YES

Problem:
 v(s(x1)) -> s(p(p(s(s(s(s(s(s(s(s(w(p(p(s(s(p(s(p(s(x1))))))))))))))))))))
 v(0(x1)) -> p(p(s(s(0(p(p(s(s(s(s(s(x1))))))))))))
 w(s(x1)) -> s(s(s(s(s(s(p(p(s(s(v(p(p(s(s(s(p(p(s(s(x1))))))))))))))))))))
 w(0(x1)) -> p(s(p(p(p(p(p(p(p(p(s(s(0(s(s(s(s(s(s(x1)))))))))))))))))))
 p(p(s(x1))) -> p(x1)
 p(s(x1)) -> x1
 p(0(x1)) -> 0(s(s(s(s(s(s(s(p(s(x1))))))))))

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {66,2,65,51,33,22,1}
   transitions:
    f50() -> 2*
    s1(128) -> 129*
    s1(189) -> 190*
    s1(206) -> 207*
    s1(119) -> 120*
    s1(231) -> 232*
    s1(253) -> 254*
    s1(251) -> 252*
    s1(184) -> 185*
    s1(113) -> 114*
    s1(250) -> 251*
    s1(153) -> 154*
    s1(230) -> 231*
    s1(276) -> 277*
    s1(272) -> 273*
    s1(209) -> 210*
    s1(151) -> 152*
    s1(181) -> 182*
    s1(233) -> 234*
    s1(158) -> 159*
    s1(155) -> 156*
    s1(120) -> 121*
    s1(118) -> 119*
    s1(210) -> 211*
    s1(114) -> 115*
    s1(125) -> 126*
    s1(273) -> 274*
    s1(121) -> 122*
    s1(185) -> 186*
    s1(157) -> 158*
    s1(186) -> 187*
    s1(156) -> 157*
    s1(225) -> 226*
    s1(274) -> 275*
    s1(269) -> 270*
    s1(227) -> 228*
    s1(208) -> 209*
    s1(252) -> 253*
    s1(228) -> 229*
    s1(109) -> 110*
    s1(122) -> 123*
    s1(229) -> 230*
    s1(275) -> 276*
    s1(203) -> 204*
    s1(205) -> 206*
    s1(247) -> 248*
    s1(111) -> 112*
    s1(159) -> 160*
    s1(124) -> 125*
    s1(255) -> 256*
    s1(188) -> 189*
    s1(183) -> 184*
    s1(154) -> 155*
    s1(254) -> 255*
    s1(123) -> 124*
    s1(211) -> 212*
    s1(187) -> 188*
    s1(249) -> 250*
    s1(271) -> 272*
    s1(277) -> 278*
    s1(207) -> 208*
    s1(232) -> 233*
    p2(173) -> 174*
    p2(177) -> 178*
    p0(5) -> 6*
    p0(58) -> 59*
    p0(31) -> 32*
    p0(59) -> 60*
    p0(44) -> 45*
    p0(34) -> 35*
    p0(60) -> 61*
    p0(57) -> 58*
    p0(39) -> 40*
    p0(20) -> 21*
    p0(27) -> 28*
    p0(32) -> 22*
    p0(23) -> 34*
    p0(62) -> 63*
    p0(3) -> 4*
    p0(38) -> 39*
    p0(26) -> 27*
    p0(61) -> 62*
    p0(8) -> 9*
    p0(43) -> 44*
    p0(55) -> 56*
    p0(19) -> 20*
    p0(64) -> 51*
    p0(9) -> 10*
    p0(56) -> 57*
    p0(2) -> 65*
    s0(41) -> 42*
    s0(21) -> 1*
    s0(68) -> 69*
    s0(6) -> 7*
    s0(30) -> 31*
    s0(67) -> 68*
    s0(17) -> 18*
    s0(69) -> 70*
    s0(36) -> 37*
    s0(13) -> 14*
    s0(71) -> 72*
    s0(35) -> 36*
    s0(46) -> 47*
    s0(12) -> 13*
    s0(47) -> 48*
    s0(42) -> 43*
    s0(48) -> 49*
    s0(25) -> 26*
    s0(45) -> 46*
    s0(4) -> 5*
    s0(2) -> 3*
    s0(49) -> 50*
    s0(53) -> 54*
    s0(63) -> 64*
    s0(54) -> 55*
    s0(16) -> 17*
    s0(29) -> 30*
    s0(26) -> 52*
    s0(24) -> 25*
    s0(23) -> 24*
    s0(7) -> 8*
    s0(5) -> 67*
    s0(70) -> 71*
    s0(15) -> 16*
    s0(18) -> 19*
    s0(3) -> 23*
    s0(50) -> 33*
    s0(14) -> 15*
    s0(37) -> 38*
    s0(11) -> 12*
    01(160) -> 161*
    01(234) -> 235*
    01(256) -> 257*
    01(212) -> 213*
    01(190) -> 191*
    01(278) -> 279*
    p1(73) -> 74*
    p1(204) -> 205*
    p1(127) -> 128*
    p1(115) -> 116*
    p1(126) -> 127*
    p1(79) -> 80*
    p1(110) -> 111*
    p1(95) -> 96*
    p1(81) -> 82*
    p1(103) -> 104*
    p1(182) -> 183*
    p1(116) -> 117*
    p1(89) -> 90*
    p1(248) -> 249*
    p1(107) -> 108*
    p1(270) -> 271*
    p1(226) -> 227*
    p1(152) -> 153*
    p1(97) -> 98*
    p1(112) -> 113*
    p1(87) -> 88*
    w0(10) -> 11*
    v0(40) -> 41*
    00(28) -> 29*
    00(72) -> 66*
    00(52) -> 53*
    w1(117) -> 118*
    247 -> 249*
    191 -> 59*
    151 -> 153*
    24 -> 96,28
    74 -> 35*
    203 -> 205*
    190 -> 203*
    160 -> 181*
    17 -> 80*
    256 -> 269*
    35 -> 109*
    42 -> 44,103
    30 -> 32,81
    113 -> 174,117
    234 -> 247*
    7 -> 9,89
    104 -> 45*
    63 -> 51*
    114 -> 116,173
    66 -> 65*
    212 -> 225*
    4 -> 6*
    2 -> 65,74,35,4
    53 -> 88,107
    82 -> 22*
    174 -> 117*
    124 -> 178*
    52 -> 151*
    54 -> 56,87
    88 -> 57*
    109 -> 111*
    6 -> 90*
    257 -> 62*
    178 -> 128*
    161 -> 108,58
    36 -> 98,40
    269 -> 271*
    235 -> 61*
    125 -> 127,177
    90 -> 10*
    37 -> 39,97
    108 -> 58*
    225 -> 227*
    213 -> 60*
    3 -> 34,73
    41 -> 104,45
    18 -> 20,79
    129 -> 41,104
    96 -> 28*
    181 -> 183*
    51 -> 118,11
    98 -> 40*
    80 -> 21*
    29 -> 82*
    25 -> 27,95
    111 -> 113*
    33 -> 118,11
    279 -> 63*
  problem:
   
  Qed