YES
Time: 0.015

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: 1
  interpretation:
   [i](x0) = x0 + 2,
   
   [one] = 0,
   
   [fAC](x0, x1) = x0 + x1 + 1
  orientation:
   fAC(x,one()) = x + 1 >= x = x
   
   fAC(i(x),x) = 2x + 3 >= 0 = 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