/export/starexec/sandbox2/solver/bin/starexec_run_Transition /export/starexec/sandbox2/benchmark/theBenchmark.smt2 /export/starexec/sandbox2/output/output_files


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YES

DP problem for innermost termination.
P =
  init#(x1, x2, x3, x4) -> f1#(rnd1, rnd2, rnd3, rnd4) 
  f4#(I0, I1, I2, I3) -> f4#(I0 - 1, I4, I5, I6) [I0 - 1 <= I0 - 1 /\ 0 <= I0 - 1]
  f5#(I7, I8, I9, I10) -> f3#(I11, I8, I9 + 1, I10) [I8 <= I10 /\ I9 <= I10 /\ 0 <= I8 - 1 /\ 0 <= y1 - 1 /\ I9 <= I8 /\ 0 <= y2 - 1 /\ 0 <= y3 - 1 /\ 0 <= I9 - 1 /\ -1 <= I10 - 1 /\ I11 <= I7 /\ 0 <= I7 - 1 /\ 0 <= I11 - 1 /\ y5 - y4 * y6 <= y4 - 1 /\ 0 <= y5 - y4 * y6]
  f3#(I12, I13, I14, I15) -> f5#(I12, I13, I14, I15) [I13 <= I15 /\ I14 <= I15 /\ 0 <= I13 - 1 /\ 0 <= I16 - 1 /\ I14 <= I13 /\ 0 <= I17 - 1 /\ 0 <= I18 - 1 /\ 0 <= I14 - 1 /\ -1 <= I15 - 1 /\ I19 <= I12 /\ 0 <= I12 - 1 /\ 0 <= I19 - 1]
  f5#(I20, I21, I22, I23) -> f3#(I24, I21, I22 + 1, I23) [0 <= I22 - 1 /\ I21 <= I23 /\ I22 <= I23 /\ 0 <= I25 - 1 /\ I21 <= I22 - 1 /\ 0 <= I26 - 1 /\ 0 <= I27 - 1 /\ 0 <= I21 - 1 /\ -1 <= I23 - 1 /\ I24 <= I20 /\ 0 <= I20 - 1 /\ 0 <= I24 - 1 /\ I28 - I29 * I30 <= I29 - 1 /\ 0 <= I28 - I29 * I30]
  f3#(I31, I32, I33, I34) -> f5#(I31, I32, I33, I34) [0 <= I33 - 1 /\ I32 <= I34 /\ I33 <= I34 /\ 0 <= I35 - 1 /\ I32 <= I33 - 1 /\ 0 <= I36 - 1 /\ 0 <= I37 - 1 /\ 0 <= I32 - 1 /\ -1 <= I34 - 1 /\ I38 <= I31 /\ 0 <= I31 - 1 /\ 0 <= I38 - 1]
  f5#(I39, I40, I41, I42) -> f3#(I43, I40, I41 + 1, I42) [I40 <= I42 /\ I41 <= I42 /\ 0 <= I40 - 1 /\ 0 <= I44 - 1 /\ I41 <= I40 /\ 1 <= I40 - I41 /\ 0 <= I45 - 1 /\ I41 <= 0 /\ -1 <= I42 - 1 /\ I43 <= I39 /\ 0 <= I39 - 1 /\ 0 <= I43 - 1 /\ I46 - I47 * I48 <= I47 - 1 /\ 0 <= I46 - I47 * I48]
  f3#(I49, I50, I51, I52) -> f5#(I49, I50, I51, I52) [I50 <= I52 /\ I51 <= I52 /\ 0 <= I50 - 1 /\ 0 <= I53 - 1 /\ I51 <= I50 /\ 1 <= I50 - I51 /\ 0 <= I54 - 1 /\ I51 <= 0 /\ -1 <= I52 - 1 /\ I55 <= I49 /\ 0 <= I49 - 1 /\ 0 <= I55 - 1]
