YES
Time: 0.229

Problem:
 Equations:
  
 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:
 AC-KBO Processor:
  precedence:
   L ~ T ~ 0 ~ plusAC
   weight function:
    [L](x0) = 8x0 + 7,
    
    [T](x0) = 4x0 + 5,
    
    [0] = 1,
    
    [plusAC](x0, x1) = x0 + x1
   problem:
    Equations:
     
    TRS:
     
   Qed