YES

TRS:

  din(der(plus(X,Y))) -> u21(din(der(X)),X,Y)
  u21(dout(DX),X,Y) -> u22(din(der(Y)),X,Y,DX)
  u22(dout(DY),X,Y,DX) -> dout(plus(DX,DY))
  din(der(times(X,Y))) -> u31(din(der(X)),X,Y)
  u31(dout(DX),X,Y) -> u32(din(der(Y)),X,Y,DX)
  u32(dout(DY),X,Y,DX) -> dout(plus(times(X,DY),times(Y,DX)))
  din(der(der(X))) -> u41(din(der(X)),X)
  u41(dout(DX),X) -> u42(din(der(DX)),X,DX)
  u42(dout(DDX),X,DX) -> dout(DDX)

max/plus interpretations on N:

  din_A(x1) = max{14, 11}
  din#_A(x1) = max{33, 9}
  der_A(x1) = max{33, 35 + x1}
  der#_A(x1) = max{35, 3}
  plus_A(x1,x2) = max{33, -36, -1}
  plus#_A(x1,x2) = max{12, 10, 15}
  u21_A(x1,x2,x3) = max{14, 13, 11, 10}
  u21#_A(x1,x2,x3) = max{8, 18 + x1, 2, 2}
  dout_A(x1) = max{37, -1}
  dout#_A(x1) = max{14, -2}
  u22_A(x1,x2,x3,x4) = max{14, x1, 14, 13, 14}
  u22#_A(x1,x2,x3,x4) = max{16, 16 + x1, 13, 13, 1}
  times_A(x1,x2) = max{1, -36 + x1, -1 + x2}
  times#_A(x1,x2) = max{14, 4, 6}
  u31_A(x1,x2,x3) = max{11, x1, 12, 11}
  u31#_A(x1,x2,x3) = max{0, -1 + x1, 8, 2}
  u32_A(x1,x2,x3,x4) = max{13, 37, 37, -1, 13}
  u32#_A(x1,x2,x3,x4) = max{1, 5, -1, 15, 7}
  u41_A(x1,x2) = max{13, 12, 14}
  u41#_A(x1,x2) = max{34, 18 + x1, 34}
  u42_A(x1,x2,x3) = max{14, x1, 12, 13}
  u42#_A(x1,x2,x3) = max{35, 13, 35, 35}

precedence:

  u22 > dout > der = u32 > plus > din > u21 = times = u31 = u41 > u42