  f5#(I56, I57, I58, I59) -> f3#(I60, 0, I58 + 1, I59) [I58 <= I59 /\ 0 <= I58 - 1 /\ -1 <= I59 - 1 /\ I58 <= 0 /\ 0 <= I61 - 1 /\ I60 <= I56 /\ 0 <= I56 - 1 /\ 0 <= I60 - 1 /\ 1 - I62 * I63 <= I62 - 1 /\ I62 * I63 <= 1 /\ 0 = I57]
  f3#(I64, I65, I66, I67) -> f5#(I64, 0, I66, I67) [I66 <= I67 /\ 0 <= I66 - 1 /\ -1 <= I67 - 1 /\ I66 <= 0 /\ 0 <= I68 - 1 /\ I69 <= I64 /\ 0 <= I64 - 1 /\ 0 <= I69 - 1 /\ 0 = I65]
  f5#(I70, I71, I72, I73) -> f3#(I74, 0, I72 + 1, I73) [0 <= I72 - 1 /\ -1 <= I73 - 1 /\ I72 <= I73 /\ 0 <= I75 - 1 /\ 0 <= I76 - 1 /\ I74 <= I70 /\ 0 <= I70 - 1 /\ 0 <= I74 - 1 /\ I77 - I78 * I79 <= I78 - 1 /\ 0 <= I77 - I78 * I79 /\ 0 = I71]
  f3#(I80, I81, I82, I83) -> f5#(I80, 0, I82, I83) [0 <= I82 - 1 /\ -1 <= I83 - 1 /\ I82 <= I83 /\ 0 <= I84 - 1 /\ 0 <= I85 - 1 /\ I86 <= I80 /\ 0 <= I80 - 1 /\ 0 <= I86 - 1 /\ 0 = I81]
  f5#(I87, I88, I89, I90) -> f3#(I91, 0, 1, I90) [-1 <= I90 - 1 /\ I91 <= I87 /\ 0 <= I87 - 1 /\ 0 <= I91 - 1 /\ 1 - I92 * I93 <= I92 - 1 /\ I92 * I93 <= 1 /\ 0 = I88 /\ 0 = I89]
  f3#(I94, I95, I96, I97) -> f5#(I94, 0, 0, I97) [-1 <= I97 - 1 /\ I98 <= I94 /\ 0 <= I94 - 1 /\ 0 <= I98 - 1 /\ 0 = I95 /\ 0 = I96]
  f5#(I99, I100, I101, I102) -> f3#(I103, 0, I101 + 1, I102) [-1 <= I102 - 1 /\ I101 <= I102 /\ I101 <= 0 /\ I103 <= I99 /\ 0 <= I99 - 1 /\ 0 <= I103 - 1 /\ 1 - I104 * I105 <= I104 - 1 /\ I104 * I105 <= 1 /\ 0 = I100]
  f3#(I106, I107, I108, I109) -> f5#(I106, 0, I108, I109) [-1 <= I109 - 1 /\ I108 <= I109 /\ I108 <= 0 /\ I110 <= I106 /\ 0 <= I106 - 1 /\ 0 <= I110 - 1 /\ 0 = I107]
  f3#(I111, I112, I113, I114) -> f4#(I112 - I113, I115, I116, I117) [I112 <= I114 /\ I113 <= I114 /\ 0 <= I112 - 1 /\ 0 <= I118 - 1 /\ I113 <= I112 /\ 0 <= I119 - 1 /\ 0 <= I120 - 1 /\ 0 <= I113 - 1 /\ 0 <= I111 - 1]
  f3#(I121, I122, I123, I124) -> f4#(I122 - I123, I125, I126, I127) [I122 <= I124 /\ I123 <= I124 /\ 0 <= I122 - 1 /\ 0 <= I128 - 1 /\ I123 <= I122 /\ 1 <= I122 - I123 /\ 0 <= I129 - 1 /\ I123 <= 0 /\ 0 <= I121 - 1]
  f3#(I130, I131, I132, I133) -> f4#(0 - I132, I134, I135, I136) [I132 <= I133 /\ 0 <= I132 - 1 /\ -1 <= I133 - 1 /\ I132 <= 0 /\ 0 <= I137 - 1 /\ 0 <= I130 - 1 /\ 0 = I131]
