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:
 DP Processor:
  DPs:
   +#(*(x,y),*(x,z)) -> +#(y,z)
   +#(+(x,y),z) -> +#(y,z)
   +#(+(x,y),z) -> +#(x,+(y,z))
   +#(*(x,y),+(*(x,z),u())) -> +#(y,z)
   +#(*(x,y),+(*(x,z),u())) -> +#(*(x,+(y,z)),u())
  TRS:
   +(*(x,y),*(x,z)) -> *(x,+(y,z))
   +(+(x,y),z) -> +(x,+(y,z))
   +(*(x,y),+(*(x,z),u())) -> +(*(x,+(y,z)),u())
  EDG Processor:
   DPs:
    +#(*(x,y),*(x,z)) -> +#(y,z)
    +#(+(x,y),z) -> +#(y,z)
    +#(+(x,y),z) -> +#(x,+(y,z))
    +#(*(x,y),+(*(x,z),u())) -> +#(y,z)
    +#(*(x,y),+(*(x,z),u())) -> +#(*(x,+(y,z)),u())
   TRS:
    +(*(x,y),*(x,z)) -> *(x,+(y,z))
    +(+(x,y),z) -> +(x,+(y,z))
    +(*(x,y),+(*(x,z),u())) -> +(*(x,+(y,z)),u())
   graph:
    +#(+(x,y),z) -> +#(y,z) -> +#(*(x,y),*(x,z)) -> +#(y,z)
    +#(+(x,y),z) -> +#(y,z) -> +#(+(x,y),z) -> +#(y,z)
    +#(+(x,y),z) -> +#(y,z) -> +#(+(x,y),z) -> +#(x,+(y,z))
    +#(+(x,y),z) -> +#(y,z) -> +#(*(x,y),+(*(x,z),u())) -> +#(y,z)
    +#(+(x,y),z) -> +#(y,z) ->
    +#(*(x,y),+(*(x,z),u())) -> +#(*(x,+(y,z)),u())
    +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(*(x,y),*(x,z)) -> +#(y,z)
    +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(+(x,y),z) -> +#(y,z)
    +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(+(x,y),z) -> +#(x,+(y,z))
    +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(*(x,y),+(*(x,z),u())) -> +#(y,z)
    +#(+(x,y),z) -> +#(x,+(y,z)) ->
    +#(*(x,y),+(*(x,z),u())) -> +#(*(x,+(y,z)),u())
    +#(*(x,y),+(*(x,z),u())) -> +#(y,z) ->
    +#(*(x,y),*(x,z)) -> +#(y,z)
    +#(*(x,y),+(*(x,z),u())) -> +#(y,z) ->
    +#(+(x,y),z) -> +#(y,z)
    +#(*(x,y),+(*(x,z),u())) -> +#(y,z) ->
    +#(+(x,y),z) -> +#(x,+(y,z))
    +#(*(x,y),+(*(x,z),u())) -> +#(y,z) ->
    +#(*(x,y),+(*(x,z),u())) -> +#(y,z)
    +#(*(x,y),+(*(x,z),u())) -> +#(y,z) ->
    +#(*(x,y),+(*(x,z),u())) -> +#(*(x,+(y,z)),u())
    +#(*(x,y),*(x,z)) -> +#(y,z) -> +#(*(x,y),*(x,z)) -> +#(y,z)
    +#(*(x,y),*(x,z)) -> +#(y,z) -> +#(+(x,y),z) -> +#(y,z)
    +#(*(x,y),*(x,z)) -> +#(y,z) -> +#(+(x,y),z) -> +#(x,+(y,z))
    +#(*(x,y),*(x,z)) -> +#(y,z) -> +#(*(x,y),+(*(x,z),u())) -> +#(y,z)
    +#(*(x,y),*(x,z)) -> +#(y,z) -> +#(*(x,y),+(*(x,z),u())) -> +#(*(x,+(y,z)),u())
   Restore Modifier:
    DPs:
     +#(*(x,y),*(x,z)) -> +#(y,z)
     +#(+(x,y),z) -> +#(y,z)
     +#(+(x,y),z) -> +#(x,+(y,z))
     +#(*(x,y),+(*(x,z),u())) -> +#(y,z)
     +#(*(x,y),+(*(x,z),u())) -> +#(*(x,+(y,z)),u())
    TRS:
     +(*(x,y),*(x,z)) -> *(x,+(y,z))
     +(+(x,y),z) -> +(x,+(y,z))
     +(*(x,y),+(*(x,z),u())) -> +(*(x,+(y,z)),u())
    SCC Processor:
     #sccs: 1
     #rules: 4
     #arcs: 20/25
     DPs:
      +#(+(x,y),z) -> +#(y,z)
      +#(*(x,y),+(*(x,z),u())) -> +#(y,z)
      +#(+(x,y),z) -> +#(x,+(y,z))
      +#(*(x,y),*(x,z)) -> +#(y,z)
     TRS:
      +(*(x,y),*(x,z)) -> *(x,+(y,z))
      +(+(x,y),z) -> +(x,+(y,z))
      +(*(x,y),+(*(x,z),u())) -> +(*(x,+(y,z)),u())
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [+#](x0, x1) = x0 + x1,
       
