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


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MAYBE

DP problem for innermost termination.
P =
  init#(x1, x2, x3, x4, x5, x6, x7) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7) 
  f9#(I0, I1, I2, I3, I4, I5, I6) -> f7#(I3, I1, I0, I7, I8, I9, I10) [I3 - I2 * y1 = 0 /\ I2 <= I3 - 1 /\ I3 - I2 * y1 <= I2 - 1 /\ 0 <= I3 - I2 * y1]
  f8#(I11, I12, I13, I14, I15, I16, I17) -> f9#(I11, I12, I13, I14, I18, I19, I20) [I13 <= I14 - 1 /\ I14 - I13 * I21 = 0]
  f7#(I22, I23, I24, I25, I26, I27, I28) -> f7#(I22 + 1, I23, I24, I29, I30, I31, I32) [I22 <= 0 /\ I23 <= I24 - 1]
  f8#(I33, I34, I35, I36, I37, I38, I39) -> f7#(I36, I34 + 1, I33, I40, I41, I42, I43) [I36 <= I35]
  f9#(I44, I45, I46, I47, I48, I49, I50) -> f8#(I44, I45, I46 + 1, I47, I51, I52, I53) [0 <= I47 - I46 * I54 - 1 /\ I47 - I46 * I54 <= I46 - 1 /\ I46 <= I47 - 1]
  f8#(I55, I56, I57, I58, I59, I60, I61) -> f9#(I55, I56, I57, I58, I62, I63, I64) [I57 <= I58 - 1 /\ 0 <= I58 - I57 * I65 - 1]
  f8#(I66, I67, I68, I69, I70, I71, I72) -> f9#(I66, I67, I68, I69, I73, I74, I75) [I68 <= I69 - 1 /\ I69 - I68 * I76 <= -1]
  f7#(I77, I78, I79, I80, I81, I82, I83) -> f8#(I79, I78, 2, I77 + 1, I84, I85, I86) [0 <= I77 - 1 /\ I78 <= I79 - 1]
  f2#(I87, I88, I89, I90, I91, I92, I93) -> f7#(1, 0, I92, I94, I95, I96, I97) [I92 + 2 <= I88 /\ I93 + 2 <= I88 /\ 0 <= I88 - 1 /\ 0 <= I87 - 1 /\ 0 <= I93 - 1 /\ 0 <= I90 - 1 /\ I89 <= I90 - 1 /\ 1 <= I91 - 1]
  f6#(I98, I99, I100, I101, I102, I103, I104) -> f4#(I105, I106, I100, I101, I102, I107, I108) [I99 - I100 * I109 = 0 /\ I105 <= I98 /\ 0 <= I98 - 1 /\ 0 <= I105 - 1 /\ I101 + 2 <= I98 /\ I102 + 2 <= I98 /\ 0 <= I99 - I100 * I106 /\ I99 - I100 * I106 <= I100 - 1 /\ I99 - I100 * I109 <= I100 - 1 /\ 0 <= I99 - I100 * I109]
  f4#(I110, I111, I112, I113, I114, I115, I116) -> f6#(I110, I111, I112, I113, I114, I117, I118) [I111 - I112 * I119 = 0 /\ y2 <= I110 /\ 0 <= I110 - 1 /\ 0 <= y2 - 1 /\ I114 + 2 <= I110 /\ I113 + 2 <= I110]
  f5#(I120, I121, I122, I123, I124, I125, I126) -> f4#(I127, I123, I121, I122 + 1, I123, I128, I129) [I122 + 2 <= I120 /\ I123 + 2 <= I120 /\ 0 <= I127 - 1 /\ 0 <= I120 - 1 /\ I127 - 1 <= I120]
  f2#(I130, I131, I132, I133, I134, I135, I136) -> f4#(I137, I136, I138, I135 + 1, I136, I139, I140) [I135 + 2 <= I131 /\ I136 + 2 <= I131 /\ 0 <= I137 - 1 /\ 0 <= I131 - 1 /\ 0 <= I130 - 1 /\ I137 - 1 <= I131 /\ 0 <= I136 - 1 /\ 0 <= I133 - 1 /\ I132 <= I133 - 1 /\ 1 <= I134 - 1]