  f3#(I138, I139, I140, I141) -> f4#(0 - I140, I142, I143, I144) [0 = I139 /\ 0 <= I138 - 1 /\ I140 <= 0 /\ I140 <= I141 /\ -1 <= I141 - 1]
  f3#(I145, I146, I147, I148) -> f4#(I147 - I146, I149, I150, I151) [0 <= I147 - 1 /\ I146 <= I148 /\ I147 <= I148 /\ 0 <= I152 - 1 /\ I146 <= I147 - 1 /\ 0 <= I153 - 1 /\ 0 <= I154 - 1 /\ 0 <= I146 - 1 /\ 0 <= I145 - 1]
  f3#(I155, I156, I157, I158) -> f4#(I157, I159, I160, I161) [0 <= I157 - 1 /\ -1 <= I158 - 1 /\ I157 <= I158 /\ 0 <= I162 - 1 /\ 0 <= I163 - 1 /\ 0 <= I155 - 1 /\ 0 = I156]
  f3#(I164, I165, I166, I167) -> f4#(I166, I168, I169, I170) [I165 <= I167 /\ I166 <= I167 /\ 0 <= I165 - 1 /\ 0 <= I171 - 1 /\ I166 <= I165 /\ 0 <= I164 - 1]
  f3#(I172, I173, I174, I175) -> f4#(I174, I176, I177, I178) [0 = I173 /\ 0 <= I172 - 1 /\ I174 <= 0 /\ I174 <= I175 /\ -1 <= I175 - 1]
  f3#(I179, I180, I181, I182) -> f4#(I180, I183, I184, I185) [0 <= I181 - 1 /\ I180 <= I182 /\ I181 <= I182 /\ 0 <= I186 - 1 /\ I180 <= I181 - 1 /\ 0 <= I179 - 1]
  f3#(I187, I188, I189, I190) -> f4#(I188, I191, I192, I193) [0 <= I187 - 1 /\ I189 <= I188 /\ I189 <= I190 /\ I188 <= I190]
  f3#(I194, I195, I196, I197) -> f4#(I196, I198, I199, I200) [0 <= I194 - 1 /\ I195 <= I196 - 1 /\ I196 <= I197 /\ I195 <= I197 /\ 0 <= I196 - 1]
  f3#(I201, I202, I203, I204) -> f2#(I205, I202 + 1, I204, I206) [0 <= I205 - 1 /\ 0 <= I201 - 1 /\ I205 <= I201 /\ -1 <= I204 - 1 /\ I204 <= I203 - 1]
  f2#(I207, I208, I209, I210) -> f3#(I211, I208, 0, I209) [0 <= I211 - 1 /\ 0 <= I207 - 1 /\ I211 <= I207 /\ -1 <= I209 - 1 /\ I208 <= I209]
  f1#(I212, I213, I214, I215) -> f2#(I216, 0, I213, I217) [0 <= I216 - 1 /\ 0 <= I212 - 1 /\ -1 <= I213 - 1 /\ I216 <= I212]
R = 
  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
  f4(I0, I1, I2, I3) -> f4(I0 - 1, I4, I5, I6) [I0 - 1 <= I0 - 1 /\ 0 <= I0 - 1]
  f5(I7, I8, I9, I10) -> f3(I11, I8, I9 + 1, I10) [I8 <= I10 /\ I9 <= I10 /\ 0 <= I8 - 1 /\ 0 <= y1 - 1 /\ I9 <= I8 /\ 0 <= y2 - 1 /\ 0 <= y3 - 1 /\ 0 <= I9 - 1 /\ -1 <= I10 - 1 /\ I11 <= I7 /\ 0 <= I7 - 1 /\ 0 <= I11 - 1 /\ y5 - y4 * y6 <= y4 - 1 /\ 0 <= y5 - y4 * y6]
