YES
Time: 0.007558
TRS:
 {  f x -> g x,
  f a() -> f b(),
  g b() -> g a()}
 DP:
  DP:
   {  f# x -> g# x,
    f# a() -> f# b(),
    g# b() -> g# a()}
  TRS:
  {  f x -> g x,
   f a() -> f b(),
   g b() -> g a()}
  UR:
   {}
   EDG:
    {(f# a() -> f# b(), f# a() -> f# b())
     (f# a() -> f# b(), f# x -> g# x)
     (g# b() -> g# a(), g# b() -> g# a())
     (f# x -> g# x, g# b() -> g# a())}
    STATUS:
     arrows: 0.555556
     SCCS (2):
      Scc:
       {f# a() -> f# b()}
      Scc:
       {g# b() -> g# a()}
      
      SCC (1):
       Strict:
        {f# a() -> f# b()}
       Weak:
       {  f x -> g x,
        f a() -> f b(),
        g b() -> g a()}
       POLY:
        Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
        Interpretation:
         [f](x0) = x0 + 1,
         
         [g](x0) = 0,
         
         [b] = 0,
         
         [a] = 1,
         
         [f#](x0) = x0 + 1
        Strict:
         f# a() -> f# b()
         2 >= 1
        Weak:
         g b() -> g a()
         0 >= 0
         f a() -> f b()
         2 >= 1
         f x -> g x
         1 + 1x >= 0 + 0x
       Qed
     
     SCC (1):
      Strict:
       {g# b() -> g# a()}
      Weak:
      {  f x -> g x,
       f a() -> f b(),
       g b() -> g a()}
      POLY:
       Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
       Interpretation:
        [f](x0) = 0,
        
        [g](x0) = 0,
        
        [b] = 1,
        
        [a] = 0,
        
        [g#](x0) = x0 + 1
       Strict:
        g# b() -> g# a()
        2 >= 1
       Weak:
        g b() -> g a()
        0 >= 0
        f a() -> f b()
        0 >= 0
        f x -> g x
        0 + 0x >= 0 + 0x
      Qed