YES

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

Proof:
 DP Processor:
  DPs:
   f#(g(x)) -> f#(x)
   f#(g(x)) -> f#(a(g(g(f(x))),g(f(x))))
  TRS:
   f(g(x)) -> f(a(g(g(f(x))),g(f(x))))
  Restore Modifier:
   DPs:
    f#(g(x)) -> f#(x)
    f#(g(x)) -> f#(a(g(g(f(x))),g(f(x))))
   TRS:
    f(g(x)) -> f(a(g(g(f(x))),g(f(x))))
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 4/4
    DPs:
     f#(g(x)) -> f#(x)
     f#(g(x)) -> f#(a(g(g(f(x))),g(f(x))))
    TRS:
     f(g(x)) -> f(a(g(g(f(x))),g(f(x))))
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [f#](x0) = x0 + 1,
      
      [a](x0, x1) = 0,
      
      [f](x0) = 1,
      
      [g](x0) = x0 + 1
     orientation:
      f#(g(x)) = x + 2 >= x + 1 = f#(x)
      
      f#(g(x)) = x + 2 >= 1 = f#(a(g(g(f(x))),g(f(x))))
      
      f(g(x)) = 1 >= 1 = f(a(g(g(f(x))),g(f(x))))
     problem:
      DPs:
       
      TRS:
       f(g(x)) -> f(a(g(g(f(x))),g(f(x))))
     Qed