s x, 0()) -> false()
        2 + 1x >= 1
        le(0(), y) -> true()
        2 + 0y >= 0
      Qed
    
    SCC (1):
     Strict:
      {le#(s x, s y) -> le#(x, y)}
     Weak:
     {               le(0(), y) -> true(),
                   le(s x, 0()) -> false(),
                   le(s x, s y) -> le(x, y),
                  minus(x, 0()) -> x,
                minus(s x, s y) -> minus(x, y),
                    mod(0(), y) -> 0(),
                  mod(s x, 0()) -> 0(),
                  mod(s x, s y) -> if_mod(le(y, x), s x, s y),
           if_mod(true(), x, y) -> mod(minus(x, y), y),
      if_mod(false(), s x, s y) -> s x}
     POLY:
      Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
      Interpretation:
       [if_mod](x0, x1, x2) = x0 + x1,
       
       [le](x0, x1) = x0 + 1,
       
       [minus](x0, x1) = x0 + 1,
       
       [mod](x0, x1) = x0 + 1,
       
       [s](x0) = x0 + 1,
       
       [true] = 0,
       
       [0] = 1,
       
       [false] = 1,
       
       [le#](x0, x1) = x0 + 1
      Strict:
       le#(s x, s y) -> le#(x, y)
       2 + 0y + 1x >= 1 + 0y + 1x
      Weak:
       if_mod(false(), s x, s y) -> s x
       2 + 0y + 1x >= 1 + 1x
       if_mod(true(), x, y) -> mod(minus(x, y), y)
       0 + 0y + 1x >= 2 + 1y + 0x
       mod(s x, s y) -> if_mod(le(y, x), s x, s y)
       2 + 0y + 1x >= 2 + 1y + 1x
       mod(s x, 0()) -> 0()
       2 + 1x >= 1
       mod(0(), y) -> 0()
       2 + 0y >= 1
       minus(s x, s y) -> minus(x, y)
       2 + 1y + 0x >= 1 + 1y + 0x
       minus(x, 0()) -> x
       2 + 0x >= 1x
       le(s x, s y) -> le(x, y)
       2 + 0y + 1x >= 1 + 0y + 1x
       le(s x, 0()) -> false()
       2 + 1x >= 1
       le(0(), y) -> true()
       2 + 0y >= 0
     Qed