YES
Time: 0.168

Problem:
 Equations:
  plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
  plusAC(x2,x3) -> plusAC(x3,x2)
  plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
  plusAC(x3,x2) -> plusAC(x2,x3)
 TRS:
  plusAC(x,0()) -> x
  plusAC(x,x) -> x
  plusAC(T(x),x) -> T(x)
  plusAC(T(plusAC(x,y)),x) -> T(plusAC(x,y))
  L(T(x)) -> L(x)
  L(plusAC(T(y),x)) -> plusAC(L(plusAC(x,y)),L(y))
  T(T(x)) -> T(x)
  T(plusAC(T(y),x)) -> plusAC(T(plusAC(x,y)),T(y))

Proof:
 Matrix Interpretation Processor:
  dimension: 1
  interpretation:
   [L](x0) = x0,
   
   [T](x0) = 3x0 + 4,
   
   [0] = 1,
   
   [plusAC](x0, x1) = x0 + x1 + 3
  orientation:
   plusAC(x,0()) = x + 4 >= x = x
   
   plusAC(x,x) = 2x + 3 >= x = x
   
   plusAC(T(x),x) = 4x + 7 >= 3x + 4 = T(x)
   
   plusAC(T(plusAC(x,y)),x) = 4x + 3y + 16 >= 3x + 3y + 13 = T(plusAC(x,y))
   
   L(T(x)) = 3x + 4 >= x = L(x)
   
   L(plusAC(T(y),x)) = x + 3y + 7 >= x + 2y + 6 = plusAC(L(plusAC(x,y)),L(y))
   
   T(T(x)) = 9x + 16 >= 3x + 4 = T(x)
   
   T(plusAC(T(y),x)) = 3x + 9y + 25 >= 3x + 6y + 20 = plusAC(T(plusAC(x,y)),T(y))
  problem:
   Equations:
    plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
    plusAC(x2,x3) -> plusAC(x3,x2)
    plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
    plusAC(x3,x2) -> plusAC(x2,x3)
   TRS:
    
  Qed