YES
Time: 0.032353
TRS:
 {   f(x, y) -> x,
  h(x, x, y) -> g x,
       g a() -> h(a(), b(), a()),
         i x -> f(x, x)}
 DP:
  DP:
   {h#(x, x, y) -> g# x,
         g# a() -> h#(a(), b(), a()),
           i# x -> f#(x, x)}
  TRS:
  {   f(x, y) -> x,
   h(x, x, y) -> g x,
        g a() -> h(a(), b(), a()),
          i x -> f(x, x)}
  UR:
   {c(z, w) -> z,
    c(z, w) -> w}
   EDG:
    {(g# a() -> h#(a(), b(), a()), h#(x, x, y) -> g# x)
     (h#(x, x, y) -> g# x, g# a() -> h#(a(), b(), a()))}
    STATUS:
     arrows: 0.777778
     SCCS (1):
      Scc:
       {h#(x, x, y) -> g# x,
             g# a() -> h#(a(), b(), a())}
      
      
      SCC (2):
       Strict:
        {h#(x, x, y) -> g# x,
              g# a() -> h#(a(), b(), a())}
       Weak:
       {   f(x, y) -> x,
        h(x, x, y) -> g x,
             g a() -> h(a(), b(), a()),
               i x -> f(x, x)}
       POLY:
        Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
        Interpretation:
         [h](x0, x1, x2) = x0 + x1 + 1,
         
         [f](x0, x1) = 0,
         
         [g](x0) = 0,
         
         [i](x0) = 0,
         
         [a] = 1,
         
         [b] = 0,
         
         [h#](x0, x1, x2) = x0,
         
         [g#](x0) = x0
        Strict:
         g# a() -> h#(a(), b(), a())
         1 >= 0
         h#(x, x, y) -> g# x
         0 + 1x + 0y >= 0 + 1x
        Weak:
         i x -> f(x, x)
         0 + 0x >= 0 + 0x
         g a() -> h(a(), b(), a())
         0 >= 2
         h(x, x, y) -> g x
         1 + 2x + 0y >= 0 + 0x
         f(x, y) -> x
         0 + 0x + 0y >= 1x
       SCCS (0):