YES

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

Proof:
 DP Processor:
  DPs:
   f#(f(a())) -> f#(g())
  TRS:
   f(f(a())) -> f(g())
  Usable Rule Processor:
   DPs:
    f#(f(a())) -> f#(g())
   TRS:
    
   Arctic Interpretation Processor:
    dimension: 1
    usable rules:
     
    interpretation:
     [f#](x0) = x0 + 0,
     
     [g] = 0,
     
     [f](x0) = x0 + 0,
     
     [a] = 3
    orientation:
     f#(f(a())) = 3 >= 0 = f#(g())
    problem:
     DPs:
      
     TRS:
      
    Qed