YES

TRS:

  U11(tt(),M,N) -> U12(tt(),activate(M),activate(N))
  U12(tt(),M,N) -> s(plus(activate(N),activate(M)))
  plus(N,0()) -> N
  plus(N,s(M)) -> U11(tt(),M,N)
  activate(X) -> X

linear polynomial interpretations on N:

  U11_A(x1,x2,x3) = x1 + x2 + x3 + 1
  U11#_A(x1,x2,x3) = x1 + x2 + x3 + 1
  tt_A = 0
  tt#_A = 0
  U12_A(x1,x2,x3) = x1 + x2 + x3 + 1
  U12#_A(x1,x2,x3) = x1 + x2 + x3 + 1
  activate_A(x1) = x1
  activate#_A(x1) = x1
  s_A(x1) = x1 + 1
  s#_A(x1) = x1 + 1
  plus_A(x1,x2) = x1 + x2
  plus#_A(x1,x2) = x1 + x2
  0_A = 0
  0#_A = 0

precedence:

  plus = 0 > U11 > U12 > activate = s > tt