/export/starexec/sandbox/solver/bin/starexec_run_Transition /export/starexec/sandbox/benchmark/theBenchmark.smt2 /export/starexec/sandbox/output/output_files


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YES

DP problem for innermost termination.
P =
  init#(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9) 
  f13#(I48, I49, I50, I51, I52, I53, I54, I55, I56) -> f3#(I57, I58, I59, I60, I61, I62, I63, I64, I65) [-1 <= I57 - 1 /\ -1 <= I51 - 1 /\ -1 <= I49 - 1 /\ 2 <= I48 - 1 /\ I57 <= I51 /\ I57 <= I49 /\ I57 + 2 <= I48]
  f3#(I66, I67, I68, I69, I70, I71, I72, I73, I74) -> f13#(I75, I76, I77, I78, I79, I80, I81, I82, I83) [-1 <= I78 - 1 /\ -1 <= I76 - 1 /\ 3 <= I75 - 1 /\ 0 <= I66 - 1 /\ I78 + 1 <= I66 /\ I76 + 1 <= I66 /\ I75 - 3 <= I66]
  f3#(I84, I85, I86, I87, I88, I89, I90, I91, I92) -> f13#(I93, I94, I95, I96, I97, I98, I99, I100, I101) [-1 <= I96 - 1 /\ -1 <= I94 - 1 /\ 4 <= I93 - 1 /\ 0 <= I84 - 1 /\ I96 + 1 <= I84 /\ I94 + 1 <= I84]
  f3#(I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f13#(I111, I112, I113, I114, I115, I116, I117, I118, I119) [-1 <= I114 - 1 /\ -1 <= I112 - 1 /\ 4 <= I111 - 1 /\ 0 <= I102 - 1 /\ I114 + 1 <= I102 /\ I112 + 1 <= I102]
  f3#(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f13#(I129, I130, I131, I132, I133, I134, I135, I136, I137) [-1 <= I132 - 1 /\ -1 <= I130 - 1 /\ 4 <= I129 - 1 /\ 0 <= I120 - 1 /\ I132 + 1 <= I120 /\ I130 + 1 <= I120]
  f3#(I138, I139, I140, I141, I142, I143, I144, I145, I146) -> f3#(I147, I148, I149, I150, I151, I152, I153, I154, I155) [-1 <= I147 - 1 /\ 1 <= I138 - 1 /\ I147 + 2 <= I138]
  f3#(I156, I157, I158, I159, I160, I161, I162, I163, I164) -> f3#(I165, I166, I167, I168, I169, I170, I171, I172, I173) [-1 <= I165 - 1 /\ 0 <= I156 - 1 /\ I165 + 1 <= I156]
  f12#(I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f7#(I183, I184, I174 - 1, I177, I178, I185, I186, I187, I188) [I179 = I180 /\ I179 + 2 <= I176 /\ I179 + 2 <= I175 /\ 3 <= I184 - 1 /\ 3 <= I183 - 1 /\ 1 <= I176 - 1 /\ 1 <= I175 - 1 /\ I184 - 2 <= I176 /\ I184 - 2 <= I175 /\ I183 - 2 <= I176 /\ I183 - 2 <= I175]
  f12#(I189, I190, I191, I192, I193, I194, I195, I196, I197) -> f7#(I198, I199, I189 - 1, I192, I193, I200, I201, I202, I203) [I195 + 2 <= I191 /\ I194 + 2 <= I190 /\ 0 <= I199 - 1 /\ 0 <= I198 - 1 /\ 1 <= I191 - 1 /\ 0 <= I190 - 1]
  f11#(I204, I205, I206, I207, I208, I209, I210, I211, I212) -> f12#(I204, I213, I214, I208, I215, I210, I216, I217, I218) [I216 + 2 <= I206 /\ I211 + 2 <= I205 /\ I210 + 2 <= I205 /\ 1 <= I214 - 1 /\ 0 <= I213 - 1 /\ 1 <= I206 - 1 /\ 0 <= I205 - 1 /\ I214 <= I206 /\ I213 <= I205 /\ 0 <= I204 - 1 /\ 0 <= I209 - 1 /\ 0 <= I207 - 1]
  f11#(I219, I220, I221, I222, I223, I224, I225, I226, I227) -> f12#(I219, I228, I229, I223, I224, I225, I230, I231, I232) [I230 + 2 <= I221 /\ I226 + 2 <= I220 /\ I225 + 2 <= I220 /\ 1 <= I229 - 1 /\ 0 <= I228 - 1 /\ 1 <= I221 - 1 /\ 0 <= I220 - 1 /\ I229 <= I221 /\ I228 <= I220 /\ 0 <= I219 - 1 /\ 0 <= I224 - 1 /\ 0 <= I222 - 1]
  f11#(I233, I234, I235, I236, I237, I238, I239, I240, I241) -> f7#(I242, I243, I233 - 1, I237, I238, I244, I245, I246, I247) [I240 + 2 <= I234 /\ I239 + 2 <= I234 /\ 0 <= I243 - 1 /\ 0 <= I242 - 1 /\ 2 <= I235 - 1 /\ 0 <= I234 - 1 /\ I243 + 2 <= I235 /\ 0 <= I236 - 1 /\ I242 <= I234]
  f11#(I248, I249, I250, I251, I252, I253, I254, I255, I256) -> f9#(I248, I257, I258, I259, I252, I253, I254, I255, I260) [0 = I251 /\ I260 + 2 <= I250 /\ I255 + 2 <= I249 /\ I254 + 2 <= I249 /\ -1 <= I259 - 1 /\ 0 <= I258 - 1 /\ 0 <= I257 - 1 /\ 0 <= I250 - 1 /\ 0 <= I249 - 1 /\ I259 + 1 <= I250 /\ I258 <= I250 /\ I257 <= I249]
  f10#(I261, I262, I263, I264, I265, I266, I267, I268, I269) -> f7#(I270, I271, I261 - 1, I264, I265, I272, I273, I274, I275) [I266 = I267 /\ I266 + 2 <= I263 /\ I266 + 2 <= I262 /\ 3 <= I271 - 1 /\ 3 <= I270 - 1 /\ 1 <= I263 - 1 /\ 1 <= I262 - 1 /\ I271 - 2 <= I263 /\ I271 - 2 <= I262 /\ I270 - 2 <= I263 /\ I270 - 2 <= I262]
  f10#(I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f7#(I285, I286, I276 - 1, I279, I280, I287, I288, I289, I290) [I282 + 2 <= I278 /\ I281 + 2 <= I277 /\ 0 <= I286 - 1 /\ 0 <= I285 - 1 /\ 1 <= I278 - 1 /\ 0 <= I277 - 1]
  f7#(I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f11#(I293, I300, I301, I302, I294, I295 + 1, I303, I304, I305) [I304 + 2 <= I291 /\ I303 + 2 <= I291 /\ 0 <= I301 - 1 /\ 0 <= I300 - 1 /\ 0 <= I292 - 1 /\ 0 <= I291 - 1 /\ I301 <= I292 /\ I300 <= I291 /\ -1 <= I302 - 1 /\ -1 <= I295 - 1 /\ I295 <= I294 - 1 /\ -1 <= I294 - 1 /\ 0 <= I293 - 1]
  f7#(I306, I307, I308, I309, I310, I311, I312, I313, I314) -> f11#(I308, I315, I316, 0, I309, I310 + 1, I317, I318, I319) [I318 + 2 <= I306 /\ I317 + 2 <= I306 /\ 0 <= I316 - 1 /\ 0 <= I315 - 1 /\ 0 <= I307 - 1 /\ 0 <= I306 - 1 /\ I316 <= I307 /\ I315 <= I306 /\ -1 <= I310 - 1 /\ I310 <= I309 - 1 /\ -1 <= I309 - 1 /\ 0 <= I308 - 1]
  f9#(I320, I321, I322, I323, I324, I325, I326, I327, I328) -> f10#(I320, I329, I330, I324, I331, I327, I328, I332, I333) [I328 + 2 <= I322 /\ I327 + 2 <= I321 /\ I326 + 2 <= I321 /\ 1 <= I330 - 1 /\ 0 <= I329 - 1 /\ -1 <= I323 - 1 /\ 1 <= I322 - 1 /\ 0 <= I321 - 1 /\ I330 <= I322 /\ I329 <= I321 /\ 0 <= I320 - 1 /\ I324 <= I325]
  f9#(I334, I335, I336, I337, I338, I339, I340, I341, I342) -> f10#(I334, I343, I344, I338, I339, I341, I342, I345, I346) [I342 + 2 <= I336 /\ I341 + 2 <= I335 /\ I340 + 2 <= I335 /\ 1 <= I344 - 1 /\ 0 <= I343 - 1 /\ -1 <= I337 - 1 /\ 1 <= I336 - 1 /\ 0 <= I335 - 1 /\ I344 <= I336 /\ I343 <= I335 /\ 0 <= I334 - 1 /\ I338 <= I339]
  f9#(I347, I348, I349, I350, I351, I352, I353, I354, I355) -> f7#(I356, I357, I347 - 1, I351, I352, I358, I359, I360, I361) [I355 + 2 <= I349 /\ I354 + 2 <= I348 /\ I353 + 2 <= I348 /\ 0 <= I357 - 1 /\ 0 <= I356 - 1 /\ 0 <= I350 - 1 /\ 2 <= I349 - 1 /\ 0 <= I348 - 1 /\ I357 <= I350 /\ I357 + 2 <= I349 /\ I356 <= I348]
  f7#(I362, I363, I364, I365, I366, I367, I368, I369, I370) -> f9#(I364, I371, I372, I373, I365, I366, I374, I375, I376) [I376 + 2 <= I363 /\ I375 + 2 <= I362 /\ I374 + 2 <= I362 /\ -1 <= I373 - 1 /\ 0 <= I372 - 1 /\ 0 <= I371 - 1 /\ 0 <= I363 - 1 /\ 0 <= I362 - 1 /\ I373 + 1 <= I363 /\ I372 <= I363 /\ I371 <= I362 /\ 0 <= I364 - 1 /\ -1 <= I365 - 1 /\ I365 <= I366]
  f8#(I377, I378, I379, I380, I381, I382, I383, I384, I385) -> f7#(I386, I387, I377, I378, I379, I388, I389, I390, I391) [1 <= I386 - 1 /\ 1 <= I387 - 1]
  f6#(I392, I393, I394, I395, I396, I397, I398, I399, I400) -> f7#(I401, I402, I392, I393, I403, I404, I405, I406, I407) [1 <= I401 - 1 /\ 1 <= I402 - 1 /\ 0 <= I393 - 1 /\ 0 <= I392 - 1]
  f6#(I408, I409, I410, I411, I412, I413, I414, I415, I416) -> f7#(I417, I418, I408, I409, 1, I419, I420, I421, I422) [1 <= I417 - 1 /\ 1 <= I418 - 1 /\ 0 <= I409 - 1 /\ 0 <= I408 - 1]
  f1#(I423, I424, I425, I426, I427, I428, I429, I430, I431) -> f6#(I432, I424, I433, I434, I435, I436, I437, I438, I439) [0 <= I423 - 1 /\ 0 <= I424 - 1 /\ -1 <= I432 - 1]
  f1#(I440, I441, I442, I443, I444, I445, I446, I447, I448) -> f6#(0, I441, I449, I450, I451, I452, I453, I454, I455) [0 <= I441 - 1 /\ 0 <= I440 - 1]
  f4#(I456, I457, I458, I459, I460, I461, I462, I463, I464) -> f3#(I465, I466, I467, I468, I469, I470, I471, I472, I473) [I458 + 2 <= I457 /\ 0 <= I465 - 1 /\ 0 <= I457 - 1 /\ 0 <= I456 - 1 /\ I465 <= I457]
  f5#(I474, I475, I476, I477, I478, I479, I480, I481, I482) -> f4#(I483, I484, I476, I485, I486, I487, I488, I489, I490) [I476 + 2 <= I475 /\ 1 <= I484 - 1 /\ 0 <= I483 - 1 /\ 1 <= I475 - 1 /\ 0 <= I474 - 1 /\ I484 <= I475 /\ I483 + 1 <= I475 /\ I483 <= I474]
  f1#(I491, I492, I493, I494, I495, I496, I497, I498, I499) -> f4#(I500, I501, I502, I503, I504, I505, I506, I507, I508) [0 <= I501 - 1 /\ 0 <= I500 - 1 /\ 0 <= I491 - 1 /\ I500 <= I491]
  f2#(I509, I510, I511, I512, I513, I514, I515, I516, I517) -> f3#(I518, I519, I520, I521, I522, I523, I524, I525, I526) [-1 <= I518 - 1 /\ 0 <= I509 - 1 /\ I510 <= 1 /\ I518 + 1 <= I509]
  f1#(I527, I528, I529, I530, I531, I532, I533, I534, I535) -> f2#(I536, 1, I528, I537, I538, I539, I540, I541, I542) [0 <= I536 - 1 /\ 0 <= I527 - 1 /\ I536 <= I527]
  f1#(I543, I544, I545, I546, I547, I548, I549, I550, I551) -> f2#(I552, 0, 0, I553, I554, I555, I556, I557, I558) [0 = I544 /\ 0 <= I552 - 1 /\ 0 <= I543 - 1 /\ I552 <= I543]
R = 
  init(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9) 
  f11(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f14(I9, I4, I5, I10, I11, I12, I13, I14, I15) [I7 + 2 <= I1 /\ I6 + 2 <= I1 /\ 1 <= I2 - 1 /\ 0 <= I1 - 1 /\ 0 <= I3 - 1 /\ -1 <= I4 - 1 /\ 0 <= I5 - 1 /\ 0 <= I0 - 1]
  f9(I16, I17, I18, I19, I20, I21, I22, I23, I24) -> f14(I25, I20, I21, I26, I27, I28, I29, I30, I31) [I24 + 2 <= I18 /\ I23 + 2 <= I17 /\ I22 + 2 <= I17 /\ -1 <= I19 - 1 /\ 1 <= I18 - 1 /\ 0 <= I17 - 1 /\ 0 <= I16 - 1 /\ I20 <= I21 /\ -1 <= I20 - 1]
  f6(I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f14(I41, I33, 1, I42, I43, I44, I45, I46, I47) [0 <= I32 - 1 /\ 0 <= I33 - 1]
  f13(I48, I49, I50, I51, I52, I53, I54, I55, I56) -> f3(I57, I58, I59, I60, I61, I62, I63, I64, I65) [-1 <= I57 - 1 /\ -1 <= I51 - 1 /\ -1 <= I49 - 1 /\ 2 <= I48 - 1 /\ I57 <= I51 /\ I57 <= I49 /\ I57 + 2 <= I48]
  f3(I66, I67, I68, I69, I70, I71, I72, I73, I74) -> f13(I75, I76, I77, I78, I79, I80, I81, I82, I83) [-1 <= I78 - 1 /\ -1 <= I76 - 1 /\ 3 <= I75 - 1 /\ 0 <= I66 - 1 /\ I78 + 1 <= I66 /\ I76 + 1 <= I66 /\ I75 - 3 <= I66]
  f3(I84, I85, I86, I87, I88, I89, I90, I91, I92) -> f13(I93, I94, I95, I96, I97, I98, I99, I100, I101) [-1 <= I96 - 1 /\ -1 <= I94 - 1 /\ 4 <= I93 - 1 /\ 0 <= I84 - 1 /\ I96 + 1 <= I84 /\ I94 + 1 <= I84]
  f3(I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f13(I111, I112, I113, I114, I115, I116, I117, I118, I119) [-1 <= I114 - 1 /\ -1 <= I112 - 1 /\ 4 <= I111 - 1 /\ 0 <= I102 - 1 /\ I114 + 1 <= I102 /\ I112 + 1 <= I102]
  f3(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f13(I129, I130, I131, I132, I133, I134, I135, I136, I137) [-1 <= I132 - 1 /\ -1 <= I130 - 1 /\ 4 <= I129 - 1 /\ 0 <= I120 - 1 /\ I132 + 1 <= I120 /\ I130 + 1 <= I120]
  f3(I138, I139, I140, I141, I142, I143, I144, I145, I146) -> f3(I147, I148, I149, I150, I151, I152, I153, I154, I155) [-1 <= I147 - 1 /\ 1 <= I138 - 1 /\ I147 + 2 <= I138]
  f3(I156, I157, I158, I159, I160, I161, I162, I163, I164) -> f3(I165, I166, I167, I168, I169, I170, I171, I172, I173) [-1 <= I165 - 1 /\ 0 <= I156 - 1 /\ I165 + 1 <= I156]
  f12(I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f7(I183, I184, I174 - 1, I177, I178, I185, I186, I187, I188) [I179 = I180 /\ I179 + 2 <= I176 /\ I179 + 2 <= I175 /\ 3 <= I184 - 1 /\ 3 <= I183 - 1 /\ 1 <= I176 - 1 /\ 1 <= I175 - 1 /\ I184 - 2 <= I176 /\ I184 - 2 <= I175 /\ I183 - 2 <= I176 /\ I183 - 2 <= I175]
  f12(I189, I190, I191, I192, I193, I194, I195, I196, I197) -> f7(I198, I199, I189 - 1, I192, I193, I200, I201, I202, I203) [I195 + 2 <= I191 /\ I194 + 2 <= I190 /\ 0 <= I199 - 1 /\ 0 <= I198 - 1 /\ 1 <= I191 - 1 /\ 0 <= I190 - 1]
  f11(I204, I205, I206, I207, I208, I209, I210, I211, I212) -> f12(I204, I213, I214, I208, I215, I210, I216, I217, I218) [I216 + 2 <= I206 /\ I211 + 2 <= I205 /\ I210 + 2 <= I205 /\ 1 <= I214 - 1 /\ 0 <= I213 - 1 /\ 1 <= I206 - 1 /\ 0 <= I205 - 1 /\ I214 <= I206 /\ I213 <= I205 /\ 0 <= I204 - 1 /\ 0 <= I209 - 1 /\ 0 <= I207 - 1]
  f11(I219, I220, I221, I222, I223, I224, I225, I226, I227) -> f12(I219, I228, I229, I223, I224, I225, I230, I231, I232) [I230 + 2 <= I221 /\ I226 + 2 <= I220 /\ I225 + 2 <= I220 /\ 1 <= I229 - 1 /\ 0 <= I228 - 1 /\ 1 <= I221 - 1 /\ 0 <= I220 - 1 /\ I229 <= I221 /\ I228 <= I220 /\ 0 <= I219 - 1 /\ 0 <= I224 - 1 /\ 0 <= I222 - 1]
  f11(I233, I234, I235, I236, I237, I238, I239, I240, I241) -> f7(I242, I243, I233 - 1, I237, I238, I244, I245, I246, I247) [I240 + 2 <= I234 /\ I239 + 2 <= I234 /\ 0 <= I243 - 1 /\ 0 <= I242 - 1 /\ 2 <= I235 - 1 /\ 0 <= I234 - 1 /\ I243 + 2 <= I235 /\ 0 <= I236 - 1 /\ I242 <= I234]
  f11(I248, I249, I250, I251, I252, I253, I254, I255, I256) -> f9(I248, I257, I258, I259, I252, I253, I254, I255, I260) [0 = I251 /\ I260 + 2 <= I250 /\ I255 + 2 <= I249 /\ I254 + 2 <= I249 /\ -1 <= I259 - 1 /\ 0 <= I258 - 1 /\ 0 <= I257 - 1 /\ 0 <= I250 - 1 /\ 0 <= I249 - 1 /\ I259 + 1 <= I250 /\ I258 <= I250 /\ I257 <= I249]
  f10(I261, I262, I263, I264, I265, I266, I267, I268, I269) -> f7(I270, I271, I261 - 1, I264, I265, I272, I273, I274, I275) [I266 = I267 /\ I266 + 2 <= I263 /\ I266 + 2 <= I262 /\ 3 <= I271 - 1 /\ 3 <= I270 - 1 /\ 1 <= I263 - 1 /\ 1 <= I262 - 1 /\ I271 - 2 <= I263 /\ I271 - 2 <= I262 /\ I270 - 2 <= I263 /\ I270 - 2 <= I262]
  f10(I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f7(I285, I286, I276 - 1, I279, I280, I287, I288, I289, I290) [I282 + 2 <= I278 /\ I281 + 2 <= I277 /\ 0 <= I286 - 1 /\ 0 <= I285 - 1 /\ 1 <= I278 - 1 /\ 0 <= I277 - 1]
  f7(I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f11(I293, I300, I301, I302, I294, I295 + 1, I303, I304, I305) [I304 + 2 <= I291 /\ I303 + 2 <= I291 /\ 0 <= I301 - 1 /\ 0 <= I300 - 1 /\ 0 <= I292 - 1 /\ 0 <= I291 - 1 /\ I301 <= I292 /\ I300 <= I291 /\ -1 <= I302 - 1 /\ -1 <= I295 - 1 /\ I295 <= I294 - 1 /\ -1 <= I294 - 1 /\ 0 <= I293 - 1]
  f7(I306, I307, I308, I309, I310, I311, I312, I313, I314) -> f11(I308, I315, I316, 0, I309, I310 + 1, I317, I318, I319) [I318 + 2 <= I306 /\ I317 + 2 <= I306 /\ 0 <= I316 - 1 /\ 0 <= I315 - 1 /\ 0 <= I307 - 1 /\ 0 <= I306 - 1 /\ I316 <= I307 /\ I315 <= I306 /\ -1 <= I310 - 1 /\ I310 <= I309 - 1 /\ -1 <= I309 - 1 /\ 0 <= I308 - 1]
  f9(I320, I321, I322, I323, I324, I325, I326, I327, I328) -> f10(I320, I329, I330, I324, I331, I327, I328, I332, I333) [I328 + 2 <= I322 /\ I327 + 2 <= I321 /\ I326 + 2 <= I321 /\ 1 <= I330 - 1 /\ 0 <= I329 - 1 /\ -1 <= I323 - 1 /\ 1 <= I322 - 1 /\ 0 <= I321 - 1 /\ I330 <= I322 /\ I329 <= I321 /\ 0 <= I320 - 1 /\ I324 <= I325]
  f9(I334, I335, I336, I337, I338, I339, I340, I341, I342) -> f10(I334, I343, I344, I338, I339, I341, I342, I345, I346) [I342 + 2 <= I336 /\ I341 + 2 <= I335 /\ I340 + 2 <= I335 /\ 1 <= I344 - 1 /\ 0 <= I343 - 1 /\ -1 <= I337 - 1 /\ 1 <= I336 - 1 /\ 0 <= I335 - 1 /\ I344 <= I336 /\ I343 <= I335 /\ 0 <= I334 - 1 /\ I338 <= I339]
  f9(I347, I348, I349, I350, I351, I352, I353, I354, I355) -> f7(I356, I357, I347 - 1, I351, I352, I358, I359, I360, I361) [I355 + 2 <= I349 /\ I354 + 2 <= I348 /\ I353 + 2 <= I348 /\ 0 <= I357 - 1 /\ 0 <= I356 - 1 /\ 0 <= I350 - 1 /\ 2 <= I349 - 1 /\ 0 <= I348 - 1 /\ I357 <= I350 /\ I357 + 2 <= I349 /\ I356 <= I348]
  f7(I362, I363, I364, I365, I366, I367, I368, I369, I370) -> f9(I364, I371, I372, I373, I365, I366, I374, I375, I376) [I376 + 2 <= I363 /\ I375 + 2 <= I362 /\ I374 + 2 <= I362 /\ -1 <= I373 - 1 /\ 0 <= I372 - 1 /\ 0 <= I371 - 1 /\ 0 <= I363 - 1 /\ 0 <= I362 - 1 /\ I373 + 1 <= I363 /\ I372 <= I363 /\ I371 <= I362 /\ 0 <= I364 - 1 /\ -1 <= I365 - 1 /\ I365 <= I366]
  f8(I377, I378, I379, I380, I381, I382, I383, I384, I385) -> f7(I386, I387, I377, I378, I379, I388, I389, I390, I391) [1 <= I386 - 1 /\ 1 <= I387 - 1]
  f6(I392, I393, I394, I395, I396, I397, I398, I399, I400) -> f7(I401, I402, I392, I393, I403, I404, I405, I406, I407) [1 <= I401 - 1 /\ 1 <= I402 - 1 /\ 0 <= I393 - 1 /\ 0 <= I392 - 1]
  f6(I408, I409, I410, I411, I412, I413, I414, I415, I416) -> f7(I417, I418, I408, I409, 1, I419, I420, I421, I422) [1 <= I417 - 1 /\ 1 <= I418 - 1 /\ 0 <= I409 - 1 /\ 0 <= I408 - 1]
  f1(I423, I424, I425, I426, I427, I428, I429, I430, I431) -> f6(I432, I424, I433, I434, I435, I436, I437, I438, I439) [0 <= I423 - 1 /\ 0 <= I424 - 1 /\ -1 <= I432 - 1]
  f1(I440, I441, I442, I443, I444, I445, I446, I447, I448) -> f6(0, I441, I449, I450, I451, I452, I453, I454, I455) [0 <= I441 - 1 /\ 0 <= I440 - 1]
  f4(I456, I457, I458, I459, I460, I461, I462, I463, I464) -> f3(I465, I466, I467, I468, I469, I470, I471, I472, I473) [I458 + 2 <= I457 /\ 0 <= I465 - 1 /\ 0 <= I457 - 1 /\ 0 <= I456 - 1 /\ I465 <= I457]
  f5(I474, I475, I476, I477, I478, I479, I480, I481, I482) -> f4(I483, I484, I476, I485, I486, I487, I488, I489, I490) [I476 + 2 <= I475 /\ 1 <= I484 - 1 /\ 0 <= I483 - 1 /\ 1 <= I475 - 1 /\ 0 <= I474 - 1 /\ I484 <= I475 /\ I483 + 1 <= I475 /\ I483 <= I474]
  f1(I491, I492, I493, I494, I495, I496, I497, I498, I499) -> f4(I500, I501, I502, I503, I504, I505, I506, I507, I508) [0 <= I501 - 1 /\ 0 <= I500 - 1 /\ 0 <= I491 - 1 /\ I500 <= I491]
  f2(I509, I510, I511, I512, I513, I514, I515, I516, I517) -> f3(I518, I519, I520, I521, I522, I523, I524, I525, I526) [-1 <= I518 - 1 /\ 0 <= I509 - 1 /\ I510 <= 1 /\ I518 + 1 <= I509]
  f1(I527, I528, I529, I530, I531, I532, I533, I534, I535) -> f2(I536, 1, I528, I537, I538, I539, I540, I541, I542) [0 <= I536 - 1 /\ 0 <= I527 - 1 /\ I536 <= I527]
  f1(I543, I544, I545, I546, I547, I548, I549, I550, I551) -> f2(I552, 0, 0, I553, I554, I555, I556, I557, I558) [0 = I544 /\ 0 <= I552 - 1 /\ 0 <= I543 - 1 /\ I552 <= I543]

