YES

Problem:
 a(x1) -> x1
 a(a(b(x1))) -> b(b(c(a(a(a(x1))))))
 a(c(x1)) -> x1

Proof:
 DP Processor:
  DPs:
   a#(a(b(x1))) -> a#(x1)
   a#(a(b(x1))) -> a#(a(x1))
   a#(a(b(x1))) -> a#(a(a(x1)))
  TRS:
   a(x1) -> x1
   a(a(b(x1))) -> b(b(c(a(a(a(x1))))))
   a(c(x1)) -> x1
  Bounds Processor:
   bound: 1
   enrichment: match-dp
   automaton:
    final states: {1}
    transitions:
     a{#,0}(11) -> 12*
     a{#,0}(2) -> 1*
     a{#,0}(17) -> 18*
     b0(39) -> 40*
     b0(38) -> 39*
     a0(36) -> 37*
     a0(55) -> 56*
     a0(10) -> 11*
     a0(16) -> 17*
     a0(70) -> 71*
     f40() -> 2*
     c0(37) -> 38*
     a{#,1}(61) -> 62*
     a{#,1}(49) -> 50*
     56 -> 11*
     70 -> 71,11,17,37
     17 -> 36*
     12 -> 1*
     16 -> 17*
     11 -> 16*
     2 -> 10*
     36 -> 37*
     38 -> 70,61
     71 -> 11*
     40 -> 16,17
     62 -> 18,12
     55 -> 56,11
     37 -> 71,11,17
     50 -> 18,12
     39 -> 55,49
     18 -> 12,1
     10 -> 11*
   problem:
    DPs:
     a#(a(b(x1))) -> a#(a(x1))
     a#(a(b(x1))) -> a#(a(a(x1)))
    TRS:
     a(x1) -> x1
     a(a(b(x1))) -> b(b(c(a(a(a(x1))))))
     a(c(x1)) -> x1
   Restore Modifier:
    DPs:
     a#(a(b(x1))) -> a#(a(x1))
     a#(a(b(x1))) -> a#(a(a(x1)))
    TRS:
     a(x1) -> x1
     a(a(b(x1))) -> b(b(c(a(a(a(x1))))))
     a(c(x1)) -> x1
    Bounds Processor:
     bound: 2
     enrichment: match-dp
     automaton:
      final states: {4}
      transitions:
       a{#,0}(7) -> 4*
       a{#,0}(30) -> 31*
       a{#,2}(59) -> 60*
       b0(13) -> 14*
       b0(14) -> 15*
       a0(6) -> 7*
       a0(38) -> 39*
       a0(5) -> 6*
       a0(11) -> 12*
       c1(41) -> 42*
       b1(43) -> 44*
       b1(42) -> 43*
       c0(12) -> 13*
       a1(40) -> 41*
       a1(49) -> 50*
       a1(47) -> 48*
       a1(24) -> 25*
       a1(32) -> 33*
       a1(25) -> 26*
       a{#,1}(26) -> 27*
       f160() -> 5*
       b2(75) -> 76*
       b2(74) -> 75*
       c2(73) -> 74*
       a2(72) -> 73*
       a2(58) -> 59*
       a2(64) -> 65*
       a2(57) -> 58*
       27 -> 31,4
       43 -> 64,47
       24 -> 25*
       47 -> 48,24
       48 -> 24*
       64 -> 65*
       42 -> 57,49
       7 -> 11*
       12 -> 33,25,26,40
       14 -> 24*
       11 -> 12*
       6 -> 7*
       72 -> 73*
       58 -> 59*
       38 -> 39*
       76 -> 59*
       26 -> 40,38
       44 -> 26*
       60 -> 27,31
       13 -> 32*
       40 -> 41*
       49 -> 50*
       31 -> 4*
       65 -> 58*
       59 -> 72*
       5 -> 6*
       57 -> 58*
       50 -> 24*
       39 -> 12*
       41 -> 58,50
       15 -> 6,7
       32 -> 33*
       25 -> 26,30
       33 -> 25*
     problem:
      DPs:
       a#(a(b(x1))) -> a#(a(x1))
      TRS:
       a(x1) -> x1
       a(a(b(x1))) -> b(b(c(a(a(a(x1))))))
       a(c(x1)) -> x1
     Restore Modifier:
      DPs:
       a#(a(b(x1))) -> a#(a(x1))
      TRS:
       a(x1) -> x1
       a(a(b(x1))) -> b(b(c(a(a(a(x1))))))
       a(c(x1)) -> x1
      Bounds Processor:
       bound: 1
       enrichment: match-dp
       automaton:
        final states: {1}
        transitions:
         a{#,0}(3) -> 1*
         f200() -> 2*
         b0(7) -> 8*
         b0(8) -> 9*
         a1(32) -> 33*
         a1(20) -> 21*
         a{#,1}(21) -> 22*
         c0(6) -> 7*
         a0(4) -> 5*
         a0(2) -> 3*
         a0(5) -> 6*
         a0(18) -> 19*
         a0(28) -> 29*
         19 -> 2*
         7 -> 20*
         28 -> 29*
         4 -> 5*
         2 -> 3*
         22 -> 1*
         6 -> 21*
         21 -> 28*
         8 -> 32,18
         20 -> 21*
         5 -> 6*
         9 -> 3*
         3 -> 4*
         18 -> 19*
         29 -> 2*
         32 -> 33,21
         33 -> 21*
       problem:
        DPs:
         
        TRS:
         a(x1) -> x1
         a(a(b(x1))) -> b(b(c(a(a(a(x1))))))
         a(c(x1)) -> x1
       Qed