  f3(I12, I13, I14, I15) -> f5(I12, I13, I14, I15) [I13 <= I15 /\ I14 <= I15 /\ 0 <= I13 - 1 /\ 0 <= I16 - 1 /\ I14 <= I13 /\ 0 <= I17 - 1 /\ 0 <= I18 - 1 /\ 0 <= I14 - 1 /\ -1 <= I15 - 1 /\ I19 <= I12 /\ 0 <= I12 - 1 /\ 0 <= I19 - 1]
  f5(I20, I21, I22, I23) -> f3(I24, I21, I22 + 1, I23) [0 <= I22 - 1 /\ I21 <= I23 /\ I22 <= I23 /\ 0 <= I25 - 1 /\ I21 <= I22 - 1 /\ 0 <= I26 - 1 /\ 0 <= I27 - 1 /\ 0 <= I21 - 1 /\ -1 <= I23 - 1 /\ I24 <= I20 /\ 0 <= I20 - 1 /\ 0 <= I24 - 1 /\ I28 - I29 * I30 <= I29 - 1 /\ 0 <= I28 - I29 * I30]
  f3(I31, I32, I33, I34) -> f5(I31, I32, I33, I34) [0 <= I33 - 1 /\ I32 <= I34 /\ I33 <= I34 /\ 0 <= I35 - 1 /\ I32 <= I33 - 1 /\ 0 <= I36 - 1 /\ 0 <= I37 - 1 /\ 0 <= I32 - 1 /\ -1 <= I34 - 1 /\ I38 <= I31 /\ 0 <= I31 - 1 /\ 0 <= I38 - 1]
  f5(I39, I40, I41, I42) -> f3(I43, I40, I41 + 1, I42) [I40 <= I42 /\ I41 <= I42 /\ 0 <= I40 - 1 /\ 0 <= I44 - 1 /\ I41 <= I40 /\ 1 <= I40 - I41 /\ 0 <= I45 - 1 /\ I41 <= 0 /\ -1 <= I42 - 1 /\ I43 <= I39 /\ 0 <= I39 - 1 /\ 0 <= I43 - 1 /\ I46 - I47 * I48 <= I47 - 1 /\ 0 <= I46 - I47 * I48]
  f3(I49, I50, I51, I52) -> f5(I49, I50, I51, I52) [I50 <= I52 /\ I51 <= I52 /\ 0 <= I50 - 1 /\ 0 <= I53 - 1 /\ I51 <= I50 /\ 1 <= I50 - I51 /\ 0 <= I54 - 1 /\ I51 <= 0 /\ -1 <= I52 - 1 /\ I55 <= I49 /\ 0 <= I49 - 1 /\ 0 <= I55 - 1]
  f5(I56, I57, I58, I59) -> f3(I60, 0, I58 + 1, I59) [I58 <= I59 /\ 0 <= I58 - 1 /\ -1 <= I59 - 1 /\ I58 <= 0 /\ 0 <= I61 - 1 /\ I60 <= I56 /\ 0 <= I56 - 1 /\ 0 <= I60 - 1 /\ 1 - I62 * I63 <= I62 - 1 /\ I62 * I63 <= 1 /\ 0 = I57]
  f3(I64, I65, I66, I67) -> f5(I64, 0, I66, I67) [I66 <= I67 /\ 0 <= I66 - 1 /\ -1 <= I67 - 1 /\ I66 <= 0 /\ 0 <= I68 - 1 /\ I69 <= I64 /\ 0 <= I64 - 1 /\ 0 <= I69 - 1 /\ 0 = I65]
  f5(I70, I71, I72, I73) -> f3(I74, 0, I72 + 1, I73) [0 <= I72 - 1 /\ -1 <= I73 - 1 /\ I72 <= I73 /\ 0 <= I75 - 1 /\ 0 <= I76 - 1 /\ I74 <= I70 /\ 0 <= I70 - 1 /\ 0 <= I74 - 1 /\ I77 - I78 * I79 <= I78 - 1 /\ 0 <= I77 - I78 * I79 /\ 0 = I71]
  f3(I80, I81, I82, I83) -> f5(I80, 0, I82, I83) [0 <= I82 - 1 /\ -1 <= I83 - 1 /\ I82 <= I83 /\ 0 <= I84 - 1 /\ 0 <= I85 - 1 /\ I86 <= I80 /\ 0 <= I80 - 1 /\ 0 <= I86 - 1 /\ 0 = I81]