  f3#(I141, I142, I143, I144, I145, I146, I147) -> f2#(I148, I149, I144 + 1, I143, I145, I146, I147) [I146 + 2 <= I142 /\ I147 + 2 <= I142 /\ 0 <= I149 - 1 /\ 0 <= I148 - 1 /\ 0 <= I142 - 1 /\ 0 <= I141 - 1 /\ I149 <= I142 /\ I148 <= I142 /\ I148 <= I141]
  f2#(I150, I151, I152, I153, I154, I155, I156) -> f2#(I157, I158, I152 + 1, I153, I154, I159, I160) [I155 + 2 <= I151 /\ I156 + 2 <= I151 /\ 0 <= I158 - 1 /\ 0 <= I157 - 1 /\ 0 <= I151 - 1 /\ 0 <= I150 - 1 /\ I157 <= I151 /\ I157 <= I150 /\ 0 <= I153 - 1 /\ 0 <= I156 - 1 /\ I152 <= I153 - 1 /\ 1 <= I154 - 1]
  f1#(I161, I162, I163, I164, I165, I166, I167) -> f2#(I168, I169, 0, I170, I162, 1, I171) [2 <= I169 - 1 /\ 0 <= I168 - 1 /\ 0 <= I161 - 1 /\ I168 <= I161 /\ 0 <= I171 - 1 /\ 1 <= I162 - 1 /\ -1 <= I170 - 1]
R = 
  init(x1, x2, x3, x4, x5, x6, x7) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7) 
  f9(I0, I1, I2, I3, I4, I5, I6) -> f7(I3, I1, I0, I7, I8, I9, I10) [I3 - I2 * y1 = 0 /\ I2 <= I3 - 1 /\ I3 - I2 * y1 <= I2 - 1 /\ 0 <= I3 - I2 * y1]
  f8(I11, I12, I13, I14, I15, I16, I17) -> f9(I11, I12, I13, I14, I18, I19, I20) [I13 <= I14 - 1 /\ I14 - I13 * I21 = 0]
  f7(I22, I23, I24, I25, I26, I27, I28) -> f7(I22 + 1, I23, I24, I29, I30, I31, I32) [I22 <= 0 /\ I23 <= I24 - 1]
  f8(I33, I34, I35, I36, I37, I38, I39) -> f7(I36, I34 + 1, I33, I40, I41, I42, I43) [I36 <= I35]
  f9(I44, I45, I46, I47, I48, I49, I50) -> f8(I44, I45, I46 + 1, I47, I51, I52, I53) [0 <= I47 - I46 * I54 - 1 /\ I47 - I46 * I54 <= I46 - 1 /\ I46 <= I47 - 1]
  f8(I55, I56, I57, I58, I59, I60, I61) -> f9(I55, I56, I57, I58, I62, I63, I64) [I57 <= I58 - 1 /\ 0 <= I58 - I57 * I65 - 1]
  f8(I66, I67, I68, I69, I70, I71, I72) -> f9(I66, I67, I68, I69, I73, I74, I75) [I68 <= I69 - 1 /\ I69 - I68 * I76 <= -1]
  f7(I77, I78, I79, I80, I81, I82, I83) -> f8(I79, I78, 2, I77 + 1, I84, I85, I86) [0 <= I77 - 1 /\ I78 <= I79 - 1]
  f2(I87, I88, I89, I90, I91, I92, I93) -> f7(1, 0, I92, I94, I95, I96, I97) [I92 + 2 <= I88 /\ I93 + 2 <= I88 /\ 0 <= I88 - 1 /\ 0 <= I87 - 1 /\ 0 <= I93 - 1 /\ 0 <= I90 - 1 /\ I89 <= I90 - 1 /\ 1 <= I91 - 1]
  f6(I98, I99, I100, I101, I102, I103, I104) -> f4(I105, I106, I100, I101, I102, I107, I108) [I99 - I100 * I109 = 0 /\ I105 <= I98 /\ 0 <= I98 - 1 /\ 0 <= I105 - 1 /\ I101 + 2 <= I98 /\ I102 + 2 <= I98 /\ 0 <= I99 - I100 * I106 /\ I99 - I100 * I106 <= I100 - 1 /\ I99 - I100 * I109 <= I100 - 1 /\ 0 <= I99 - I100 * I109]
