YES

TRS:

  a__and(tt(),X) -> mark(X)
  a__plus(N,0()) -> mark(N)
  a__plus(N,s(M)) -> s(a__plus(mark(N),mark(M)))
  mark(and(X1,X2)) -> a__and(mark(X1),X2)
  mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
  mark(tt()) -> tt()
  mark(0()) -> 0()
  mark(s(X)) -> s(mark(X))
  a__and(X1,X2) -> and(X1,X2)
  a__plus(X1,X2) -> plus(X1,X2)

linear polynomial interpretations on N:

  a__and_A(x1,x2) = x1 + x2 + 1
  a__and#_A(x1,x2) = x1 + x2 + 1
  tt_A = 0
  tt#_A = 0
  mark_A(x1) = x1
  mark#_A(x1) = x1
  a__plus_A(x1,x2) = x1 + x2 + 1
  a__plus#_A(x1,x2) = x1 + x2 + 1
  0_A = 0
  0#_A = 0
  s_A(x1) = x1 + 1
  s#_A(x1) = x1 + 1
  and_A(x1,x2) = x1 + x2 + 1
  and#_A(x1,x2) = x1 + x2 + 1
  plus_A(x1,x2) = x1 + x2 + 1
  plus#_A(x1,x2) = x1 + x2 + 1

precedence:

  mark > a__and = tt = a__plus = 0 > s = and = plus