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To complement @rburing answer, you can specify an algorithm to solve the simplified system of equations:

sage: %time solve(list(map(SR, G)), list(map(SR, R.gens())), algorithm='giac', solution_dict=True)
CPU times: user 128 ms, sys: 0 ns, total: 128 ms
Wall time: 127 ms
[{a15: a15,
  x13_14: x13_14,
  a4: a4,
  a11: a11,
  a0: 1,
  x14_15: x14_15,
  x11_13: x11_13,
  x5_5: x5_5,
  x9_12: x9_12,
  a5: 1/x5_5,
  a12: a12,
  x3_4: 0,
  a1: 1,
  x7_7: x7_7,
  x11_14: x11_14,
  x12_15: x12_15,
  x5_6: x5_6,
  x4_4: 1/a4,
  x9_9: x9_9,
  a6: a6,
  a13: a13,
  x3_5: x3_5,
  a2: 1,
  x10_10: x10_10,
  x7_8: x7_8,
  x6_6: 1/a6,
  x5_7: x5_7,
  x12_12: 1/a12,
  x8_8: x8_8,
  a7: 1/x7_7,
  x3_6: x3_6,
  x6_7: x6_7,
  x14_14: x14_14,
  a9: 1/x9_9,
  x15_15: 1/a15,
  x4_6: x4_6,
  x11_11: 1/a11,
  x8_9: 0,
  a8: 1/x8_8,
  x10_12: x10_12,
  a14: 1/x14_14,
  x13_13: 1/a13,
  a3: 1,
  a10: 1/x10_10,
  x4_7: x4_7,
  x12_14: x12_14,
  x11_12: 0,
  x13_15: x13_15,
  x10_13: x10_13},
 {a15: a15,
  x13_14: x13_14,
  a4: a4,
  a11: a11,
  a0: 1,
  x14_15: x14_15,
  x11_13: x11_13,
  x5_5: x5_5,
  x9_12: x9_12,
  a5: 1/x5_5,
  a12: a12,
  x3_4: 0,
  a1: 1,
  x7_7: x7_7,
  x11_14: x11_14,
  x12_15: x12_15,
  x5_6: x5_6,
  x4_4: 1/a4,
  x9_9: x9_9,
  a6: a6,
  a13: a13,
  x3_5: x3_5,
  a2: 1,
  x10_10: x10_10,
  x7_8: 0,
  x6_6: 1/a6,
  x5_7: x5_7,
  x12_12: 1/a12,
  x8_8: x8_8,
  a7: 1/x7_7,
  x3_6: x3_6,
  x6_7: x6_7,
  x14_14: x14_14,
  a9: 1/x9_9,
  x15_15: 1/a15,
  x4_6: x4_6,
  x11_11: 1/a11,
  x8_9: x8_9,
  a8: 1/x8_8,
  x10_12: x10_12,
  a14: 1/x14_14,
  x13_13: 1/a13,
  a3: 1,
  a10: 1/x10_10,
  x4_7: x4_7,
  x12_14: x12_14,
  x11_12: 0,
  x13_15: x13_15,
  x10_13: x10_13}]

Note that, in contrast with maxima, giac does not seem to introduce free parameter like r19 to describe the solutions, instead the values of the dict are unchanged if they are free.

