MAYBE
Time: 0.110468
TRS:
 {               le(0(), y) -> true(),
               le(s x, 0()) -> false(),
               le(s x, s y) -> le(x, y),
                   pred s x -> x,
              minus(x, 0()) -> x,
              minus(x, s y) -> pred 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#(x, s y) -> pred# minus(x, y),
               minus#(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(), 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),
                    pred s x -> x,
               minus(x, 0()) -> x,
               minus(x, s y) -> pred 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}
  UR:
   {   le(0(), y) -> true(),
     le(s x, 0()) -> false(),
     le(s x, s y) -> le(x, y),
         pred s x -> x,
    minus(x, 0()) -> x,
    minus(x, s y) -> pred minus(x, y),
          a(z, w) -> z,
          a(z, w) -> w}
   EDG:
    {(le#(s x, s y) -> le#(x, y), le#(s x, s y) -> le#(x, y))
     (if_mod#(true(), s x, s y) -> minus#(x, y), minus#(x, s y) -> minus#(x, y))
     (if_mod#(true(), s x, s y) -> minus#(x, y), minus#(x, s y) -> pred# minus(x, y))
     (mod#(s x, s y) -> le#(y, x), 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(), 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))
     (if_mod#(true(), s x, s y) -> mod#(minus(x, y), s y), mod#(s x, s y) -> le#(y, x))
     (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))
     (minus#(x, s y) -> minus#(x, y), minus#(x, s y) -> pred# minus(x, y))
     (minus#(x, s y) -> minus#(x, y), minus#(x, s y) -> minus#(x, y))}
    STATUS:
     arrows: 0.795918
     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#(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(), 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),
                         pred s x -> x,
                    minus(x, 0()) -> x,
                    minus(x, s y) -> pred 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:
        {minus#(x, s y) -> minus#(x, y)}
       Weak:
       {               le(0(), y) -> true(),
                     le(s x, 0()) -> false(),
                     le(s x, s y) -> le(x, y),
                         pred s x -> x,
                    minus(x, 0()) -> x,
                    minus(x, s y) -> pred 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),
                         pred s x -> x,
                    minus(x, 0()) -> x,
                    minus(x, s y) -> pred 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