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: 2
  enrichment: match
  automaton:
   final states: {5,4,3}
   transitions:
    01(10) -> 11*
    01(78) -> 79*
    01(58) -> 59*
    s1(65) -> 66*
    s1(35) -> 36*
    s1(12) -> 13*
    s1(7) -> 8*
    s1(59) -> 60*
    s1(34) -> 35*
    s1(9) -> 10*
    s1(61) -> 62*
    s1(36) -> 37*
    s1(11) -> 12*
    s1(6) -> 7*
    s1(68) -> 69*
    s1(33) -> 34*
    s1(28) -> 29*
    s1(8) -> 9*
    p1(60) -> 61*
    p1(55) -> 56*
    p1(30) -> 31*
    p1(62) -> 63*
    p1(57) -> 58*
    p1(64) -> 65*
    p1(14) -> 15*
    p1(66) -> 67*
    p1(56) -> 57*
    p1(31) -> 32*
    p1(13) -> 14*
    q1(67) -> 68*
    r1(32) -> 33*
    p2(80) -> 81*
    p2(86) -> 87*
    p2(88) -> 89*
    q0(2) -> 3*
    q0(1) -> 3*
    00(2) -> 1*
    00(1) -> 1*
    p0(2) -> 5*
    p0(1) -> 5*
    s0(2) -> 2*
    s0(1) -> 2*
    r0(2) -> 4*
    r0(1) -> 4*
    1 -> 5,28
    2 -> 5,6
    6 -> 87,65
    7 -> 89,57,31,86,64
    8 -> 56,88,30
    9 -> 78,55
    11 -> 81,15
    12 -> 14,80
    15 -> 68,3
    28 -> 87,65
    29 -> 7*
    37 -> 11*
    59 -> 61*
    61 -> 63*
    63 -> 33,4
    65 -> 67*
    69 -> 59*
    79 -> 5*
    81 -> 15,3
    87 -> 58,32
    89 -> 57*
  problem:
   
  Qed