To complement @rburing answer, you You can specify an algorithm to solve the simplified system of equations:

sage: %time solve(polys, vs, algorithm='giac', solution_dict=True)
// Giac share root-directory:/opt/sagemath/sage-source/local/share/giac/
// Giac share root-directory:/opt/sagemath/sage-source/local/share/giac/
Help file /opt/sagemath/sage-source/local/share/giac/doc/fr/aide_cas not found
Added 0 synonyms
CPU times: user 531 ms, sys: 32.8 ms, total: 564 ms
Wall time: 563 ms
[{a15: 1/x15_15,
  x13_14: x13_14,
  a4: 1/x4_4,
  a11: 1/x11_11,
  a0: 1,
  x14_15: x14_15,
  x11_13: x11_13,
  x5_5: 1/a5,
  x9_12: x9_12,
  a5: a5,
  a12: 1/x12_12,
  x3_4: 0,
  a1: 1,
  x7_7: x7_7,
  x11_14: x11_14,
  x12_15: x12_15,
  x5_6: x5_6,
  x4_4: x4_4,
  x9_9: x9_9,
  a6: a6,
  a13: a13,
  x3_5: x3_5,
  a2: 1,
  x10_10: x10_10,
  x7_8: x7_8,
  x6_6: 1/a6,
  x5_7: x5_7,
  x12_12: x12_12,
  x8_8: x8_8,
  a7: 1/x7_7,
  x3_6: x3_6,
  x6_7: x6_7,
  x14_14: x14_14,
  a9: 1/x9_9,
  x15_15: x15_15,
  x4_6: x4_6,
  x11_11: x11_11,
  x8_9: 0,
  a8: 1/x8_8,
  x10_12: x10_12,
  a14: 1/x14_14,
  x13_13: 1/a13,
  a3: 1,
  a10: 1/x10_10,
  x4_7: x4_7,
  x12_14: x12_14,
  x11_12: 0,
  x13_15: x13_15,
  x10_13: x10_13},
 {a15: 1/x15_15,
  x13_14: x13_14,
  a4: 1/x4_4,
  a11: 1/x11_11,
  a0: 1,
  x14_15: x14_15,
  x11_13: x11_13,
  x5_5: 1/a5,
  x9_12: x9_12,
  a5: a5,
  a12: 1/x12_12,
  x3_4: 0,
  a1: 1,
  x7_7: x7_7,
  x11_14: x11_14,
  x12_15: x12_15,
  x5_6: x5_6,
  x4_4: x4_4,
  x9_9: x9_9,
  a6: a6,
  a13: a13,
  x3_5: x3_5,
  a2: 1,
  x10_10: x10_10,
  x7_8: x7_8,
  x6_6: 1/a6,
  x5_7: x5_7,
  x12_12: x12_12,
  x8_8: x8_8,
  a7: 1/x7_7,
  x3_6: x3_6,
  x6_7: x6_7,
  x14_14: x14_14,
  a9: 1/x9_9,
  x15_15: x15_15,
  x4_6: x4_6,
  x11_11: x11_11,
  x8_9: 0,
  a8: 1/x8_8,
  x10_12: x10_12,
  a14: 1/x14_14,
  x13_13: 1/a13,
  a3: 1,
  a10: 1/x10_10,
  x4_7: x4_7,
  x12_14: x12_14,
  x11_12: 0,
  x13_15: x13_15,
  x10_13: 0},
 {a15: 1/x15_15,
  x13_14: x13_14,
  a4: 1/x4_4,
  a11: 1/x11_11,
  a0: 1,
  x14_15: x14_15,
  x11_13: x11_13,
  x5_5: 1/a5,
  x9_12: x9_12,
  a5: a5,
  a12: 1/x12_12,
  x3_4: 0,
  a1: 1,
  x7_7: x7_7,
  x11_14: x11_14,
  x12_15: x12_15,
  x5_6: x5_6,
  x4_4: x4_4,
  x9_9: x9_9,
  a6: a6,
  a13: a13,
  x3_5: x3_5,
  a2: 1,
  x10_10: x10_10,
  x7_8: x7_8,
  x6_6: 1/a6,
  x5_7: x5_7,
  x12_12: x12_12,
  x8_8: x8_8,
  a7: 1/x7_7,
  x3_6: x3_6,
  x6_7: x6_7,
  x14_14: x14_14,
  a9: 1/x9_9,
  x15_15: x15_15,
  x4_6: x4_6,
  x11_11: x11_11,
  x8_9: 0,
  a8: 1/x8_8,
  x10_12: 0,
  a14: 1/x14_14,
  x13_13: 1/a13,
  a3: 1,
  a10: 1/x10_10,
  x4_7: x4_7,
  x12_14: x12_14,
  x11_12: 0,
  x13_15: x13_15,
  x10_13: 0},
 {a15: 1/x15_15,
  x13_14: x13_14,
  a4: 1/x4_4,
  a11: 1/x11_11,
  a0: 1,
  x14_15: x14_15,
  x11_13: x11_13,
