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)
  Restore Modifier:
   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)
   SCC Processor:
    #sccs: 1
    #rules: 5
    #arcs: 25/25
    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:
     dimension: 1
     interpretation:
      [+#](x0, x1) = x0 + x1 + 1,
      
      [*](x0, x1) = x1,
      
      [+](x0, x1) = x0 + x1 + 1
     orientation:
      +#(x,+(y,z)) = x + y + z + 2 >= x + y + 1 = +#(x,y)
      
      +#(x,+(y,z)) = x + y + z + 2 >= x + y + z + 2 = +#(+(x,y),z)
      
      +#(*(x,y),+(x,z)) = x + y + z + 2 >= y + z + 1 = +#(y,z)
      
      +#(*(x,y),+(*(x,z),u)) = u + y + z + 2 >= y + z + 1 = +#(y,z)
      
      +#(*(x,y),+(*(x,z),u)) = u + y + z + 2 >= u + y + z + 2 = +#(*(x,+(y,z)),u)
      
      +(x,+(y,z)) = x + y + z + 2 >= x + y + z + 2 = +(+(x,y),z)
      
      +(*(x,y),+(x,z)) = x + y + z + 2 >= y + z + 1 = *(x,+(y,z))
      
      +(*(x,y),+(*(x,z),u)) = u + y + z + 2 >= u + y + z + 2 = +(*(x,+(y,z)),u)
     problem:
      DPs:
       +#(x,+(y,z)) -> +#(+(x,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:
      dimension: 1
      interpretation:
       [+#](x0, x1) = x1,
       
       [*](x0, x1) = x0 + 1,
       
       [+](x0, x1) = x0 + x1
      orientation:
       +#(x,+(y,z)) = y + z >= z = +#(+(x,y),z)
       
       +#(*(x,y),+(*(x,z),u)) = u + x + 1 >= u = +#(*(x,+(y,z)),u)
       
       +(x,+(y,z)) = x + y + z >= x + y + z = +(+(x,y),z)
       
       +(*(x,y),+(x,z)) = 2x + z + 1 >= x + 1 = *(x,+(y,z))
       
       +(*(x,y),+(*(x,z),u)) = u + 2x + 2 >= u + x + 1 = +(*(x,+(y,z)),u)
      problem:
       DPs:
        +#(x,+(y,z)) -> +#(+(x,y),z)
       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:
       dimension: 1
       interpretation:
        [+#](x0, x1) = x1,
        
        [*](x0, x1) = x1 + 1,
        
        [+](x0, x1) = x1 + 1
       orientation:
        +#(x,+(y,z)) = z + 1 >= z = +#(+(x,y),z)
        
        +(x,+(y,z)) = z + 2 >= z + 1 = +(+(x,y),z)
        
        +(*(x,y),+(x,z)) = z + 2 >= z + 2 = *(x,+(y,z))
        
        +(*(x,y),+(*(x,z),u)) = u + 2 >= u + 1 = +(*(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