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))

linear polynomial interpretations on N:

  ._A(x1,x2) = x1 + x2 + 1
  .#_A(x1,x2) = x1
  1_A = 1
  1#_A = 1
  i_A(x1) = x1
  i#_A(x1) = x1 + 2

precedence:

  . > i > 1