  f4(I110, I111, I112, I113, I114, I115, I116) -> f6(I110, I111, I112, I113, I114, I117, I118) [I111 - I112 * I119 = 0 /\ y2 <= I110 /\ 0 <= I110 - 1 /\ 0 <= y2 - 1 /\ I114 + 2 <= I110 /\ I113 + 2 <= I110]
  f5(I120, I121, I122, I123, I124, I125, I126) -> f4(I127, I123, I121, I122 + 1, I123, I128, I129) [I122 + 2 <= I120 /\ I123 + 2 <= I120 /\ 0 <= I127 - 1 /\ 0 <= I120 - 1 /\ I127 - 1 <= I120]
  f2(I130, I131, I132, I133, I134, I135, I136) -> f4(I137, I136, I138, I135 + 1, I136, I139, I140) [I135 + 2 <= I131 /\ I136 + 2 <= I131 /\ 0 <= I137 - 1 /\ 0 <= I131 - 1 /\ 0 <= I130 - 1 /\ I137 - 1 <= I131 /\ 0 <= I136 - 1 /\ 0 <= I133 - 1 /\ I132 <= I133 - 1 /\ 1 <= I134 - 1]
  f3(I141, I142, I143, I144, I145, I146, I147) -> f2(I148, I149, I144 + 1, I143, I145, I146, I147) [I146 + 2 <= I142 /\ I147 + 2 <= I142 /\ 0 <= I149 - 1 /\ 0 <= I148 - 1 /\ 0 <= I142 - 1 /\ 0 <= I141 - 1 /\ I149 <= I142 /\ I148 <= I142 /\ I148 <= I141]
  f2(I150, I151, I152, I153, I154, I155, I156) -> f2(I157, I158, I152 + 1, I153, I154, I159, I160) [I155 + 2 <= I151 /\ I156 + 2 <= I151 /\ 0 <= I158 - 1 /\ 0 <= I157 - 1 /\ 0 <= I151 - 1 /\ 0 <= I150 - 1 /\ I157 <= I151 /\ I157 <= I150 /\ 0 <= I153 - 1 /\ 0 <= I156 - 1 /\ I152 <= I153 - 1 /\ 1 <= I154 - 1]
  f1(I161, I162, I163, I164, I165, I166, I167) -> f2(I168, I169, 0, I170, I162, 1, I171) [2 <= I169 - 1 /\ 0 <= I168 - 1 /\ 0 <= I161 - 1 /\ I168 <= I161 /\ 0 <= I171 - 1 /\ 1 <= I162 - 1 /\ -1 <= I170 - 1]

The dependency graph for this problem is:
  0 -> 16
  1 -> 8
  2 -> 1, 5
  3 -> 3, 8
  4 -> 3, 8
  5 -> 2, 4, 6, 7
  6 -> 1, 5
  7 -> 1, 5
  8 -> 2, 4, 6, 7
  9 -> 8
  10 -> 11
  11 -> 10
  12 -> 11
  13 -> 11
  14 -> 9, 13, 15
  15 -> 9, 13, 15
  16 -> 9, 13, 15
Where:
  0) init#(x1, x2, x3, x4, x5, x6, x7) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7) 
  1) f9#(I0, I1, I2, I3, I4, I5, I6) -> f7#(I3, I1, I0, I7, I8, I9, I10) [I3 - I2 * y1 = 0 /\ I2 <= I3 - 1 /\ I3 - I2 * y1 <= I2 - 1 /\ 0 <= I3 - I2 * y1]
  2) f8#(I11, I12, I13, I14, I15, I16, I17) -> f9#(I11, I12, I13, I14, I18, I19, I20) [I13 <= I14 - 1 /\ I14 - I13 * I21 = 0]
  3) f7#(I22, I23, I24, I25, I26, I27, I28) -> f7#(I22 + 1, I23, I24, I29, I30, I31, I32) [I22 <= 0 /\ I23 <= I24 - 1]
  4) f8#(I33, I34, I35, I36, I37, I38, I39) -> f7#(I36, I34 + 1, I33, I40, I41, I42, I43) [I36 <= I35]
  5) f9#(I44, I45, I46, I47, I48, I49, I50) -> f8#(I44, I45, I46 + 1, I47, I51, I52, I53) [0 <= I47 - I46 * I54 - 1 /\ I47 - I46 * I54 <= I46 - 1 /\ I46 <= I47 - 1]
