YES(?,O(n^1))

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

Proof:
 Bounds Processor:
  bound: 3
  enrichment: match
  automaton:
   final states: {4}
   transitions:
    a3(92) -> 93*
    a3(93) -> 94*
    a3(88) -> 89*
    a1(20) -> 21*
    a1(49) -> 50*
    a1(19) -> 20*
    a1(11) -> 12*
    a1(13) -> 14*
    b3(89) -> 90*
    b3(91) -> 92*
    b1(45) -> 46*
    b1(12) -> 13*
    b1(14) -> 15*
    b1(43) -> 44*
    b1(18) -> 19*
    c3(90) -> 91*
    c1(15) -> 16*
    c1(17) -> 18*
    a2(62) -> 63*
    a2(57) -> 58*
    a2(84) -> 85*
    a2(79) -> 80*
    a2(26) -> 27*
    a2(83) -> 84*
    a2(73) -> 74*
    a2(58) -> 59*
    a2(53) -> 54*
    a2(28) -> 29*
    a0(4) -> 4*
    b2(102) -> 103*
    b2(82) -> 83*
    b2(27) -> 28*
    b2(64) -> 65*
    b2(54) -> 55*
    b2(29) -> 30*
    b2(56) -> 57*
    b2(80) -> 81*
    b0(4) -> 4*
    c2(55) -> 56*
    c2(30) -> 31*
    c2(81) -> 82*
    c0(4) -> 4*
    4 -> 11*
    13 -> 73,17
    14 -> 53,49
    16 -> 74,27,12,14,4
    19 -> 62*
    20 -> 43,26
    21 -> 12,45,4
    29 -> 88,79
    31 -> 74,27,29,14
    44 -> 13*
    46 -> 13*
    50 -> 12*
    58 -> 64*
    59 -> 54,50,12
    63 -> 27*
    65 -> 28*
    74 -> 27*
    84 -> 102*
    85 -> 50*
    94 -> 89,80,54
    103 -> 28*
  problem:
   
  Qed