YES

Problem:
 *(x,*(y,z)) -> *(*(x,y),z)
 *(x,x) -> x

Proof:
 DP Processor:
  DPs:
   *#(x,*(y,z)) -> *#(x,y)
   *#(x,*(y,z)) -> *#(*(x,y),z)
  TRS:
   *(x,*(y,z)) -> *(*(x,y),z)
   *(x,x) -> x
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [*#](x0, x1) = 4x0 + 5x1 + 2,
    
    [*](x0, x1) = x0 + x1 + 1
   orientation:
    *#(x,*(y,z)) = 4x + 5y + 5z + 7 >= 4x + 5y + 2 = *#(x,y)
    
    *#(x,*(y,z)) = 4x + 5y + 5z + 7 >= 4x + 4y + 5z + 6 = *#(*(x,y),z)
    
    *(x,*(y,z)) = x + y + z + 2 >= x + y + z + 2 = *(*(x,y),z)
    
    *(x,x) = 2x + 1 >= x = x
   problem:
    DPs:
     
    TRS:
     *(x,*(y,z)) -> *(*(x,y),z)
     *(x,x) -> x
   Qed