MAYBE
Time: 0.016184
TRS:
 {f(g x, s 0(), y) -> f(g s 0(), y, g x),
             g s x -> s g x,
             g 0() -> 0()}
 DP:
  DP:
   {f#(g x, s 0(), y) -> f#(g s 0(), y, g x),
    f#(g x, s 0(), y) -> g# s 0(),
               g# s x -> g# x}
  TRS:
  {f(g x, s 0(), y) -> f(g s 0(), y, g x),
              g s x -> s g x,
              g 0() -> 0()}
  EDG:
   {(g# s x -> g# x, g# s x -> g# x)
    (f#(g x, s 0(), y) -> f#(g s 0(), y, g x), f#(g x, s 0(), y) -> f#(g s 0(), y, g x))
    (f#(g x, s 0(), y) -> f#(g s 0(), y, g x), f#(g x, s 0(), y) -> g# s 0())
    (f#(g x, s 0(), y) -> g# s 0(), g# s x -> g# x)}
   STATUS:
    arrows: 0.555556
    SCCS (2):
     Scc:
      {f#(g x, s 0(), y) -> f#(g s 0(), y, g x)}
     Scc:
      {g# s x -> g# x}
     
     SCC (1):
      Strict:
       {f#(g x, s 0(), y) -> f#(g s 0(), y, g x)}
      Weak:
      {f(g x, s 0(), y) -> f(g s 0(), y, g x),
                  g s x -> s g x,
                  g 0() -> 0()}
      Fail
     
     SCC (1):
      Strict:
       {g# s x -> g# x}
      Weak:
      {f(g x, s 0(), y) -> f(g s 0(), y, g x),
                  g s x -> s g x,
                  g 0() -> 0()}
      POLY:
       Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
       Interpretation:
        [f](x0, x1, x2) = x0 + 1,
        
        [g](x0) = 1,
        
        [s](x0) = x0 + 1,
        
        [0] = 1,
        
        [g#](x0) = x0
       Strict:
        g# s x -> g# x
        1 + 1x >= 0 + 1x
       Weak:
        g 0() -> 0()
        1 >= 1
        g s x -> s g x
        1 + 0x >= 2 + 0x
        f(g x, s 0(), y) -> f(g s 0(), y, g x)
        2 + 0y + 0x >= 2 + 0y + 0x
      Qed