  6) f8#(I55, I56, I57, I58, I59, I60, I61) -> f9#(I55, I56, I57, I58, I62, I63, I64) [I57 <= I58 - 1 /\ 0 <= I58 - I57 * I65 - 1]
  7) f8#(I66, I67, I68, I69, I70, I71, I72) -> f9#(I66, I67, I68, I69, I73, I74, I75) [I68 <= I69 - 1 /\ I69 - I68 * I76 <= -1]
  8) f7#(I77, I78, I79, I80, I81, I82, I83) -> f8#(I79, I78, 2, I77 + 1, I84, I85, I86) [0 <= I77 - 1 /\ I78 <= I79 - 1]
  9) f2#(I87, I88, I89, I90, I91, I92, I93) -> f7#(1, 0, I92, I94, I95, I96, I97) [I92 + 2 <= I88 /\ I93 + 2 <= I88 /\ 0 <= I88 - 1 /\ 0 <= I87 - 1 /\ 0 <= I93 - 1 /\ 0 <= I90 - 1 /\ I89 <= I90 - 1 /\ 1 <= I91 - 1]
  10) f6#(I98, I99, I100, I101, I102, I103, I104) -> f4#(I105, I106, I100, I101, I102, I107, I108) [I99 - I100 * I109 = 0 /\ I105 <= I98 /\ 0 <= I98 - 1 /\ 0 <= I105 - 1 /\ I101 + 2 <= I98 /\ I102 + 2 <= I98 /\ 0 <= I99 - I100 * I106 /\ I99 - I100 * I106 <= I100 - 1 /\ I99 - I100 * I109 <= I100 - 1 /\ 0 <= I99 - I100 * I109]
  11) f4#(I110, I111, I112, I113, I114, I115, I116) -> f6#(I110, I111, I112, I113, I114, I117, I118) [I111 - I112 * I119 = 0 /\ y2 <= I110 /\ 0 <= I110 - 1 /\ 0 <= y2 - 1 /\ I114 + 2 <= I110 /\ I113 + 2 <= I110]
  12) f5#(I120, I121, I122, I123, I124, I125, I126) -> f4#(I127, I123, I121, I122 + 1, I123, I128, I129) [I122 + 2 <= I120 /\ I123 + 2 <= I120 /\ 0 <= I127 - 1 /\ 0 <= I120 - 1 /\ I127 - 1 <= I120]
  13) f2#(I130, I131, I132, I133, I134, I135, I136) -> f4#(I137, I136, I138, I135 + 1, I136, I139, I140) [I135 + 2 <= I131 /\ I136 + 2 <= I131 /\ 0 <= I137 - 1 /\ 0 <= I131 - 1 /\ 0 <= I130 - 1 /\ I137 - 1 <= I131 /\ 0 <= I136 - 1 /\ 0 <= I133 - 1 /\ I132 <= I133 - 1 /\ 1 <= I134 - 1]
  14) f3#(I141, I142, I143, I144, I145, I146, I147) -> f2#(I148, I149, I144 + 1, I143, I145, I146, I147) [I146 + 2 <= I142 /\ I147 + 2 <= I142 /\ 0 <= I149 - 1 /\ 0 <= I148 - 1 /\ 0 <= I142 - 1 /\ 0 <= I141 - 1 /\ I149 <= I142 /\ I148 <= I142 /\ I148 <= I141]
  15) f2#(I150, I151, I152, I153, I154, I155, I156) -> f2#(I157, I158, I152 + 1, I153, I154, I159, I160) [I155 + 2 <= I151 /\ I156 + 2 <= I151 /\ 0 <= I158 - 1 /\ 0 <= I157 - 1 /\ 0 <= I151 - 1 /\ 0 <= I150 - 1 /\ I157 <= I151 /\ I157 <= I150 /\ 0 <= I153 - 1 /\ 0 <= I156 - 1 /\ I152 <= I153 - 1 /\ 1 <= I154 - 1]
  16) f1#(I161, I162, I163, I164, I165, I166, I167) -> f2#(I168, I169, 0, I170, I162, 1, I171) [2 <= I169 - 1 /\ 0 <= I168 - 1 /\ 0 <= I161 - 1 /\ I168 <= I161 /\ 0 <= I171 - 1 /\ 1 <= I162 - 1 /\ -1 <= I170 - 1]

We have the following SCCs.