  x5_5: 1/a5,
  x9_12: x9_12,
  a5: a5,
  a12: 1/x12_12,
  x3_4: 0,
  a1: 1,
  x7_7: x7_7,
  x11_14: x11_14,
  x12_15: x12_15,
  x5_6: x5_6,
  x4_4: x4_4,
  x9_9: x9_9,
  a6: a6,
  a13: a13,
  x3_5: x3_5,
  a2: 1,
  x10_10: x10_10,
  x7_8: x7_8,
  x6_6: 1/a6,
  x5_7: x5_7,
  x12_12: x12_12,
  x8_8: x8_8,
  a7: 1/x7_7,
  x3_6: 0,
  x6_7: x6_7,
  x14_14: x14_14,
  a9: 1/x9_9,
  x15_15: x15_15,
  x4_6: x12_14,
  x11_11: x11_11,
  x8_9: 0,
  a8: 1/x8_8,
  x10_12: 0,
  a14: 1/x14_14,
  x13_13: 1/a13,
  a3: 1,
  a10: 1/x10_10,
  x4_7: x4_7,
  x12_14: x12_14,
  x11_12: 0,
  x13_15: x13_15,
  x10_13: 0},
 {a15: 1/x15_15,
  x13_14: x13_14,
  a4: 1/x4_4,
  a11: 1/x11_11,
  a0: 1,
  x14_15: x14_15,
  x11_13: x11_13,
  x5_5: 1/a5,
  x9_12: x9_12,
  a5: a5,
  a12: 1/x12_12,
  x3_4: 0,
  a1: 1,
  x7_7: x7_7,
  x11_14: x11_14,
  x12_15: x12_15,
  x5_6: x5_6,
  x4_4: x4_4,
  x9_9: x9_9,
  a6: a6,
  a13: a13,
  x3_5: x3_5,
  a2: 1,
  x10_10: x10_10,
  x7_8: x7_8,
  x6_6: 1/a6,
  x5_7: x13_15,
  x12_12: x12_12,
  x8_8: x8_8,
  a7: 1/x7_7,
  x3_6: 0,
  x6_7: x6_7,
  x14_14: x14_14,
  a9: 1/x9_9,
  x15_15: x15_15,
  x4_6: x12_14,
  x11_11: x11_11,
  x8_9: 0,
  a8: 1/x8_8,
  x10_12: 0,
  a14: 1/x14_14,
  x13_13: 1/a13,
  a3: 1,
  a10: 1/x10_10,
  x4_7: x4_7,
  x12_14: x12_14,
  x11_12: 0,
  x13_15: x13_15,
  x10_13: 0},
 {a15: 1/x15_15,
  x13_14: x13_14,
  a4: 1/x4_4,
  a11: 1/x11_11,
  a0: 1,
  x14_15: x14_15,
  x11_13: x11_13,
  x5_5: 1/a5,
  x9_12: x9_12,
  a5: a5,
  a12: 1/x12_12,
  x3_4: 0,
  a1: 1,
  x7_7: x7_7,
  x11_14: x11_14,
  x12_15: x12_15,
  x5_6: x5_6,
  x4_4: x4_4,
  x9_9: x9_9,
  a6: 1/x14_14,
  a13: a13,
  x3_5: 0,
  a2: 1,
  x10_10: x10_10,
  x7_8: 0,
  x6_6: x14_14,
  x5_7: x13_15,
  x12_12: x12_12,
  x8_8: x8_8,
  a7: 1/x7_7,
  x3_6: 0,
  x6_7: x6_7,
  x14_14: x14_14,
  a9: 1/x9_9,
  x15_15: x15_15,
  x4_6: x12_14,
  x11_11: x11_11,
  x8_9: 0,
  a8: 1/x8_8,
  x10_12: 0,
  a14: 1/x14_14,
  x13_13: 1/a13,
  a3: 1,
  a10: 1/x10_10,
  x4_7: x4_7,
  x12_14: x12_14,
  x11_12: 0,
  x13_15: x13_15,
  x10_13: 0},
 {a15: 1/x15_15,
  x13_14: x13_14,
  a4: 1/x12_12,
  a11: 1/x11_11,
  a0: 1,
  x14_15: x14_15,
  x11_13: x11_13,
  x5_5: 1/a5,
  x9_12: x9_12,
  a5: a5,
  a12: 1/x12_12,
  x3_4: 0,
  a1: 1,
  x7_7: x7_7,
  x11_14: x11_14,
  x12_15: x12_15,
  x5_6: x5_6,
  x4_4: x12_12,
  x9_9: x9_9,
  a6: 1/x14_14,
  a13: a13,
  x3_5: 0,
  a2: 1,
  x10_10: x10_10,
  x7_8: 0,
  x6_6: x14_14,
  x5_7: x13_15,
  x12_12: x12_12,
  x8_8: x8_8,
  a7: 1/x7_7,
  x3_6: 0,
  x6_7: x6_7,
  x14_14: x14_14,
  a9: 1/x9_9,
  x15_15: x15_15,
  x4_6: x12_14,
  x11_11: x11_11,
  x8_9: 0,
  a8: 1/x8_8,
  x10_12: 0,
  a14: 1/x14_14,
  x13_13: 1/a13,
  a3: 1,
  a10: 1/x10_10,
  x4_7: x4_7,
  x12_14: x12_14,
  x11_12: 0,
  x13_15: x13_15,
