YES

Problem:
 c(c(c(y))) -> c(c(a(y,0())))
 c(a(a(0(),x),y)) -> a(c(c(c(0()))),y)
 c(y) -> y

Proof:
 Bounds Processor:
  bound: 3
  enrichment: match
  automaton:
   final states: {4}
   transitions:
    c3(27) -> 28*
    c3(28) -> 25*
    a1(9,8) -> 9*
    a1(4,8) -> 9*
    a1(13,4) -> 4*
    a1(13,8) -> 10*
    a1(10,8) -> 9*
    a3(17,26) -> 27*
    c1(10) -> 4*
    c1(12) -> 13*
    c1(9) -> 10*
    c1(11) -> 12*
    c1(8) -> 11*
    03() -> 26*
    01() -> 8*
    c2(17) -> 23*
    c2(24) -> 25*
    c2(19) -> 13*
    c2(23) -> 24*
    c2(18) -> 19*
    c0(4) -> 4*
    a2(8,17) -> 18*
    a2(25,8) -> 10,4
    a0(4,4) -> 4*
    02() -> 17*
    00() -> 4*
    8 -> 11*
    9 -> 10*
    10 -> 4*
    11 -> 12*
    12 -> 13*
    17 -> 23*
    18 -> 19*
    19 -> 13*
    23 -> 24*
    24 -> 25*
    27 -> 28*
    28 -> 25*
  problem:
   
  Qed