The dependency graph for this problem is:
  0 -> 25, 26, 29, 31, 32
  1 -> 2, 3, 4, 5, 6, 7
  2 -> 1
  3 -> 1
  4 -> 1
  5 -> 1
  6 -> 2, 3, 4, 5, 6, 7
  7 -> 2, 3, 4, 5, 6, 7
  8 -> 16, 17, 21
  9 -> 16, 17, 21
  10 -> 8, 9
  11 -> 8, 9
  12 -> 16, 17, 21
  13 -> 18, 19, 20
  14 -> 16, 17, 21
  15 -> 16, 17, 21
  16 -> 10, 11, 12, 13
  17 -> 13
  18 -> 14, 15
  19 -> 14, 15
  20 -> 16, 17, 21
  21 -> 18, 19, 20
  22 -> 16, 17, 21
  23 -> 16, 17, 21
  24 -> 16, 17, 21
  25 -> 23, 24
  26 -> 
  27 -> 2, 3, 4, 5, 6, 7
  28 -> 27
  29 -> 27
  30 -> 2, 3, 4, 5, 6, 7
  31 -> 30
  32 -> 30
Where:
  0) init#(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9) 
  1) f13#(I48, I49, I50, I51, I52, I53, I54, I55, I56) -> f3#(I57, I58, I59, I60, I61, I62, I63, I64, I65) [-1 <= I57 - 1 /\ -1 <= I51 - 1 /\ -1 <= I49 - 1 /\ 2 <= I48 - 1 /\ I57 <= I51 /\ I57 <= I49 /\ I57 + 2 <= I48]
  2) f3#(I66, I67, I68, I69, I70, I71, I72, I73, I74) -> f13#(I75, I76, I77, I78, I79, I80, I81, I82, I83) [-1 <= I78 - 1 /\ -1 <= I76 - 1 /\ 3 <= I75 - 1 /\ 0 <= I66 - 1 /\ I78 + 1 <= I66 /\ I76 + 1 <= I66 /\ I75 - 3 <= I66]
  3) f3#(I84, I85, I86, I87, I88, I89, I90, I91, I92) -> f13#(I93, I94, I95, I96, I97, I98, I99, I100, I101) [-1 <= I96 - 1 /\ -1 <= I94 - 1 /\ 4 <= I93 - 1 /\ 0 <= I84 - 1 /\ I96 + 1 <= I84 /\ I94 + 1 <= I84]
  4) f3#(I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f13#(I111, I112, I113, I114, I115, I116, I117, I118, I119) [-1 <= I114 - 1 /\ -1 <= I112 - 1 /\ 4 <= I111 - 1 /\ 0 <= I102 - 1 /\ I114 + 1 <= I102 /\ I112 + 1 <= I102]
  5) f3#(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f13#(I129, I130, I131, I132, I133, I134, I135, I136, I137) [-1 <= I132 - 1 /\ -1 <= I130 - 1 /\ 4 <= I129 - 1 /\ 0 <= I120 - 1 /\ I132 + 1 <= I120 /\ I130 + 1 <= I120]
  6) f3#(I138, I139, I140, I141, I142, I143, I144, I145, I146) -> f3#(I147, I148, I149, I150, I151, I152, I153, I154, I155) [-1 <= I147 - 1 /\ 1 <= I138 - 1 /\ I147 + 2 <= I138]
  7) f3#(I156, I157, I158, I159, I160, I161, I162, I163, I164) -> f3#(I165, I166, I167, I168, I169, I170, I171, I172, I173) [-1 <= I165 - 1 /\ 0 <= I156 - 1 /\ I165 + 1 <= I156]
  8) f12#(I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f7#(I183, I184, I174 - 1, I177, I178, I185, I186, I187, I188) [I179 = I180 /\ I179 + 2 <= I176 /\ I179 + 2 <= I175 /\ 3 <= I184 - 1 /\ 3 <= I183 - 1 /\ 1 <= I176 - 1 /\ 1 <= I175 - 1 /\ I184 - 2 <= I176 /\ I184 - 2 <= I175 /\ I183 - 2 <= I176 /\ I183 - 2 <= I175]
  9) f12#(I189, I190, I191, I192, I193, I194, I195, I196, I197) -> f7#(I198, I199, I189 - 1, I192, I193, I200, I201, I202, I203) [I195 + 2 <= I191 /\ I194 + 2 <= I190 /\ 0 <= I199 - 1 /\ 0 <= I198 - 1 /\ 1 <= I191 - 1 /\ 0 <= I190 - 1]
  10) f11#(I204, I205, I206, I207, I208, I209, I210, I211, I212) -> f12#(I204, I213, I214, I208, I215, I210, I216, I217, I218) [I216 + 2 <= I206 /\ I211 + 2 <= I205 /\ I210 + 2 <= I205 /\ 1 <= I214 - 1 /\ 0 <= I213 - 1 /\ 1 <= I206 - 1 /\ 0 <= I205 - 1 /\ I214 <= I206 /\ I213 <= I205 /\ 0 <= I204 - 1 /\ 0 <= I209 - 1 /\ 0 <= I207 - 1]
  11) f11#(I219, I220, I221, I222, I223, I224, I225, I226, I227) -> f12#(I219, I228, I229, I223, I224, I225, I230, I231, I232) [I230 + 2 <= I221 /\ I226 + 2 <= I220 /\ I225 + 2 <= I220 /\ 1 <= I229 - 1 /\ 0 <= I228 - 1 /\ 1 <= I221 - 1 /\ 0 <= I220 - 1 /\ I229 <= I221 /\ I228 <= I220 /\ 0 <= I219 - 1 /\ 0 <= I224 - 1 /\ 0 <= I222 - 1]
  12) f11#(I233, I234, I235, I236, I237, I238, I239, I240, I241) -> f7#(I242, I243, I233 - 1, I237, I238, I244, I245, I246, I247) [I240 + 2 <= I234 /\ I239 + 2 <= I234 /\ 0 <= I243 - 1 /\ 0 <= I242 - 1 /\ 2 <= I235 - 1 /\ 0 <= I234 - 1 /\ I243 + 2 <= I235 /\ 0 <= I236 - 1 /\ I242 <= I234]
  13) f11#(I248, I249, I250, I251, I252, I253, I254, I255, I256) -> f9#(I248, I257, I258, I259, I252, I253, I254, I255, I260) [0 = I251 /\ I260 + 2 <= I250 /\ I255 + 2 <= I249 /\ I254 + 2 <= I249 /\ -1 <= I259 - 1 /\ 0 <= I258 - 1 /\ 0 <= I257 - 1 /\ 0 <= I250 - 1 /\ 0 <= I249 - 1 /\ I259 + 1 <= I250 /\ I258 <= I250 /\ I257 <= I249]
  14) f10#(I261, I262, I263, I264, I265, I266, I267, I268, I269) -> f7#(I270, I271, I261 - 1, I264, I265, I272, I273, I274, I275) [I266 = I267 /\ I266 + 2 <= I263 /\ I266 + 2 <= I262 /\ 3 <= I271 - 1 /\ 3 <= I270 - 1 /\ 1 <= I263 - 1 /\ 1 <= I262 - 1 /\ I271 - 2 <= I263 /\ I271 - 2 <= I262 /\ I270 - 2 <= I263 /\ I270 - 2 <= I262]
  15) f10#(I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f7#(I285, I286, I276 - 1, I279, I280, I287, I288, I289, I290) [I282 + 2 <= I278 /\ I281 + 2 <= I277 /\ 0 <= I286 - 1 /\ 0 <= I285 - 1 /\ 1 <= I278 - 1 /\ 0 <= I277 - 1]
  16) f7#(I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f11#(I293, I300, I301, I302, I294, I295 + 1, I303, I304, I305) [I304 + 2 <= I291 /\ I303 + 2 <= I291 /\ 0 <= I301 - 1 /\ 0 <= I300 - 1 /\ 0 <= I292 - 1 /\ 0 <= I291 - 1 /\ I301 <= I292 /\ I300 <= I291 /\ -1 <= I302 - 1 /\ -1 <= I295 - 1 /\ I295 <= I294 - 1 /\ -1 <= I294 - 1 /\ 0 <= I293 - 1]
  17) f7#(I306, I307, I308, I309, I310, I311, I312, I313, I314) -> f11#(I308, I315, I316, 0, I309, I310 + 1, I317, I318, I319) [I318 + 2 <= I306 /\ I317 + 2 <= I306 /\ 0 <= I316 - 1 /\ 0 <= I315 - 1 /\ 0 <= I307 - 1 /\ 0 <= I306 - 1 /\ I316 <= I307 /\ I315 <= I306 /\ -1 <= I310 - 1 /\ I310 <= I309 - 1 /\ -1 <= I309 - 1 /\ 0 <= I308 - 1]
  18) f9#(I320, I321, I322, I323, I324, I325, I326, I327, I328) -> f10#(I320, I329, I330, I324, I331, I327, I328, I332, I333) [I328 + 2 <= I322 /\ I327 + 2 <= I321 /\ I326 + 2 <= I321 /\ 1 <= I330 - 1 /\ 0 <= I329 - 1 /\ -1 <= I323 - 1 /\ 1 <= I322 - 1 /\ 0 <= I321 - 1 /\ I330 <= I322 /\ I329 <= I321 /\ 0 <= I320 - 1 /\ I324 <= I325]
  19) f9#(I334, I335, I336, I337, I338, I339, I340, I341, I342) -> f10#(I334, I343, I344, I338, I339, I341, I342, I345, I346) [I342 + 2 <= I336 /\ I341 + 2 <= I335 /\ I340 + 2 <= I335 /\ 1 <= I344 - 1 /\ 0 <= I343 - 1 /\ -1 <= I337 - 1 /\ 1 <= I336 - 1 /\ 0 <= I335 - 1 /\ I344 <= I336 /\ I343 <= I335 /\ 0 <= I334 - 1 /\ I338 <= I339]
  20) f9#(I347, I348, I349, I350, I351, I352, I353, I354, I355) -> f7#(I356, I357, I347 - 1, I351, I352, I358, I359, I360, I361) [I355 + 2 <= I349 /\ I354 + 2 <= I348 /\ I353 + 2 <= I348 /\ 0 <= I357 - 1 /\ 0 <= I356 - 1 /\ 0 <= I350 - 1 /\ 2 <= I349 - 1 /\ 0 <= I348 - 1 /\ I357 <= I350 /\ I357 + 2 <= I349 /\ I356 <= I348]
  21) f7#(I362, I363, I364, I365, I366, I367, I368, I369, I370) -> f9#(I364, I371, I372, I373, I365, I366, I374, I375, I376) [I376 + 2 <= I363 /\ I375 + 2 <= I362 /\ I374 + 2 <= I362 /\ -1 <= I373 - 1 /\ 0 <= I372 - 1 /\ 0 <= I371 - 1 /\ 0 <= I363 - 1 /\ 0 <= I362 - 1 /\ I373 + 1 <= I363 /\ I372 <= I363 /\ I371 <= I362 /\ 0 <= I364 - 1 /\ -1 <= I365 - 1 /\ I365 <= I366]
  22) f8#(I377, I378, I379, I380, I381, I382, I383, I384, I385) -> f7#(I386, I387, I377, I378, I379, I388, I389, I390, I391) [1 <= I386 - 1 /\ 1 <= I387 - 1]
  23) f6#(I392, I393, I394, I395, I396, I397, I398, I399, I400) -> f7#(I401, I402, I392, I393, I403, I404, I405, I406, I407) [1 <= I401 - 1 /\ 1 <= I402 - 1 /\ 0 <= I393 - 1 /\ 0 <= I392 - 1]
  24) f6#(I408, I409, I410, I411, I412, I413, I414, I415, I416) -> f7#(I417, I418, I408, I409, 1, I419, I420, I421, I422) [1 <= I417 - 1 /\ 1 <= I418 - 1 /\ 0 <= I409 - 1 /\ 0 <= I408 - 1]
  25) f1#(I423, I424, I425, I426, I427, I428, I429, I430, I431) -> f6#(I432, I424, I433, I434, I435, I436, I437, I438, I439) [0 <= I423 - 1 /\ 0 <= I424 - 1 /\ -1 <= I432 - 1]
  26) f1#(I440, I441, I442, I443, I444, I445, I446, I447, I448) -> f6#(0, I441, I449, I450, I451, I452, I453, I454, I455) [0 <= I441 - 1 /\ 0 <= I440 - 1]
  27) f4#(I456, I457, I458, I459, I460, I461, I462, I463, I464) -> f3#(I465, I466, I467, I468, I469, I470, I471, I472, I473) [I458 + 2 <= I457 /\ 0 <= I465 - 1 /\ 0 <= I457 - 1 /\ 0 <= I456 - 1 /\ I465 <= I457]
  28) f5#(I474, I475, I476, I477, I478, I479, I480, I481, I482) -> f4#(I483, I484, I476, I485, I486, I487, I488, I489, I490) [I476 + 2 <= I475 /\ 1 <= I484 - 1 /\ 0 <= I483 - 1 /\ 1 <= I475 - 1 /\ 0 <= I474 - 1 /\ I484 <= I475 /\ I483 + 1 <= I475 /\ I483 <= I474]
  29) f1#(I491, I492, I493, I494, I495, I496, I497, I498, I499) -> f4#(I500, I501, I502, I503, I504, I505, I506, I507, I508) [0 <= I501 - 1 /\ 0 <= I500 - 1 /\ 0 <= I491 - 1 /\ I500 <= I491]
  30) f2#(I509, I510, I511, I512, I513, I514, I515, I516, I517) -> f3#(I518, I519, I520, I521, I522, I523, I524, I525, I526) [-1 <= I518 - 1 /\ 0 <= I509 - 1 /\ I510 <= 1 /\ I518 + 1 <= I509]
  31) f1#(I527, I528, I529, I530, I531, I532, I533, I534, I535) -> f2#(I536, 1, I528, I537, I538, I539, I540, I541, I542) [0 <= I536 - 1 /\ 0 <= I527 - 1 /\ I536 <= I527]
  32) f1#(I543, I544, I545, I546, I547, I548, I549, I550, I551) -> f2#(I552, 0, 0, I553, I554, I555, I556, I557, I558) [0 = I544 /\ 0 <= I552 - 1 /\ 0 <= I543 - 1 /\ I552 <= I543]

