YES

TRS:

  +(p1(),p1()) -> p2()
  +(p1(),+(p2(),p2())) -> p5()
  +(p5(),p5()) -> p10()
  +(+(x,y),z) -> +(x,+(y,z))
  +(p1(),+(p1(),x)) -> +(p2(),x)
  +(p1(),+(p2(),+(p2(),x))) -> +(p5(),x)
  +(p2(),p1()) -> +(p1(),p2())
  +(p2(),+(p1(),x)) -> +(p1(),+(p2(),x))
  +(p2(),+(p2(),p2())) -> +(p1(),p5())
  +(p2(),+(p2(),+(p2(),x))) -> +(p1(),+(p5(),x))
  +(p5(),p1()) -> +(p1(),p5())
  +(p5(),+(p1(),x)) -> +(p1(),+(p5(),x))
  +(p5(),p2()) -> +(p2(),p5())
  +(p5(),+(p2(),x)) -> +(p2(),+(p5(),x))
  +(p5(),+(p5(),x)) -> +(p10(),x)
  +(p10(),p1()) -> +(p1(),p10())
  +(p10(),+(p1(),x)) -> +(p1(),+(p10(),x))
  +(p10(),p2()) -> +(p2(),p10())
  +(p10(),+(p2(),x)) -> +(p2(),+(p10(),x))
  +(p10(),p5()) -> +(p5(),p10())
  +(p10(),+(p5(),x)) -> +(p5(),+(p10(),x))

linear polynomial interpretations on N:

  +_A(x1,x2) = x1 + x2 + 9
  +#_A(x1,x2) = x1 + x2
  p1_A = 28
  p1#_A = 10
  p2_A = 11
  p2#_A = 12
  p5_A = 14
  p5#_A = 26
  p10_A = 2
  p10#_A = 27

precedence:

  + > p10 > p5 > p2 > p1