YES

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

Proof:
 DP Processor:
  DPs:
   +#(x,+(y,z)) -> +#(x,y)
   +#(x,+(y,z)) -> +#(+(x,y),z)
   +#(*(x,y),+(x,z)) -> +#(y,z)
   +#(*(x,y),+(*(x,z),u)) -> +#(y,z)
   +#(*(x,y),+(*(x,z),u)) -> +#(*(x,+(y,z)),u)
  TRS:
   +(x,+(y,z)) -> +(+(x,y),z)
   +(*(x,y),+(x,z)) -> *(x,+(y,z))
   +(*(x,y),+(*(x,z),u)) -> +(*(x,+(y,z)),u)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [+#](x0, x1) = 3x1 + 4,
    
    [*](x0, x1) = x1 + 6,
    
    [+](x0, x1) = x0 + x1 + 3
   orientation:
    +#(x,+(y,z)) = 3y + 3z + 13 >= 3y + 4 = +#(x,y)
    
    +#(x,+(y,z)) = 3y + 3z + 13 >= 3z + 4 = +#(+(x,y),z)
    
    +#(*(x,y),+(x,z)) = 3x + 3z + 13 >= 3z + 4 = +#(y,z)
    
    +#(*(x,y),+(*(x,z),u)) = 3u + 3z + 31 >= 3z + 4 = +#(y,z)
    
    +#(*(x,y),+(*(x,z),u)) = 3u + 3z + 31 >= 3u + 4 = +#(*(x,+(y,z)),u)
    
    +(x,+(y,z)) = x + y + z + 6 >= x + y + z + 6 = +(+(x,y),z)
    
    +(*(x,y),+(x,z)) = x + y + z + 12 >= y + z + 9 = *(x,+(y,z))
    
    +(*(x,y),+(*(x,z),u)) = u + y + z + 18 >= u + y + z + 12 = +(*(x,+(y,z)),u)
   problem:
    DPs:
     
    TRS:
     +(x,+(y,z)) -> +(+(x,y),z)
     +(*(x,y),+(x,z)) -> *(x,+(y,z))
     +(*(x,y),+(*(x,z),u)) -> +(*(x,+(y,z)),u)
   Qed