We have the following SCCs.
  { 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21 }
  { 1, 2, 3, 4, 5, 6, 7 }

DP problem for innermost termination.
P =
  f13#(I48, I49, I50, I51, I52, I53, I54, I55, I56) -> f3#(I57, I58, I59, I60, I61, I62, I63, I64, I65) [-1 <= I57 - 1 /\ -1 <= I51 - 1 /\ -1 <= I49 - 1 /\ 2 <= I48 - 1 /\ I57 <= I51 /\ I57 <= I49 /\ I57 + 2 <= I48]
  f3#(I66, I67, I68, I69, I70, I71, I72, I73, I74) -> f13#(I75, I76, I77, I78, I79, I80, I81, I82, I83) [-1 <= I78 - 1 /\ -1 <= I76 - 1 /\ 3 <= I75 - 1 /\ 0 <= I66 - 1 /\ I78 + 1 <= I66 /\ I76 + 1 <= I66 /\ I75 - 3 <= I66]
  f3#(I84, I85, I86, I87, I88, I89, I90, I91, I92) -> f13#(I93, I94, I95, I96, I97, I98, I99, I100, I101) [-1 <= I96 - 1 /\ -1 <= I94 - 1 /\ 4 <= I93 - 1 /\ 0 <= I84 - 1 /\ I96 + 1 <= I84 /\ I94 + 1 <= I84]
  f3#(I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f13#(I111, I112, I113, I114, I115, I116, I117, I118, I119) [-1 <= I114 - 1 /\ -1 <= I112 - 1 /\ 4 <= I111 - 1 /\ 0 <= I102 - 1 /\ I114 + 1 <= I102 /\ I112 + 1 <= I102]
  f3#(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f13#(I129, I130, I131, I132, I133, I134, I135, I136, I137) [-1 <= I132 - 1 /\ -1 <= I130 - 1 /\ 4 <= I129 - 1 /\ 0 <= I120 - 1 /\ I132 + 1 <= I120 /\ I130 + 1 <= I120]
  f3#(I138, I139, I140, I141, I142, I143, I144, I145, I146) -> f3#(I147, I148, I149, I150, I151, I152, I153, I154, I155) [-1 <= I147 - 1 /\ 1 <= I138 - 1 /\ I147 + 2 <= I138]
  f3#(I156, I157, I158, I159, I160, I161, I162, I163, I164) -> f3#(I165, I166, I167, I168, I169, I170, I171, I172, I173) [-1 <= I165 - 1 /\ 0 <= I156 - 1 /\ I165 + 1 <= I156]
R = 
  init(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9) 
  f11(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f14(I9, I4, I5, I10, I11, I12, I13, I14, I15) [I7 + 2 <= I1 /\ I6 + 2 <= I1 /\ 1 <= I2 - 1 /\ 0 <= I1 - 1 /\ 0 <= I3 - 1 /\ -1 <= I4 - 1 /\ 0 <= I5 - 1 /\ 0 <= I0 - 1]
  f9(I16, I17, I18, I19, I20, I21, I22, I23, I24) -> f14(I25, I20, I21, I26, I27, I28, I29, I30, I31) [I24 + 2 <= I18 /\ I23 + 2 <= I17 /\ I22 + 2 <= I17 /\ -1 <= I19 - 1 /\ 1 <= I18 - 1 /\ 0 <= I17 - 1 /\ 0 <= I16 - 1 /\ I20 <= I21 /\ -1 <= I20 - 1]
  f6(I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f14(I41, I33, 1, I42, I43, I44, I45, I46, I47) [0 <= I32 - 1 /\ 0 <= I33 - 1]
  f13(I48, I49, I50, I51, I52, I53, I54, I55, I56) -> f3(I57, I58, I59, I60, I61, I62, I63, I64, I65) [-1 <= I57 - 1 /\ -1 <= I51 - 1 /\ -1 <= I49 - 1 /\ 2 <= I48 - 1 /\ I57 <= I51 /\ I57 <= I49 /\ I57 + 2 <= I48]
  f3(I66, I67, I68, I69, I70, I71, I72, I73, I74) -> f13(I75, I76, I77, I78, I79, I80, I81, I82, I83) [-1 <= I78 - 1 /\ -1 <= I76 - 1 /\ 3 <= I75 - 1 /\ 0 <= I66 - 1 /\ I78 + 1 <= I66 /\ I76 + 1 <= I66 /\ I75 - 3 <= I66]
  f3(I84, I85, I86, I87, I88, I89, I90, I91, I92) -> f13(I93, I94, I95, I96, I97, I98, I99, I100, I101) [-1 <= I96 - 1 /\ -1 <= I94 - 1 /\ 4 <= I93 - 1 /\ 0 <= I84 - 1 /\ I96 + 1 <= I84 /\ I94 + 1 <= I84]
  f3(I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f13(I111, I112, I113, I114, I115, I116, I117, I118, I119) [-1 <= I114 - 1 /\ -1 <= I112 - 1 /\ 4 <= I111 - 1 /\ 0 <= I102 - 1 /\ I114 + 1 <= I102 /\ I112 + 1 <= I102]
  f3(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f13(I129, I130, I131, I132, I133, I134, I135, I136, I137) [-1 <= I132 - 1 /\ -1 <= I130 - 1 /\ 4 <= I129 - 1 /\ 0 <= I120 - 1 /\ I132 + 1 <= I120 /\ I130 + 1 <= I120]
  f3(I138, I139, I140, I141, I142, I143, I144, I145, I146) -> f3(I147, I148, I149, I150, I151, I152, I153, I154, I155) [-1 <= I147 - 1 /\ 1 <= I138 - 1 /\ I147 + 2 <= I138]
  f3(I156, I157, I158, I159, I160, I161, I162, I163, I164) -> f3(I165, I166, I167, I168, I169, I170, I171, I172, I173) [-1 <= I165 - 1 /\ 0 <= I156 - 1 /\ I165 + 1 <= I156]
  f12(I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f7(I183, I184, I174 - 1, I177, I178, I185, I186, I187, I188) [I179 = I180 /\ I179 + 2 <= I176 /\ I179 + 2 <= I175 /\ 3 <= I184 - 1 /\ 3 <= I183 - 1 /\ 1 <= I176 - 1 /\ 1 <= I175 - 1 /\ I184 - 2 <= I176 /\ I184 - 2 <= I175 /\ I183 - 2 <= I176 /\ I183 - 2 <= I175]
  f12(I189, I190, I191, I192, I193, I194, I195, I196, I197) -> f7(I198, I199, I189 - 1, I192, I193, I200, I201, I202, I203) [I195 + 2 <= I191 /\ I194 + 2 <= I190 /\ 0 <= I199 - 1 /\ 0 <= I198 - 1 /\ 1 <= I191 - 1 /\ 0 <= I190 - 1]
  f11(I204, I205, I206, I207, I208, I209, I210, I211, I212) -> f12(I204, I213, I214, I208, I215, I210, I216, I217, I218) [I216 + 2 <= I206 /\ I211 + 2 <= I205 /\ I210 + 2 <= I205 /\ 1 <= I214 - 1 /\ 0 <= I213 - 1 /\ 1 <= I206 - 1 /\ 0 <= I205 - 1 /\ I214 <= I206 /\ I213 <= I205 /\ 0 <= I204 - 1 /\ 0 <= I209 - 1 /\ 0 <= I207 - 1]
  f11(I219, I220, I221, I222, I223, I224, I225, I226, I227) -> f12(I219, I228, I229, I223, I224, I225, I230, I231, I232) [I230 + 2 <= I221 /\ I226 + 2 <= I220 /\ I225 + 2 <= I220 /\ 1 <= I229 - 1 /\ 0 <= I228 - 1 /\ 1 <= I221 - 1 /\ 0 <= I220 - 1 /\ I229 <= I221 /\ I228 <= I220 /\ 0 <= I219 - 1 /\ 0 <= I224 - 1 /\ 0 <= I222 - 1]
  f11(I233, I234, I235, I236, I237, I238, I239, I240, I241) -> f7(I242, I243, I233 - 1, I237, I238, I244, I245, I246, I247) [I240 + 2 <= I234 /\ I239 + 2 <= I234 /\ 0 <= I243 - 1 /\ 0 <= I242 - 1 /\ 2 <= I235 - 1 /\ 0 <= I234 - 1 /\ I243 + 2 <= I235 /\ 0 <= I236 - 1 /\ I242 <= I234]
  f11(I248, I249, I250, I251, I252, I253, I254, I255, I256) -> f9(I248, I257, I258, I259, I252, I253, I254, I255, I260) [0 = I251 /\ I260 + 2 <= I250 /\ I255 + 2 <= I249 /\ I254 + 2 <= I249 /\ -1 <= I259 - 1 /\ 0 <= I258 - 1 /\ 0 <= I257 - 1 /\ 0 <= I250 - 1 /\ 0 <= I249 - 1 /\ I259 + 1 <= I250 /\ I258 <= I250 /\ I257 <= I249]
  f10(I261, I262, I263, I264, I265, I266, I267, I268, I269) -> f7(I270, I271, I261 - 1, I264, I265, I272, I273, I274, I275) [I266 = I267 /\ I266 + 2 <= I263 /\ I266 + 2 <= I262 /\ 3 <= I271 - 1 /\ 3 <= I270 - 1 /\ 1 <= I263 - 1 /\ 1 <= I262 - 1 /\ I271 - 2 <= I263 /\ I271 - 2 <= I262 /\ I270 - 2 <= I263 /\ I270 - 2 <= I262]
  f10(I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f7(I285, I286, I276 - 1, I279, I280, I287, I288, I289, I290) [I282 + 2 <= I278 /\ I281 + 2 <= I277 /\ 0 <= I286 - 1 /\ 0 <= I285 - 1 /\ 1 <= I278 - 1 /\ 0 <= I277 - 1]
  f7(I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f11(I293, I300, I301, I302, I294, I295 + 1, I303, I304, I305) [I304 + 2 <= I291 /\ I303 + 2 <= I291 /\ 0 <= I301 - 1 /\ 0 <= I300 - 1 /\ 0 <= I292 - 1 /\ 0 <= I291 - 1 /\ I301 <= I292 /\ I300 <= I291 /\ -1 <= I302 - 1 /\ -1 <= I295 - 1 /\ I295 <= I294 - 1 /\ -1 <= I294 - 1 /\ 0 <= I293 - 1]
  f7(I306, I307, I308, I309, I310, I311, I312, I313, I314) -> f11(I308, I315, I316, 0, I309, I310 + 1, I317, I318, I319) [I318 + 2 <= I306 /\ I317 + 2 <= I306 /\ 0 <= I316 - 1 /\ 0 <= I315 - 1 /\ 0 <= I307 - 1 /\ 0 <= I306 - 1 /\ I316 <= I307 /\ I315 <= I306 /\ -1 <= I310 - 1 /\ I310 <= I309 - 1 /\ -1 <= I309 - 1 /\ 0 <= I308 - 1]
  f9(I320, I321, I322, I323, I324, I325, I326, I327, I328) -> f10(I320, I329, I330, I324, I331, I327, I328, I332, I333) [I328 + 2 <= I322 /\ I327 + 2 <= I321 /\ I326 + 2 <= I321 /\ 1 <= I330 - 1 /\ 0 <= I329 - 1 /\ -1 <= I323 - 1 /\ 1 <= I322 - 1 /\ 0 <= I321 - 1 /\ I330 <= I322 /\ I329 <= I321 /\ 0 <= I320 - 1 /\ I324 <= I325]
  f9(I334, I335, I336, I337, I338, I339, I340, I341, I342) -> f10(I334, I343, I344, I338, I339, I341, I342, I345, I346) [I342 + 2 <= I336 /\ I341 + 2 <= I335 /\ I340 + 2 <= I335 /\ 1 <= I344 - 1 /\ 0 <= I343 - 1 /\ -1 <= I337 - 1 /\ 1 <= I336 - 1 /\ 0 <= I335 - 1 /\ I344 <= I336 /\ I343 <= I335 /\ 0 <= I334 - 1 /\ I338 <= I339]
  f9(I347, I348, I349, I350, I351, I352, I353, I354, I355) -> f7(I356, I357, I347 - 1, I351, I352, I358, I359, I360, I361) [I355 + 2 <= I349 /\ I354 + 2 <= I348 /\ I353 + 2 <= I348 /\ 0 <= I357 - 1 /\ 0 <= I356 - 1 /\ 0 <= I350 - 1 /\ 2 <= I349 - 1 /\ 0 <= I348 - 1 /\ I357 <= I350 /\ I357 + 2 <= I349 /\ I356 <= I348]
  f7(I362, I363, I364, I365, I366, I367, I368, I369, I370) -> f9(I364, I371, I372, I373, I365, I366, I374, I375, I376) [I376 + 2 <= I363 /\ I375 + 2 <= I362 /\ I374 + 2 <= I362 /\ -1 <= I373 - 1 /\ 0 <= I372 - 1 /\ 0 <= I371 - 1 /\ 0 <= I363 - 1 /\ 0 <= I362 - 1 /\ I373 + 1 <= I363 /\ I372 <= I363 /\ I371 <= I362 /\ 0 <= I364 - 1 /\ -1 <= I365 - 1 /\ I365 <= I366]
  f8(I377, I378, I379, I380, I381, I382, I383, I384, I385) -> f7(I386, I387, I377, I378, I379, I388, I389, I390, I391) [1 <= I386 - 1 /\ 1 <= I387 - 1]
  f6(I392, I393, I394, I395, I396, I397, I398, I399, I400) -> f7(I401, I402, I392, I393, I403, I404, I405, I406, I407) [1 <= I401 - 1 /\ 1 <= I402 - 1 /\ 0 <= I393 - 1 /\ 0 <= I392 - 1]
  f6(I408, I409, I410, I411, I412, I413, I414, I415, I416) -> f7(I417, I418, I408, I409, 1, I419, I420, I421, I422) [1 <= I417 - 1 /\ 1 <= I418 - 1 /\ 0 <= I409 - 1 /\ 0 <= I408 - 1]
  f1(I423, I424, I425, I426, I427, I428, I429, I430, I431) -> f6(I432, I424, I433, I434, I435, I436, I437, I438, I439) [0 <= I423 - 1 /\ 0 <= I424 - 1 /\ -1 <= I432 - 1]
  f1(I440, I441, I442, I443, I444, I445, I446, I447, I448) -> f6(0, I441, I449, I450, I451, I452, I453, I454, I455) [0 <= I441 - 1 /\ 0 <= I440 - 1]
  f4(I456, I457, I458, I459, I460, I461, I462, I463, I464) -> f3(I465, I466, I467, I468, I469, I470, I471, I472, I473) [I458 + 2 <= I457 /\ 0 <= I465 - 1 /\ 0 <= I457 - 1 /\ 0 <= I456 - 1 /\ I465 <= I457]
  f5(I474, I475, I476, I477, I478, I479, I480, I481, I482) -> f4(I483, I484, I476, I485, I486, I487, I488, I489, I490) [I476 + 2 <= I475 /\ 1 <= I484 - 1 /\ 0 <= I483 - 1 /\ 1 <= I475 - 1 /\ 0 <= I474 - 1 /\ I484 <= I475 /\ I483 + 1 <= I475 /\ I483 <= I474]
  f1(I491, I492, I493, I494, I495, I496, I497, I498, I499) -> f4(I500, I501, I502, I503, I504, I505, I506, I507, I508) [0 <= I501 - 1 /\ 0 <= I500 - 1 /\ 0 <= I491 - 1 /\ I500 <= I491]
  f2(I509, I510, I511, I512, I513, I514, I515, I516, I517) -> f3(I518, I519, I520, I521, I522, I523, I524, I525, I526) [-1 <= I518 - 1 /\ 0 <= I509 - 1 /\ I510 <= 1 /\ I518 + 1 <= I509]
  f1(I527, I528, I529, I530, I531, I532, I533, I534, I535) -> f2(I536, 1, I528, I537, I538, I539, I540, I541, I542) [0 <= I536 - 1 /\ 0 <= I527 - 1 /\ I536 <= I527]
  f1(I543, I544, I545, I546, I547, I548, I549, I550, I551) -> f2(I552, 0, 0, I553, I554, I555, I556, I557, I558) [0 = I544 /\ 0 <= I552 - 1 /\ 0 <= I543 - 1 /\ I552 <= I543]

We use the basic value criterion with the projection function NU:
  NU[f3#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = z1
  NU[f13#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = z4

This gives the following inequalities:
  -1 <= I57 - 1 /\ -1 <= I51 - 1 /\ -1 <= I49 - 1 /\ 2 <= I48 - 1 /\ I57 <= I51 /\ I57 <= I49 /\ I57 + 2 <= I48  ==>  I51 (>! \union =) I57
  -1 <= I78 - 1 /\ -1 <= I76 - 1 /\ 3 <= I75 - 1 /\ 0 <= I66 - 1 /\ I78 + 1 <= I66 /\ I76 + 1 <= I66 /\ I75 - 3 <= I66  ==>  I66 >! I78
  -1 <= I96 - 1 /\ -1 <= I94 - 1 /\ 4 <= I93 - 1 /\ 0 <= I84 - 1 /\ I96 + 1 <= I84 /\ I94 + 1 <= I84  ==>  I84 >! I96
  -1 <= I114 - 1 /\ -1 <= I112 - 1 /\ 4 <= I111 - 1 /\ 0 <= I102 - 1 /\ I114 + 1 <= I102 /\ I112 + 1 <= I102  ==>  I102 >! I114
  -1 <= I132 - 1 /\ -1 <= I130 - 1 /\ 4 <= I129 - 1 /\ 0 <= I120 - 1 /\ I132 + 1 <= I120 /\ I130 + 1 <= I120  ==>  I120 >! I132
  -1 <= I147 - 1 /\ 1 <= I138 - 1 /\ I147 + 2 <= I138  ==>  I138 >! I147
  -1 <= I165 - 1 /\ 0 <= I156 - 1 /\ I165 + 1 <= I156  ==>  I156 >! I165

