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: {3,6,1}
   transitions:
    03() -> 41*
    a1(25,13) -> 15*
    a1(15,13) -> 14*
    a1(5,13) -> 14*
    a1(2,13) -> 16*
    a1(14,13) -> 14*
    a1(25,2) -> 1*
    c1(15) -> 5*
    c1(17) -> 9*
    c1(24) -> 25*
    c1(14) -> 15*
    c1(16) -> 17*
    c1(23) -> 24*
    c1(13) -> 23*
    01() -> 13*
    c2(35) -> 36*
    c2(27) -> 28*
    c2(36) -> 37*
    c2(26) -> 35*
    c2(28) -> 25*
    a2(37,13) -> 15,5
    a2(13,26) -> 27*
    f30() -> 3*
    02() -> 26*
    c0(5) -> 1*
    c0(7) -> 8*
    c0(2) -> 7*
    c0(4) -> 5*
    c0(8) -> 9*
    c3(42) -> 43*
    c3(43) -> 37*
    a0(9,2) -> 1*
    a0(3,2) -> 4*
    a0(9,3) -> 6*
    a0(5,2) -> 4*
    a0(2,2) -> 7*
    a3(26,41) -> 42*
    00() -> 2*
    1 -> 5*
    2 -> 7*
    4 -> 5*
    5 -> 1*
    7 -> 8*
    8 -> 9*
    13 -> 23*
    14 -> 15*
    15 -> 5*
    16 -> 17*
    17 -> 9*
    23 -> 24*
    24 -> 25*
    26 -> 35*
    27 -> 28*
    28 -> 25*
    35 -> 36*
    36 -> 37*
    42 -> 43*
    43 -> 37*
  problem:
   
  Qed