       [u] = 0,
       
       [+](x0, x1) = x0 + x1,
       
       [*](x0, x1) = x1 + 1
      orientation:
       +#(+(x,y),z) = x + y + z >= y + z = +#(y,z)
       
       +#(*(x,y),+(*(x,z),u())) = y + z + 2 >= y + z = +#(y,z)
       
       +#(+(x,y),z) = x + y + z >= x + y + z = +#(x,+(y,z))
       
       +#(*(x,y),*(x,z)) = y + z + 2 >= y + z = +#(y,z)
       
       +(*(x,y),*(x,z)) = y + z + 2 >= y + z + 1 = *(x,+(y,z))
       
       +(+(x,y),z) = x + y + z >= x + y + z = +(x,+(y,z))
       
       +(*(x,y),+(*(x,z),u())) = y + z + 2 >= y + z + 1 = +(*(x,+(y,z)),u())
      problem:
       DPs:
        +#(+(x,y),z) -> +#(y,z)
        +#(+(x,y),z) -> +#(x,+(y,z))
       TRS:
        +(*(x,y),*(x,z)) -> *(x,+(y,z))
        +(+(x,y),z) -> +(x,+(y,z))
        +(*(x,y),+(*(x,z),u())) -> +(*(x,+(y,z)),u())
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [+#](x0, x1) = x0 + x1,
        
        [u] = 1,
        
        [+](x0, x1) = x0 + x1 + 1,
        
        [*](x0, x1) = 0
       orientation:
        +#(+(x,y),z) = x + y + z + 1 >= y + z = +#(y,z)
        
        +#(+(x,y),z) = x + y + z + 1 >= x + y + z + 1 = +#(x,+(y,z))
        
        +(*(x,y),*(x,z)) = 1 >= 0 = *(x,+(y,z))
        
        +(+(x,y),z) = x + y + z + 2 >= x + y + z + 2 = +(x,+(y,z))
        
        +(*(x,y),+(*(x,z),u())) = 3 >= 2 = +(*(x,+(y,z)),u())
       problem:
        DPs:
         +#(+(x,y),z) -> +#(x,+(y,z))
        TRS:
         +(*(x,y),*(x,z)) -> *(x,+(y,z))
         +(+(x,y),z) -> +(x,+(y,z))
         +(*(x,y),+(*(x,z),u())) -> +(*(x,+(y,z)),u())
       Matrix Interpretation Processor:
        dimension: 1
        interpretation:
         [+#](x0, x1) = x0,
         
         [u] = 1,
         
         [+](x0, x1) = x0 + x1 + 1,
         
         [*](x0, x1) = x1
        orientation:
         +#(+(x,y),z) = x + y + 1 >= x = +#(x,+(y,z))
         
         +(*(x,y),*(x,z)) = y + z + 1 >= y + z + 1 = *(x,+(y,z))
         
         +(+(x,y),z) = x + y + z + 2 >= x + y + z + 2 = +(x,+(y,z))
         
         +(*(x,y),+(*(x,z),u())) = y + z + 3 >= y + z + 3 = +(*(x,+(y,z)),u())
        problem:
         DPs:
          
         TRS:
          +(*(x,y),*(x,z)) -> *(x,+(y,z))
          +(+(x,y),z) -> +(x,+(y,z))
          +(*(x,y),+(*(x,z),u())) -> +(*(x,+(y,z)),u())
        Qed