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f13#(I48, I49, I50, I51, I52, I53, I54, I55, I56) -> f3#(I57, I58, I59, I60, I61, I62, I63, I64, I65) [-1 <= I57 - 1 /\ -1 <= I51 - 1 /\ -1 <= I49 - 1 /\ 2 <= I48 - 1 /\ I57 <= I51 /\ I57 <= I49 /\ I57 + 2 <= I48]
R = 
  init(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9) 
  f11(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f14(I9, I4, I5, I10, I11, I12, I13, I14, I15) [I7 + 2 <= I1 /\ I6 + 2 <= I1 /\ 1 <= I2 - 1 /\ 0 <= I1 - 1 /\ 0 <= I3 - 1 /\ -1 <= I4 - 1 /\ 0 <= I5 - 1 /\ 0 <= I0 - 1]
  f9(I16, I17, I18, I19, I20, I21, I22, I23, I24) -> f14(I25, I20, I21, I26, I27, I28, I29, I30, I31) [I24 + 2 <= I18 /\ I23 + 2 <= I17 /\ I22 + 2 <= I17 /\ -1 <= I19 - 1 /\ 1 <= I18 - 1 /\ 0 <= I17 - 1 /\ 0 <= I16 - 1 /\ I20 <= I21 /\ -1 <= I20 - 1]
  f6(I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f14(I41, I33, 1, I42, I43, I44, I45, I46, I47) [0 <= I32 - 1 /\ 0 <= I33 - 1]
  f13(I48, I49, I50, I51, I52, I53, I54, I55, I56) -> f3(I57, I58, I59, I60, I61, I62, I63, I64, I65) [-1 <= I57 - 1 /\ -1 <= I51 - 1 /\ -1 <= I49 - 1 /\ 2 <= I48 - 1 /\ I57 <= I51 /\ I57 <= I49 /\ I57 + 2 <= I48]
  f3(I66, I67, I68, I69, I70, I71, I72, I73, I74) -> f13(I75, I76, I77, I78, I79, I80, I81, I82, I83) [-1 <= I78 - 1 /\ -1 <= I76 - 1 /\ 3 <= I75 - 1 /\ 0 <= I66 - 1 /\ I78 + 1 <= I66 /\ I76 + 1 <= I66 /\ I75 - 3 <= I66]
  f3(I84, I85, I86, I87, I88, I89, I90, I91, I92) -> f13(I93, I94, I95, I96, I97, I98, I99, I100, I101) [-1 <= I96 - 1 /\ -1 <= I94 - 1 /\ 4 <= I93 - 1 /\ 0 <= I84 - 1 /\ I96 + 1 <= I84 /\ I94 + 1 <= I84]
  f3(I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f13(I111, I112, I113, I114, I115, I116, I117, I118, I119) [-1 <= I114 - 1 /\ -1 <= I112 - 1 /\ 4 <= I111 - 1 /\ 0 <= I102 - 1 /\ I114 + 1 <= I102 /\ I112 + 1 <= I102]
  f3(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f13(I129, I130, I131, I132, I133, I134, I135, I136, I137) [-1 <= I132 - 1 /\ -1 <= I130 - 1 /\ 4 <= I129 - 1 /\ 0 <= I120 - 1 /\ I132 + 1 <= I120 /\ I130 + 1 <= I120]
  f3(I138, I139, I140, I141, I142, I143, I144, I145, I146) -> f3(I147, I148, I149, I150, I151, I152, I153, I154, I155) [-1 <= I147 - 1 /\ 1 <= I138 - 1 /\ I147 + 2 <= I138]
  f3(I156, I157, I158, I159, I160, I161, I162, I163, I164) -> f3(I165, I166, I167, I168, I169, I170, I171, I172, I173) [-1 <= I165 - 1 /\ 0 <= I156 - 1 /\ I165 + 1 <= I156]
  f12(I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f7(I183, I184, I174 - 1, I177, I178, I185, I186, I187, I188) [I179 = I180 /\ I179 + 2 <= I176 /\ I179 + 2 <= I175 /\ 3 <= I184 - 1 /\ 3 <= I183 - 1 /\ 1 <= I176 - 1 /\ 1 <= I175 - 1 /\ I184 - 2 <= I176 /\ I184 - 2 <= I175 /\ I183 - 2 <= I176 /\ I183 - 2 <= I175]
  f12(I189, I190, I191, I192, I193, I194, I195, I196, I197) -> f7(I198, I199, I189 - 1, I192, I193, I200, I201, I202, I203) [I195 + 2 <= I191 /\ I194 + 2 <= I190 /\ 0 <= I199 - 1 /\ 0 <= I198 - 1 /\ 1 <= I191 - 1 /\ 0 <= I190 - 1]
  f11(I204, I205, I206, I207, I208, I209, I210, I211, I212) -> f12(I204, I213, I214, I208, I215, I210, I216, I217, I218) [I216 + 2 <= I206 /\ I211 + 2 <= I205 /\ I210 + 2 <= I205 /\ 1 <= I214 - 1 /\ 0 <= I213 - 1 /\ 1 <= I206 - 1 /\ 0 <= I205 - 1 /\ I214 <= I206 /\ I213 <= I205 /\ 0 <= I204 - 1 /\ 0 <= I209 - 1 /\ 0 <= I207 - 1]
  f11(I219, I220, I221, I222, I223, I224, I225, I226, I227) -> f12(I219, I228, I229, I223, I224, I225, I230, I231, I232) [I230 + 2 <= I221 /\ I226 + 2 <= I220 /\ I225 + 2 <= I220 /\ 1 <= I229 - 1 /\ 0 <= I228 - 1 /\ 1 <= I221 - 1 /\ 0 <= I220 - 1 /\ I229 <= I221 /\ I228 <= I220 /\ 0 <= I219 - 1 /\ 0 <= I224 - 1 /\ 0 <= I222 - 1]
  f11(I233, I234, I235, I236, I237, I238, I239, I240, I241) -> f7(I242, I243, I233 - 1, I237, I238, I244, I245, I246, I247) [I240 + 2 <= I234 /\ I239 + 2 <= I234 /\ 0 <= I243 - 1 /\ 0 <= I242 - 1 /\ 2 <= I235 - 1 /\ 0 <= I234 - 1 /\ I243 + 2 <= I235 /\ 0 <= I236 - 1 /\ I242 <= I234]
  f11(I248, I249, I250, I251, I252, I253, I254, I255, I256) -> f9(I248, I257, I258, I259, I252, I253, I254, I255, I260) [0 = I251 /\ I260 + 2 <= I250 /\ I255 + 2 <= I249 /\ I254 + 2 <= I249 /\ -1 <= I259 - 1 /\ 0 <= I258 - 1 /\ 0 <= I257 - 1 /\ 0 <= I250 - 1 /\ 0 <= I249 - 1 /\ I259 + 1 <= I250 /\ I258 <= I250 /\ I257 <= I249]
  f10(I261, I262, I263, I264, I265, I266, I267, I268, I269) -> f7(I270, I271, I261 - 1, I264, I265, I272, I273, I274, I275) [I266 = I267 /\ I266 + 2 <= I263 /\ I266 + 2 <= I262 /\ 3 <= I271 - 1 /\ 3 <= I270 - 1 /\ 1 <= I263 - 1 /\ 1 <= I262 - 1 /\ I271 - 2 <= I263 /\ I271 - 2 <= I262 /\ I270 - 2 <= I263 /\ I270 - 2 <= I262]
  f10(I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f7(I285, I286, I276 - 1, I279, I280, I287, I288, I289, I290) [I282 + 2 <= I278 /\ I281 + 2 <= I277 /\ 0 <= I286 - 1 /\ 0 <= I285 - 1 /\ 1 <= I278 - 1 /\ 0 <= I277 - 1]
  f7(I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f11(I293, I300, I301, I302, I294, I295 + 1, I303, I304, I305) [I304 + 2 <= I291 /\ I303 + 2 <= I291 /\ 0 <= I301 - 1 /\ 0 <= I300 - 1 /\ 0 <= I292 - 1 /\ 0 <= I291 - 1 /\ I301 <= I292 /\ I300 <= I291 /\ -1 <= I302 - 1 /\ -1 <= I295 - 1 /\ I295 <= I294 - 1 /\ -1 <= I294 - 1 /\ 0 <= I293 - 1]
  f7(I306, I307, I308, I309, I310, I311, I312, I313, I314) -> f11(I308, I315, I316, 0, I309, I310 + 1, I317, I318, I319) [I318 + 2 <= I306 /\ I317 + 2 <= I306 /\ 0 <= I316 - 1 /\ 0 <= I315 - 1 /\ 0 <= I307 - 1 /\ 0 <= I306 - 1 /\ I316 <= I307 /\ I315 <= I306 /\ -1 <= I310 - 1 /\ I310 <= I309 - 1 /\ -1 <= I309 - 1 /\ 0 <= I308 - 1]
  f9(I320, I321, I322, I323, I324, I325, I326, I327, I328) -> f10(I320, I329, I330, I324, I331, I327, I328, I332, I333) [I328 + 2 <= I322 /\ I327 + 2 <= I321 /\ I326 + 2 <= I321 /\ 1 <= I330 - 1 /\ 0 <= I329 - 1 /\ -1 <= I323 - 1 /\ 1 <= I322 - 1 /\ 0 <= I321 - 1 /\ I330 <= I322 /\ I329 <= I321 /\ 0 <= I320 - 1 /\ I324 <= I325]
  f9(I334, I335, I336, I337, I338, I339, I340, I341, I342) -> f10(I334, I343, I344, I338, I339, I341, I342, I345, I346) [I342 + 2 <= I336 /\ I341 + 2 <= I335 /\ I340 + 2 <= I335 /\ 1 <= I344 - 1 /\ 0 <= I343 - 1 /\ -1 <= I337 - 1 /\ 1 <= I336 - 1 /\ 0 <= I335 - 1 /\ I344 <= I336 /\ I343 <= I335 /\ 0 <= I334 - 1 /\ I338 <= I339]
  f9(I347, I348, I349, I350, I351, I352, I353, I354, I355) -> f7(I356, I357, I347 - 1, I351, I352, I358, I359, I360, I361) [I355 + 2 <= I349 /\ I354 + 2 <= I348 /\ I353 + 2 <= I348 /\ 0 <= I357 - 1 /\ 0 <= I356 - 1 /\ 0 <= I350 - 1 /\ 2 <= I349 - 1 /\ 0 <= I348 - 1 /\ I357 <= I350 /\ I357 + 2 <= I349 /\ I356 <= I348]
  f7(I362, I363, I364, I365, I366, I367, I368, I369, I370) -> f9(I364, I371, I372, I373, I365, I366, I374, I375, I376) [I376 + 2 <= I363 /\ I375 + 2 <= I362 /\ I374 + 2 <= I362 /\ -1 <= I373 - 1 /\ 0 <= I372 - 1 /\ 0 <= I371 - 1 /\ 0 <= I363 - 1 /\ 0 <= I362 - 1 /\ I373 + 1 <= I363 /\ I372 <= I363 /\ I371 <= I362 /\ 0 <= I364 - 1 /\ -1 <= I365 - 1 /\ I365 <= I366]
  f8(I377, I378, I379, I380, I381, I382, I383, I384, I385) -> f7(I386, I387, I377, I378, I379, I388, I389, I390, I391) [1 <= I386 - 1 /\ 1 <= I387 - 1]
  f6(I392, I393, I394, I395, I396, I397, I398, I399, I400) -> f7(I401, I402, I392, I393, I403, I404, I405, I406, I407) [1 <= I401 - 1 /\ 1 <= I402 - 1 /\ 0 <= I393 - 1 /\ 0 <= I392 - 1]
  f6(I408, I409, I410, I411, I412, I413, I414, I415, I416) -> f7(I417, I418, I408, I409, 1, I419, I420, I421, I422) [1 <= I417 - 1 /\ 1 <= I418 - 1 /\ 0 <= I409 - 1 /\ 0 <= I408 - 1]
  f1(I423, I424, I425, I426, I427, I428, I429, I430, I431) -> f6(I432, I424, I433, I434, I435, I436, I437, I438, I439) [0 <= I423 - 1 /\ 0 <= I424 - 1 /\ -1 <= I432 - 1]
  f1(I440, I441, I442, I443, I444, I445, I446, I447, I448) -> f6(0, I441, I449, I450, I451, I452, I453, I454, I455) [0 <= I441 - 1 /\ 0 <= I440 - 1]
  f4(I456, I457, I458, I459, I460, I461, I462, I463, I464) -> f3(I465, I466, I467, I468, I469, I470, I471, I472, I473) [I458 + 2 <= I457 /\ 0 <= I465 - 1 /\ 0 <= I457 - 1 /\ 0 <= I456 - 1 /\ I465 <= I457]
  f5(I474, I475, I476, I477, I478, I479, I480, I481, I482) -> f4(I483, I484, I476, I485, I486, I487, I488, I489, I490) [I476 + 2 <= I475 /\ 1 <= I484 - 1 /\ 0 <= I483 - 1 /\ 1 <= I475 - 1 /\ 0 <= I474 - 1 /\ I484 <= I475 /\ I483 + 1 <= I475 /\ I483 <= I474]
  f1(I491, I492, I493, I494, I495, I496, I497, I498, I499) -> f4(I500, I501, I502, I503, I504, I505, I506, I507, I508) [0 <= I501 - 1 /\ 0 <= I500 - 1 /\ 0 <= I491 - 1 /\ I500 <= I491]
  f2(I509, I510, I511, I512, I513, I514, I515, I516, I517) -> f3(I518, I519, I520, I521, I522, I523, I524, I525, I526) [-1 <= I518 - 1 /\ 0 <= I509 - 1 /\ I510 <= 1 /\ I518 + 1 <= I509]
  f1(I527, I528, I529, I530, I531, I532, I533, I534, I535) -> f2(I536, 1, I528, I537, I538, I539, I540, I541, I542) [0 <= I536 - 1 /\ 0 <= I527 - 1 /\ I536 <= I527]
  f1(I543, I544, I545, I546, I547, I548, I549, I550, I551) -> f2(I552, 0, 0, I553, I554, I555, I556, I557, I558) [0 = I544 /\ 0 <= I552 - 1 /\ 0 <= I543 - 1 /\ I552 <= I543]

The dependency graph for this problem is:
  1 -> 
Where:
  1) f13#(I48, I49, I50, I51, I52, I53, I54, I55, I56) -> f3#(I57, I58, I59, I60, I61, I62, I63, I64, I65) [-1 <= I57 - 1 /\ -1 <= I51 - 1 /\ -1 <= I49 - 1 /\ 2 <= I48 - 1 /\ I57 <= I51 /\ I57 <= I49 /\ I57 + 2 <= I48]

We have the following SCCs.
  

