YES

TRS:

  \(x,x) -> e()
  /(x,x) -> e()
  .(e(),x) -> x
  .(x,e()) -> x
  \(e(),x) -> x
  /(x,e()) -> x
  .(x,\(x,y)) -> y
  .(/(y,x),x) -> y
  \(x,.(x,y)) -> y
  /(.(y,x),x) -> y
  /(x,\(y,x)) -> y
  \(/(x,y),x) -> y

max/plus interpretations on N:

  \_A(x1,x2) = max{2, 2 + x1, x2}
  \#_A(x1,x2) = max{2, 2 + x1, x2}
  e_A = 1
  e#_A = 1
  /_A(x1,x2) = max{2, 2 + x1, 2 + x2}
  /#_A(x1,x2) = max{2, 2 + x1, 2 + x2}
  ._A(x1,x2) = max{0, x1, x2}
  .#_A(x1,x2) = max{0, x1, x2}

precedence:

  e > \ = / = .