YES

TRS:

  a(h(),h(),h(),x) -> s(x)
  a(l,x,s(y),h()) -> a(l,x,y,s(h()))
  a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z))
  a(l,s(x),h(),z) -> a(l,x,z,z)
  a(s(l),h(),h(),z) -> a(l,z,h(),z)
  +(x,h()) -> x
  +(h(),x) -> x
  +(s(x),s(y)) -> s(s(+(x,y)))
  +(+(x,y),z) -> +(x,+(y,z))
  s(h()) -> 1()
  *(h(),x) -> h()
  *(x,h()) -> h()
  *(s(x),s(y)) -> s(+(+(*(x,y),x),y))

max/plus interpretations on N:

  a_A(x1,x2,x3,x4) = max{4, 2, 1, 1, 2}
  a#_A(x1,x2,x3,x4) = max{10, 2, 9, 7, 12}
  h_A = 4
  h#_A = 1
  s_A(x1) = max{3, -1}
  s#_A(x1) = max{8, 3}
  +_A(x1,x2) = max{2, 3 + x1, x2}
  +#_A(x1,x2) = max{4, 5, 9}
  1_A = 0
  1#_A = 0
  *_A(x1,x2) = max{2, -2, 4}
  *#_A(x1,x2) = max{7, 10, 6}

precedence:

  a = * > h = + > s > 1