YES

Problem:
 foo(0(x1)) -> 0(s(p(p(p(s(s(s(p(s(x1))))))))))
 foo(s(x1)) -> p(s(p(p(p(s(s(p(s(s(p(s(foo(p(p(s(s(p(s(bar(p(p(s(s(p(s(x1))))))))))))))))))))))))))
 bar(0(x1)) -> 0(p(s(s(s(x1)))))
 bar(s(x1)) -> p(s(p(p(s(s(foo(s(p(p(s(s(x1))))))))))))
 p(p(s(x1))) -> p(x1)
 p(s(x1)) -> x1
 p(0(x1)) -> 0(s(s(s(s(x1)))))

Proof:
 String Reversal Processor:
  0(foo(x1)) -> s(p(s(s(s(p(p(p(s(0(x1))))))))))
  s(foo(x1)) ->
  s(p(s(s(p(p(bar(s(p(s(s(p(p(foo(s(p(s(s(p(s(s(p(p(p(s(p(x1))))))))))))))))))))))))))
  0(bar(x1)) -> s(s(s(p(0(x1)))))
  s(bar(x1)) -> s(s(p(p(s(foo(s(s(p(p(s(p(x1))))))))))))
  s(p(p(x1))) -> p(x1)
  s(p(x1)) -> x1
  0(p(x1)) -> s(s(s(s(0(x1)))))
  Bounds Processor:
   bound: 2
   enrichment: match
   automaton:
    final states: {50,2,13,42,38,12,1}
    transitions:
     f50() -> 2*
     p1(113) -> 114*
     p1(104) -> 105*
     p1(115) -> 116*
     p1(121) -> 122*
     p1(137) -> 138*
     p1(80) -> 81*
     p1(83) -> 84*
     p1(107) -> 108*
     p1(93) -> 94*
     p1(90) -> 91*
     p1(84) -> 85*
     p1(94) -> 95*
     p1(129) -> 130*
     p1(123) -> 124*
     p1(82) -> 83*
     p1(97) -> 98*
     p1(100) -> 101*
     p1(101) -> 102*
     p1(87) -> 88*
     p2(139) -> 140*
     p2(147) -> 148*
     p2(145) -> 146*
     p2(133) -> 134*
     foo1(92) -> 93*
     p0(47) -> 48*
     p0(5) -> 6*
     p0(16) -> 17*
     p0(22) -> 23*
     p0(15) -> 16*
     p0(33) -> 34*
     p0(29) -> 30*
     p0(32) -> 33*
     p0(14) -> 15*
     p0(6) -> 7*
     p0(3) -> 39*
     p0(26) -> 27*
     p0(4) -> 5*
     p0(25) -> 26*
     p0(36) -> 37*
     p0(19) -> 20*
     p0(10) -> 11*
     p0(46) -> 47*
     p0(2) -> 13*
     foo0(24) -> 25*
     foo0(44) -> 45*
     bar1(99) -> 100*
     bar0(31) -> 32*
     00(2) -> 3*
     s1(81) -> 82*
     s1(86) -> 87*
     s1(102) -> 103*
     s1(103) -> 104*
     s1(89) -> 90*
     s1(85) -> 86*
     s1(91) -> 92*
     s1(98) -> 99*
     s1(95) -> 96*
     s1(88) -> 89*
     s1(96) -> 97*
     s1(105) -> 106*
     s0(41) -> 38*
     s0(21) -> 22*
     s0(30) -> 31*
     s0(17) -> 18*
     s0(13) -> 14*
     s0(35) -> 36*
     s0(20) -> 21*
     s0(27) -> 28*
     s0(34) -> 35*
     s0(48) -> 49*
     s0(43) -> 44*
     s0(52) -> 50*
     s0(45) -> 46*
     s0(4) -> 51*
     s0(49) -> 42*
     s0(39) -> 40*
     s0(16) -> 43*
     s0(23) -> 24*
     s0(7) -> 8*
     s0(40) -> 41*
     s0(51) -> 52*
     s0(18) -> 19*
     s0(3) -> 4*
     s0(37) -> 12*
     s0(28) -> 29*
     s0(8) -> 9*
     s0(11) -> 1*
     s0(9) -> 10*
     94 -> 96*
     19 -> 21*
     148 -> 82,90,87,89
     47 -> 49*
     83 -> 133*
     115 -> 9*
     46 -> 113*
     137 -> 10,1
     113 -> 42*
     100 -> 145*
     104 -> 106*
     140 -> 96*
     93 -> 139*
     14 -> 121*
     16 -> 18*
     114 -> 49*
     106 -> 46*
     4 -> 137*
     2 -> 14*
     82 -> 147*
     124 -> 35*
     22 -> 24*
     116 -> 8*
     6 -> 8*
     121 -> 22,24,44
     138 -> 9*
     36 -> 12*
     38 -> 3,40
     26 -> 28*
     44 -> 80*
     139 -> 97,99
     101 -> 103*
     13 -> 14,121,44,22
     123 -> 36*
     1 -> 3,40
     107 -> 29,31
     90 -> 92*
     130 -> 18*
     147 -> 90,92
     5 -> 115*
     134 -> 86*
     108 -> 28*
     146 -> 103*
     3 -> 40*
     133 -> 87,89
     122 -> 19,43
     145 -> 104,106
     84 -> 86*
     129 -> 19,21
     15 -> 43,129
     97 -> 99*
     10 -> 1*
     80 -> 82*
     87 -> 89*
     81 -> 22,44,82,147,24
     29 -> 31*
     32 -> 123*
     25 -> 107*
     33 -> 35*
   problem:
    
   Qed