YES
TRS:
 {        and(x, false()) -> false(),
     and(x, not(false())) -> x,
              not(not(x)) -> x,
      implies(x, false()) -> not(x),
      implies(false(), y) -> not(false()),
  implies(not(x), not(y)) -> implies(y, and(x, y))}
 DP:
  Strict:
   {    implies#(x, false()) -> not#(x),
        implies#(false(), y) -> not#(false()),
    implies#(not(x), not(y)) -> and#(x, y),
    implies#(not(x), not(y)) -> implies#(y, and(x, y))}
  Weak:
  {        and(x, false()) -> false(),
      and(x, not(false())) -> x,
               not(not(x)) -> x,
       implies(x, false()) -> not(x),
       implies(false(), y) -> not(false()),
   implies(not(x), not(y)) -> implies(y, and(x, y))}
  EDG:
   {(implies#(not(x), not(y)) -> implies#(y, and(x, y)), implies#(x, false()) -> not#(x))
    (implies#(not(x), not(y)) -> implies#(y, and(x, y)), implies#(false(), y) -> not#(false()))
    (implies#(not(x), not(y)) -> implies#(y, and(x, y)), implies#(not(x), not(y)) -> and#(x, y))
    (implies#(not(x), not(y)) -> implies#(y, and(x, y)), implies#(not(x), not(y)) -> implies#(y, and(x, y)))}
   SCCS:
    Scc:
     {implies#(not(x), not(y)) -> implies#(y, and(x, y))}
    SCC:
     Strict:
      {implies#(not(x), not(y)) -> implies#(y, and(x, y))}
     Weak:
     {        and(x, false()) -> false(),
         and(x, not(false())) -> x,
                  not(not(x)) -> x,
          implies(x, false()) -> not(x),
          implies(false(), y) -> not(false()),
      implies(not(x), not(y)) -> implies(y, and(x, y))}
     POLY:
      Argument Filtering:
       pi(implies#) = [0,1], pi(implies) = [], pi(not) = [0], pi(and) = 0, pi(false) = []
      Usable Rules:
       {}
      Interpretation:
       [implies#](x0, x1) = x0 + x1,
       [not](x0) = x0 + 1
      Strict:
       {}
      Weak:
       {        and(x, false()) -> false(),
           and(x, not(false())) -> x,
                    not(not(x)) -> x,
            implies(x, false()) -> not(x),
            implies(false(), y) -> not(false()),
        implies(not(x), not(y)) -> implies(y, and(x, y))}
      Qed