YES

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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {2,28,23,12,1}
   transitions:
    f50() -> 2*
    p0(5) -> 6*
    p0(27) -> 23*
    p0(14) -> 15*
    p0(3) -> 13*
    p0(8) -> 9*
    p0(4) -> 5*
    p0(25) -> 26*
    p0(19) -> 20*
    p0(18) -> 19*
    p0(2) -> 28*
    s0(21) -> 22*
    s0(17) -> 18*
    s0(13) -> 14*
    s0(20) -> 21*
    s0(2) -> 3*
    s0(10) -> 11*
    s0(16) -> 17*
    s0(26) -> 27*
    s0(24) -> 25*
    s0(7) -> 8*
    s0(3) -> 4*
    s0(22) -> 12*
    s0(11) -> 1*
    s0(9) -> 10*
    p1(35) -> 36*
    p1(29) -> 30*
    b0(6) -> 7*
    a0(15) -> 24*
    c0(15) -> 16*
    24 -> 26*
    17 -> 19,29
    30 -> 20*
    7 -> 9*
    12 -> 7,9
    16 -> 30*
    2 -> 28,36,6,13
    36 -> 6*
    26 -> 23*
    13 -> 15*
    1 -> 24,26,23
    3 -> 5,35
    23 -> 16,30,20
  problem:
   
  Qed