YES

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

Proof:
 DP Processor:
  DPs:
   f#(f(a())) -> f#(g())
  TRS:
   f(f(a())) -> f(g())
  Arctic Interpretation Processor:
   dimension: 1
   interpretation:
    [f#](x0) = 2x0 + 2,
    
    [g] = 0,
    
    [f](x0) = x0 + 0,
    
    [a] = 2
   orientation:
    f#(f(a())) = 4 >= 2 = f#(g())
    
    f(f(a())) = 2 >= 0 = f(g())
   problem:
    DPs:
     
    TRS:
     f(f(a())) -> f(g())
   Qed