  f5(I87, I88, I89, I90) -> f3(I91, 0, 1, I90) [-1 <= I90 - 1 /\ I91 <= I87 /\ 0 <= I87 - 1 /\ 0 <= I91 - 1 /\ 1 - I92 * I93 <= I92 - 1 /\ I92 * I93 <= 1 /\ 0 = I88 /\ 0 = I89]
  f3(I94, I95, I96, I97) -> f5(I94, 0, 0, I97) [-1 <= I97 - 1 /\ I98 <= I94 /\ 0 <= I94 - 1 /\ 0 <= I98 - 1 /\ 0 = I95 /\ 0 = I96]
  f5(I99, I100, I101, I102) -> f3(I103, 0, I101 + 1, I102) [-1 <= I102 - 1 /\ I101 <= I102 /\ I101 <= 0 /\ I103 <= I99 /\ 0 <= I99 - 1 /\ 0 <= I103 - 1 /\ 1 - I104 * I105 <= I104 - 1 /\ I104 * I105 <= 1 /\ 0 = I100]
  f3(I106, I107, I108, I109) -> f5(I106, 0, I108, I109) [-1 <= I109 - 1 /\ I108 <= I109 /\ I108 <= 0 /\ I110 <= I106 /\ 0 <= I106 - 1 /\ 0 <= I110 - 1 /\ 0 = I107]
  f3(I111, I112, I113, I114) -> f4(I112 - I113, I115, I116, I117) [I112 <= I114 /\ I113 <= I114 /\ 0 <= I112 - 1 /\ 0 <= I118 - 1 /\ I113 <= I112 /\ 0 <= I119 - 1 /\ 0 <= I120 - 1 /\ 0 <= I113 - 1 /\ 0 <= I111 - 1]
  f3(I121, I122, I123, I124) -> f4(I122 - I123, I125, I126, I127) [I122 <= I124 /\ I123 <= I124 /\ 0 <= I122 - 1 /\ 0 <= I128 - 1 /\ I123 <= I122 /\ 1 <= I122 - I123 /\ 0 <= I129 - 1 /\ I123 <= 0 /\ 0 <= I121 - 1]
  f3(I130, I131, I132, I133) -> f4(0 - I132, I134, I135, I136) [I132 <= I133 /\ 0 <= I132 - 1 /\ -1 <= I133 - 1 /\ I132 <= 0 /\ 0 <= I137 - 1 /\ 0 <= I130 - 1 /\ 0 = I131]
  f3(I138, I139, I140, I141) -> f4(0 - I140, I142, I143, I144) [0 = I139 /\ 0 <= I138 - 1 /\ I140 <= 0 /\ I140 <= I141 /\ -1 <= I141 - 1]
  f3(I145, I146, I147, I148) -> f4(I147 - I146, I149, I150, I151) [0 <= I147 - 1 /\ I146 <= I148 /\ I147 <= I148 /\ 0 <= I152 - 1 /\ I146 <= I147 - 1 /\ 0 <= I153 - 1 /\ 0 <= I154 - 1 /\ 0 <= I146 - 1 /\ 0 <= I145 - 1]
  f3(I155, I156, I157, I158) -> f4(I157, I159, I160, I161) [0 <= I157 - 1 /\ -1 <= I158 - 1 /\ I157 <= I158 /\ 0 <= I162 - 1 /\ 0 <= I163 - 1 /\ 0 <= I155 - 1 /\ 0 = I156]
  f3(I164, I165, I166, I167) -> f4(I166, I168, I169, I170) [I165 <= I167 /\ I166 <= I167 /\ 0 <= I165 - 1 /\ 0 <= I171 - 1 /\ I166 <= I165 /\ 0 <= I164 - 1]
  f3(I172, I173, I174, I175) -> f4(I174, I176, I177, I178) [0 = I173 /\ 0 <= I172 - 1 /\ I174 <= 0 /\ I174 <= I175 /\ -1 <= I175 - 1]
