YES
TRS:
 {        xor(x, x) -> F(),
        xor(x, F()) -> x,
     xor(x, neg(x)) -> F(),
             neg(x) -> xor(x, T()),
          and(x, x) -> x,
        and(x, F()) -> F(),
        and(x, T()) -> x,
  and(xor(x, y), z) -> xor(and(x, z), and(y, z)),
         impl(x, y) -> xor(and(x, y), xor(x, T())),
           or(x, y) -> xor(and(x, y), xor(x, y)),
        equiv(x, y) -> xor(x, xor(y, T()))}
 DP:
  Strict:
   {           neg#(x) -> xor#(x, T()),
    and#(xor(x, y), z) -> xor#(and(x, z), and(y, z)),
    and#(xor(x, y), z) -> and#(x, z),
    and#(xor(x, y), z) -> and#(y, z),
           impl#(x, y) -> xor#(x, T()),
           impl#(x, y) -> xor#(and(x, y), xor(x, T())),
           impl#(x, y) -> and#(x, y),
             or#(x, y) -> xor#(x, y),
             or#(x, y) -> xor#(and(x, y), xor(x, y)),
             or#(x, y) -> and#(x, y),
          equiv#(x, y) -> xor#(x, xor(y, T())),
          equiv#(x, y) -> xor#(y, T())}
  Weak:
  {        xor(x, x) -> F(),
         xor(x, F()) -> x,
      xor(x, neg(x)) -> F(),
              neg(x) -> xor(x, T()),
           and(x, x) -> x,
         and(x, F()) -> F(),
         and(x, T()) -> x,
   and(xor(x, y), z) -> xor(and(x, z), and(y, z)),
          impl(x, y) -> xor(and(x, y), xor(x, T())),
            or(x, y) -> xor(and(x, y), xor(x, y)),
         equiv(x, y) -> xor(x, xor(y, T()))}
  EDG:
   {(and#(xor(x, y), z) -> and#(x, z), and#(xor(x, y), z) -> and#(y, z))
    (and#(xor(x, y), z) -> and#(x, z), and#(xor(x, y), z) -> and#(x, z))
    (and#(xor(x, y), z) -> and#(x, z), and#(xor(x, y), z) -> xor#(and(x, z), and(y, z)))
    (and#(xor(x, y), z) -> and#(y, z), and#(xor(x, y), z) -> xor#(and(x, z), and(y, z)))
    (and#(xor(x, y), z) -> and#(y, z), and#(xor(x, y), z) -> and#(x, z))
    (and#(xor(x, y), z) -> and#(y, z), and#(xor(x, y), z) -> and#(y, z))
    (or#(x, y) -> and#(x, y), and#(xor(x, y), z) -> xor#(and(x, z), and(y, z)))
    (or#(x, y) -> and#(x, y), and#(xor(x, y), z) -> and#(x, z))
    (or#(x, y) -> and#(x, y), and#(xor(x, y), z) -> and#(y, z))
    (impl#(x, y) -> and#(x, y), and#(xor(x, y), z) -> xor#(and(x, z), and(y, z)))
    (impl#(x, y) -> and#(x, y), and#(xor(x, y), z) -> and#(x, z))
    (impl#(x, y) -> and#(x, y), and#(xor(x, y), z) -> and#(y, z))}
   SCCS:
    Scc:
     {and#(xor(x, y), z) -> and#(x, z),
      and#(xor(x, y), z) -> and#(y, z)}
    SCC:
     Strict:
      {and#(xor(x, y), z) -> and#(x, z),
       and#(xor(x, y), z) -> and#(y, z)}
     Weak:
     {        xor(x, x) -> F(),
            xor(x, F()) -> x,
         xor(x, neg(x)) -> F(),
                 neg(x) -> xor(x, T()),
              and(x, x) -> x,
            and(x, F()) -> F(),
            and(x, T()) -> x,
      and(xor(x, y), z) -> xor(and(x, z), and(y, z)),
             impl(x, y) -> xor(and(x, y), xor(x, T())),
               or(x, y) -> xor(and(x, y), xor(x, y)),
            equiv(x, y) -> xor(x, xor(y, T()))}
     SPSC:
      Simple Projection:
       pi(and#) = 0
      Strict:
       {and#(xor(x, y), z) -> and#(x, z)}
      EDG:
       {(and#(xor(x, y), z) -> and#(x, z), and#(xor(x, y), z) -> and#(x, z))}
       SCCS:
        Scc:
         {and#(xor(x, y), z) -> and#(x, z)}
        SCC:
         Strict:
          {and#(xor(x, y), z) -> and#(x, z)}
         Weak:
         {        xor(x, x) -> F(),
                xor(x, F()) -> x,
             xor(x, neg(x)) -> F(),
                     neg(x) -> xor(x, T()),
                  and(x, x) -> x,
                and(x, F()) -> F(),
                and(x, T()) -> x,
          and(xor(x, y), z) -> xor(and(x, z), and(y, z)),
                 impl(x, y) -> xor(and(x, y), xor(x, T())),
                   or(x, y) -> xor(and(x, y), xor(x, y)),
                equiv(x, y) -> xor(x, xor(y, T()))}
         SPSC:
          Simple Projection:
           pi(and#) = 0
          Strict:
           {}
          Qed