MAYBE
Time: 0.003211
TRS:
 {               le(0(), y) -> true(),
               le(s x, 0()) -> false(),
               le(s x, s y) -> le(x, y),
              minus(0(), y) -> 0(),
              minus(s x, y) -> if_minus(le(s x, y), s x, y),
   if_minus(true(), s x, y) -> 0(),
  if_minus(false(), s x, y) -> s 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(), s x, s y) -> mod(minus(x, y), s y),
  if_mod(false(), s x, s y) -> s x}
 DP:
  DP:
   {             le#(s x, s y) -> le#(x, y),
                minus#(s x, y) -> le#(s x, y),
                minus#(s x, y) -> if_minus#(le(s x, y), s x, y),
    if_minus#(false(), s x, 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(), s x, s y) -> minus#(x, y),
     if_mod#(true(), s x, s y) -> mod#(minus(x, y), s y)}
  TRS:
  {               le(0(), y) -> true(),
                le(s x, 0()) -> false(),
                le(s x, s y) -> le(x, y),
               minus(0(), y) -> 0(),
               minus(s x, y) -> if_minus(le(s x, y), s x, y),
    if_minus(true(), s x, y) -> 0(),
   if_minus(false(), s x, y) -> s 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(), s x, s y) -> mod(minus(x, y), s y),
   if_mod(false(), s x, s y) -> s x}
  EDG:
   {(mod#(s x, s y) -> le#(y, x), le#(s x, s y) -> le#(x, y))
    (if_mod#(true(), s x, s y) -> mod#(minus(x, y), s y), mod#(s x, s y) -> if_mod#(le(y, x), s x, s y))
    (if_mod#(true(), s x, s y) -> mod#(minus(x, y), s y), mod#(s x, s y) -> le#(y, x))
    (if_minus#(false(), s x, y) -> minus#(x, y), minus#(s x, y) -> if_minus#(le(s x, y), s x, y))
    (if_minus#(false(), s x, y) -> minus#(x, y), minus#(s x, y) -> le#(s x, y))
    (if_mod#(true(), s x, s y) -> minus#(x, y), minus#(s x, y) -> if_minus#(le(s x, y), s x, y))
    (if_mod#(true(), s x, s y) -> minus#(x, y), minus#(s x, y) -> le#(s x, y))
    (mod#(s x, s y) -> if_mod#(le(y, x), s x, s y), if_mod#(true(), s x, s y) -> minus#(x, y))
    (mod#(s x, s y) -> if_mod#(le(y, x), s x, s y), if_mod#(true(), s x, s y) -> mod#(minus(x, y), s y))
    (le#(s x, s y) -> le#(x, y), le#(s x, s y) -> le#(x, y))
    (minus#(s x, y) -> le#(s x, y), le#(s x, s y) -> le#(x, y))
    (minus#(s x, y) -> if_minus#(le(s x, y), s x, y), if_minus#(false(), s x, y) -> minus#(x, y))}
   STATUS:
    arrows: 0.812500
    SCCS (3):
     Scc:
      {           mod#(s x, s y) -> if_mod#(le(y, x), s x, s y),
       if_mod#(true(), s x, s y) -> mod#(minus(x, y), s y)}
     Scc:
      {            minus#(s x, y) -> if_minus#(le(s x, y), s x, y),
       if_minus#(false(), s x, 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(), s x, s y) -> mod#(minus(x, y), s y)}
      Weak:
      {               le(0(), y) -> true(),
                    le(s x, 0()) -> false(),
                    le(s x, s y) -> le(x, y),
                   minus(0(), y) -> 0(),
                   minus(s x, y) -> if_minus(le(s x, y), s x, y),
        if_minus(true(), s x, y) -> 0(),
       if_minus(false(), s x, y) -> s 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(), s x, s y) -> mod(minus(x, y), s y),
       if_mod(false(), s x, s y) -> s x}
      Open
     
     
     SCC (2):
      Strict:
       {            minus#(s x, y) -> if_minus#(le(s x, y), s x, y),
        if_minus#(false(), s x, y) -> minus#(x, y)}
      Weak:
      {               le(0(), y) -> true(),
                    le(s x, 0()) -> false(),
                    le(s x, s y) -> le(x, y),
                   minus(0(), y) -> 0(),
                   minus(s x, y) -> if_minus(le(s x, y), s x, y),
        if_minus(true(), s x, y) -> 0(),
       if_minus(false(), s x, y) -> s 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(), s x, s y) -> mod(minus(x, y), s y),
       if_mod(false(), s x, s y) -> s x}
      Open
     
     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(0(), y) -> 0(),
                   minus(s x, y) -> if_minus(le(s x, y), s x, y),
        if_minus(true(), s x, y) -> 0(),
       if_minus(false(), s x, y) -> s 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(), s x, s y) -> mod(minus(x, y), s y),
       if_mod(false(), s x, s y) -> s x}
      Open