  x10_13: 0},
 {a15: 1/x15_15,
  x13_14: x13_14,
  a4: 1/x12_12,
  a11: 1/x11_11,
  a0: 1,
  x14_15: x14_15,
  x11_13: x11_13,
  x5_5: 1/a5,
  x9_12: x9_12,
  a5: a5,
  a12: 1/x12_12,
  x3_4: 0,
  a1: 1,
  x7_7: x7_7,
  x11_14: x11_14,
  x12_15: x4_7,
  x5_6: x5_6,
  x4_4: x12_12,
  x9_9: x9_9,
  a6: 1/x14_14,
  a13: a13,
  x3_5: 0,
  a2: 1,
  x10_10: x10_10,
  x7_8: 0,
  x6_6: x14_14,
  x5_7: x13_15,
  x12_12: x12_12,
  x8_8: x8_8,
  a7: 1/x7_7,
  x3_6: 0,
  x6_7: x6_7,
  x14_14: x14_14,
  a9: 1/x9_9,
  x15_15: x15_15,
  x4_6: x12_14,
  x11_11: x11_11,
  x8_9: 0,
  a8: 1/x8_8,
  x10_12: 0,
  a14: 1/x14_14,
  x13_13: 1/a13,
  a3: 1,
  a10: 1/x10_10,
  x4_7: x4_7,
  x12_14: x12_14,
  x11_12: 0,
  x13_15: x13_15,
  x10_13: 0},
 {a15: 1/x15_15,
  x13_14: x13_14,
  a4: 1/x12_12,
  a11: 1/x11_11,
  a0: 1,
  x14_15: x14_15,
  x11_13: x11_13,
  x5_5: 1/a5,
  x9_12: x9_12,
  a5: a5,
  a12: 1/x12_12,
  x3_4: 0,
  a1: 1,
  x7_7: x7_7,
  x11_14: 0,
  x12_15: x4_7,
  x5_6: x5_6,
  x4_4: x12_12,
  x9_9: x9_9,
  a6: 1/x14_14,
  a13: a13,
  x3_5: 0,
  a2: 1,
  x10_10: x10_10,
  x7_8: 0,
  x6_6: x14_14,
  x5_7: x13_15,
  x12_12: x12_12,
  x8_8: x8_8,
  a7: 1/x7_7,
  x3_6: 0,
  x6_7: x6_7,
  x14_14: x14_14,
  a9: 1/x9_9,
  x15_15: x15_15,
  x4_6: x12_14,
  x11_11: x11_11,
  x8_9: 0,
  a8: 1/x8_8,
  x10_12: 0,
  a14: 1/x14_14,
  x13_13: 1/a13,
  a3: 1,
  a10: 1/x10_10,
  x4_7: x4_7,
  x12_14: x12_14,
  x11_12: 0,
  x13_15: x13_15,
  x10_13: 0},
 {a15: 1/x15_15,
  x13_14: x13_14,
  a4: 1/x4_4,
  a11: 1/x11_11,
  a0: 1,
  x14_15: x14_15,
  x11_13: x11_13,
  x5_5: 1/a5,
  x9_12: x9_12,
  a5: a5,
  a12: 1/x12_12,
  x3_4: 0,
  a1: 1,
  x7_7: x7_7,
  x11_14: x11_14,
  x12_15: x12_15,
  x5_6: x5_6,
  x4_4: x4_4,
  x9_9: x9_9,
  a6: 1/x14_14,
  a13: a13,
  x3_5: x3_5,
  a2: 1,
  x10_10: x10_10,
  x7_8: 0,
  x6_6: x14_14,
  x5_7: x13_15,
  x12_12: x12_12,
  x8_8: x8_8,
  a7: 1/x7_7,
  x3_6: 0,
  x6_7: x6_7,
  x14_14: x14_14,
  a9: 1/x9_9,
  x15_15: x15_15,
  x4_6: x12_14,
  x11_11: x11_11,
  x8_9: 0,
  a8: 1/x8_8,
  x10_12: 0,
  a14: 1/x14_14,
  x13_13: 1/a13,
  a3: 1,
  a10: 1/x10_10,
  x4_7: x4_7,
  x12_14: x12_14,
  x11_12: 0,
  x13_15: x13_15,
  x10_13: 0},
 {a15: 1/x15_15,
  x13_14: x13_14,
  a4: 1/x4_4,
  a11: 1/x11_11,
  a0: 1,
  x14_15: x14_15,
  x11_13: x11_13,
  x5_5: 1/a5,
  x9_12: x9_12,
  a5: a5,
  a12: 1/x12_12,
  x3_4: 0,
  a1: 1,
  x7_7: x7_7,
  x11_14: x11_14,
  x12_15: x12_15,
  x5_6: x5_6,
  x4_4: x4_4,
  x9_9: x9_9,
  a6: 1/x14_14,
  a13: a13,
  x3_5: x3_5,
  a2: 1,
  x10_10: x10_10,
  x7_8: x7_8,
  x6_6: x14_14,
  x5_7: x13_15,
  x12_12: x12_12,
  x8_8: x8_8,
  a7: 1/x7_7,
  x3_6: 0,
  x6_7: x6_7,
  x14_14: x14_14,
  a9: 1/x9_9,
  x15_15: x15_15,
  x4_6: x12_14,
  x11_11: x11_11,
  x8_9: 0,
  a8: 1/x8_8,
  x10_12: 0,