  { 15 }
  { 10, 11 }
  { 1, 2, 3, 4, 5, 6, 7, 8 }

DP problem for innermost termination.
P =
  f9#(I0, I1, I2, I3, I4, I5, I6) -> f7#(I3, I1, I0, I7, I8, I9, I10) [I3 - I2 * y1 = 0 /\ I2 <= I3 - 1 /\ I3 - I2 * y1 <= I2 - 1 /\ 0 <= I3 - I2 * y1]
  f8#(I11, I12, I13, I14, I15, I16, I17) -> f9#(I11, I12, I13, I14, I18, I19, I20) [I13 <= I14 - 1 /\ I14 - I13 * I21 = 0]
  f7#(I22, I23, I24, I25, I26, I27, I28) -> f7#(I22 + 1, I23, I24, I29, I30, I31, I32) [I22 <= 0 /\ I23 <= I24 - 1]
  f8#(I33, I34, I35, I36, I37, I38, I39) -> f7#(I36, I34 + 1, I33, I40, I41, I42, I43) [I36 <= I35]
  f9#(I44, I45, I46, I47, I48, I49, I50) -> f8#(I44, I45, I46 + 1, I47, I51, I52, I53) [0 <= I47 - I46 * I54 - 1 /\ I47 - I46 * I54 <= I46 - 1 /\ I46 <= I47 - 1]
  f8#(I55, I56, I57, I58, I59, I60, I61) -> f9#(I55, I56, I57, I58, I62, I63, I64) [I57 <= I58 - 1 /\ 0 <= I58 - I57 * I65 - 1]
  f8#(I66, I67, I68, I69, I70, I71, I72) -> f9#(I66, I67, I68, I69, I73, I74, I75) [I68 <= I69 - 1 /\ I69 - I68 * I76 <= -1]
  f7#(I77, I78, I79, I80, I81, I82, I83) -> f8#(I79, I78, 2, I77 + 1, I84, I85, I86) [0 <= I77 - 1 /\ I78 <= I79 - 1]
R = 
  init(x1, x2, x3, x4, x5, x6, x7) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7) 
  f9(I0, I1, I2, I3, I4, I5, I6) -> f7(I3, I1, I0, I7, I8, I9, I10) [I3 - I2 * y1 = 0 /\ I2 <= I3 - 1 /\ I3 - I2 * y1 <= I2 - 1 /\ 0 <= I3 - I2 * y1]
  f8(I11, I12, I13, I14, I15, I16, I17) -> f9(I11, I12, I13, I14, I18, I19, I20) [I13 <= I14 - 1 /\ I14 - I13 * I21 = 0]
  f7(I22, I23, I24, I25, I26, I27, I28) -> f7(I22 + 1, I23, I24, I29, I30, I31, I32) [I22 <= 0 /\ I23 <= I24 - 1]
  f8(I33, I34, I35, I36, I37, I38, I39) -> f7(I36, I34 + 1, I33, I40, I41, I42, I43) [I36 <= I35]
  f9(I44, I45, I46, I47, I48, I49, I50) -> f8(I44, I45, I46 + 1, I47, I51, I52, I53) [0 <= I47 - I46 * I54 - 1 /\ I47 - I46 * I54 <= I46 - 1 /\ I46 <= I47 - 1]
  f8(I55, I56, I57, I58, I59, I60, I61) -> f9(I55, I56, I57, I58, I62, I63, I64) [I57 <= I58 - 1 /\ 0 <= I58 - I57 * I65 - 1]
  f8(I66, I67, I68, I69, I70, I71, I72) -> f9(I66, I67, I68, I69, I73, I74, I75) [I68 <= I69 - 1 /\ I69 - I68 * I76 <= -1]
  f7(I77, I78, I79, I80, I81, I82, I83) -> f8(I79, I78, 2, I77 + 1, I84, I85, I86) [0 <= I77 - 1 /\ I78 <= I79 - 1]
