MAYBE
Time: 0.036080
TRS:
 {   f c(s x, y) -> g c(x, y),
           f s x -> f id_inc c(x, x),
  id_inc c(x, y) -> c(id_inc x, id_inc y),
      id_inc s x -> s id_inc x,
      id_inc 0() -> s 0(),
      id_inc 0() -> 0(),
       g c(x, x) -> f x,
     g c(x, s y) -> g c(y, x),
     g c(s x, y) -> g c(y, x)}
 DP:
  DP:
   {   f# c(s x, y) -> g# c(x, y),
             f# s x -> f# id_inc c(x, x),
             f# s x -> id_inc# c(x, x),
    id_inc# c(x, y) -> id_inc# x,
    id_inc# c(x, y) -> id_inc# y,
        id_inc# s x -> id_inc# x,
         g# c(x, x) -> f# x,
       g# c(x, s y) -> g# c(y, x),
       g# c(s x, y) -> g# c(y, x)}
  TRS:
  {   f c(s x, y) -> g c(x, y),
            f s x -> f id_inc c(x, x),
   id_inc c(x, y) -> c(id_inc x, id_inc y),
       id_inc s x -> s id_inc x,
       id_inc 0() -> s 0(),
       id_inc 0() -> 0(),
        g c(x, x) -> f x,
      g c(x, s y) -> g c(y, x),
      g c(s x, y) -> g c(y, x)}
  UR:
   {id_inc c(x, y) -> c(id_inc x, id_inc y),
        id_inc s x -> s id_inc x,
        id_inc 0() -> s 0(),
        id_inc 0() -> 0(),
           a(z, w) -> z,
           a(z, w) -> w}
   EDG:
    {(id_inc# s x -> id_inc# x, id_inc# s x -> id_inc# x)
     (id_inc# s x -> id_inc# x, id_inc# c(x, y) -> id_inc# y)
     (id_inc# s x -> id_inc# x, id_inc# c(x, y) -> id_inc# x)
     (f# s x -> f# id_inc c(x, x), f# s x -> id_inc# c(x, x))
     (f# s x -> f# id_inc c(x, x), f# s x -> f# id_inc c(x, x))
     (f# s x -> f# id_inc c(x, x), f# c(s x, y) -> g# c(x, y))
     (f# c(s x, y) -> g# c(x, y), g# c(s x, y) -> g# c(y, x))
     (f# c(s x, y) -> g# c(x, y), g# c(x, s y) -> g# c(y, x))
     (f# c(s x, y) -> g# c(x, y), g# c(x, x) -> f# x)
     (g# c(x, s y) -> g# c(y, x), g# c(s x, y) -> g# c(y, x))
     (g# c(x, s y) -> g# c(y, x), g# c(x, s y) -> g# c(y, x))
     (g# c(x, s y) -> g# c(y, x), g# c(x, x) -> f# x)
     (g# c(s x, y) -> g# c(y, x), g# c(x, x) -> f# x)
     (g# c(s x, y) -> g# c(y, x), g# c(x, s y) -> g# c(y, x))
     (g# c(s x, y) -> g# c(y, x), g# c(s x, y) -> g# c(y, x))
     (f# s x -> id_inc# c(x, x), id_inc# c(x, y) -> id_inc# x)
     (f# s x -> id_inc# c(x, x), id_inc# c(x, y) -> id_inc# y)
     (f# s x -> id_inc# c(x, x), id_inc# s x -> id_inc# x)
     (id_inc# c(x, y) -> id_inc# y, id_inc# c(x, y) -> id_inc# x)
     (id_inc# c(x, y) -> id_inc# y, id_inc# c(x, y) -> id_inc# y)
     (id_inc# c(x, y) -> id_inc# y, id_inc# s x -> id_inc# x)
     (g# c(x, x) -> f# x, f# c(s x, y) -> g# c(x, y))
     (g# c(x, x) -> f# x, f# s x -> f# id_inc c(x, x))
     (g# c(x, x) -> f# x, f# s x -> id_inc# c(x, x))
     (id_inc# c(x, y) -> id_inc# x, id_inc# c(x, y) -> id_inc# x)
     (id_inc# c(x, y) -> id_inc# x, id_inc# c(x, y) -> id_inc# y)
     (id_inc# c(x, y) -> id_inc# x, id_inc# s x -> id_inc# x)}
    EDG:
     {(id_inc# s x -> id_inc# x, id_inc# s x -> id_inc# x)
      (id_inc# s x -> id_inc# x, id_inc# c(x, y) -> id_inc# y)
      (id_inc# s x -> id_inc# x, id_inc# c(x, y) -> id_inc# x)
      (f# s x -> f# id_inc c(x, x), f# s x -> id_inc# c(x, x))