  a14: 1/x14_14,
  x13_13: 1/a13,
  a3: 1,
  a10: 1/x10_10,
  x4_7: x4_7,
  x12_14: x12_14,
  x11_12: 0,
  x13_15: x13_15,
  x10_13: 0},
 {a15: 1,
  x13_14: x13_14,
  a4: 1/x4_4,
  a11: 1/x11_11,
  a0: 1,
  x14_15: x14_15,
  x11_13: x11_13,
  x5_5: 1/a5,
  x9_12: x9_12,
  a5: a5,
  a12: 1/x12_12,
  x3_4: 0,
  a1: 1,
  x7_7: x7_7,
  x11_14: x11_14,
  x12_15: x12_15,
  x5_6: x5_6,
  x4_4: x4_4,
  x9_9: x9_9,
  a6: 1/x14_14,
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  a9: 1/x9_9,
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  x13_13: 1/a13,
  a3: 1,
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  x4_7: x4_7,
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 {a15: 1,
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  a4: 1/x12_12,
  a11: 1/x11_11,
  a0: 1,
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  x7_8: x7_8,
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  a9: 1/x9_9,
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  x11_11: x11_11,
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  a14: 1/x14_14,
  x13_13: 1/a13,
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  x4_7: x4_7,
  x12_14: x12_14,
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 {a15: 1,
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  a4: 1/x12_12,
  a11: 1/x11_11,
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  x11_13: x11_13,
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  a13: a13,
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  a14: 1/x14_14,
  x13_13: 1/a13,
  a3: 1,
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 {a15: 1,
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  a4: 1/x12_12,
  a11: 1/x11_11,
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  x7_7: x7_7,
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  x4_4: x12_12,
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  a6: 1/x14_14,
  a13: a13,
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  x7_8: x7_8,
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  a9: 1/x9_9,
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 {a15: 1,
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  a4: 1/x4_4,
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  a6: 1/x14_14,
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  a7: 1/x7_7,
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  a9: 1/x9_9,
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  x11_11: x11_11,
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  x13_13: 1/a13,
  a3: 1,
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  x4_7: x4_7,
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 {a15: 1/x15_15,
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  a4: 1/x4_4,
  a11: 1/x11_11,
