YES

TRS:

  and(tt(),X) -> activate(X)
  plus(N,0()) -> N
  plus(N,s(M)) -> s(plus(N,M))
  x(N,0()) -> 0()
  x(N,s(M)) -> plus(x(N,M),N)
  activate(X) -> X

linear polynomial interpretations on N:

  and_A(x1,x2) = x1 + x2
  and#_A(x1,x2) = x2 + 1
  tt_A = 1
  tt#_A = 0
  activate_A(x1) = x1
  activate#_A(x1) = 0
  plus_A(x1,x2) = x1
  plus#_A(x1,x2) = 1
  0_A = 1
  0#_A = 3
  s_A(x1) = x1
  s#_A(x1) = 0
  x_A(x1,x2) = x1 + x2 + 1
  x#_A(x1,x2) = 2

precedence:

  and = 0 > tt = activate = plus = s = x