DP problem for innermost termination.
P =
  f12#(I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f7#(I183, I184, I174 - 1, I177, I178, I185, I186, I187, I188) [I179 = I180 /\ I179 + 2 <= I176 /\ I179 + 2 <= I175 /\ 3 <= I184 - 1 /\ 3 <= I183 - 1 /\ 1 <= I176 - 1 /\ 1 <= I175 - 1 /\ I184 - 2 <= I176 /\ I184 - 2 <= I175 /\ I183 - 2 <= I176 /\ I183 - 2 <= I175]
  f12#(I189, I190, I191, I192, I193, I194, I195, I196, I197) -> f7#(I198, I199, I189 - 1, I192, I193, I200, I201, I202, I203) [I195 + 2 <= I191 /\ I194 + 2 <= I190 /\ 0 <= I199 - 1 /\ 0 <= I198 - 1 /\ 1 <= I191 - 1 /\ 0 <= I190 - 1]
  f11#(I204, I205, I206, I207, I208, I209, I210, I211, I212) -> f12#(I204, I213, I214, I208, I215, I210, I216, I217, I218) [I216 + 2 <= I206 /\ I211 + 2 <= I205 /\ I210 + 2 <= I205 /\ 1 <= I214 - 1 /\ 0 <= I213 - 1 /\ 1 <= I206 - 1 /\ 0 <= I205 - 1 /\ I214 <= I206 /\ I213 <= I205 /\ 0 <= I204 - 1 /\ 0 <= I209 - 1 /\ 0 <= I207 - 1]
  f11#(I219, I220, I221, I222, I223, I224, I225, I226, I227) -> f12#(I219, I228, I229, I223, I224, I225, I230, I231, I232) [I230 + 2 <= I221 /\ I226 + 2 <= I220 /\ I225 + 2 <= I220 /\ 1 <= I229 - 1 /\ 0 <= I228 - 1 /\ 1 <= I221 - 1 /\ 0 <= I220 - 1 /\ I229 <= I221 /\ I228 <= I220 /\ 0 <= I219 - 1 /\ 0 <= I224 - 1 /\ 0 <= I222 - 1]
  f11#(I233, I234, I235, I236, I237, I238, I239, I240, I241) -> f7#(I242, I243, I233 - 1, I237, I238, I244, I245, I246, I247) [I240 + 2 <= I234 /\ I239 + 2 <= I234 /\ 0 <= I243 - 1 /\ 0 <= I242 - 1 /\ 2 <= I235 - 1 /\ 0 <= I234 - 1 /\ I243 + 2 <= I235 /\ 0 <= I236 - 1 /\ I242 <= I234]
  f11#(I248, I249, I250, I251, I252, I253, I254, I255, I256) -> f9#(I248, I257, I258, I259, I252, I253, I254, I255, I260) [0 = I251 /\ I260 + 2 <= I250 /\ I255 + 2 <= I249 /\ I254 + 2 <= I249 /\ -1 <= I259 - 1 /\ 0 <= I258 - 1 /\ 0 <= I257 - 1 /\ 0 <= I250 - 1 /\ 0 <= I249 - 1 /\ I259 + 1 <= I250 /\ I258 <= I250 /\ I257 <= I249]
  f10#(I261, I262, I263, I264, I265, I266, I267, I268, I269) -> f7#(I270, I271, I261 - 1, I264, I265, I272, I273, I274, I275) [I266 = I267 /\ I266 + 2 <= I263 /\ I266 + 2 <= I262 /\ 3 <= I271 - 1 /\ 3 <= I270 - 1 /\ 1 <= I263 - 1 /\ 1 <= I262 - 1 /\ I271 - 2 <= I263 /\ I271 - 2 <= I262 /\ I270 - 2 <= I263 /\ I270 - 2 <= I262]
  f10#(I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f7#(I285, I286, I276 - 1, I279, I280, I287, I288, I289, I290) [I282 + 2 <= I278 /\ I281 + 2 <= I277 /\ 0 <= I286 - 1 /\ 0 <= I285 - 1 /\ 1 <= I278 - 1 /\ 0 <= I277 - 1]
  f7#(I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f11#(I293, I300, I301, I302, I294, I295 + 1, I303, I304, I305) [I304 + 2 <= I291 /\ I303 + 2 <= I291 /\ 0 <= I301 - 1 /\ 0 <= I300 - 1 /\ 0 <= I292 - 1 /\ 0 <= I291 - 1 /\ I301 <= I292 /\ I300 <= I291 /\ -1 <= I302 - 1 /\ -1 <= I295 - 1 /\ I295 <= I294 - 1 /\ -1 <= I294 - 1 /\ 0 <= I293 - 1]
  f7#(I306, I307, I308, I309, I310, I311, I312, I313, I314) -> f11#(I308, I315, I316, 0, I309, I310 + 1, I317, I318, I319) [I318 + 2 <= I306 /\ I317 + 2 <= I306 /\ 0 <= I316 - 1 /\ 0 <= I315 - 1 /\ 0 <= I307 - 1 /\ 0 <= I306 - 1 /\ I316 <= I307 /\ I315 <= I306 /\ -1 <= I310 - 1 /\ I310 <= I309 - 1 /\ -1 <= I309 - 1 /\ 0 <= I308 - 1]
  f9#(I320, I321, I322, I323, I324, I325, I326, I327, I328) -> f10#(I320, I329, I330, I324, I331, I327, I328, I332, I333) [I328 + 2 <= I322 /\ I327 + 2 <= I321 /\ I326 + 2 <= I321 /\ 1 <= I330 - 1 /\ 0 <= I329 - 1 /\ -1 <= I323 - 1 /\ 1 <= I322 - 1 /\ 0 <= I321 - 1 /\ I330 <= I322 /\ I329 <= I321 /\ 0 <= I320 - 1 /\ I324 <= I325]
  f9#(I334, I335, I336, I337, I338, I339, I340, I341, I342) -> f10#(I334, I343, I344, I338, I339, I341, I342, I345, I346) [I342 + 2 <= I336 /\ I341 + 2 <= I335 /\ I340 + 2 <= I335 /\ 1 <= I344 - 1 /\ 0 <= I343 - 1 /\ -1 <= I337 - 1 /\ 1 <= I336 - 1 /\ 0 <= I335 - 1 /\ I344 <= I336 /\ I343 <= I335 /\ 0 <= I334 - 1 /\ I338 <= I339]
  f9#(I347, I348, I349, I350, I351, I352, I353, I354, I355) -> f7#(I356, I357, I347 - 1, I351, I352, I358, I359, I360, I361) [I355 + 2 <= I349 /\ I354 + 2 <= I348 /\ I353 + 2 <= I348 /\ 0 <= I357 - 1 /\ 0 <= I356 - 1 /\ 0 <= I350 - 1 /\ 2 <= I349 - 1 /\ 0 <= I348 - 1 /\ I357 <= I350 /\ I357 + 2 <= I349 /\ I356 <= I348]
  f7#(I362, I363, I364, I365, I366, I367, I368, I369, I370) -> f9#(I364, I371, I372, I373, I365, I366, I374, I375, I376) [I376 + 2 <= I363 /\ I375 + 2 <= I362 /\ I374 + 2 <= I362 /\ -1 <= I373 - 1 /\ 0 <= I372 - 1 /\ 0 <= I371 - 1 /\ 0 <= I363 - 1 /\ 0 <= I362 - 1 /\ I373 + 1 <= I363 /\ I372 <= I363 /\ I371 <= I362 /\ 0 <= I364 - 1 /\ -1 <= I365 - 1 /\ I365 <= I366]
R = 
  init(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9) 
  f11(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f14(I9, I4, I5, I10, I11, I12, I13, I14, I15) [I7 + 2 <= I1 /\ I6 + 2 <= I1 /\ 1 <= I2 - 1 /\ 0 <= I1 - 1 /\ 0 <= I3 - 1 /\ -1 <= I4 - 1 /\ 0 <= I5 - 1 /\ 0 <= I0 - 1]
  f9(I16, I17, I18, I19, I20, I21, I22, I23, I24) -> f14(I25, I20, I21, I26, I27, I28, I29, I30, I31) [I24 + 2 <= I18 /\ I23 + 2 <= I17 /\ I22 + 2 <= I17 /\ -1 <= I19 - 1 /\ 1 <= I18 - 1 /\ 0 <= I17 - 1 /\ 0 <= I16 - 1 /\ I20 <= I21 /\ -1 <= I20 - 1]
  f6(I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f14(I41, I33, 1, I42, I43, I44, I45, I46, I47) [0 <= I32 - 1 /\ 0 <= I33 - 1]
  f13(I48, I49, I50, I51, I52, I53, I54, I55, I56) -> f3(I57, I58, I59, I60, I61, I62, I63, I64, I65) [-1 <= I57 - 1 /\ -1 <= I51 - 1 /\ -1 <= I49 - 1 /\ 2 <= I48 - 1 /\ I57 <= I51 /\ I57 <= I49 /\ I57 + 2 <= I48]
  f3(I66, I67, I68, I69, I70, I71, I72, I73, I74) -> f13(I75, I76, I77, I78, I79, I80, I81, I82, I83) [-1 <= I78 - 1 /\ -1 <= I76 - 1 /\ 3 <= I75 - 1 /\ 0 <= I66 - 1 /\ I78 + 1 <= I66 /\ I76 + 1 <= I66 /\ I75 - 3 <= I66]
  f3(I84, I85, I86, I87, I88, I89, I90, I91, I92) -> f13(I93, I94, I95, I96, I97, I98, I99, I100, I101) [-1 <= I96 - 1 /\ -1 <= I94 - 1 /\ 4 <= I93 - 1 /\ 0 <= I84 - 1 /\ I96 + 1 <= I84 /\ I94 + 1 <= I84]
  f3(I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f13(I111, I112, I113, I114, I115, I116, I117, I118, I119) [-1 <= I114 - 1 /\ -1 <= I112 - 1 /\ 4 <= I111 - 1 /\ 0 <= I102 - 1 /\ I114 + 1 <= I102 /\ I112 + 1 <= I102]
  f3(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f13(I129, I130, I131, I132, I133, I134, I135, I136, I137) [-1 <= I132 - 1 /\ -1 <= I130 - 1 /\ 4 <= I129 - 1 /\ 0 <= I120 - 1 /\ I132 + 1 <= I120 /\ I130 + 1 <= I120]
  f3(I138, I139, I140, I141, I142, I143, I144, I145, I146) -> f3(I147, I148, I149, I150, I151, I152, I153, I154, I155) [-1 <= I147 - 1 /\ 1 <= I138 - 1 /\ I147 + 2 <= I138]
  f3(I156, I157, I158, I159, I160, I161, I162, I163, I164) -> f3(I165, I166, I167, I168, I169, I170, I171, I172, I173) [-1 <= I165 - 1 /\ 0 <= I156 - 1 /\ I165 + 1 <= I156]
  f12(I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f7(I183, I184, I174 - 1, I177, I178, I185, I186, I187, I188) [I179 = I180 /\ I179 + 2 <= I176 /\ I179 + 2 <= I175 /\ 3 <= I184 - 1 /\ 3 <= I183 - 1 /\ 1 <= I176 - 1 /\ 1 <= I175 - 1 /\ I184 - 2 <= I176 /\ I184 - 2 <= I175 /\ I183 - 2 <= I176 /\ I183 - 2 <= I175]
  f12(I189, I190, I191, I192, I193, I194, I195, I196, I197) -> f7(I198, I199, I189 - 1, I192, I193, I200, I201, I202, I203) [I195 + 2 <= I191 /\ I194 + 2 <= I190 /\ 0 <= I199 - 1 /\ 0 <= I198 - 1 /\ 1 <= I191 - 1 /\ 0 <= I190 - 1]
  f11(I204, I205, I206, I207, I208, I209, I210, I211, I212) -> f12(I204, I213, I214, I208, I215, I210, I216, I217, I218) [I216 + 2 <= I206 /\ I211 + 2 <= I205 /\ I210 + 2 <= I205 /\ 1 <= I214 - 1 /\ 0 <= I213 - 1 /\ 1 <= I206 - 1 /\ 0 <= I205 - 1 /\ I214 <= I206 /\ I213 <= I205 /\ 0 <= I204 - 1 /\ 0 <= I209 - 1 /\ 0 <= I207 - 1]
  f11(I219, I220, I221, I222, I223, I224, I225, I226, I227) -> f12(I219, I228, I229, I223, I224, I225, I230, I231, I232) [I230 + 2 <= I221 /\ I226 + 2 <= I220 /\ I225 + 2 <= I220 /\ 1 <= I229 - 1 /\ 0 <= I228 - 1 /\ 1 <= I221 - 1 /\ 0 <= I220 - 1 /\ I229 <= I221 /\ I228 <= I220 /\ 0 <= I219 - 1 /\ 0 <= I224 - 1 /\ 0 <= I222 - 1]
  f11(I233, I234, I235, I236, I237, I238, I239, I240, I241) -> f7(I242, I243, I233 - 1, I237, I238, I244, I245, I246, I247) [I240 + 2 <= I234 /\ I239 + 2 <= I234 /\ 0 <= I243 - 1 /\ 0 <= I242 - 1 /\ 2 <= I235 - 1 /\ 0 <= I234 - 1 /\ I243 + 2 <= I235 /\ 0 <= I236 - 1 /\ I242 <= I234]
  f11(I248, I249, I250, I251, I252, I253, I254, I255, I256) -> f9(I248, I257, I258, I259, I252, I253, I254, I255, I260) [0 = I251 /\ I260 + 2 <= I250 /\ I255 + 2 <= I249 /\ I254 + 2 <= I249 /\ -1 <= I259 - 1 /\ 0 <= I258 - 1 /\ 0 <= I257 - 1 /\ 0 <= I250 - 1 /\ 0 <= I249 - 1 /\ I259 + 1 <= I250 /\ I258 <= I250 /\ I257 <= I249]
  f10(I261, I262, I263, I264, I265, I266, I267, I268, I269) -> f7(I270, I271, I261 - 1, I264, I265, I272, I273, I274, I275) [I266 = I267 /\ I266 + 2 <= I263 /\ I266 + 2 <= I262 /\ 3 <= I271 - 1 /\ 3 <= I270 - 1 /\ 1 <= I263 - 1 /\ 1 <= I262 - 1 /\ I271 - 2 <= I263 /\ I271 - 2 <= I262 /\ I270 - 2 <= I263 /\ I270 - 2 <= I262]
  f10(I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f7(I285, I286, I276 - 1, I279, I280, I287, I288, I289, I290) [I282 + 2 <= I278 /\ I281 + 2 <= I277 /\ 0 <= I286 - 1 /\ 0 <= I285 - 1 /\ 1 <= I278 - 1 /\ 0 <= I277 - 1]
  f7(I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f11(I293, I300, I301, I302, I294, I295 + 1, I303, I304, I305) [I304 + 2 <= I291 /\ I303 + 2 <= I291 /\ 0 <= I301 - 1 /\ 0 <= I300 - 1 /\ 0 <= I292 - 1 /\ 0 <= I291 - 1 /\ I301 <= I292 /\ I300 <= I291 /\ -1 <= I302 - 1 /\ -1 <= I295 - 1 /\ I295 <= I294 - 1 /\ -1 <= I294 - 1 /\ 0 <= I293 - 1]
  f7(I306, I307, I308, I309, I310, I311, I312, I313, I314) -> f11(I308, I315, I316, 0, I309, I310 + 1, I317, I318, I319) [I318 + 2 <= I306 /\ I317 + 2 <= I306 /\ 0 <= I316 - 1 /\ 0 <= I315 - 1 /\ 0 <= I307 - 1 /\ 0 <= I306 - 1 /\ I316 <= I307 /\ I315 <= I306 /\ -1 <= I310 - 1 /\ I310 <= I309 - 1 /\ -1 <= I309 - 1 /\ 0 <= I308 - 1]
  f9(I320, I321, I322, I323, I324, I325, I326, I327, I328) -> f10(I320, I329, I330, I324, I331, I327, I328, I332, I333) [I328 + 2 <= I322 /\ I327 + 2 <= I321 /\ I326 + 2 <= I321 /\ 1 <= I330 - 1 /\ 0 <= I329 - 1 /\ -1 <= I323 - 1 /\ 1 <= I322 - 1 /\ 0 <= I321 - 1 /\ I330 <= I322 /\ I329 <= I321 /\ 0 <= I320 - 1 /\ I324 <= I325]
  f9(I334, I335, I336, I337, I338, I339, I340, I341, I342) -> f10(I334, I343, I344, I338, I339, I341, I342, I345, I346) [I342 + 2 <= I336 /\ I341 + 2 <= I335 /\ I340 + 2 <= I335 /\ 1 <= I344 - 1 /\ 0 <= I343 - 1 /\ -1 <= I337 - 1 /\ 1 <= I336 - 1 /\ 0 <= I335 - 1 /\ I344 <= I336 /\ I343 <= I335 /\ 0 <= I334 - 1 /\ I338 <= I339]
  f9(I347, I348, I349, I350, I351, I352, I353, I354, I355) -> f7(I356, I357, I347 - 1, I351, I352, I358, I359, I360, I361) [I355 + 2 <= I349 /\ I354 + 2 <= I348 /\ I353 + 2 <= I348 /\ 0 <= I357 - 1 /\ 0 <= I356 - 1 /\ 0 <= I350 - 1 /\ 2 <= I349 - 1 /\ 0 <= I348 - 1 /\ I357 <= I350 /\ I357 + 2 <= I349 /\ I356 <= I348]
  f7(I362, I363, I364, I365, I366, I367, I368, I369, I370) -> f9(I364, I371, I372, I373, I365, I366, I374, I375, I376) [I376 + 2 <= I363 /\ I375 + 2 <= I362 /\ I374 + 2 <= I362 /\ -1 <= I373 - 1 /\ 0 <= I372 - 1 /\ 0 <= I371 - 1 /\ 0 <= I363 - 1 /\ 0 <= I362 - 1 /\ I373 + 1 <= I363 /\ I372 <= I363 /\ I371 <= I362 /\ 0 <= I364 - 1 /\ -1 <= I365 - 1 /\ I365 <= I366]
  f8(I377, I378, I379, I380, I381, I382, I383, I384, I385) -> f7(I386, I387, I377, I378, I379, I388, I389, I390, I391) [1 <= I386 - 1 /\ 1 <= I387 - 1]
  f6(I392, I393, I394, I395, I396, I397, I398, I399, I400) -> f7(I401, I402, I392, I393, I403, I404, I405, I406, I407) [1 <= I401 - 1 /\ 1 <= I402 - 1 /\ 0 <= I393 - 1 /\ 0 <= I392 - 1]
  f6(I408, I409, I410, I411, I412, I413, I414, I415, I416) -> f7(I417, I418, I408, I409, 1, I419, I420, I421, I422) [1 <= I417 - 1 /\ 1 <= I418 - 1 /\ 0 <= I409 - 1 /\ 0 <= I408 - 1]
  f1(I423, I424, I425, I426, I427, I428, I429, I430, I431) -> f6(I432, I424, I433, I434, I435, I436, I437, I438, I439) [0 <= I423 - 1 /\ 0 <= I424 - 1 /\ -1 <= I432 - 1]
  f1(I440, I441, I442, I443, I444, I445, I446, I447, I448) -> f6(0, I441, I449, I450, I451, I452, I453, I454, I455) [0 <= I441 - 1 /\ 0 <= I440 - 1]
  f4(I456, I457, I458, I459, I460, I461, I462, I463, I464) -> f3(I465, I466, I467, I468, I469, I470, I471, I472, I473) [I458 + 2 <= I457 /\ 0 <= I465 - 1 /\ 0 <= I457 - 1 /\ 0 <= I456 - 1 /\ I465 <= I457]
  f5(I474, I475, I476, I477, I478, I479, I480, I481, I482) -> f4(I483, I484, I476, I485, I486, I487, I488, I489, I490) [I476 + 2 <= I475 /\ 1 <= I484 - 1 /\ 0 <= I483 - 1 /\ 1 <= I475 - 1 /\ 0 <= I474 - 1 /\ I484 <= I475 /\ I483 + 1 <= I475 /\ I483 <= I474]
  f1(I491, I492, I493, I494, I495, I496, I497, I498, I499) -> f4(I500, I501, I502, I503, I504, I505, I506, I507, I508) [0 <= I501 - 1 /\ 0 <= I500 - 1 /\ 0 <= I491 - 1 /\ I500 <= I491]
  f2(I509, I510, I511, I512, I513, I514, I515, I516, I517) -> f3(I518, I519, I520, I521, I522, I523, I524, I525, I526) [-1 <= I518 - 1 /\ 0 <= I509 - 1 /\ I510 <= 1 /\ I518 + 1 <= I509]
  f1(I527, I528, I529, I530, I531, I532, I533, I534, I535) -> f2(I536, 1, I528, I537, I538, I539, I540, I541, I542) [0 <= I536 - 1 /\ 0 <= I527 - 1 /\ I536 <= I527]
  f1(I543, I544, I545, I546, I547, I548, I549, I550, I551) -> f2(I552, 0, 0, I553, I554, I555, I556, I557, I558) [0 = I544 /\ 0 <= I552 - 1 /\ 0 <= I543 - 1 /\ I552 <= I543]

We use the reverse value criterion with the projection function NU:
  NU[f10#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = z1 - 1 - 1 + -1 * 0
  NU[f9#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = z1 - 1 + -1 * 0
  NU[f11#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = z1 - 1 + -1 * 0
  NU[f7#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = z3 - 1 + -1 * 0
  NU[f12#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = z1 - 1 - 1 + -1 * 0

This gives the following inequalities:
  I179 = I180 /\ I179 + 2 <= I176 /\ I179 + 2 <= I175 /\ 3 <= I184 - 1 /\ 3 <= I183 - 1 /\ 1 <= I176 - 1 /\ 1 <= I175 - 1 /\ I184 - 2 <= I176 /\ I184 - 2 <= I175 /\ I183 - 2 <= I176 /\ I183 - 2 <= I175  ==>  I174 - 1 - 1 + -1 * 0 >= I174 - 1 - 1 + -1 * 0
  I195 + 2 <= I191 /\ I194 + 2 <= I190 /\ 0 <= I199 - 1 /\ 0 <= I198 - 1 /\ 1 <= I191 - 1 /\ 0 <= I190 - 1  ==>  I189 - 1 - 1 + -1 * 0 >= I189 - 1 - 1 + -1 * 0
  I216 + 2 <= I206 /\ I211 + 2 <= I205 /\ I210 + 2 <= I205 /\ 1 <= I214 - 1 /\ 0 <= I213 - 1 /\ 1 <= I206 - 1 /\ 0 <= I205 - 1 /\ I214 <= I206 /\ I213 <= I205 /\ 0 <= I204 - 1 /\ 0 <= I209 - 1 /\ 0 <= I207 - 1  ==>  I204 - 1 + -1 * 0 > I204 - 1 - 1 + -1 * 0  with  I204 - 1 + -1 * 0 >= 0
  I230 + 2 <= I221 /\ I226 + 2 <= I220 /\ I225 + 2 <= I220 /\ 1 <= I229 - 1 /\ 0 <= I228 - 1 /\ 1 <= I221 - 1 /\ 0 <= I220 - 1 /\ I229 <= I221 /\ I228 <= I220 /\ 0 <= I219 - 1 /\ 0 <= I224 - 1 /\ 0 <= I222 - 1  ==>  I219 - 1 + -1 * 0 > I219 - 1 - 1 + -1 * 0  with  I219 - 1 + -1 * 0 >= 0
  I240 + 2 <= I234 /\ I239 + 2 <= I234 /\ 0 <= I243 - 1 /\ 0 <= I242 - 1 /\ 2 <= I235 - 1 /\ 0 <= I234 - 1 /\ I243 + 2 <= I235 /\ 0 <= I236 - 1 /\ I242 <= I234  ==>  I233 - 1 + -1 * 0 >= I233 - 1 - 1 + -1 * 0
  0 = I251 /\ I260 + 2 <= I250 /\ I255 + 2 <= I249 /\ I254 + 2 <= I249 /\ -1 <= I259 - 1 /\ 0 <= I258 - 1 /\ 0 <= I257 - 1 /\ 0 <= I250 - 1 /\ 0 <= I249 - 1 /\ I259 + 1 <= I250 /\ I258 <= I250 /\ I257 <= I249  ==>  I248 - 1 + -1 * 0 >= I248 - 1 + -1 * 0
  I266 = I267 /\ I266 + 2 <= I263 /\ I266 + 2 <= I262 /\ 3 <= I271 - 1 /\ 3 <= I270 - 1 /\ 1 <= I263 - 1 /\ 1 <= I262 - 1 /\ I271 - 2 <= I263 /\ I271 - 2 <= I262 /\ I270 - 2 <= I263 /\ I270 - 2 <= I262  ==>  I261 - 1 - 1 + -1 * 0 >= I261 - 1 - 1 + -1 * 0
  I282 + 2 <= I278 /\ I281 + 2 <= I277 /\ 0 <= I286 - 1 /\ 0 <= I285 - 1 /\ 1 <= I278 - 1 /\ 0 <= I277 - 1  ==>  I276 - 1 - 1 + -1 * 0 >= I276 - 1 - 1 + -1 * 0
  I304 + 2 <= I291 /\ I303 + 2 <= I291 /\ 0 <= I301 - 1 /\ 0 <= I300 - 1 /\ 0 <= I292 - 1 /\ 0 <= I291 - 1 /\ I301 <= I292 /\ I300 <= I291 /\ -1 <= I302 - 1 /\ -1 <= I295 - 1 /\ I295 <= I294 - 1 /\ -1 <= I294 - 1 /\ 0 <= I293 - 1  ==>  I293 - 1 + -1 * 0 >= I293 - 1 + -1 * 0
  I318 + 2 <= I306 /\ I317 + 2 <= I306 /\ 0 <= I316 - 1 /\ 0 <= I315 - 1 /\ 0 <= I307 - 1 /\ 0 <= I306 - 1 /\ I316 <= I307 /\ I315 <= I306 /\ -1 <= I310 - 1 /\ I310 <= I309 - 1 /\ -1 <= I309 - 1 /\ 0 <= I308 - 1  ==>  I308 - 1 + -1 * 0 >= I308 - 1 + -1 * 0
  I328 + 2 <= I322 /\ I327 + 2 <= I321 /\ I326 + 2 <= I321 /\ 1 <= I330 - 1 /\ 0 <= I329 - 1 /\ -1 <= I323 - 1 /\ 1 <= I322 - 1 /\ 0 <= I321 - 1 /\ I330 <= I322 /\ I329 <= I321 /\ 0 <= I320 - 1 /\ I324 <= I325  ==>  I320 - 1 + -1 * 0 > I320 - 1 - 1 + -1 * 0  with  I320 - 1 + -1 * 0 >= 0
  I342 + 2 <= I336 /\ I341 + 2 <= I335 /\ I340 + 2 <= I335 /\ 1 <= I344 - 1 /\ 0 <= I343 - 1 /\ -1 <= I337 - 1 /\ 1 <= I336 - 1 /\ 0 <= I335 - 1 /\ I344 <= I336 /\ I343 <= I335 /\ 0 <= I334 - 1 /\ I338 <= I339  ==>  I334 - 1 + -1 * 0 > I334 - 1 - 1 + -1 * 0  with  I334 - 1 + -1 * 0 >= 0
  I355 + 2 <= I349 /\ I354 + 2 <= I348 /\ I353 + 2 <= I348 /\ 0 <= I357 - 1 /\ 0 <= I356 - 1 /\ 0 <= I350 - 1 /\ 2 <= I349 - 1 /\ 0 <= I348 - 1 /\ I357 <= I350 /\ I357 + 2 <= I349 /\ I356 <= I348  ==>  I347 - 1 + -1 * 0 >= I347 - 1 - 1 + -1 * 0
  I376 + 2 <= I363 /\ I375 + 2 <= I362 /\ I374 + 2 <= I362 /\ -1 <= I373 - 1 /\ 0 <= I372 - 1 /\ 0 <= I371 - 1 /\ 0 <= I363 - 1 /\ 0 <= I362 - 1 /\ I373 + 1 <= I363 /\ I372 <= I363 /\ I371 <= I362 /\ 0 <= I364 - 1 /\ -1 <= I365 - 1 /\ I365 <= I366  ==>  I364 - 1 + -1 * 0 >= I364 - 1 + -1 * 0

