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

linear polynomial interpretations on N:

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

precedence:

  \ = / = . > e