YES

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

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [u] = 3,
   
   [+](x0, x1) = x0 + x1 + 1,
   
   [*](x0, x1) = 2x0 + x1 + 2
  orientation:
   +(*(x,y),*(x,z)) = 4x + y + z + 5 >= 2x + y + z + 3 = *(x,+(y,z))
   
   +(+(x,y),z) = x + y + z + 2 >= x + y + z + 2 = +(x,+(y,z))
   
   +(*(x,y),+(*(x,z),u())) = 4x + y + z + 9 >= 2x + y + z + 7 = +(*(x,+(y,z)),u())
  problem:
   +(+(x,y),z) -> +(x,+(y,z))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [+](x0, x1) = 2x0 + x1 + 1
   orientation:
    +(+(x,y),z) = 4x + 2y + z + 3 >= 2x + 2y + z + 2 = +(x,+(y,z))
   problem:
    
   Qed