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f12#(I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f7#(I183, I184, I174 - 1, I177, I178, I185, I186, I187, I188) [I179 = I180 /\ I179 + 2 <= I176 /\ I179 + 2 <= I175 /\ 3 <= I184 - 1 /\ 3 <= I183 - 1 /\ 1 <= I176 - 1 /\ 1 <= I175 - 1 /\ I184 - 2 <= I176 /\ I184 - 2 <= I175 /\ I183 - 2 <= I176 /\ I183 - 2 <= I175]
  f12#(I189, I190, I191, I192, I193, I194, I195, I196, I197) -> f7#(I198, I199, I189 - 1, I192, I193, I200, I201, I202, I203) [I195 + 2 <= I191 /\ I194 + 2 <= I190 /\ 0 <= I199 - 1 /\ 0 <= I198 - 1 /\ 1 <= I191 - 1 /\ 0 <= I190 - 1]
  f11#(I233, I234, I235, I236, I237, I238, I239, I240, I241) -> f7#(I242, I243, I233 - 1, I237, I238, I244, I245, I246, I247) [I240 + 2 <= I234 /\ I239 + 2 <= I234 /\ 0 <= I243 - 1 /\ 0 <= I242 - 1 /\ 2 <= I235 - 1 /\ 0 <= I234 - 1 /\ I243 + 2 <= I235 /\ 0 <= I236 - 1 /\ I242 <= I234]
  f11#(I248, I249, I250, I251, I252, I253, I254, I255, I256) -> f9#(I248, I257, I258, I259, I252, I253, I254, I255, I260) [0 = I251 /\ I260 + 2 <= I250 /\ I255 + 2 <= I249 /\ I254 + 2 <= I249 /\ -1 <= I259 - 1 /\ 0 <= I258 - 1 /\ 0 <= I257 - 1 /\ 0 <= I250 - 1 /\ 0 <= I249 - 1 /\ I259 + 1 <= I250 /\ I258 <= I250 /\ I257 <= I249]
  f10#(I261, I262, I263, I264, I265, I266, I267, I268, I269) -> f7#(I270, I271, I261 - 1, I264, I265, I272, I273, I274, I275) [I266 = I267 /\ I266 + 2 <= I263 /\ I266 + 2 <= I262 /\ 3 <= I271 - 1 /\ 3 <= I270 - 1 /\ 1 <= I263 - 1 /\ 1 <= I262 - 1 /\ I271 - 2 <= I263 /\ I271 - 2 <= I262 /\ I270 - 2 <= I263 /\ I270 - 2 <= I262]
  f10#(I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f7#(I285, I286, I276 - 1, I279, I280, I287, I288, I289, I290) [I282 + 2 <= I278 /\ I281 + 2 <= I277 /\ 0 <= I286 - 1 /\ 0 <= I285 - 1 /\ 1 <= I278 - 1 /\ 0 <= I277 - 1]
  f7#(I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f11#(I293, I300, I301, I302, I294, I295 + 1, I303, I304, I305) [I304 + 2 <= I291 /\ I303 + 2 <= I291 /\ 0 <= I301 - 1 /\ 0 <= I300 - 1 /\ 0 <= I292 - 1 /\ 0 <= I291 - 1 /\ I301 <= I292 /\ I300 <= I291 /\ -1 <= I302 - 1 /\ -1 <= I295 - 1 /\ I295 <= I294 - 1 /\ -1 <= I294 - 1 /\ 0 <= I293 - 1]
  f7#(I306, I307, I308, I309, I310, I311, I312, I313, I314) -> f11#(I308, I315, I316, 0, I309, I310 + 1, I317, I318, I319) [I318 + 2 <= I306 /\ I317 + 2 <= I306 /\ 0 <= I316 - 1 /\ 0 <= I315 - 1 /\ 0 <= I307 - 1 /\ 0 <= I306 - 1 /\ I316 <= I307 /\ I315 <= I306 /\ -1 <= I310 - 1 /\ I310 <= I309 - 1 /\ -1 <= I309 - 1 /\ 0 <= I308 - 1]
  f9#(I347, I348, I349, I350, I351, I352, I353, I354, I355) -> f7#(I356, I357, I347 - 1, I351, I352, I358, I359, I360, I361) [I355 + 2 <= I349 /\ I354 + 2 <= I348 /\ I353 + 2 <= I348 /\ 0 <= I357 - 1 /\ 0 <= I356 - 1 /\ 0 <= I350 - 1 /\ 2 <= I349 - 1 /\ 0 <= I348 - 1 /\ I357 <= I350 /\ I357 + 2 <= I349 /\ I356 <= I348]
  f7#(I362, I363, I364, I365, I366, I367, I368, I369, I370) -> f9#(I364, I371, I372, I373, I365, I366, I374, I375, I376) [I376 + 2 <= I363 /\ I375 + 2 <= I362 /\ I374 + 2 <= I362 /\ -1 <= I373 - 1 /\ 0 <= I372 - 1 /\ 0 <= I371 - 1 /\ 0 <= I363 - 1 /\ 0 <= I362 - 1 /\ I373 + 1 <= I363 /\ I372 <= I363 /\ I371 <= I362 /\ 0 <= I364 - 1 /\ -1 <= I365 - 1 /\ I365 <= I366]
R = 
  init(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9) 
  f11(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f14(I9, I4, I5, I10, I11, I12, I13, I14, I15) [I7 + 2 <= I1 /\ I6 + 2 <= I1 /\ 1 <= I2 - 1 /\ 0 <= I1 - 1 /\ 0 <= I3 - 1 /\ -1 <= I4 - 1 /\ 0 <= I5 - 1 /\ 0 <= I0 - 1]
  f9(I16, I17, I18, I19, I20, I21, I22, I23, I24) -> f14(I25, I20, I21, I26, I27, I28, I29, I30, I31) [I24 + 2 <= I18 /\ I23 + 2 <= I17 /\ I22 + 2 <= I17 /\ -1 <= I19 - 1 /\ 1 <= I18 - 1 /\ 0 <= I17 - 1 /\ 0 <= I16 - 1 /\ I20 <= I21 /\ -1 <= I20 - 1]
  f6(I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f14(I41, I33, 1, I42, I43, I44, I45, I46, I47) [0 <= I32 - 1 /\ 0 <= I33 - 1]
  f13(I48, I49, I50, I51, I52, I53, I54, I55, I56) -> f3(I57, I58, I59, I60, I61, I62, I63, I64, I65) [-1 <= I57 - 1 /\ -1 <= I51 - 1 /\ -1 <= I49 - 1 /\ 2 <= I48 - 1 /\ I57 <= I51 /\ I57 <= I49 /\ I57 + 2 <= I48]
  f3(I66, I67, I68, I69, I70, I71, I72, I73, I74) -> f13(I75, I76, I77, I78, I79, I80, I81, I82, I83) [-1 <= I78 - 1 /\ -1 <= I76 - 1 /\ 3 <= I75 - 1 /\ 0 <= I66 - 1 /\ I78 + 1 <= I66 /\ I76 + 1 <= I66 /\ I75 - 3 <= I66]
  f3(I84, I85, I86, I87, I88, I89, I90, I91, I92) -> f13(I93, I94, I95, I96, I97, I98, I99, I100, I101) [-1 <= I96 - 1 /\ -1 <= I94 - 1 /\ 4 <= I93 - 1 /\ 0 <= I84 - 1 /\ I96 + 1 <= I84 /\ I94 + 1 <= I84]
  f3(I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f13(I111, I112, I113, I114, I115, I116, I117, I118, I119) [-1 <= I114 - 1 /\ -1 <= I112 - 1 /\ 4 <= I111 - 1 /\ 0 <= I102 - 1 /\ I114 + 1 <= I102 /\ I112 + 1 <= I102]
  f3(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f13(I129, I130, I131, I132, I133, I134, I135, I136, I137) [-1 <= I132 - 1 /\ -1 <= I130 - 1 /\ 4 <= I129 - 1 /\ 0 <= I120 - 1 /\ I132 + 1 <= I120 /\ I130 + 1 <= I120]
  f3(I138, I139, I140, I141, I142, I143, I144, I145, I146) -> f3(I147, I148, I149, I150, I151, I152, I153, I154, I155) [-1 <= I147 - 1 /\ 1 <= I138 - 1 /\ I147 + 2 <= I138]
  f3(I156, I157, I158, I159, I160, I161, I162, I163, I164) -> f3(I165, I166, I167, I168, I169, I170, I171, I172, I173) [-1 <= I165 - 1 /\ 0 <= I156 - 1 /\ I165 + 1 <= I156]
  f12(I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f7(I183, I184, I174 - 1, I177, I178, I185, I186, I187, I188) [I179 = I180 /\ I179 + 2 <= I176 /\ I179 + 2 <= I175 /\ 3 <= I184 - 1 /\ 3 <= I183 - 1 /\ 1 <= I176 - 1 /\ 1 <= I175 - 1 /\ I184 - 2 <= I176 /\ I184 - 2 <= I175 /\ I183 - 2 <= I176 /\ I183 - 2 <= I175]
  f12(I189, I190, I191, I192, I193, I194, I195, I196, I197) -> f7(I198, I199, I189 - 1, I192, I193, I200, I201, I202, I203) [I195 + 2 <= I191 /\ I194 + 2 <= I190 /\ 0 <= I199 - 1 /\ 0 <= I198 - 1 /\ 1 <= I191 - 1 /\ 0 <= I190 - 1]
  f11(I204, I205, I206, I207, I208, I209, I210, I211, I212) -> f12(I204, I213, I214, I208, I215, I210, I216, I217, I218) [I216 + 2 <= I206 /\ I211 + 2 <= I205 /\ I210 + 2 <= I205 /\ 1 <= I214 - 1 /\ 0 <= I213 - 1 /\ 1 <= I206 - 1 /\ 0 <= I205 - 1 /\ I214 <= I206 /\ I213 <= I205 /\ 0 <= I204 - 1 /\ 0 <= I209 - 1 /\ 0 <= I207 - 1]
  f11(I219, I220, I221, I222, I223, I224, I225, I226, I227) -> f12(I219, I228, I229, I223, I224, I225, I230, I231, I232) [I230 + 2 <= I221 /\ I226 + 2 <= I220 /\ I225 + 2 <= I220 /\ 1 <= I229 - 1 /\ 0 <= I228 - 1 /\ 1 <= I221 - 1 /\ 0 <= I220 - 1 /\ I229 <= I221 /\ I228 <= I220 /\ 0 <= I219 - 1 /\ 0 <= I224 - 1 /\ 0 <= I222 - 1]
  f11(I233, I234, I235, I236, I237, I238, I239, I240, I241) -> f7(I242, I243, I233 - 1, I237, I238, I244, I245, I246, I247) [I240 + 2 <= I234 /\ I239 + 2 <= I234 /\ 0 <= I243 - 1 /\ 0 <= I242 - 1 /\ 2 <= I235 - 1 /\ 0 <= I234 - 1 /\ I243 + 2 <= I235 /\ 0 <= I236 - 1 /\ I242 <= I234]
  f11(I248, I249, I250, I251, I252, I253, I254, I255, I256) -> f9(I248, I257, I258, I259, I252, I253, I254, I255, I260) [0 = I251 /\ I260 + 2 <= I250 /\ I255 + 2 <= I249 /\ I254 + 2 <= I249 /\ -1 <= I259 - 1 /\ 0 <= I258 - 1 /\ 0 <= I257 - 1 /\ 0 <= I250 - 1 /\ 0 <= I249 - 1 /\ I259 + 1 <= I250 /\ I258 <= I250 /\ I257 <= I249]
  f10(I261, I262, I263, I264, I265, I266, I267, I268, I269) -> f7(I270, I271, I261 - 1, I264, I265, I272, I273, I274, I275) [I266 = I267 /\ I266 + 2 <= I263 /\ I266 + 2 <= I262 /\ 3 <= I271 - 1 /\ 3 <= I270 - 1 /\ 1 <= I263 - 1 /\ 1 <= I262 - 1 /\ I271 - 2 <= I263 /\ I271 - 2 <= I262 /\ I270 - 2 <= I263 /\ I270 - 2 <= I262]
  f10(I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f7(I285, I286, I276 - 1, I279, I280, I287, I288, I289, I290) [I282 + 2 <= I278 /\ I281 + 2 <= I277 /\ 0 <= I286 - 1 /\ 0 <= I285 - 1 /\ 1 <= I278 - 1 /\ 0 <= I277 - 1]
  f7(I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f11(I293, I300, I301, I302, I294, I295 + 1, I303, I304, I305) [I304 + 2 <= I291 /\ I303 + 2 <= I291 /\ 0 <= I301 - 1 /\ 0 <= I300 - 1 /\ 0 <= I292 - 1 /\ 0 <= I291 - 1 /\ I301 <= I292 /\ I300 <= I291 /\ -1 <= I302 - 1 /\ -1 <= I295 - 1 /\ I295 <= I294 - 1 /\ -1 <= I294 - 1 /\ 0 <= I293 - 1]
  f7(I306, I307, I308, I309, I310, I311, I312, I313, I314) -> f11(I308, I315, I316, 0, I309, I310 + 1, I317, I318, I319) [I318 + 2 <= I306 /\ I317 + 2 <= I306 /\ 0 <= I316 - 1 /\ 0 <= I315 - 1 /\ 0 <= I307 - 1 /\ 0 <= I306 - 1 /\ I316 <= I307 /\ I315 <= I306 /\ -1 <= I310 - 1 /\ I310 <= I309 - 1 /\ -1 <= I309 - 1 /\ 0 <= I308 - 1]
  f9(I320, I321, I322, I323, I324, I325, I326, I327, I328) -> f10(I320, I329, I330, I324, I331, I327, I328, I332, I333) [I328 + 2 <= I322 /\ I327 + 2 <= I321 /\ I326 + 2 <= I321 /\ 1 <= I330 - 1 /\ 0 <= I329 - 1 /\ -1 <= I323 - 1 /\ 1 <= I322 - 1 /\ 0 <= I321 - 1 /\ I330 <= I322 /\ I329 <= I321 /\ 0 <= I320 - 1 /\ I324 <= I325]
  f9(I334, I335, I336, I337, I338, I339, I340, I341, I342) -> f10(I334, I343, I344, I338, I339, I341, I342, I345, I346) [I342 + 2 <= I336 /\ I341 + 2 <= I335 /\ I340 + 2 <= I335 /\ 1 <= I344 - 1 /\ 0 <= I343 - 1 /\ -1 <= I337 - 1 /\ 1 <= I336 - 1 /\ 0 <= I335 - 1 /\ I344 <= I336 /\ I343 <= I335 /\ 0 <= I334 - 1 /\ I338 <= I339]
  f9(I347, I348, I349, I350, I351, I352, I353, I354, I355) -> f7(I356, I357, I347 - 1, I351, I352, I358, I359, I360, I361) [I355 + 2 <= I349 /\ I354 + 2 <= I348 /\ I353 + 2 <= I348 /\ 0 <= I357 - 1 /\ 0 <= I356 - 1 /\ 0 <= I350 - 1 /\ 2 <= I349 - 1 /\ 0 <= I348 - 1 /\ I357 <= I350 /\ I357 + 2 <= I349 /\ I356 <= I348]
  f7(I362, I363, I364, I365, I366, I367, I368, I369, I370) -> f9(I364, I371, I372, I373, I365, I366, I374, I375, I376) [I376 + 2 <= I363 /\ I375 + 2 <= I362 /\ I374 + 2 <= I362 /\ -1 <= I373 - 1 /\ 0 <= I372 - 1 /\ 0 <= I371 - 1 /\ 0 <= I363 - 1 /\ 0 <= I362 - 1 /\ I373 + 1 <= I363 /\ I372 <= I363 /\ I371 <= I362 /\ 0 <= I364 - 1 /\ -1 <= I365 - 1 /\ I365 <= I366]
  f8(I377, I378, I379, I380, I381, I382, I383, I384, I385) -> f7(I386, I387, I377, I378, I379, I388, I389, I390, I391) [1 <= I386 - 1 /\ 1 <= I387 - 1]
  f6(I392, I393, I394, I395, I396, I397, I398, I399, I400) -> f7(I401, I402, I392, I393, I403, I404, I405, I406, I407) [1 <= I401 - 1 /\ 1 <= I402 - 1 /\ 0 <= I393 - 1 /\ 0 <= I392 - 1]
  f6(I408, I409, I410, I411, I412, I413, I414, I415, I416) -> f7(I417, I418, I408, I409, 1, I419, I420, I421, I422) [1 <= I417 - 1 /\ 1 <= I418 - 1 /\ 0 <= I409 - 1 /\ 0 <= I408 - 1]
  f1(I423, I424, I425, I426, I427, I428, I429, I430, I431) -> f6(I432, I424, I433, I434, I435, I436, I437, I438, I439) [0 <= I423 - 1 /\ 0 <= I424 - 1 /\ -1 <= I432 - 1]
  f1(I440, I441, I442, I443, I444, I445, I446, I447, I448) -> f6(0, I441, I449, I450, I451, I452, I453, I454, I455) [0 <= I441 - 1 /\ 0 <= I440 - 1]
  f4(I456, I457, I458, I459, I460, I461, I462, I463, I464) -> f3(I465, I466, I467, I468, I469, I470, I471, I472, I473) [I458 + 2 <= I457 /\ 0 <= I465 - 1 /\ 0 <= I457 - 1 /\ 0 <= I456 - 1 /\ I465 <= I457]
  f5(I474, I475, I476, I477, I478, I479, I480, I481, I482) -> f4(I483, I484, I476, I485, I486, I487, I488, I489, I490) [I476 + 2 <= I475 /\ 1 <= I484 - 1 /\ 0 <= I483 - 1 /\ 1 <= I475 - 1 /\ 0 <= I474 - 1 /\ I484 <= I475 /\ I483 + 1 <= I475 /\ I483 <= I474]
  f1(I491, I492, I493, I494, I495, I496, I497, I498, I499) -> f4(I500, I501, I502, I503, I504, I505, I506, I507, I508) [0 <= I501 - 1 /\ 0 <= I500 - 1 /\ 0 <= I491 - 1 /\ I500 <= I491]
  f2(I509, I510, I511, I512, I513, I514, I515, I516, I517) -> f3(I518, I519, I520, I521, I522, I523, I524, I525, I526) [-1 <= I518 - 1 /\ 0 <= I509 - 1 /\ I510 <= 1 /\ I518 + 1 <= I509]
  f1(I527, I528, I529, I530, I531, I532, I533, I534, I535) -> f2(I536, 1, I528, I537, I538, I539, I540, I541, I542) [0 <= I536 - 1 /\ 0 <= I527 - 1 /\ I536 <= I527]
  f1(I543, I544, I545, I546, I547, I548, I549, I550, I551) -> f2(I552, 0, 0, I553, I554, I555, I556, I557, I558) [0 = I544 /\ 0 <= I552 - 1 /\ 0 <= I543 - 1 /\ I552 <= I543]