  a0: 1,
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  x5_5: 1/a5,
  x9_12: x9_12,
  a5: a5,
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  x7_7: x7_7,
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  a6: a6,
  a13: a13,
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  x10_10: x10_10,
  x7_8: x7_8,
  x6_6: 1/a6,
  x5_7: x5_7,
  x12_12: x12_12,
  x8_8: x8_8,
  a7: 1/x7_7,
  x3_6: x3_6,
  x6_7: x6_7,
  x14_14: x14_14,
  a9: 1/x9_9,
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  a14: 1/x14_14,
  x13_13: 1/a13,
  a3: 1,
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 {a15: 1/x15_15,
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  a4: 1/x4_4,
  a11: 1/x11_11,
  a0: 1,
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  x5_5: 1/a5,
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  a6: a6,
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  x8_8: x8_8,
  a7: 1/x7_7,
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  a8: 1/x8_8,
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  a14: 1/x14_14,
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 {a15: 1/x15_15,
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  a4: 1/x4_4,
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  a6: a6,
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  a7: 1/x7_7,
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  a8: 1/x8_8,
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  a14: 1/x14_14,
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 {a15: 1/x15_15,
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  a4: 1/x4_4,
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 {a15: 1/x15_15,
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  a6: a6,
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  x12_12: x12_12,
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  a7: 1/x7_7,
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  a8: 1/x8_8,
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  a14: 1/x14_14,
  x13_13: 1/a13,
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 {a15: 1/x15_15,
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  a4: 1/x4_4,
  a11: 1/x11_11,
  a0: 1,
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  x5_5: 1/a5,
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  x5_6: x5_6,
  x4_4: x4_4,
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  a6: 1/x14_14,
  a13: a13,
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  a2: 1,
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  x12_12: x12_12,
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  a7: 1/x7_7,
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  a6: 1/x14_14,
  a13: a13,
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  a2: 1,
