YES

TRS:

  .(1(),x) -> x
  .(x,1()) -> x
  .(i(x),x) -> 1()
  .(x,i(x)) -> 1()
  i(1()) -> 1()
  i(i(x)) -> x
  .(i(y),.(y,z)) -> z
  .(y,.(i(y),z)) -> z
  .(.(x,y),z) -> .(x,.(y,z))
  i(.(x,y)) -> .(i(y),i(x))

max/plus interpretations on N:

  ._A(x1,x2) = max{1, x1, x2}
  .#_A(x1,x2) = max{2, 2, 1}
  1_A = 3
  1#_A = 0
  i_A(x1) = max{3, 1 + x1}
  i#_A(x1) = max{3, 4}

precedence:

  i > 1 > .