YES
Time: 0.067

Problem:
 Equations:
  fAC(fAC(x3,x4),x5) -> fAC(x3,fAC(x4,x5))
  fAC(x3,x4) -> fAC(x4,x3)
  fAC(x3,fAC(x4,x5)) -> fAC(fAC(x3,x4),x5)
  fAC(x4,x3) -> fAC(x3,x4)
 TRS:
  g(fAC(x,y)) -> fAC(g(x),g(y))
  fAC(a(),g(g(a()))) -> fAC(g(a()),g(a()))

Proof:
 Matrix Interpretation Processor:
  dimension: 1
  interpretation:
   [a] = 1,
   
   [g](x0) = 2x0 + 3,
   
   [fAC](x0, x1) = x0 + x1 + 10
  orientation:
   g(fAC(x,y)) = 2x + 2y + 23 >= 2x + 2y + 16 = fAC(g(x),g(y))
   
   fAC(a(),g(g(a()))) = 24 >= 20 = fAC(g(a()),g(a()))
  problem:
   Equations:
    fAC(fAC(x3,x4),x5) -> fAC(x3,fAC(x4,x5))
    fAC(x3,x4) -> fAC(x4,x3)
    fAC(x3,fAC(x4,x5)) -> fAC(fAC(x3,x4),x5)
    fAC(x4,x3) -> fAC(x3,x4)
   TRS:
    
  Qed