The dependency graph for this problem is:
  8 -> 16, 17, 21
  9 -> 16, 17, 21
  12 -> 16, 17, 21
  13 -> 20
  14 -> 16, 17, 21
  15 -> 16, 17, 21
  16 -> 12, 13
  17 -> 13
  20 -> 16, 17, 21
  21 -> 20
Where:
  8) f12#(I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f7#(I183, I184, I174 - 1, I177, I178, I185, I186, I187, I188) [I179 = I180 /\ I179 + 2 <= I176 /\ I179 + 2 <= I175 /\ 3 <= I184 - 1 /\ 3 <= I183 - 1 /\ 1 <= I176 - 1 /\ 1 <= I175 - 1 /\ I184 - 2 <= I176 /\ I184 - 2 <= I175 /\ I183 - 2 <= I176 /\ I183 - 2 <= I175]
  9) f12#(I189, I190, I191, I192, I193, I194, I195, I196, I197) -> f7#(I198, I199, I189 - 1, I192, I193, I200, I201, I202, I203) [I195 + 2 <= I191 /\ I194 + 2 <= I190 /\ 0 <= I199 - 1 /\ 0 <= I198 - 1 /\ 1 <= I191 - 1 /\ 0 <= I190 - 1]
  12) f11#(I233, I234, I235, I236, I237, I238, I239, I240, I241) -> f7#(I242, I243, I233 - 1, I237, I238, I244, I245, I246, I247) [I240 + 2 <= I234 /\ I239 + 2 <= I234 /\ 0 <= I243 - 1 /\ 0 <= I242 - 1 /\ 2 <= I235 - 1 /\ 0 <= I234 - 1 /\ I243 + 2 <= I235 /\ 0 <= I236 - 1 /\ I242 <= I234]
  13) f11#(I248, I249, I250, I251, I252, I253, I254, I255, I256) -> f9#(I248, I257, I258, I259, I252, I253, I254, I255, I260) [0 = I251 /\ I260 + 2 <= I250 /\ I255 + 2 <= I249 /\ I254 + 2 <= I249 /\ -1 <= I259 - 1 /\ 0 <= I258 - 1 /\ 0 <= I257 - 1 /\ 0 <= I250 - 1 /\ 0 <= I249 - 1 /\ I259 + 1 <= I250 /\ I258 <= I250 /\ I257 <= I249]
  14) f10#(I261, I262, I263, I264, I265, I266, I267, I268, I269) -> f7#(I270, I271, I261 - 1, I264, I265, I272, I273, I274, I275) [I266 = I267 /\ I266 + 2 <= I263 /\ I266 + 2 <= I262 /\ 3 <= I271 - 1 /\ 3 <= I270 - 1 /\ 1 <= I263 - 1 /\ 1 <= I262 - 1 /\ I271 - 2 <= I263 /\ I271 - 2 <= I262 /\ I270 - 2 <= I263 /\ I270 - 2 <= I262]
  15) f10#(I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f7#(I285, I286, I276 - 1, I279, I280, I287, I288, I289, I290) [I282 + 2 <= I278 /\ I281 + 2 <= I277 /\ 0 <= I286 - 1 /\ 0 <= I285 - 1 /\ 1 <= I278 - 1 /\ 0 <= I277 - 1]
  16) f7#(I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f11#(I293, I300, I301, I302, I294, I295 + 1, I303, I304, I305) [I304 + 2 <= I291 /\ I303 + 2 <= I291 /\ 0 <= I301 - 1 /\ 0 <= I300 - 1 /\ 0 <= I292 - 1 /\ 0 <= I291 - 1 /\ I301 <= I292 /\ I300 <= I291 /\ -1 <= I302 - 1 /\ -1 <= I295 - 1 /\ I295 <= I294 - 1 /\ -1 <= I294 - 1 /\ 0 <= I293 - 1]
  17) f7#(I306, I307, I308, I309, I310, I311, I312, I313, I314) -> f11#(I308, I315, I316, 0, I309, I310 + 1, I317, I318, I319) [I318 + 2 <= I306 /\ I317 + 2 <= I306 /\ 0 <= I316 - 1 /\ 0 <= I315 - 1 /\ 0 <= I307 - 1 /\ 0 <= I306 - 1 /\ I316 <= I307 /\ I315 <= I306 /\ -1 <= I310 - 1 /\ I310 <= I309 - 1 /\ -1 <= I309 - 1 /\ 0 <= I308 - 1]
  20) f9#(I347, I348, I349, I350, I351, I352, I353, I354, I355) -> f7#(I356, I357, I347 - 1, I351, I352, I358, I359, I360, I361) [I355 + 2 <= I349 /\ I354 + 2 <= I348 /\ I353 + 2 <= I348 /\ 0 <= I357 - 1 /\ 0 <= I356 - 1 /\ 0 <= I350 - 1 /\ 2 <= I349 - 1 /\ 0 <= I348 - 1 /\ I357 <= I350 /\ I357 + 2 <= I349 /\ I356 <= I348]
  21) f7#(I362, I363, I364, I365, I366, I367, I368, I369, I370) -> f9#(I364, I371, I372, I373, I365, I366, I374, I375, I376) [I376 + 2 <= I363 /\ I375 + 2 <= I362 /\ I374 + 2 <= I362 /\ -1 <= I373 - 1 /\ 0 <= I372 - 1 /\ 0 <= I371 - 1 /\ 0 <= I363 - 1 /\ 0 <= I362 - 1 /\ I373 + 1 <= I363 /\ I372 <= I363 /\ I371 <= I362 /\ 0 <= I364 - 1 /\ -1 <= I365 - 1 /\ I365 <= I366]

We have the following SCCs.
  { 12, 13, 16, 17, 20, 21 }

DP problem for innermost termination.
P =
  f11#(I233, I234, I235, I236, I237, I238, I239, I240, I241) -> f7#(I242, I243, I233 - 1, I237, I238, I244, I245, I246, I247) [I240 + 2 <= I234 /\ I239 + 2 <= I234 /\ 0 <= I243 - 1 /\ 0 <= I242 - 1 /\ 2 <= I235 - 1 /\ 0 <= I234 - 1 /\ I243 + 2 <= I235 /\ 0 <= I236 - 1 /\ I242 <= I234]
  f11#(I248, I249, I250, I251, I252, I253, I254, I255, I256) -> f9#(I248, I257, I258, I259, I252, I253, I254, I255, I260) [0 = I251 /\ I260 + 2 <= I250 /\ I255 + 2 <= I249 /\ I254 + 2 <= I249 /\ -1 <= I259 - 1 /\ 0 <= I258 - 1 /\ 0 <= I257 - 1 /\ 0 <= I250 - 1 /\ 0 <= I249 - 1 /\ I259 + 1 <= I250 /\ I258 <= I250 /\ I257 <= I249]
  f7#(I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f11#(I293, I300, I301, I302, I294, I295 + 1, I303, I304, I305) [I304 + 2 <= I291 /\ I303 + 2 <= I291 /\ 0 <= I301 - 1 /\ 0 <= I300 - 1 /\ 0 <= I292 - 1 /\ 0 <= I291 - 1 /\ I301 <= I292 /\ I300 <= I291 /\ -1 <= I302 - 1 /\ -1 <= I295 - 1 /\ I295 <= I294 - 1 /\ -1 <= I294 - 1 /\ 0 <= I293 - 1]
  f7#(I306, I307, I308, I309, I310, I311, I312, I313, I314) -> f11#(I308, I315, I316, 0, I309, I310 + 1, I317, I318, I319) [I318 + 2 <= I306 /\ I317 + 2 <= I306 /\ 0 <= I316 - 1 /\ 0 <= I315 - 1 /\ 0 <= I307 - 1 /\ 0 <= I306 - 1 /\ I316 <= I307 /\ I315 <= I306 /\ -1 <= I310 - 1 /\ I310 <= I309 - 1 /\ -1 <= I309 - 1 /\ 0 <= I308 - 1]
  f9#(I347, I348, I349, I350, I351, I352, I353, I354, I355) -> f7#(I356, I357, I347 - 1, I351, I352, I358, I359, I360, I361) [I355 + 2 <= I349 /\ I354 + 2 <= I348 /\ I353 + 2 <= I348 /\ 0 <= I357 - 1 /\ 0 <= I356 - 1 /\ 0 <= I350 - 1 /\ 2 <= I349 - 1 /\ 0 <= I348 - 1 /\ I357 <= I350 /\ I357 + 2 <= I349 /\ I356 <= I348]
  f7#(I362, I363, I364, I365, I366, I367, I368, I369, I370) -> f9#(I364, I371, I372, I373, I365, I366, I374, I375, I376) [I376 + 2 <= I363 /\ I375 + 2 <= I362 /\ I374 + 2 <= I362 /\ -1 <= I373 - 1 /\ 0 <= I372 - 1 /\ 0 <= I371 - 1 /\ 0 <= I363 - 1 /\ 0 <= I362 - 1 /\ I373 + 1 <= I363 /\ I372 <= I363 /\ I371 <= I362 /\ 0 <= I364 - 1 /\ -1 <= I365 - 1 /\ I365 <= I366]
R = 
  init(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9) 
  f11(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f14(I9, I4, I5, I10, I11, I12, I13, I14, I15) [I7 + 2 <= I1 /\ I6 + 2 <= I1 /\ 1 <= I2 - 1 /\ 0 <= I1 - 1 /\ 0 <= I3 - 1 /\ -1 <= I4 - 1 /\ 0 <= I5 - 1 /\ 0 <= I0 - 1]
  f9(I16, I17, I18, I19, I20, I21, I22, I23, I24) -> f14(I25, I20, I21, I26, I27, I28, I29, I30, I31) [I24 + 2 <= I18 /\ I23 + 2 <= I17 /\ I22 + 2 <= I17 /\ -1 <= I19 - 1 /\ 1 <= I18 - 1 /\ 0 <= I17 - 1 /\ 0 <= I16 - 1 /\ I20 <= I21 /\ -1 <= I20 - 1]
  f6(I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f14(I41, I33, 1, I42, I43, I44, I45, I46, I47) [0 <= I32 - 1 /\ 0 <= I33 - 1]
  f13(I48, I49, I50, I51, I52, I53, I54, I55, I56) -> f3(I57, I58, I59, I60, I61, I62, I63, I64, I65) [-1 <= I57 - 1 /\ -1 <= I51 - 1 /\ -1 <= I49 - 1 /\ 2 <= I48 - 1 /\ I57 <= I51 /\ I57 <= I49 /\ I57 + 2 <= I48]
  f3(I66, I67, I68, I69, I70, I71, I72, I73, I74) -> f13(I75, I76, I77, I78, I79, I80, I81, I82, I83) [-1 <= I78 - 1 /\ -1 <= I76 - 1 /\ 3 <= I75 - 1 /\ 0 <= I66 - 1 /\ I78 + 1 <= I66 /\ I76 + 1 <= I66 /\ I75 - 3 <= I66]
  f3(I84, I85, I86, I87, I88, I89, I90, I91, I92) -> f13(I93, I94, I95, I96, I97, I98, I99, I100, I101) [-1 <= I96 - 1 /\ -1 <= I94 - 1 /\ 4 <= I93 - 1 /\ 0 <= I84 - 1 /\ I96 + 1 <= I84 /\ I94 + 1 <= I84]
  f3(I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f13(I111, I112, I113, I114, I115, I116, I117, I118, I119) [-1 <= I114 - 1 /\ -1 <= I112 - 1 /\ 4 <= I111 - 1 /\ 0 <= I102 - 1 /\ I114 + 1 <= I102 /\ I112 + 1 <= I102]
  f3(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f13(I129, I130, I131, I132, I133, I134, I135, I136, I137) [-1 <= I132 - 1 /\ -1 <= I130 - 1 /\ 4 <= I129 - 1 /\ 0 <= I120 - 1 /\ I132 + 1 <= I120 /\ I130 + 1 <= I120]
  f3(I138, I139, I140, I141, I142, I143, I144, I145, I146) -> f3(I147, I148, I149, I150, I151, I152, I153, I154, I155) [-1 <= I147 - 1 /\ 1 <= I138 - 1 /\ I147 + 2 <= I138]
  f3(I156, I157, I158, I159, I160, I161, I162, I163, I164) -> f3(I165, I166, I167, I168, I169, I170, I171, I172, I173) [-1 <= I165 - 1 /\ 0 <= I156 - 1 /\ I165 + 1 <= I156]
  f12(I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f7(I183, I184, I174 - 1, I177, I178, I185, I186, I187, I188) [I179 = I180 /\ I179 + 2 <= I176 /\ I179 + 2 <= I175 /\ 3 <= I184 - 1 /\ 3 <= I183 - 1 /\ 1 <= I176 - 1 /\ 1 <= I175 - 1 /\ I184 - 2 <= I176 /\ I184 - 2 <= I175 /\ I183 - 2 <= I176 /\ I183 - 2 <= I175]
  f12(I189, I190, I191, I192, I193, I194, I195, I196, I197) -> f7(I198, I199, I189 - 1, I192, I193, I200, I201, I202, I203) [I195 + 2 <= I191 /\ I194 + 2 <= I190 /\ 0 <= I199 - 1 /\ 0 <= I198 - 1 /\ 1 <= I191 - 1 /\ 0 <= I190 - 1]
  f11(I204, I205, I206, I207, I208, I209, I210, I211, I212) -> f12(I204, I213, I214, I208, I215, I210, I216, I217, I218) [I216 + 2 <= I206 /\ I211 + 2 <= I205 /\ I210 + 2 <= I205 /\ 1 <= I214 - 1 /\ 0 <= I213 - 1 /\ 1 <= I206 - 1 /\ 0 <= I205 - 1 /\ I214 <= I206 /\ I213 <= I205 /\ 0 <= I204 - 1 /\ 0 <= I209 - 1 /\ 0 <= I207 - 1]
  f11(I219, I220, I221, I222, I223, I224, I225, I226, I227) -> f12(I219, I228, I229, I223, I224, I225, I230, I231, I232) [I230 + 2 <= I221 /\ I226 + 2 <= I220 /\ I225 + 2 <= I220 /\ 1 <= I229 - 1 /\ 0 <= I228 - 1 /\ 1 <= I221 - 1 /\ 0 <= I220 - 1 /\ I229 <= I221 /\ I228 <= I220 /\ 0 <= I219 - 1 /\ 0 <= I224 - 1 /\ 0 <= I222 - 1]
  f11(I233, I234, I235, I236, I237, I238, I239, I240, I241) -> f7(I242, I243, I233 - 1, I237, I238, I244, I245, I246, I247) [I240 + 2 <= I234 /\ I239 + 2 <= I234 /\ 0 <= I243 - 1 /\ 0 <= I242 - 1 /\ 2 <= I235 - 1 /\ 0 <= I234 - 1 /\ I243 + 2 <= I235 /\ 0 <= I236 - 1 /\ I242 <= I234]
  f11(I248, I249, I250, I251, I252, I253, I254, I255, I256) -> f9(I248, I257, I258, I259, I252, I253, I254, I255, I260) [0 = I251 /\ I260 + 2 <= I250 /\ I255 + 2 <= I249 /\ I254 + 2 <= I249 /\ -1 <= I259 - 1 /\ 0 <= I258 - 1 /\ 0 <= I257 - 1 /\ 0 <= I250 - 1 /\ 0 <= I249 - 1 /\ I259 + 1 <= I250 /\ I258 <= I250 /\ I257 <= I249]
  f10(I261, I262, I263, I264, I265, I266, I267, I268, I269) -> f7(I270, I271, I261 - 1, I264, I265, I272, I273, I274, I275) [I266 = I267 /\ I266 + 2 <= I263 /\ I266 + 2 <= I262 /\ 3 <= I271 - 1 /\ 3 <= I270 - 1 /\ 1 <= I263 - 1 /\ 1 <= I262 - 1 /\ I271 - 2 <= I263 /\ I271 - 2 <= I262 /\ I270 - 2 <= I263 /\ I270 - 2 <= I262]
  f10(I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f7(I285, I286, I276 - 1, I279, I280, I287, I288, I289, I290) [I282 + 2 <= I278 /\ I281 + 2 <= I277 /\ 0 <= I286 - 1 /\ 0 <= I285 - 1 /\ 1 <= I278 - 1 /\ 0 <= I277 - 1]
  f7(I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f11(I293, I300, I301, I302, I294, I295 + 1, I303, I304, I305) [I304 + 2 <= I291 /\ I303 + 2 <= I291 /\ 0 <= I301 - 1 /\ 0 <= I300 - 1 /\ 0 <= I292 - 1 /\ 0 <= I291 - 1 /\ I301 <= I292 /\ I300 <= I291 /\ -1 <= I302 - 1 /\ -1 <= I295 - 1 /\ I295 <= I294 - 1 /\ -1 <= I294 - 1 /\ 0 <= I293 - 1]
  f7(I306, I307, I308, I309, I310, I311, I312, I313, I314) -> f11(I308, I315, I316, 0, I309, I310 + 1, I317, I318, I319) [I318 + 2 <= I306 /\ I317 + 2 <= I306 /\ 0 <= I316 - 1 /\ 0 <= I315 - 1 /\ 0 <= I307 - 1 /\ 0 <= I306 - 1 /\ I316 <= I307 /\ I315 <= I306 /\ -1 <= I310 - 1 /\ I310 <= I309 - 1 /\ -1 <= I309 - 1 /\ 0 <= I308 - 1]
  f9(I320, I321, I322, I323, I324, I325, I326, I327, I328) -> f10(I320, I329, I330, I324, I331, I327, I328, I332, I333) [I328 + 2 <= I322 /\ I327 + 2 <= I321 /\ I326 + 2 <= I321 /\ 1 <= I330 - 1 /\ 0 <= I329 - 1 /\ -1 <= I323 - 1 /\ 1 <= I322 - 1 /\ 0 <= I321 - 1 /\ I330 <= I322 /\ I329 <= I321 /\ 0 <= I320 - 1 /\ I324 <= I325]
  f9(I334, I335, I336, I337, I338, I339, I340, I341, I342) -> f10(I334, I343, I344, I338, I339, I341, I342, I345, I346) [I342 + 2 <= I336 /\ I341 + 2 <= I335 /\ I340 + 2 <= I335 /\ 1 <= I344 - 1 /\ 0 <= I343 - 1 /\ -1 <= I337 - 1 /\ 1 <= I336 - 1 /\ 0 <= I335 - 1 /\ I344 <= I336 /\ I343 <= I335 /\ 0 <= I334 - 1 /\ I338 <= I339]
  f9(I347, I348, I349, I350, I351, I352, I353, I354, I355) -> f7(I356, I357, I347 - 1, I351, I352, I358, I359, I360, I361) [I355 + 2 <= I349 /\ I354 + 2 <= I348 /\ I353 + 2 <= I348 /\ 0 <= I357 - 1 /\ 0 <= I356 - 1 /\ 0 <= I350 - 1 /\ 2 <= I349 - 1 /\ 0 <= I348 - 1 /\ I357 <= I350 /\ I357 + 2 <= I349 /\ I356 <= I348]
  f7(I362, I363, I364, I365, I366, I367, I368, I369, I370) -> f9(I364, I371, I372, I373, I365, I366, I374, I375, I376) [I376 + 2 <= I363 /\ I375 + 2 <= I362 /\ I374 + 2 <= I362 /\ -1 <= I373 - 1 /\ 0 <= I372 - 1 /\ 0 <= I371 - 1 /\ 0 <= I363 - 1 /\ 0 <= I362 - 1 /\ I373 + 1 <= I363 /\ I372 <= I363 /\ I371 <= I362 /\ 0 <= I364 - 1 /\ -1 <= I365 - 1 /\ I365 <= I366]
  f8(I377, I378, I379, I380, I381, I382, I383, I384, I385) -> f7(I386, I387, I377, I378, I379, I388, I389, I390, I391) [1 <= I386 - 1 /\ 1 <= I387 - 1]
  f6(I392, I393, I394, I395, I396, I397, I398, I399, I400) -> f7(I401, I402, I392, I393, I403, I404, I405, I406, I407) [1 <= I401 - 1 /\ 1 <= I402 - 1 /\ 0 <= I393 - 1 /\ 0 <= I392 - 1]
  f6(I408, I409, I410, I411, I412, I413, I414, I415, I416) -> f7(I417, I418, I408, I409, 1, I419, I420, I421, I422) [1 <= I417 - 1 /\ 1 <= I418 - 1 /\ 0 <= I409 - 1 /\ 0 <= I408 - 1]
  f1(I423, I424, I425, I426, I427, I428, I429, I430, I431) -> f6(I432, I424, I433, I434, I435, I436, I437, I438, I439) [0 <= I423 - 1 /\ 0 <= I424 - 1 /\ -1 <= I432 - 1]
  f1(I440, I441, I442, I443, I444, I445, I446, I447, I448) -> f6(0, I441, I449, I450, I451, I452, I453, I454, I455) [0 <= I441 - 1 /\ 0 <= I440 - 1]
  f4(I456, I457, I458, I459, I460, I461, I462, I463, I464) -> f3(I465, I466, I467, I468, I469, I470, I471, I472, I473) [I458 + 2 <= I457 /\ 0 <= I465 - 1 /\ 0 <= I457 - 1 /\ 0 <= I456 - 1 /\ I465 <= I457]
  f5(I474, I475, I476, I477, I478, I479, I480, I481, I482) -> f4(I483, I484, I476, I485, I486, I487, I488, I489, I490) [I476 + 2 <= I475 /\ 1 <= I484 - 1 /\ 0 <= I483 - 1 /\ 1 <= I475 - 1 /\ 0 <= I474 - 1 /\ I484 <= I475 /\ I483 + 1 <= I475 /\ I483 <= I474]
  f1(I491, I492, I493, I494, I495, I496, I497, I498, I499) -> f4(I500, I501, I502, I503, I504, I505, I506, I507, I508) [0 <= I501 - 1 /\ 0 <= I500 - 1 /\ 0 <= I491 - 1 /\ I500 <= I491]
  f2(I509, I510, I511, I512, I513, I514, I515, I516, I517) -> f3(I518, I519, I520, I521, I522, I523, I524, I525, I526) [-1 <= I518 - 1 /\ 0 <= I509 - 1 /\ I510 <= 1 /\ I518 + 1 <= I509]
  f1(I527, I528, I529, I530, I531, I532, I533, I534, I535) -> f2(I536, 1, I528, I537, I538, I539, I540, I541, I542) [0 <= I536 - 1 /\ 0 <= I527 - 1 /\ I536 <= I527]
  f1(I543, I544, I545, I546, I547, I548, I549, I550, I551) -> f2(I552, 0, 0, I553, I554, I555, I556, I557, I558) [0 = I544 /\ 0 <= I552 - 1 /\ 0 <= I543 - 1 /\ I552 <= I543]

