YES

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

Proof:
 DP Processor:
  DPs:
   *#(x,+(y,z)) -> *#(x,z)
   *#(x,+(y,z)) -> *#(x,y)
  TRS:
   *(x,+(y,z)) -> +(*(x,y),*(x,z))
  Usable Rule Processor:
   DPs:
    *#(x,+(y,z)) -> *#(x,z)
    *#(x,+(y,z)) -> *#(x,y)
   TRS:
    
   Restore Modifier:
    DPs:
     *#(x,+(y,z)) -> *#(x,z)
     *#(x,+(y,z)) -> *#(x,y)
    TRS:
     *(x,+(y,z)) -> +(*(x,y),*(x,z))
    SCC Processor:
     #sccs: 1
     #rules: 2
     #arcs: 4/4
     DPs:
      *#(x,+(y,z)) -> *#(x,z)
      *#(x,+(y,z)) -> *#(x,y)
     TRS:
      *(x,+(y,z)) -> +(*(x,y),*(x,z))
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [*#](x0, x1) = x1 + 1,
       
       [*](x0, x1) = x1,
       
       [+](x0, x1) = x0 + x1 + 1
      orientation:
       *#(x,+(y,z)) = y + z + 2 >= z + 1 = *#(x,z)
       
       *#(x,+(y,z)) = y + z + 2 >= y + 1 = *#(x,y)
       
       *(x,+(y,z)) = y + z + 1 >= y + z + 1 = +(*(x,y),*(x,z))
      problem:
       DPs:
        
       TRS:
        *(x,+(y,z)) -> +(*(x,y),*(x,z))
      Qed