YES

Problem:
 q(0(x1)) -> p(p(s(s(0(s(s(s(s(x1)))))))))
 q(s(x1)) -> p(p(s(s(s(s(s(s(r(p(p(s(s(x1)))))))))))))
 r(0(x1)) -> p(s(p(s(0(p(p(p(s(s(s(x1)))))))))))
 r(s(x1)) -> p(s(p(s(s(q(p(s(p(s(x1))))))))))
 p(p(s(x1))) -> p(x1)
 p(s(x1)) -> x1
 p(0(x1)) -> 0(s(s(s(x1))))

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {40,2,39,30,22,11,1}
   transitions:
    f50() -> 2*
    s0(5) -> 6*
    s0(31) -> 32*
    s0(16) -> 17*
    s0(34) -> 35*
    s0(35) -> 36*
    s0(15) -> 16*
    s0(7) -> 8*
    s0(14) -> 15*
    s0(17) -> 18*
    s0(3) -> 4*
    s0(37) -> 38*
    s0(26) -> 27*
    s0(8) -> 9*
    s0(4) -> 5*
    s0(19) -> 20*
    s0(28) -> 29*
    s0(18) -> 19*
    s0(2) -> 3*
    p0(21) -> 11*
    p0(32) -> 33*
    p0(36) -> 37*
    p0(12) -> 13*
    p0(20) -> 21*
    p0(27) -> 28*
    p0(4) -> 12*
    p0(2) -> 39*
    p0(10) -> 1*
    p0(38) -> 30*
    p0(29) -> 22*
    p0(24) -> 25*
    p0(23) -> 24*
    p0(5) -> 23*
    p0(3) -> 31*
    p0(9) -> 10*
    p1(55) -> 56*
    p1(49) -> 50*
    p1(41) -> 42*
    p1(47) -> 48*
    00(5) -> 40*
    00(25) -> 26*
    00(6) -> 7*
    q0(33) -> 34*
    r0(13) -> 14*
    56 -> 11*
    19 -> 21,55
    48 -> 24*
    35 -> 37*
    42 -> 25,13
    30 -> 14*
    7 -> 50*
    28 -> 22*
    4 -> 23,47
    11 -> 34*
    2 -> 39,42,13,31
    22 -> 14*
    26 -> 28*
    8 -> 10,49
    40 -> 39*
    1 -> 34*
    31 -> 33*
    37 -> 30*
    50 -> 1*
    3 -> 48,12,41
    18 -> 56,11
  problem:
   
  Qed