YES
TRS:
 {f(x, x) -> f(a(), b()),
      b() -> c()}
 DP:
  Strict:
   {f#(x, x) -> f#(a(), b()),
    f#(x, x) -> b#()}
  Weak:
  {f(x, x) -> f(a(), b()),
       b() -> c()}
  EDG:
   {(f#(x, x) -> f#(a(), b()), f#(x, x) -> b#())
    (f#(x, x) -> f#(a(), b()), f#(x, x) -> f#(a(), b()))}
   SCCS:
    Scc:
     {f#(x, x) -> f#(a(), b())}
    SCC:
     Strict:
      {f#(x, x) -> f#(a(), b())}
     Weak:
     {f(x, x) -> f(a(), b()),
          b() -> c()}
     BOUND:
      Bound: match(-raise)-bounded by 1
      Automaton:
       {     c_1() -> 7* | 6 | 3
             c_0() -> 6*
             b_0() -> 3*
             a_0() -> 2*
        f#_0(2, 7) -> 4*
        f#_0(2, 6) -> 4*
        f#_0(2, 3) -> 4*
         f_0(2, 7) -> 1*
         f_0(2, 6) -> 1*
         f_0(2, 3) -> 1*}
      Strict:
       {}
      Qed