      (f# s x -> f# id_inc c(x, x), f# s x -> f# id_inc c(x, x))
      (f# s x -> f# id_inc c(x, x), f# c(s x, y) -> g# c(x, y))
      (f# c(s x, y) -> g# c(x, y), g# c(s x, y) -> g# c(y, x))
      (f# c(s x, y) -> g# c(x, y), g# c(x, s y) -> g# c(y, x))
      (f# c(s x, y) -> g# c(x, y), g# c(x, x) -> f# x)
      (g# c(x, s y) -> g# c(y, x), g# c(s x, y) -> g# c(y, x))
      (g# c(x, s y) -> g# c(y, x), g# c(x, s y) -> g# c(y, x))
      (g# c(x, s y) -> g# c(y, x), g# c(x, x) -> f# x)
      (g# c(s x, y) -> g# c(y, x), g# c(x, x) -> f# x)
      (g# c(s x, y) -> g# c(y, x), g# c(x, s y) -> g# c(y, x))
      (g# c(s x, y) -> g# c(y, x), g# c(s x, y) -> g# c(y, x))
      (f# s x -> id_inc# c(x, x), id_inc# c(x, y) -> id_inc# x)
      (f# s x -> id_inc# c(x, x), id_inc# c(x, y) -> id_inc# y)
      (id_inc# c(x, y) -> id_inc# y, id_inc# c(x, y) -> id_inc# x)
      (id_inc# c(x, y) -> id_inc# y, id_inc# c(x, y) -> id_inc# y)
      (id_inc# c(x, y) -> id_inc# y, id_inc# s x -> id_inc# x)
      (g# c(x, x) -> f# x, f# c(s x, y) -> g# c(x, y))
      (g# c(x, x) -> f# x, f# s x -> f# id_inc c(x, x))
      (g# c(x, x) -> f# x, f# s x -> id_inc# c(x, x))
      (id_inc# c(x, y) -> id_inc# x, id_inc# c(x, y) -> id_inc# x)
      (id_inc# c(x, y) -> id_inc# x, id_inc# c(x, y) -> id_inc# y)
      (id_inc# c(x, y) -> id_inc# x, id_inc# s x -> id_inc# x)}
     EDG:
      {(id_inc# s x -> id_inc# x, id_inc# s x -> id_inc# x)
       (id_inc# s x -> id_inc# x, id_inc# c(x, y) -> id_inc# y)
       (id_inc# s x -> id_inc# x, id_inc# c(x, y) -> id_inc# x)
       (f# s x -> f# id_inc c(x, x), f# c(s x, y) -> g# c(x, y))
       (f# c(s x, y) -> g# c(x, y), g# c(s x, y) -> g# c(y, x))
       (f# c(s x, y) -> g# c(x, y), g# c(x, s y) -> g# c(y, x))
       (f# c(s x, y) -> g# c(x, y), g# c(x, x) -> f# x)
       (g# c(x, s y) -> g# c(y, x), g# c(s x, y) -> g# c(y, x))
       (g# c(x, s y) -> g# c(y, x), g# c(x, s y) -> g# c(y, x))
       (g# c(x, s y) -> g# c(y, x), g# c(x, x) -> f# x)
       (g# c(s x, y) -> g# c(y, x), g# c(x, x) -> f# x)
       (g# c(s x, y) -> g# c(y, x), g# c(x, s y) -> g# c(y, x))
       (g# c(s x, y) -> g# c(y, x), g# c(s x, y) -> g# c(y, x))
       (f# s x -> id_inc# c(x, x), id_inc# c(x, y) -> id_inc# x)
       (f# s x -> id_inc# c(x, x), id_inc# c(x, y) -> id_inc# y)
       (id_inc# c(x, y) -> id_inc# y, id_inc# c(x, y) -> id_inc# x)
       (id_inc# c(x, y) -> id_inc# y, id_inc# c(x, y) -> id_inc# y)
       (id_inc# c(x, y) -> id_inc# y, id_inc# s x -> id_inc# x)
       (g# c(x, x) -> f# x, f# c(s x, y) -> g# c(x, y))
       (g# c(x, x) -> f# x, f# s x -> f# id_inc c(x, x))
       (g# c(x, x) -> f# x, f# s x -> id_inc# c(x, x))
       (id_inc# c(x, y) -> id_inc# x, id_inc# c(x, y) -> id_inc# x)
       (id_inc# c(x, y) -> id_inc# x, id_inc# c(x, y) -> id_inc# y)
       (id_inc# c(x, y) -> id_inc# x, id_inc# s x -> id_inc# x)}
      EDG:
       {(id_inc# s x -> id_inc# x, id_inc# s x -> id_inc# x)
        (id_inc# s x -> id_inc# x, id_inc# c(x, y) -> id_inc# y)
