YES
Time: 0.004483
TRS:
 {  g g x -> g h g x,
  g h g x -> g x,
    h h x -> h f(h x, x)}
 DP:
  DP:
   {g# g x -> g# h g x,
    g# g x -> h# g x,
    h# h x -> h# f(h x, x)}
  TRS:
  {  g g x -> g h g x,
   g h g x -> g x,
     h h x -> h f(h x, x)}
  EDG:
   {(g# g x -> h# g x, h# h x -> h# f(h x, x))
    (g# g x -> g# h g x, g# g x -> g# h g x)
    (g# g x -> g# h g x, g# g x -> h# g x)}
   SCCS (1):
    Scc:
     {g# g x -> g# h g x}
    SCC (1):
     Strict:
      {g# g x -> g# h g x}
     Weak:
     {  g g x -> g h g x,
      g h g x -> g x,
        h h x -> h f(h x, x)}
     POLY:
      Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
      Interpretation:
       [f](x0, x1) = 0,
       
       [g](x0) = 1,
       
       [h](x0) = 0,
       
       [g#](x0) = x0
      Strict:
       g# g x -> g# h g x
       1 + 0x >= 0 + 0x
      Weak:
       
     Qed