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  a7: 1/x7_7,
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  a9: 1/x9_9,
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  a8: 1/x8_8,
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  a3: 1,
  a10: 1/x10_10,
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 {a15: 1/x15_15,
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  a4: 1/x12_12,
  a11: 1/x11_11,
  a0: 1,
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  x11_13: x11_13,
  x5_5: 1/a5,
  x9_12: x9_12,
  a5: a5,
  a12: 1/x12_12,
  x3_4: 0,
  a1: 1,
  x7_7: x7_7,
  x11_14: 0,
  x12_15: x4_7,
  x5_6: x5_6,
  x4_4: x12_12,
  x9_9: x9_9,
  a6: 1/x14_14,
  a13: a13,
  x3_5: 0,
  a2: 1,
  x10_10: x10_10,
  x7_8: 0,
  x6_6: x14_14,
  x5_7: x13_15,
  x12_12: x12_12,
  x8_8: x8_8,
  a7: 1/x7_7,
  x3_6: 0,
  x6_7: x6_7,
  x14_14: x14_14,
  a9: 1/x9_9,
  x15_15: x15_15,
  x4_6: x12_14,
  x11_11: x11_11,
  x8_9: x8_9,
  a8: 1/x8_8,
  x10_12: 0,
  a14: 1/x14_14,
  x13_13: 1/a13,
  a3: 1,
  a10: 1/x10_10,
  x4_7: x4_7,
  x12_14: x12_14,
  x11_12: 0,
  x13_15: x13_15,
  x10_13: 0},
 {a15: 1/x15_15,
  x13_14: x13_14,
  a4: 1/x4_4,
  a11: 1/x11_11,
  a0: 1,
  x14_15: x14_15,
  x11_13: x11_13,
  x5_5: 1/a5,
  x9_12: x9_12,
  a5: a5,
  a12: 1/x12_12,
  x3_4: 0,
  a1: 1,
  x7_7: x7_7,
  x11_14: x11_14,
  x12_15: x12_15,
  x5_6: x5_6,
  x4_4: x4_4,
  x9_9: x9_9,
  a6: 1/x14_14,
  a13: a13,
  x3_5: x3_5,
  a2: 1,
  x10_10: x10_10,
  x7_8: 0,
  x6_6: x14_14,
  x5_7: x13_15,
  x12_12: x12_12,
  x8_8: x8_8,
  a7: 1/x7_7,
  x3_6: 0,
  x6_7: x6_7,
  x14_14: x14_14,
  a9: 1/x9_9,
  x15_15: x15_15,
  x4_6: x12_14,
  x11_11: x11_11,
  x8_9: x8_9,
  a8: 1/x8_8,
  x10_12: 0,
  a14: 1/x14_14,
  x13_13: 1/a13,
  a3: 1,
  a10: 1/x10_10,
  x4_7: x4_7,
  x12_14: x12_14,
  x11_12: 0,
  x13_15: x13_15,
  x10_13: 0},
 {a15: 1/x15_15,
  x13_14: x13_14,
  a4: 1/x4_4,
  a11: 1/x11_11,
  a0: 1,
  x14_15: x14_15,
  x11_13: x11_13,
  x5_5: 1/a5,
  x9_12: x9_12,
  a5: a5,
  a12: 1/x12_12,
  x3_4: 0,
  a1: 1,
  x7_7: x7_7,
  x11_14: x11_14,
  x12_15: x12_15,
  x5_6: x5_6,
  x4_4: x4_4,
  x9_9: x9_9,
  a6: a6,
  a13: a13,
  x3_5: x3_5,
  a2: 1,
  x10_10: x10_10,
  x7_8: 0,
  x6_6: 1/a6,
  x5_7: x5_7,
  x12_12: x12_12,
  x8_8: x8_8,
  a7: 1/x7_7,
  x3_6: x3_6,
  x6_7: x6_7,
  x14_14: x14_14,
  a9: 1/x9_9,
  x15_15: x15_15,
  x4_6: x12_14,
  x11_11: x11_11,
  x8_9: x8_9,
  a8: 1/x8_8,
  x10_12: 0,
  a14: 1/x14_14,
  x13_13: 1/a13,
  a3: 1,
  a10: 1/x10_10,
  x4_7: x4_7,
  x12_14: x12_14,
  x11_12: 0,
  x13_15: x13_15,
  x10_13: 0}]

Note that, in contrast with maxima, giac does not seem to introduce free parameter like r19 to describe the solutions, instead the values of the dict are unchanged if they are free.

