YES
Time: 0.044

Problem:
 Equations:
  fAC(fAC(x1,x2),x3) -> fAC(x1,fAC(x2,x3))
  fAC(x1,x2) -> fAC(x2,x1)
  fAC(x1,fAC(x2,x3)) -> fAC(fAC(x1,x2),x3)
  fAC(x2,x1) -> fAC(x1,x2)
 TRS:
  fAC(x,one()) -> x
  fAC(i(x),x) -> one()

Proof:
 Matrix Interpretation Processor:
  dimension: 2
  interpretation:
             [4 0]     [0]
   [i](x0) = [0 0]x0 + [1],
   
           [0]
   [one] = [1],
   
                             [1]
   [fAC](x0, x1) = x0 + x1 + [0]
  orientation:
                      [1]         
   fAC(x,one()) = x + [1] >= x = x
   
                 [5 0]    [1]    [0]        
   fAC(i(x),x) = [0 1]x + [1] >= [1] = one()
  problem:
   Equations:
    fAC(fAC(x1,x2),x3) -> fAC(x1,fAC(x2,x3))
    fAC(x1,x2) -> fAC(x2,x1)
    fAC(x1,fAC(x2,x3)) -> fAC(fAC(x1,x2),x3)
    fAC(x2,x1) -> fAC(x1,x2)
   TRS:
    
  Qed