We use the basic value criterion with the projection function NU:
  NU[f9#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = z4
  NU[f7#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = z2
  NU[f11#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = z3

This gives the following inequalities:
  I240 + 2 <= I234 /\ I239 + 2 <= I234 /\ 0 <= I243 - 1 /\ 0 <= I242 - 1 /\ 2 <= I235 - 1 /\ 0 <= I234 - 1 /\ I243 + 2 <= I235 /\ 0 <= I236 - 1 /\ I242 <= I234  ==>  I235 >! I243
  0 = I251 /\ I260 + 2 <= I250 /\ I255 + 2 <= I249 /\ I254 + 2 <= I249 /\ -1 <= I259 - 1 /\ 0 <= I258 - 1 /\ 0 <= I257 - 1 /\ 0 <= I250 - 1 /\ 0 <= I249 - 1 /\ I259 + 1 <= I250 /\ I258 <= I250 /\ I257 <= I249  ==>  I250 >! I259
  I304 + 2 <= I291 /\ I303 + 2 <= I291 /\ 0 <= I301 - 1 /\ 0 <= I300 - 1 /\ 0 <= I292 - 1 /\ 0 <= I291 - 1 /\ I301 <= I292 /\ I300 <= I291 /\ -1 <= I302 - 1 /\ -1 <= I295 - 1 /\ I295 <= I294 - 1 /\ -1 <= I294 - 1 /\ 0 <= I293 - 1  ==>  I292 (>! \union =) I301
  I318 + 2 <= I306 /\ I317 + 2 <= I306 /\ 0 <= I316 - 1 /\ 0 <= I315 - 1 /\ 0 <= I307 - 1 /\ 0 <= I306 - 1 /\ I316 <= I307 /\ I315 <= I306 /\ -1 <= I310 - 1 /\ I310 <= I309 - 1 /\ -1 <= I309 - 1 /\ 0 <= I308 - 1  ==>  I307 (>! \union =) I316
  I355 + 2 <= I349 /\ I354 + 2 <= I348 /\ I353 + 2 <= I348 /\ 0 <= I357 - 1 /\ 0 <= I356 - 1 /\ 0 <= I350 - 1 /\ 2 <= I349 - 1 /\ 0 <= I348 - 1 /\ I357 <= I350 /\ I357 + 2 <= I349 /\ I356 <= I348  ==>  I350 (>! \union =) I357
  I376 + 2 <= I363 /\ I375 + 2 <= I362 /\ I374 + 2 <= I362 /\ -1 <= I373 - 1 /\ 0 <= I372 - 1 /\ 0 <= I371 - 1 /\ 0 <= I363 - 1 /\ 0 <= I362 - 1 /\ I373 + 1 <= I363 /\ I372 <= I363 /\ I371 <= I362 /\ 0 <= I364 - 1 /\ -1 <= I365 - 1 /\ I365 <= I366  ==>  I363 >! I373

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f7#(I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f11#(I293, I300, I301, I302, I294, I295 + 1, I303, I304, I305) [I304 + 2 <= I291 /\ I303 + 2 <= I291 /\ 0 <= I301 - 1 /\ 0 <= I300 - 1 /\ 0 <= I292 - 1 /\ 0 <= I291 - 1 /\ I301 <= I292 /\ I300 <= I291 /\ -1 <= I302 - 1 /\ -1 <= I295 - 1 /\ I295 <= I294 - 1 /\ -1 <= I294 - 1 /\ 0 <= I293 - 1]
  f7#(I306, I307, I308, I309, I310, I311, I312, I313, I314) -> f11#(I308, I315, I316, 0, I309, I310 + 1, I317, I318, I319) [I318 + 2 <= I306 /\ I317 + 2 <= I306 /\ 0 <= I316 - 1 /\ 0 <= I315 - 1 /\ 0 <= I307 - 1 /\ 0 <= I306 - 1 /\ I316 <= I307 /\ I315 <= I306 /\ -1 <= I310 - 1 /\ I310 <= I309 - 1 /\ -1 <= I309 - 1 /\ 0 <= I308 - 1]
  f9#(I347, I348, I349, I350, I351, I352, I353, I354, I355) -> f7#(I356, I357, I347 - 1, I351, I352, I358, I359, I360, I361) [I355 + 2 <= I349 /\ I354 + 2 <= I348 /\ I353 + 2 <= I348 /\ 0 <= I357 - 1 /\ 0 <= I356 - 1 /\ 0 <= I350 - 1 /\ 2 <= I349 - 1 /\ 0 <= I348 - 1 /\ I357 <= I350 /\ I357 + 2 <= I349 /\ I356 <= I348]
R = 
  init(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9) 
  f11(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f14(I9, I4, I5, I10, I11, I12, I13, I14, I15) [I7 + 2 <= I1 /\ I6 + 2 <= I1 /\ 1 <= I2 - 1 /\ 0 <= I1 - 1 /\ 0 <= I3 - 1 /\ -1 <= I4 - 1 /\ 0 <= I5 - 1 /\ 0 <= I0 - 1]
  f9(I16, I17, I18, I19, I20, I21, I22, I23, I24) -> f14(I25, I20, I21, I26, I27, I28, I29, I30, I31) [I24 + 2 <= I18 /\ I23 + 2 <= I17 /\ I22 + 2 <= I17 /\ -1 <= I19 - 1 /\ 1 <= I18 - 1 /\ 0 <= I17 - 1 /\ 0 <= I16 - 1 /\ I20 <= I21 /\ -1 <= I20 - 1]
  f6(I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f14(I41, I33, 1, I42, I43, I44, I45, I46, I47) [0 <= I32 - 1 /\ 0 <= I33 - 1]
  f13(I48, I49, I50, I51, I52, I53, I54, I55, I56) -> f3(I57, I58, I59, I60, I61, I62, I63, I64, I65) [-1 <= I57 - 1 /\ -1 <= I51 - 1 /\ -1 <= I49 - 1 /\ 2 <= I48 - 1 /\ I57 <= I51 /\ I57 <= I49 /\ I57 + 2 <= I48]
  f3(I66, I67, I68, I69, I70, I71, I72, I73, I74) -> f13(I75, I76, I77, I78, I79, I80, I81, I82, I83) [-1 <= I78 - 1 /\ -1 <= I76 - 1 /\ 3 <= I75 - 1 /\ 0 <= I66 - 1 /\ I78 + 1 <= I66 /\ I76 + 1 <= I66 /\ I75 - 3 <= I66]
  f3(I84, I85, I86, I87, I88, I89, I90, I91, I92) -> f13(I93, I94, I95, I96, I97, I98, I99, I100, I101) [-1 <= I96 - 1 /\ -1 <= I94 - 1 /\ 4 <= I93 - 1 /\ 0 <= I84 - 1 /\ I96 + 1 <= I84 /\ I94 + 1 <= I84]
  f3(I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f13(I111, I112, I113, I114, I115, I116, I117, I118, I119) [-1 <= I114 - 1 /\ -1 <= I112 - 1 /\ 4 <= I111 - 1 /\ 0 <= I102 - 1 /\ I114 + 1 <= I102 /\ I112 + 1 <= I102]
  f3(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f13(I129, I130, I131, I132, I133, I134, I135, I136, I137) [-1 <= I132 - 1 /\ -1 <= I130 - 1 /\ 4 <= I129 - 1 /\ 0 <= I120 - 1 /\ I132 + 1 <= I120 /\ I130 + 1 <= I120]
  f3(I138, I139, I140, I141, I142, I143, I144, I145, I146) -> f3(I147, I148, I149, I150, I151, I152, I153, I154, I155) [-1 <= I147 - 1 /\ 1 <= I138 - 1 /\ I147 + 2 <= I138]
  f3(I156, I157, I158, I159, I160, I161, I162, I163, I164) -> f3(I165, I166, I167, I168, I169, I170, I171, I172, I173) [-1 <= I165 - 1 /\ 0 <= I156 - 1 /\ I165 + 1 <= I156]
  f12(I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f7(I183, I184, I174 - 1, I177, I178, I185, I186, I187, I188) [I179 = I180 /\ I179 + 2 <= I176 /\ I179 + 2 <= I175 /\ 3 <= I184 - 1 /\ 3 <= I183 - 1 /\ 1 <= I176 - 1 /\ 1 <= I175 - 1 /\ I184 - 2 <= I176 /\ I184 - 2 <= I175 /\ I183 - 2 <= I176 /\ I183 - 2 <= I175]
  f12(I189, I190, I191, I192, I193, I194, I195, I196, I197) -> f7(I198, I199, I189 - 1, I192, I193, I200, I201, I202, I203) [I195 + 2 <= I191 /\ I194 + 2 <= I190 /\ 0 <= I199 - 1 /\ 0 <= I198 - 1 /\ 1 <= I191 - 1 /\ 0 <= I190 - 1]
  f11(I204, I205, I206, I207, I208, I209, I210, I211, I212) -> f12(I204, I213, I214, I208, I215, I210, I216, I217, I218) [I216 + 2 <= I206 /\ I211 + 2 <= I205 /\ I210 + 2 <= I205 /\ 1 <= I214 - 1 /\ 0 <= I213 - 1 /\ 1 <= I206 - 1 /\ 0 <= I205 - 1 /\ I214 <= I206 /\ I213 <= I205 /\ 0 <= I204 - 1 /\ 0 <= I209 - 1 /\ 0 <= I207 - 1]
  f11(I219, I220, I221, I222, I223, I224, I225, I226, I227) -> f12(I219, I228, I229, I223, I224, I225, I230, I231, I232) [I230 + 2 <= I221 /\ I226 + 2 <= I220 /\ I225 + 2 <= I220 /\ 1 <= I229 - 1 /\ 0 <= I228 - 1 /\ 1 <= I221 - 1 /\ 0 <= I220 - 1 /\ I229 <= I221 /\ I228 <= I220 /\ 0 <= I219 - 1 /\ 0 <= I224 - 1 /\ 0 <= I222 - 1]
  f11(I233, I234, I235, I236, I237, I238, I239, I240, I241) -> f7(I242, I243, I233 - 1, I237, I238, I244, I245, I246, I247) [I240 + 2 <= I234 /\ I239 + 2 <= I234 /\ 0 <= I243 - 1 /\ 0 <= I242 - 1 /\ 2 <= I235 - 1 /\ 0 <= I234 - 1 /\ I243 + 2 <= I235 /\ 0 <= I236 - 1 /\ I242 <= I234]
  f11(I248, I249, I250, I251, I252, I253, I254, I255, I256) -> f9(I248, I257, I258, I259, I252, I253, I254, I255, I260) [0 = I251 /\ I260 + 2 <= I250 /\ I255 + 2 <= I249 /\ I254 + 2 <= I249 /\ -1 <= I259 - 1 /\ 0 <= I258 - 1 /\ 0 <= I257 - 1 /\ 0 <= I250 - 1 /\ 0 <= I249 - 1 /\ I259 + 1 <= I250 /\ I258 <= I250 /\ I257 <= I249]
  f10(I261, I262, I263, I264, I265, I266, I267, I268, I269) -> f7(I270, I271, I261 - 1, I264, I265, I272, I273, I274, I275) [I266 = I267 /\ I266 + 2 <= I263 /\ I266 + 2 <= I262 /\ 3 <= I271 - 1 /\ 3 <= I270 - 1 /\ 1 <= I263 - 1 /\ 1 <= I262 - 1 /\ I271 - 2 <= I263 /\ I271 - 2 <= I262 /\ I270 - 2 <= I263 /\ I270 - 2 <= I262]
  f10(I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f7(I285, I286, I276 - 1, I279, I280, I287, I288, I289, I290) [I282 + 2 <= I278 /\ I281 + 2 <= I277 /\ 0 <= I286 - 1 /\ 0 <= I285 - 1 /\ 1 <= I278 - 1 /\ 0 <= I277 - 1]
  f7(I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f11(I293, I300, I301, I302, I294, I295 + 1, I303, I304, I305) [I304 + 2 <= I291 /\ I303 + 2 <= I291 /\ 0 <= I301 - 1 /\ 0 <= I300 - 1 /\ 0 <= I292 - 1 /\ 0 <= I291 - 1 /\ I301 <= I292 /\ I300 <= I291 /\ -1 <= I302 - 1 /\ -1 <= I295 - 1 /\ I295 <= I294 - 1 /\ -1 <= I294 - 1 /\ 0 <= I293 - 1]
  f7(I306, I307, I308, I309, I310, I311, I312, I313, I314) -> f11(I308, I315, I316, 0, I309, I310 + 1, I317, I318, I319) [I318 + 2 <= I306 /\ I317 + 2 <= I306 /\ 0 <= I316 - 1 /\ 0 <= I315 - 1 /\ 0 <= I307 - 1 /\ 0 <= I306 - 1 /\ I316 <= I307 /\ I315 <= I306 /\ -1 <= I310 - 1 /\ I310 <= I309 - 1 /\ -1 <= I309 - 1 /\ 0 <= I308 - 1]
  f9(I320, I321, I322, I323, I324, I325, I326, I327, I328) -> f10(I320, I329, I330, I324, I331, I327, I328, I332, I333) [I328 + 2 <= I322 /\ I327 + 2 <= I321 /\ I326 + 2 <= I321 /\ 1 <= I330 - 1 /\ 0 <= I329 - 1 /\ -1 <= I323 - 1 /\ 1 <= I322 - 1 /\ 0 <= I321 - 1 /\ I330 <= I322 /\ I329 <= I321 /\ 0 <= I320 - 1 /\ I324 <= I325]
  f9(I334, I335, I336, I337, I338, I339, I340, I341, I342) -> f10(I334, I343, I344, I338, I339, I341, I342, I345, I346) [I342 + 2 <= I336 /\ I341 + 2 <= I335 /\ I340 + 2 <= I335 /\ 1 <= I344 - 1 /\ 0 <= I343 - 1 /\ -1 <= I337 - 1 /\ 1 <= I336 - 1 /\ 0 <= I335 - 1 /\ I344 <= I336 /\ I343 <= I335 /\ 0 <= I334 - 1 /\ I338 <= I339]
  f9(I347, I348, I349, I350, I351, I352, I353, I354, I355) -> f7(I356, I357, I347 - 1, I351, I352, I358, I359, I360, I361) [I355 + 2 <= I349 /\ I354 + 2 <= I348 /\ I353 + 2 <= I348 /\ 0 <= I357 - 1 /\ 0 <= I356 - 1 /\ 0 <= I350 - 1 /\ 2 <= I349 - 1 /\ 0 <= I348 - 1 /\ I357 <= I350 /\ I357 + 2 <= I349 /\ I356 <= I348]
  f7(I362, I363, I364, I365, I366, I367, I368, I369, I370) -> f9(I364, I371, I372, I373, I365, I366, I374, I375, I376) [I376 + 2 <= I363 /\ I375 + 2 <= I362 /\ I374 + 2 <= I362 /\ -1 <= I373 - 1 /\ 0 <= I372 - 1 /\ 0 <= I371 - 1 /\ 0 <= I363 - 1 /\ 0 <= I362 - 1 /\ I373 + 1 <= I363 /\ I372 <= I363 /\ I371 <= I362 /\ 0 <= I364 - 1 /\ -1 <= I365 - 1 /\ I365 <= I366]
  f8(I377, I378, I379, I380, I381, I382, I383, I384, I385) -> f7(I386, I387, I377, I378, I379, I388, I389, I390, I391) [1 <= I386 - 1 /\ 1 <= I387 - 1]
  f6(I392, I393, I394, I395, I396, I397, I398, I399, I400) -> f7(I401, I402, I392, I393, I403, I404, I405, I406, I407) [1 <= I401 - 1 /\ 1 <= I402 - 1 /\ 0 <= I393 - 1 /\ 0 <= I392 - 1]
  f6(I408, I409, I410, I411, I412, I413, I414, I415, I416) -> f7(I417, I418, I408, I409, 1, I419, I420, I421, I422) [1 <= I417 - 1 /\ 1 <= I418 - 1 /\ 0 <= I409 - 1 /\ 0 <= I408 - 1]
  f1(I423, I424, I425, I426, I427, I428, I429, I430, I431) -> f6(I432, I424, I433, I434, I435, I436, I437, I438, I439) [0 <= I423 - 1 /\ 0 <= I424 - 1 /\ -1 <= I432 - 1]
  f1(I440, I441, I442, I443, I444, I445, I446, I447, I448) -> f6(0, I441, I449, I450, I451, I452, I453, I454, I455) [0 <= I441 - 1 /\ 0 <= I440 - 1]
  f4(I456, I457, I458, I459, I460, I461, I462, I463, I464) -> f3(I465, I466, I467, I468, I469, I470, I471, I472, I473) [I458 + 2 <= I457 /\ 0 <= I465 - 1 /\ 0 <= I457 - 1 /\ 0 <= I456 - 1 /\ I465 <= I457]
  f5(I474, I475, I476, I477, I478, I479, I480, I481, I482) -> f4(I483, I484, I476, I485, I486, I487, I488, I489, I490) [I476 + 2 <= I475 /\ 1 <= I484 - 1 /\ 0 <= I483 - 1 /\ 1 <= I475 - 1 /\ 0 <= I474 - 1 /\ I484 <= I475 /\ I483 + 1 <= I475 /\ I483 <= I474]
  f1(I491, I492, I493, I494, I495, I496, I497, I498, I499) -> f4(I500, I501, I502, I503, I504, I505, I506, I507, I508) [0 <= I501 - 1 /\ 0 <= I500 - 1 /\ 0 <= I491 - 1 /\ I500 <= I491]
  f2(I509, I510, I511, I512, I513, I514, I515, I516, I517) -> f3(I518, I519, I520, I521, I522, I523, I524, I525, I526) [-1 <= I518 - 1 /\ 0 <= I509 - 1 /\ I510 <= 1 /\ I518 + 1 <= I509]
  f1(I527, I528, I529, I530, I531, I532, I533, I534, I535) -> f2(I536, 1, I528, I537, I538, I539, I540, I541, I542) [0 <= I536 - 1 /\ 0 <= I527 - 1 /\ I536 <= I527]
  f1(I543, I544, I545, I546, I547, I548, I549, I550, I551) -> f2(I552, 0, 0, I553, I554, I555, I556, I557, I558) [0 = I544 /\ 0 <= I552 - 1 /\ 0 <= I543 - 1 /\ I552 <= I543]

The dependency graph for this problem is:
  16 -> 
  17 -> 
  20 -> 16, 17
Where:
  16) f7#(I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f11#(I293, I300, I301, I302, I294, I295 + 1, I303, I304, I305) [I304 + 2 <= I291 /\ I303 + 2 <= I291 /\ 0 <= I301 - 1 /\ 0 <= I300 - 1 /\ 0 <= I292 - 1 /\ 0 <= I291 - 1 /\ I301 <= I292 /\ I300 <= I291 /\ -1 <= I302 - 1 /\ -1 <= I295 - 1 /\ I295 <= I294 - 1 /\ -1 <= I294 - 1 /\ 0 <= I293 - 1]
  17) f7#(I306, I307, I308, I309, I310, I311, I312, I313, I314) -> f11#(I308, I315, I316, 0, I309, I310 + 1, I317, I318, I319) [I318 + 2 <= I306 /\ I317 + 2 <= I306 /\ 0 <= I316 - 1 /\ 0 <= I315 - 1 /\ 0 <= I307 - 1 /\ 0 <= I306 - 1 /\ I316 <= I307 /\ I315 <= I306 /\ -1 <= I310 - 1 /\ I310 <= I309 - 1 /\ -1 <= I309 - 1 /\ 0 <= I308 - 1]
  20) f9#(I347, I348, I349, I350, I351, I352, I353, I354, I355) -> f7#(I356, I357, I347 - 1, I351, I352, I358, I359, I360, I361) [I355 + 2 <= I349 /\ I354 + 2 <= I348 /\ I353 + 2 <= I348 /\ 0 <= I357 - 1 /\ 0 <= I356 - 1 /\ 0 <= I350 - 1 /\ 2 <= I349 - 1 /\ 0 <= I348 - 1 /\ I357 <= I350 /\ I357 + 2 <= I349 /\ I356 <= I348]

We have the following SCCs.