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))
  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),*(a(),y)) -> *(+(x,a()),y)
    *(*(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())
   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))
    Subterm Criterion Processor:
     simple projection:
      pi(+#) = 1
     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))
    Subterm Criterion Processor:
     simple projection:
      pi(*#) = 0
     problem:
      DPs:
       
      TRS:
       +(*(x,y),*(a(),y)) -> *(+(x,a()),y)
       *(*(x,y),z) -> *(x,*(y,z))
     Qed