YES

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

Proof:
 DP Processor:
  DPs:
   +#(*(x,y),*(a(),y)) -> +#(x,a())
   +#(*(x,y),*(a(),y)) -> *#(+(x,a()),y)
   *#(*(x,y),z) -> *#(y,z)
   *#(*(x,y),z) -> *#(x,*(y,z))
  TRS:
   +(*(x,y),*(a(),y)) -> *(+(x,a()),y)
   *(*(x,y),z) -> *(x,*(y,z))
  Usable Rule Processor:
   DPs:
    +#(*(x,y),*(a(),y)) -> +#(x,a())
    +#(*(x,y),*(a(),y)) -> *#(+(x,a()),y)
    *#(*(x,y),z) -> *#(y,z)
    *#(*(x,y),z) -> *#(x,*(y,z))
   TRS:
    *(*(x,y),z) -> *(x,*(y,z))
   TDG Processor:
    DPs:
     +#(*(x,y),*(a(),y)) -> +#(x,a())
     +#(*(x,y),*(a(),y)) -> *#(+(x,a()),y)
     *#(*(x,y),z) -> *#(y,z)
     *#(*(x,y),z) -> *#(x,*(y,z))
    TRS:
     *(*(x,y),z) -> *(x,*(y,z))
    graph:
     *#(*(x,y),z) -> *#(y,z) -> *#(*(x,y),z) -> *#(x,*(y,z))
     *#(*(x,y),z) -> *#(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),z) -> *#(y,z)
     +#(*(x,y),*(a(),y)) -> *#(+(x,a()),y) ->
     *#(*(x,y),z) -> *#(x,*(y,z))
     +#(*(x,y),*(a(),y)) -> *#(+(x,a()),y) ->
     *#(*(x,y),z) -> *#(y,z)
     +#(*(x,y),*(a(),y)) -> +#(x,a()) ->
     +#(*(x,y),*(a(),y)) -> *#(+(x,a()),y)
     +#(*(x,y),*(a(),y)) -> +#(x,a()) -> +#(*(x,y),*(a(),y)) -> +#(x,a())
    Restore Modifier:
     DPs:
      +#(*(x,y),*(a(),y)) -> +#(x,a())
      +#(*(x,y),*(a(),y)) -> *#(+(x,a()),y)
      *#(*(x,y),z) -> *#(y,z)
      *#(*(x,y),z) -> *#(x,*(y,z))
     TRS:
      +(*(x,y),*(a(),y)) -> *(+(x,a()),y)
      *(*(x,y),z) -> *(x,*(y,z))
     SCC Processor:
      #sccs: 2
      #rules: 3
      #arcs: 8/16
      DPs:
       +#(*(x,y),*(a(),y)) -> +#(x,a())
      TRS:
       +(*(x,y),*(a(),y)) -> *(+(x,a()),y)
       *(*(x,y),z) -> *(x,*(y,z))
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [+#](x0, x1) = x1,
        
        [+](x0, x1) = x0 + 1,
        
        [a] = 0,
        
        [*](x0, x1) = x0 + 1
       orientation:
        +#(*(x,y),*(a(),y)) = 1 >= 0 = +#(x,a())
        
        +(*(x,y),*(a(),y)) = x + 2 >= x + 2 = *(+(x,a()),y)
        
        *(*(x,y),z) = x + 2 >= x + 1 = *(x,*(y,z))
       problem:
        DPs:
         
        TRS:
         +(*(x,y),*(a(),y)) -> *(+(x,a()),y)
         *(*(x,y),z) -> *(x,*(y,z))
       Qed
      
      DPs:
       *#(*(x,y),z) -> *#(y,z)
       *#(*(x,y),z) -> *#(x,*(y,z))
      TRS:
       +(*(x,y),*(a(),y)) -> *(+(x,a()),y)
       *(*(x,y),z) -> *(x,*(y,z))
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [*#](x0, x1) = x0 + x1,
        
        [+](x0, x1) = x0 + x1,
        
        [a] = 0,
        
        [*](x0, x1) = x0 + x1 + 1
       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),*(a(),y)) = x + 2y + 2 >= x + y + 1 = *(+(x,a()),y)
        
        *(*(x,y),z) = x + y + z + 2 >= x + y + z + 2 = *(x,*(y,z))
       problem:
        DPs:
         *#(*(x,y),z) -> *#(x,*(y,z))
        TRS:
         +(*(x,y),*(a(),y)) -> *(+(x,a()),y)
         *(*(x,y),z) -> *(x,*(y,z))
       Matrix Interpretation Processor:
        dimension: 1
        interpretation:
         [*#](x0, x1) = x0,
         
         [+](x0, x1) = x1,
         
         [a] = 1,
         
         [*](x0, x1) = x0 + x1 + 1
        orientation:
         *#(*(x,y),z) = x + y + 1 >= x = *#(x,*(y,z))
         
         +(*(x,y),*(a(),y)) = y + 2 >= y + 2 = *(+(x,a()),y)
         
         *(*(x,y),z) = x + y + z + 2 >= x + y + z + 2 = *(x,*(y,z))
        problem:
         DPs:
          
         TRS:
          +(*(x,y),*(a(),y)) -> *(+(x,a()),y)
          *(*(x,y),z) -> *(x,*(y,z))
        Qed