YES

Problem:
 f(f(X)) -> f(a(b(f(X))))
 f(a(g(X))) -> b(X)
 b(X) -> a(X)

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