  f2(I87, I88, I89, I90, I91, I92, I93) -> f7(1, 0, I92, I94, I95, I96, I97) [I92 + 2 <= I88 /\ I93 + 2 <= I88 /\ 0 <= I88 - 1 /\ 0 <= I87 - 1 /\ 0 <= I93 - 1 /\ 0 <= I90 - 1 /\ I89 <= I90 - 1 /\ 1 <= I91 - 1]
  f6(I98, I99, I100, I101, I102, I103, I104) -> f4(I105, I106, I100, I101, I102, I107, I108) [I99 - I100 * I109 = 0 /\ I105 <= I98 /\ 0 <= I98 - 1 /\ 0 <= I105 - 1 /\ I101 + 2 <= I98 /\ I102 + 2 <= I98 /\ 0 <= I99 - I100 * I106 /\ I99 - I100 * I106 <= I100 - 1 /\ I99 - I100 * I109 <= I100 - 1 /\ 0 <= I99 - I100 * I109]
  f4(I110, I111, I112, I113, I114, I115, I116) -> f6(I110, I111, I112, I113, I114, I117, I118) [I111 - I112 * I119 = 0 /\ y2 <= I110 /\ 0 <= I110 - 1 /\ 0 <= y2 - 1 /\ I114 + 2 <= I110 /\ I113 + 2 <= I110]
  f5(I120, I121, I122, I123, I124, I125, I126) -> f4(I127, I123, I121, I122 + 1, I123, I128, I129) [I122 + 2 <= I120 /\ I123 + 2 <= I120 /\ 0 <= I127 - 1 /\ 0 <= I120 - 1 /\ I127 - 1 <= I120]
  f2(I130, I131, I132, I133, I134, I135, I136) -> f4(I137, I136, I138, I135 + 1, I136, I139, I140) [I135 + 2 <= I131 /\ I136 + 2 <= I131 /\ 0 <= I137 - 1 /\ 0 <= I131 - 1 /\ 0 <= I130 - 1 /\ I137 - 1 <= I131 /\ 0 <= I136 - 1 /\ 0 <= I133 - 1 /\ I132 <= I133 - 1 /\ 1 <= I134 - 1]
  f3(I141, I142, I143, I144, I145, I146, I147) -> f2(I148, I149, I144 + 1, I143, I145, I146, I147) [I146 + 2 <= I142 /\ I147 + 2 <= I142 /\ 0 <= I149 - 1 /\ 0 <= I148 - 1 /\ 0 <= I142 - 1 /\ 0 <= I141 - 1 /\ I149 <= I142 /\ I148 <= I142 /\ I148 <= I141]
  f2(I150, I151, I152, I153, I154, I155, I156) -> f2(I157, I158, I152 + 1, I153, I154, I159, I160) [I155 + 2 <= I151 /\ I156 + 2 <= I151 /\ 0 <= I158 - 1 /\ 0 <= I157 - 1 /\ 0 <= I151 - 1 /\ 0 <= I150 - 1 /\ I157 <= I151 /\ I157 <= I150 /\ 0 <= I153 - 1 /\ 0 <= I156 - 1 /\ I152 <= I153 - 1 /\ 1 <= I154 - 1]
  f1(I161, I162, I163, I164, I165, I166, I167) -> f2(I168, I169, 0, I170, I162, 1, I171) [2 <= I169 - 1 /\ 0 <= I168 - 1 /\ 0 <= I161 - 1 /\ I168 <= I161 /\ 0 <= I171 - 1 /\ 1 <= I162 - 1 /\ -1 <= I170 - 1]

We use the reverse value criterion with the projection function NU:
  NU[f8#(z1,z2,z3,z4,z5,z6,z7)] = 0 + -1 * z4
  NU[f7#(z1,z2,z3,z4,z5,z6,z7)] = 0 + -1 * z1
  NU[f9#(z1,z2,z3,z4,z5,z6,z7)] = 0 + -1 * z4

This gives the following inequalities:
  I3 - I2 * y1 = 0 /\ I2 <= I3 - 1 /\ I3 - I2 * y1 <= I2 - 1 /\ 0 <= I3 - I2 * y1  ==>  0 + -1 * I3 >= 0 + -1 * I3
