YES

Problem:
 f(a(),x) -> g(a(),x)
 g(a(),x) -> f(b(),x)
 f(a(),x) -> f(b(),x)

Proof:
 DP Processor:
  DPs:
   f#(a(),x) -> g#(a(),x)
   g#(a(),x) -> f#(b(),x)
   f#(a(),x) -> f#(b(),x)
  TRS:
   f(a(),x) -> g(a(),x)
   g(a(),x) -> f(b(),x)
   f(a(),x) -> f(b(),x)
  Usable Rule Processor:
   DPs:
    f#(a(),x) -> g#(a(),x)
    g#(a(),x) -> f#(b(),x)
    f#(a(),x) -> f#(b(),x)
   TRS:
    
   TDG Processor:
    DPs:
     f#(a(),x) -> g#(a(),x)
     g#(a(),x) -> f#(b(),x)
     f#(a(),x) -> f#(b(),x)
    TRS:
     
    graph:
     g#(a(),x) -> f#(b(),x) -> f#(a(),x) -> f#(b(),x)
     g#(a(),x) -> f#(b(),x) -> f#(a(),x) -> g#(a(),x)
     f#(a(),x) -> g#(a(),x) -> g#(a(),x) -> f#(b(),x)
     f#(a(),x) -> f#(b(),x) -> f#(a(),x) -> f#(b(),x)
     f#(a(),x) -> f#(b(),x) -> f#(a(),x) -> g#(a(),x)
    Restore Modifier:
     DPs:
      f#(a(),x) -> g#(a(),x)
      g#(a(),x) -> f#(b(),x)
      f#(a(),x) -> f#(b(),x)
     TRS:
      f(a(),x) -> g(a(),x)
      g(a(),x) -> f(b(),x)
      f(a(),x) -> f(b(),x)
     SCC Processor:
      #sccs: 1
      #rules: 3
      #arcs: 5/9
      DPs:
       g#(a(),x) -> f#(b(),x)
       f#(a(),x) -> g#(a(),x)
       f#(a(),x) -> f#(b(),x)
      TRS:
       f(a(),x) -> g(a(),x)
       g(a(),x) -> f(b(),x)
       f(a(),x) -> f(b(),x)
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [g#](x0, x1) = 0,
        
        [f#](x0, x1) = x0,
        
        [b] = 0,
        
        [g](x0, x1) = 1,
        
        [f](x0, x1) = 1,
        
        [a] = 1
       orientation:
        g#(a(),x) = 0 >= 0 = f#(b(),x)
        
        f#(a(),x) = 1 >= 0 = g#(a(),x)
        
        f#(a(),x) = 1 >= 0 = f#(b(),x)
        
        f(a(),x) = 1 >= 1 = g(a(),x)
        
        g(a(),x) = 1 >= 1 = f(b(),x)
        
        f(a(),x) = 1 >= 1 = f(b(),x)
       problem:
        DPs:
         g#(a(),x) -> f#(b(),x)
        TRS:
         f(a(),x) -> g(a(),x)
         g(a(),x) -> f(b(),x)
         f(a(),x) -> f(b(),x)
       Matrix Interpretation Processor:
        dimension: 1
        interpretation:
         [g#](x0, x1) = 1,
         
         [f#](x0, x1) = 0,
         
         [b] = 0,
         
         [g](x0, x1) = 0,
         
         [f](x0, x1) = 0,
         
         [a] = 0
        orientation:
         g#(a(),x) = 1 >= 0 = f#(b(),x)
         
         f(a(),x) = 0 >= 0 = g(a(),x)
         
         g(a(),x) = 0 >= 0 = f(b(),x)
         
         f(a(),x) = 0 >= 0 = f(b(),x)
        problem:
         DPs:
          
         TRS:
          f(a(),x) -> g(a(),x)
          g(a(),x) -> f(b(),x)
          f(a(),x) -> f(b(),x)
        Qed