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())
  KBO Processor:
   argument filtering:
    pi(*) = [0,1]
    pi(+) = [0,1]
    pi(u) = []
    pi(+#) = [0,1]
   usable rules:
    +(*(x,y),*(x,z)) -> *(x,+(y,z))
    +(+(x,y),z) -> +(x,+(y,z))
    +(*(x,y),+(*(x,z),u())) -> +(*(x,+(y,z)),u())
   weight function:
    w0 = 1
    w(+#) = w(u) = w(+) = w(*) = 1
   precedence:
    +# ~ 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