You can also use this to work with @rburing answer (giac knows about Groebner basis, but the solution is shorted here, perhaps because of a different monomial ordering):

sage: %time solve(list(map(SR, G)), list(map(SR, R.gens())), algorithm='giac', solution_dict=True)
CPU times: user 128 ms, sys: 0 ns, total: 128 ms
Wall time: 127 ms
[{a15: a15,
  x13_14: x13_14,
  a4: a4,
  a11: a11,
  a0: 1,
  x14_15: x14_15,
  x11_13: x11_13,
  x5_5: x5_5,
  x9_12: x9_12,
  a5: 1/x5_5,
  a12: a12,
  x3_4: 0,
  a1: 1,
  x7_7: x7_7,
  x11_14: x11_14,
  x12_15: x12_15,
  x5_6: x5_6,
  x4_4: 1/a4,
  x9_9: x9_9,
  a6: a6,
  a13: a13,
  x3_5: x3_5,
  a2: 1,
  x10_10: x10_10,
  x7_8: x7_8,
  x6_6: 1/a6,
  x5_7: x5_7,
  x12_12: 1/a12,
  x8_8: x8_8,
  a7: 1/x7_7,
  x3_6: x3_6,
  x6_7: x6_7,
  x14_14: x14_14,
  a9: 1/x9_9,
  x15_15: 1/a15,
  x4_6: x4_6,
  x11_11: 1/a11,
  x8_9: 0,
  a8: 1/x8_8,
  x10_12: x10_12,
  a14: 1/x14_14,
  x13_13: 1/a13,
  a3: 1,
  a10: 1/x10_10,
  x4_7: x4_7,
  x12_14: x12_14,
  x11_12: 0,
  x13_15: x13_15,
  x10_13: x10_13},
 {a15: a15,
  x13_14: x13_14,
  a4: a4,
  a11: a11,
  a0: 1,
  x14_15: x14_15,
  x11_13: x11_13,
  x5_5: x5_5,
  x9_12: x9_12,
  a5: 1/x5_5,
  a12: a12,
  x3_4: 0,
  a1: 1,
  x7_7: x7_7,
  x11_14: x11_14,
  x12_15: x12_15,
  x5_6: x5_6,
  x4_4: 1/a4,
  x9_9: x9_9,
  a6: a6,
  a13: a13,
  x3_5: x3_5,
  a2: 1,
  x10_10: x10_10,
  x7_8: 0,
  x6_6: 1/a6,
  x5_7: x5_7,
  x12_12: 1/a12,
  x8_8: x8_8,
  a7: 1/x7_7,
  x3_6: x3_6,
  x6_7: x6_7,
  x14_14: x14_14,
  a9: 1/x9_9,
  x15_15: 1/a15,
  x4_6: x4_6,
  x11_11: 1/a11,
  x8_9: x8_9,
  a8: 1/x8_8,
  x10_12: x10_12,
  a14: 1/x14_14,
  x13_13: 1/a13,
  a3: 1,
  a10: 1/x10_10,
  x4_7: x4_7,
  x12_14: x12_14,
  x11_12: 0,
  x13_15: x13_15,
  x10_13: x10_13}]

Note that, in contrast with maxima, giac does not seem to introduce free parameter like r19 to describe the solutions, instead the values of the dict are unchanged if they are free.