  I13 <= I14 - 1 /\ I14 - I13 * I21 = 0  ==>  0 + -1 * I14 >= 0 + -1 * I14
  I22 <= 0 /\ I23 <= I24 - 1  ==>  0 + -1 * I22 > 0 + -1 * (I22 + 1)  with  0 + -1 * I22 >= 0
  I36 <= I35  ==>  0 + -1 * I36 >= 0 + -1 * I36
  0 <= I47 - I46 * I54 - 1 /\ I47 - I46 * I54 <= I46 - 1 /\ I46 <= I47 - 1  ==>  0 + -1 * I47 >= 0 + -1 * I47
  I57 <= I58 - 1 /\ 0 <= I58 - I57 * I65 - 1  ==>  0 + -1 * I58 >= 0 + -1 * I58
  I68 <= I69 - 1 /\ I69 - I68 * I76 <= -1  ==>  0 + -1 * I69 >= 0 + -1 * I69
  0 <= I77 - 1 /\ I78 <= I79 - 1  ==>  0 + -1 * I77 >= 0 + -1 * (I77 + 1)

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f9#(I0, I1, I2, I3, I4, I5, I6) -> f7#(I3, I1, I0, I7, I8, I9, I10) [I3 - I2 * y1 = 0 /\ I2 <= I3 - 1 /\ I3 - I2 * y1 <= I2 - 1 /\ 0 <= I3 - I2 * y1]
  f8#(I11, I12, I13, I14, I15, I16, I17) -> f9#(I11, I12, I13, I14, I18, I19, I20) [I13 <= I14 - 1 /\ I14 - I13 * I21 = 0]
  f8#(I33, I34, I35, I36, I37, I38, I39) -> f7#(I36, I34 + 1, I33, I40, I41, I42, I43) [I36 <= I35]
  f9#(I44, I45, I46, I47, I48, I49, I50) -> f8#(I44, I45, I46 + 1, I47, I51, I52, I53) [0 <= I47 - I46 * I54 - 1 /\ I47 - I46 * I54 <= I46 - 1 /\ I46 <= I47 - 1]
  f8#(I55, I56, I57, I58, I59, I60, I61) -> f9#(I55, I56, I57, I58, I62, I63, I64) [I57 <= I58 - 1 /\ 0 <= I58 - I57 * I65 - 1]
  f8#(I66, I67, I68, I69, I70, I71, I72) -> f9#(I66, I67, I68, I69, I73, I74, I75) [I68 <= I69 - 1 /\ I69 - I68 * I76 <= -1]
  f7#(I77, I78, I79, I80, I81, I82, I83) -> f8#(I79, I78, 2, I77 + 1, I84, I85, I86) [0 <= I77 - 1 /\ I78 <= I79 - 1]
R = 
  init(x1, x2, x3, x4, x5, x6, x7) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7) 
  f9(I0, I1, I2, I3, I4, I5, I6) -> f7(I3, I1, I0, I7, I8, I9, I10) [I3 - I2 * y1 = 0 /\ I2 <= I3 - 1 /\ I3 - I2 * y1 <= I2 - 1 /\ 0 <= I3 - I2 * y1]
  f8(I11, I12, I13, I14, I15, I16, I17) -> f9(I11, I12, I13, I14, I18, I19, I20) [I13 <= I14 - 1 /\ I14 - I13 * I21 = 0]
  f7(I22, I23, I24, I25, I26, I27, I28) -> f7(I22 + 1, I23, I24, I29, I30, I31, I32) [I22 <= 0 /\ I23 <= I24 - 1]
  f8(I33, I34, I35, I36, I37, I38, I39) -> f7(I36, I34 + 1, I33, I40, I41, I42, I43) [I36 <= I35]
  f9(I44, I45, I46, I47, I48, I49, I50) -> f8(I44, I45, I46 + 1, I47, I51, I52, I53) [0 <= I47 - I46 * I54 - 1 /\ I47 - I46 * I54 <= I46 - 1 /\ I46 <= I47 - 1]
