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:
 Arctic Interpretation Processor:
  dimension: 1
  interpretation:
   [0](x0) = x0,
   
   [w](x0) = 2x0,
   
   [p](x0) = x0,
   
   [v](x0) = 2x0,
   
   [s](x0) = x0
  orientation:
   v(s(x1)) = 2x1 >= 2x1 = s(p(p(s(s(s(s(s(s(s(s(w(p(p(s(s(p(s(p(s(x1))))))))))))))))))))
   
   v(0(x1)) = 2x1 >= x1 = p(p(s(s(0(p(p(s(s(s(s(s(x1))))))))))))
   
   w(s(x1)) = 2x1 >= 2x1 = s(s(s(s(s(s(p(p(s(s(v(p(p(s(s(s(p(p(s(s(x1))))))))))))))))))))
   
   w(0(x1)) = 2x1 >= 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))) = x1 >= x1 = p(x1)
   
   p(s(x1)) = x1 >= x1 = x1
   
   p(0(x1)) = x1 >= x1 = 0(s(s(s(s(s(s(s(p(s(x1))))))))))
  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))))))))))))))))))))
   w(s(x1)) -> s(s(s(s(s(s(p(p(s(s(v(p(p(s(s(s(p(p(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))))))))))
  Bounds Processor:
   bound: 2
   enrichment: match
   automaton:
    final states: {42,2,41,22,1}
    transitions:
     f50() -> 2*
     s0(45) -> 46*
     s0(40) -> 22*
     s0(35) -> 36*
     s0(25) -> 26*
     s0(15) -> 16*
     s0(5) -> 43*
     s0(47) -> 48*
     s0(37) -> 38*
     s0(32) -> 33*
     s0(27) -> 28*
     s0(17) -> 18*
     s0(12) -> 13*
     s0(7) -> 8*
     s0(2) -> 3*
     s0(44) -> 45*
     s0(39) -> 40*
     s0(14) -> 15*
     s0(4) -> 5*
     s0(46) -> 47*
     s0(36) -> 37*
     s0(31) -> 32*
     s0(26) -> 27*
     s0(21) -> 1*
     s0(16) -> 17*
     s0(11) -> 12*
     s0(6) -> 7*
     s0(43) -> 44*
     s0(38) -> 39*
     s0(18) -> 19*
     s0(13) -> 14*
     s0(3) -> 23*
     p0(20) -> 21*
     p0(5) -> 6*
     p0(2) -> 41*
     p0(34) -> 35*
     p0(29) -> 30*
     p0(24) -> 25*
     p0(19) -> 20*
     p0(9) -> 10*
     p0(33) -> 34*
     p0(28) -> 29*
     p0(23) -> 24*
     p0(8) -> 9*
     p0(3) -> 4*
     w0(10) -> 11*
     v0(30) -> 31*
     00(48) -> 42*
     p1(107) -> 108*
     p1(97) -> 98*
     p1(67) -> 68*
     p1(59) -> 60*
     p1(96) -> 97*
     p1(91) -> 92*
     p1(61) -> 62*
     p1(51) -> 52*
     p1(108) -> 109*
     p1(93) -> 94*
     p1(53) -> 54*
     s1(102) -> 103*
     s1(92) -> 93*
     s1(109) -> 110*
     s1(104) -> 105*
     s1(99) -> 100*
     s1(94) -> 95*
     s1(106) -> 107*
     s1(101) -> 102*
     s1(103) -> 104*
     s1(105) -> 106*
     s1(100) -> 101*
     s1(95) -> 96*
     s1(90) -> 91*
     w1(98) -> 99*
     p2(117) -> 118*
     p2(111) -> 112*
     2 -> 41,54,25,4
     3 -> 24,53
     4 -> 6*
     6 -> 60*
     7 -> 9,59
     17 -> 68,21
     18 -> 20,67
     22 -> 99,11
     25 -> 90*
     26 -> 62,30
     27 -> 29,61
     31 -> 52*
     32 -> 34,51
     42 -> 41*
     52 -> 35*
     54 -> 25*
     60 -> 10*
     62 -> 30*
     68 -> 21*
     90 -> 92*
     92 -> 94*
     94 -> 118,98
     95 -> 97,117
     105 -> 112*
     106 -> 108,111
     110 -> 31,52,35
     112 -> 109*
     118 -> 98*
   problem:
    
   Qed