YES

Problem:
 i(0(x1)) -> p(s(p(s(0(p(s(p(s(x1)))))))))
 i(s(x1)) -> p(s(p(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1))))))))))))))))))
 j(0(x1)) -> p(s(p(p(s(s(0(p(s(p(s(x1)))))))))))
 j(s(x1)) -> s(s(s(s(p(p(s(s(i(p(s(p(s(x1)))))))))))))
 p(p(s(x1))) -> p(x1)
 p(s(x1)) -> x1
 p(0(x1)) -> 0(s(s(s(s(s(s(s(s(x1)))))))))

Proof:
 Arctic Interpretation Processor:
  dimension: 1
  interpretation:
   [j](x0) = 9x0,
   
   [p](x0) = x0,
   
   [s](x0) = x0,
   
   [i](x0) = 9x0,
   
   [0](x0) = 1x0
  orientation:
   i(0(x1)) = 10x1 >= 1x1 = p(s(p(s(0(p(s(p(s(x1)))))))))
   
   i(s(x1)) = 9x1 >= 9x1 = p(s(p(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1))))))))))))))))))
   
   j(0(x1)) = 10x1 >= 1x1 = p(s(p(p(s(s(0(p(s(p(s(x1)))))))))))
   
   j(s(x1)) = 9x1 >= 9x1 = s(s(s(s(p(p(s(s(i(p(s(p(s(x1)))))))))))))
   
   p(p(s(x1))) = x1 >= x1 = p(x1)
   
   p(s(x1)) = x1 >= x1 = x1
   
   p(0(x1)) = 1x1 >= 1x1 = 0(s(s(s(s(s(s(s(s(x1)))))))))
  problem:
   i(s(x1)) -> p(s(p(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1))))))))))))))))))
   j(s(x1)) -> s(s(s(s(p(p(s(s(i(p(s(p(s(x1)))))))))))))
   p(p(s(x1))) -> p(x1)
   p(s(x1)) -> x1
   p(0(x1)) -> 0(s(s(s(s(s(s(s(s(x1)))))))))
  Bounds Processor:
   bound: 1
   enrichment: match
   automaton:
    final states: {33,2,32,20,1}
    transitions:
     p1(50) -> 51*
     p1(44) -> 45*
     p1(46) -> 47*
     p1(38) -> 39*
     f50() -> 2*
     p0(27) -> 28*
     p0(22) -> 23*
     p0(17) -> 18*
     p0(7) -> 8*
     p0(2) -> 32*
     p0(19) -> 1*
     p0(9) -> 10*
     p0(26) -> 27*
     p0(11) -> 12*
     p0(6) -> 7*
     p0(13) -> 14*
     p0(8) -> 9*
     p0(3) -> 21*
     s0(35) -> 36*
     s0(30) -> 31*
     s0(25) -> 26*
     s0(15) -> 16*
     s0(10) -> 11*
     s0(5) -> 6*
     s0(12) -> 13*
     s0(2) -> 3*
     s0(34) -> 35*
     s0(29) -> 30*
     s0(24) -> 25*
     s0(4) -> 5*
     s0(36) -> 37*
     s0(31) -> 20*
     s0(21) -> 22*
     s0(16) -> 17*
     s0(6) -> 34*
     s0(28) -> 29*
     s0(18) -> 19*
     s0(3) -> 4*
     j0(14) -> 15*
     i0(23) -> 24*
     00(37) -> 33*
     1 -> 24,45
     2 -> 32,51,10,21
     3 -> 47,50
     4 -> 39,46
     5 -> 7,38
     10 -> 12*
     12 -> 14*
     16 -> 18*
     18 -> 1*
     20 -> 15*
     21 -> 23*
     24 -> 45,28
     25 -> 27,44
     33 -> 32*
     39 -> 8*
     45 -> 28*
     47 -> 9*
     51 -> 10,12,14
   problem:
    
   Qed