YES
TRS:
 {   a__f(X1, X2, X3) -> f(X1, X2, X3),
      a__f(a(), X, X) -> a__f(X, a__b(), b()),
               a__b() -> b(),
               a__b() -> a(),
            mark(b()) -> a__b(),
            mark(a()) -> a(),
  mark(f(X1, X2, X3)) -> a__f(X1, mark(X2), X3)}
 DP:
  Strict:
   {    a__f#(a(), X, X) -> a__f#(X, a__b(), b()),
        a__f#(a(), X, X) -> a__b#(),
              mark#(b()) -> a__b#(),
    mark#(f(X1, X2, X3)) -> a__f#(X1, mark(X2), X3),
    mark#(f(X1, X2, X3)) -> mark#(X2)}
  Weak:
  {   a__f(X1, X2, X3) -> f(X1, X2, X3),
       a__f(a(), X, X) -> a__f(X, a__b(), b()),
                a__b() -> b(),
                a__b() -> a(),
             mark(b()) -> a__b(),
             mark(a()) -> a(),
   mark(f(X1, X2, X3)) -> a__f(X1, mark(X2), X3)}
  EDG:
   {(mark#(f(X1, X2, X3)) -> a__f#(X1, mark(X2), X3), a__f#(a(), X, X) -> a__b#())
    (mark#(f(X1, X2, X3)) -> a__f#(X1, mark(X2), X3), a__f#(a(), X, X) -> a__f#(X, a__b(), b()))
    (a__f#(a(), X, X) -> a__f#(X, a__b(), b()), a__f#(a(), X, X) -> a__f#(X, a__b(), b()))
    (a__f#(a(), X, X) -> a__f#(X, a__b(), b()), a__f#(a(), X, X) -> a__b#())
    (mark#(f(X1, X2, X3)) -> mark#(X2), mark#(b()) -> a__b#())
    (mark#(f(X1, X2, X3)) -> mark#(X2), mark#(f(X1, X2, X3)) -> a__f#(X1, mark(X2), X3))
    (mark#(f(X1, X2, X3)) -> mark#(X2), mark#(f(X1, X2, X3)) -> mark#(X2))}
   SCCS:
    Scc:
     {mark#(f(X1, X2, X3)) -> mark#(X2)}
    Scc:
     {a__f#(a(), X, X) -> a__f#(X, a__b(), b())}
    SCC:
     Strict:
      {mark#(f(X1, X2, X3)) -> mark#(X2)}
     Weak:
     {   a__f(X1, X2, X3) -> f(X1, X2, X3),
          a__f(a(), X, X) -> a__f(X, a__b(), b()),
                   a__b() -> b(),
                   a__b() -> a(),
                mark(b()) -> a__b(),
                mark(a()) -> a(),
      mark(f(X1, X2, X3)) -> a__f(X1, mark(X2), X3)}
     SPSC:
      Simple Projection:
       pi(mark#) = 0
      Strict:
       {}
      Qed
    SCC:
     Strict:
      {a__f#(a(), X, X) -> a__f#(X, a__b(), b())}
     Weak:
     {   a__f(X1, X2, X3) -> f(X1, X2, X3),
          a__f(a(), X, X) -> a__f(X, a__b(), b()),
                   a__b() -> b(),
                   a__b() -> a(),
                mark(b()) -> a__b(),
                mark(a()) -> a(),
      mark(f(X1, X2, X3)) -> a__f(X1, mark(X2), X3)}
     POLY:
      Argument Filtering:
       pi(f) = [], pi(mark) = [], pi(a) = [], pi(b) = [], pi(a__b) = [], pi(a__f#) = [0,2], pi(a__f) = []
      Usable Rules:
       {}
      Interpretation:
       [a__f#](x0, x1) = x0 + x1,
       [a] = 1,
       [b] = 0
      Strict:
       {}
      Weak:
       {   a__f(X1, X2, X3) -> f(X1, X2, X3),
            a__f(a(), X, X) -> a__f(X, a__b(), b()),
                     a__b() -> b(),
                     a__b() -> a(),
                  mark(b()) -> a__b(),
                  mark(a()) -> a(),
        mark(f(X1, X2, X3)) -> a__f(X1, mark(X2), X3)}
      Qed