        (id_inc# s x -> id_inc# x, id_inc# c(x, y) -> id_inc# x)
        (f# s x -> f# id_inc c(x, x), f# c(s x, y) -> g# c(x, y))
        (f# c(s x, y) -> g# c(x, y), g# c(s x, y) -> g# c(y, x))
        (f# c(s x, y) -> g# c(x, y), g# c(x, s y) -> g# c(y, x))
        (f# c(s x, y) -> g# c(x, y), g# c(x, x) -> f# x)
        (g# c(x, s y) -> g# c(y, x), g# c(s x, y) -> g# c(y, x))
        (g# c(x, s y) -> g# c(y, x), g# c(x, s y) -> g# c(y, x))
        (g# c(x, s y) -> g# c(y, x), g# c(x, x) -> f# x)
        (g# c(s x, y) -> g# c(y, x), g# c(x, x) -> f# x)
        (g# c(s x, y) -> g# c(y, x), g# c(x, s y) -> g# c(y, x))
        (g# c(s x, y) -> g# c(y, x), g# c(s x, y) -> g# c(y, x))
        (f# s x -> id_inc# c(x, x), id_inc# c(x, y) -> id_inc# x)
        (f# s x -> id_inc# c(x, x), id_inc# c(x, y) -> id_inc# y)
        (id_inc# c(x, y) -> id_inc# y, id_inc# c(x, y) -> id_inc# x)
        (id_inc# c(x, y) -> id_inc# y, id_inc# c(x, y) -> id_inc# y)
        (id_inc# c(x, y) -> id_inc# y, id_inc# s x -> id_inc# x)
        (g# c(x, x) -> f# x, f# c(s x, y) -> g# c(x, y))
        (g# c(x, x) -> f# x, f# s x -> f# id_inc c(x, x))
        (g# c(x, x) -> f# x, f# s x -> id_inc# c(x, x))
        (id_inc# c(x, y) -> id_inc# x, id_inc# c(x, y) -> id_inc# x)
        (id_inc# c(x, y) -> id_inc# x, id_inc# c(x, y) -> id_inc# y)
        (id_inc# c(x, y) -> id_inc# x, id_inc# s x -> id_inc# x)}
       STATUS:
        arrows: 0.703704
        SCCS (2):
         Scc:
          {f# c(s x, y) -> g# c(x, y),
                 f# s x -> f# id_inc c(x, x),
             g# c(x, x) -> f# x,
           g# c(x, s y) -> g# c(y, x),
           g# c(s x, y) -> g# c(y, x)}
         Scc:
          {id_inc# c(x, y) -> id_inc# x,
           id_inc# c(x, y) -> id_inc# y,
               id_inc# s x -> id_inc# x}
         
         SCC (5):
          Strict:
           {f# c(s x, y) -> g# c(x, y),
                  f# s x -> f# id_inc c(x, x),
              g# c(x, x) -> f# x,
            g# c(x, s y) -> g# c(y, x),
            g# c(s x, y) -> g# c(y, x)}
          Weak:
          {   f c(s x, y) -> g c(x, y),
                    f s x -> f id_inc c(x, x),
           id_inc c(x, y) -> c(id_inc x, id_inc y),
               id_inc s x -> s id_inc x,
               id_inc 0() -> s 0(),
               id_inc 0() -> 0(),
                g c(x, x) -> f x,
              g c(x, s y) -> g c(y, x),
              g c(s x, y) -> g c(y, x)}
          Open
         
         SCC (3):
          Strict:
           {id_inc# c(x, y) -> id_inc# x,
            id_inc# c(x, y) -> id_inc# y,
                id_inc# s x -> id_inc# x}
          Weak:
          {   f c(s x, y) -> g c(x, y),
                    f s x -> f id_inc c(x, x),
           id_inc c(x, y) -> c(id_inc x, id_inc y),
               id_inc s x -> s id_inc x,
               id_inc 0() -> s 0(),
               id_inc 0() -> 0(),
                g c(x, x) -> f x,
              g c(x, s y) -> g c(y, x),
              g c(s x, y) -> g c(y, x)}
          Open