YES
O(n)
TRS:
 {
     c(c(b(c(y), 0()))) -> a(0(), c(c(a(y, 0())))),
       c(c(c(a(x, y)))) -> b(c(c(c(c(y)))), x),
  c(c(a(a(y, 0()), x))) -> c(y)
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
       c(c(b(c(y), 0()))) -> a(0(), c(c(a(y, 0())))),
         c(c(c(a(x, y)))) -> b(c(c(c(c(y)))), x),
    c(c(a(a(y, 0()), x))) -> c(y)
   }
  BOUND:
   Automaton:
    {
           0_3() -> 79,
           0_2() -> 25,
           0_1() -> 5,
           0_0() -> 4,
     a_3(79, 82) -> 71 | 70 | 69 | 47 | 46 | 45 | 16 | 15 | 14,
     a_3(46, 79) -> 80,
     a_2(46, 25) -> 26,
     a_2(39, 25) -> 26,
     a_2(25, 28) ->
     71 |
     70 |
     69 |
     68 |
     47 |
     46 |
     45 |
     44 |
     40 | 39 | 38 | 37 | 28 | 16 | 15 | 14 | 13 | 12 | 11 | 10 | 9 | 8 | 4,
     a_2(15, 25) -> 26,
     a_2(11, 25) -> 26,
      a_2(4, 25) -> 26,
      a_1(62, 5) -> 98,
      a_1(58, 5) -> 95,
      a_1(46, 5) -> 6,
      a_1(39, 5) -> 6,
      a_1(23, 5) -> 41,
      a_1(15, 5) -> 6,
      a_1(11, 5) -> 6,
     a_1(5, 100) -> 70 | 46,
      a_1(5, 97) -> 39,
      a_1(5, 43) -> 15 | 11,
       a_1(5, 8) ->
     71 |
     70 |
     69 |
     68 |
     47 |
     46 |
     45 |
     44 |
     40 | 39 | 38 | 37 | 28 | 16 | 15 | 14 | 13 | 12 | 11 | 10 | 9 | 8 | 4,
       a_1(4, 5) -> 6,
       a_0(4, 4) -> 4,
         c_3(81) -> 82,
         c_3(80) -> 81,
         c_3(70) -> 71,
         c_3(69) -> 70,
         c_3(68) -> 69,
         c_3(62) -> 63,
         c_3(61) -> 62,
         c_3(60) -> 61,
         c_3(28) -> 68,
         c_3(25) -> 60,
         c_2(58) -> 59,
         c_2(57) -> 58,
         c_2(56) -> 57,
         c_2(46) -> 47,
         c_2(45) -> 46,
         c_2(44) -> 45,
         c_2(28) -> 44,
         c_2(27) -> 28,
         c_2(26) -> 27,
         c_2(25) -> 56,
         c_2(23) -> 24,
         c_2(22) -> 23,
         c_2(21) -> 22,
         c_2(15) -> 16,
         c_2(14) -> 15,
         c_2(13) -> 14,
          c_2(8) -> 13,
          c_2(5) -> 21,
         c_1(99) -> 100,
         c_1(98) -> 99,
         c_1(96) -> 97,
         c_1(95) -> 96,
         c_1(42) -> 43,
         c_1(41) -> 42,
         c_1(39) -> 40,
         c_1(38) -> 39,
         c_1(37) -> 38,
         c_1(28) -> 37,
         c_1(11) -> 12,
         c_1(10) -> 11,
          c_1(9) -> 10,
          c_1(8) -> 9,
          c_1(7) -> 8,
          c_1(6) -> 7,
          c_1(4) ->
     71 |
     70 |
     69 |
     68 |
     47 |
     46 |
     45 |
     44 |
     40 | 39 | 38 | 37 | 28 | 16 | 15 | 14 | 13 | 12 | 11 | 10 | 9 | 8 | 4,
          c_0(4) -> 4,
     b_3(71, 25) -> 71 | 70 | 47 | 46 | 16 | 15,
     b_3(63, 46) -> 68 | 44,
     b_3(63, 39) -> 68 | 44,
     b_3(63, 15) -> 68 | 44,
     b_3(63, 11) -> 68 | 44,
      b_3(63, 4) -> 68 | 44,
     b_2(59, 46) -> 37,
     b_2(59, 39) -> 37,
     b_2(59, 15) -> 37,
     b_2(59, 11) -> 37,
      b_2(59, 4) -> 37,
     b_2(47, 25) ->
     71 |
     70 |
     69 |
     68 |
     47 |
     46 |
     45 |
     44 |
     40 | 39 | 38 | 37 | 28 | 16 | 15 | 14 | 13 | 12 | 11 | 10 | 9 | 8 | 4,
     b_2(24, 46) -> 13 | 9,
     b_2(24, 39) -> 13 | 9,
     b_2(24, 15) -> 13 | 9,
     b_2(24, 11) -> 13 | 9,
      b_2(24, 4) -> 13 | 9,
      b_2(16, 5) ->
     71 |
     70 |
     69 |
     68 |
     47 |
     46 |
     45 |
     44 |
     40 | 39 | 38 | 37 | 28 | 16 | 15 | 14 | 13 | 12 | 11 | 10 | 9 | 8 | 4,
     b_1(40, 25) ->
     71 |
     70 |
     69 |
     68 |
     47 |
     46 |
     45 |
     44 |
     40 | 39 | 38 | 37 | 28 | 16 | 15 | 14 | 13 | 12 | 11 | 10 | 9 | 8 | 4,
      b_1(12, 5) ->
     71 |
     70 |
     69 |
     68 |
     47 |
     46 |
     45 |
     44 |
     40 | 39 | 38 | 37 | 28 | 16 | 15 | 14 | 13 | 12 | 11 | 10 | 9 | 8 | 4,
       b_1(4, 4) ->
     71 |
     70 |
     69 |
     68 |
     47 |
     46 |
     45 |
     44 |
     40 | 39 | 38 | 37 | 28 | 16 | 15 | 14 | 13 | 12 | 11 | 10 | 9 | 8 | 4,
       b_0(4, 4) -> 4
    }
   Strict:
    {}
   Qed