  f8(I55, I56, I57, I58, I59, I60, I61) -> f9(I55, I56, I57, I58, I62, I63, I64) [I57 <= I58 - 1 /\ 0 <= I58 - I57 * I65 - 1]
  f8(I66, I67, I68, I69, I70, I71, I72) -> f9(I66, I67, I68, I69, I73, I74, I75) [I68 <= I69 - 1 /\ I69 - I68 * I76 <= -1]
  f7(I77, I78, I79, I80, I81, I82, I83) -> f8(I79, I78, 2, I77 + 1, I84, I85, I86) [0 <= I77 - 1 /\ I78 <= I79 - 1]
  f2(I87, I88, I89, I90, I91, I92, I93) -> f7(1, 0, I92, I94, I95, I96, I97) [I92 + 2 <= I88 /\ I93 + 2 <= I88 /\ 0 <= I88 - 1 /\ 0 <= I87 - 1 /\ 0 <= I93 - 1 /\ 0 <= I90 - 1 /\ I89 <= I90 - 1 /\ 1 <= I91 - 1]
  f6(I98, I99, I100, I101, I102, I103, I104) -> f4(I105, I106, I100, I101, I102, I107, I108) [I99 - I100 * I109 = 0 /\ I105 <= I98 /\ 0 <= I98 - 1 /\ 0 <= I105 - 1 /\ I101 + 2 <= I98 /\ I102 + 2 <= I98 /\ 0 <= I99 - I100 * I106 /\ I99 - I100 * I106 <= I100 - 1 /\ I99 - I100 * I109 <= I100 - 1 /\ 0 <= I99 - I100 * I109]
  f4(I110, I111, I112, I113, I114, I115, I116) -> f6(I110, I111, I112, I113, I114, I117, I118) [I111 - I112 * I119 = 0 /\ y2 <= I110 /\ 0 <= I110 - 1 /\ 0 <= y2 - 1 /\ I114 + 2 <= I110 /\ I113 + 2 <= I110]
  f5(I120, I121, I122, I123, I124, I125, I126) -> f4(I127, I123, I121, I122 + 1, I123, I128, I129) [I122 + 2 <= I120 /\ I123 + 2 <= I120 /\ 0 <= I127 - 1 /\ 0 <= I120 - 1 /\ I127 - 1 <= I120]
  f2(I130, I131, I132, I133, I134, I135, I136) -> f4(I137, I136, I138, I135 + 1, I136, I139, I140) [I135 + 2 <= I131 /\ I136 + 2 <= I131 /\ 0 <= I137 - 1 /\ 0 <= I131 - 1 /\ 0 <= I130 - 1 /\ I137 - 1 <= I131 /\ 0 <= I136 - 1 /\ 0 <= I133 - 1 /\ I132 <= I133 - 1 /\ 1 <= I134 - 1]
  f3(I141, I142, I143, I144, I145, I146, I147) -> f2(I148, I149, I144 + 1, I143, I145, I146, I147) [I146 + 2 <= I142 /\ I147 + 2 <= I142 /\ 0 <= I149 - 1 /\ 0 <= I148 - 1 /\ 0 <= I142 - 1 /\ 0 <= I141 - 1 /\ I149 <= I142 /\ I148 <= I142 /\ I148 <= I141]
  f2(I150, I151, I152, I153, I154, I155, I156) -> f2(I157, I158, I152 + 1, I153, I154, I159, I160) [I155 + 2 <= I151 /\ I156 + 2 <= I151 /\ 0 <= I158 - 1 /\ 0 <= I157 - 1 /\ 0 <= I151 - 1 /\ 0 <= I150 - 1 /\ I157 <= I151 /\ I157 <= I150 /\ 0 <= I153 - 1 /\ 0 <= I156 - 1 /\ I152 <= I153 - 1 /\ 1 <= I154 - 1]
  f1(I161, I162, I163, I164, I165, I166, I167) -> f2(I168, I169, 0, I170, I162, 1, I171) [2 <= I169 - 1 /\ 0 <= I168 - 1 /\ 0 <= I161 - 1 /\ I168 <= I161 /\ 0 <= I171 - 1 /\ 1 <= I162 - 1 /\ -1 <= I170 - 1]