YES
Time: 0.047

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:
  fAC(x,one()) -> x
  fAC(i(x),x) -> one()
  phi(one(),y1) -> y1
  phi(y1,phi(y2,x)) -> phi(fAC(y1,y2),x)

Proof:
 Matrix Interpretation Processor:
  dimension: 1
  interpretation:
   [phi](x0, x1) = 4x0 + 2x1 + 5,
   
   [i](x0) = 2x0 + 9,
   
   [one] = 5,
   
   [fAC](x0, x1) = x0 + x1 + 2
  orientation:
   fAC(x,one()) = x + 7 >= x = x
   
   fAC(i(x),x) = 3x + 11 >= 5 = one()
   
   phi(one(),y1) = 2y1 + 25 >= y1 = y1
   
   phi(y1,phi(y2,x)) = 4x + 4y1 + 8y2 + 15 >= 2x + 4y1 + 4y2 + 13 = phi(fAC(y1,y2),x)
  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