  f3(I179, I180, I181, I182) -> f4(I180, I183, I184, I185) [0 <= I181 - 1 /\ I180 <= I182 /\ I181 <= I182 /\ 0 <= I186 - 1 /\ I180 <= I181 - 1 /\ 0 <= I179 - 1]
  f3(I187, I188, I189, I190) -> f4(I188, I191, I192, I193) [0 <= I187 - 1 /\ I189 <= I188 /\ I189 <= I190 /\ I188 <= I190]
  f3(I194, I195, I196, I197) -> f4(I196, I198, I199, I200) [0 <= I194 - 1 /\ I195 <= I196 - 1 /\ I196 <= I197 /\ I195 <= I197 /\ 0 <= I196 - 1]
  f3(I201, I202, I203, I204) -> f2(I205, I202 + 1, I204, I206) [0 <= I205 - 1 /\ 0 <= I201 - 1 /\ I205 <= I201 /\ -1 <= I204 - 1 /\ I204 <= I203 - 1]
  f2(I207, I208, I209, I210) -> f3(I211, I208, 0, I209) [0 <= I211 - 1 /\ 0 <= I207 - 1 /\ I211 <= I207 /\ -1 <= I209 - 1 /\ I208 <= I209]
  f1(I212, I213, I214, I215) -> f2(I216, 0, I213, I217) [0 <= I216 - 1 /\ 0 <= I212 - 1 /\ -1 <= I213 - 1 /\ I216 <= I212]

The dependency graph for this problem is:
  0 -> 29
  1 -> 1
  2 -> 3, 5, 16, 20, 22, 24, 25, 26, 27
  3 -> 2
  4 -> 5, 20, 24, 26, 27
  5 -> 4
  6 -> 3, 7, 16, 17, 22, 25
  7 -> 6
  8 -> 
  9 -> 
  10 -> 11, 21, 24, 26, 27
  11 -> 10
  12 -> 11, 21, 24, 26, 27
  13 -> 12, 14
  14 -> 11, 13, 15, 19, 21, 23, 24, 25, 26, 27
  15 -> 12, 14
  16 -> 1
  17 -> 1
  18 -> 
  19 -> 1
  20 -> 1
  21 -> 1
  22 -> 1
  23 -> 
  24 -> 1
  25 -> 1
  26 -> 1
  27 -> 28
  28 -> 7, 13, 15, 17, 19, 22, 23, 25
  29 -> 28
Where:
  0) init#(x1, x2, x3, x4) -> f1#(rnd1, rnd2, rnd3, rnd4) 
  1) f4#(I0, I1, I2, I3) -> f4#(I0 - 1, I4, I5, I6) [I0 - 1 <= I0 - 1 /\ 0 <= I0 - 1]
  2) f5#(I7, I8, I9, I10) -> f3#(I11, I8, I9 + 1, I10) [I8 <= I10 /\ I9 <= I10 /\ 0 <= I8 - 1 /\ 0 <= y1 - 1 /\ I9 <= I8 /\ 0 <= y2 - 1 /\ 0 <= y3 - 1 /\ 0 <= I9 - 1 /\ -1 <= I10 - 1 /\ I11 <= I7 /\ 0 <= I7 - 1 /\ 0 <= I11 - 1 /\ y5 - y4 * y6 <= y4 - 1 /\ 0 <= y5 - y4 * y6]
  3) f3#(I12, I13, I14, I15) -> f5#(I12, I13, I14, I15) [I13 <= I15 /\ I14 <= I15 /\ 0 <= I13 - 1 /\ 0 <= I16 - 1 /\ I14 <= I13 /\ 0 <= I17 - 1 /\ 0 <= I18 - 1 /\ 0 <= I14 - 1 /\ -1 <= I15 - 1 /\ I19 <= I12 /\ 0 <= I12 - 1 /\ 0 <= I19 - 1]
  4) f5#(I20, I21, I22, I23) -> f3#(I24, I21, I22 + 1, I23) [0 <= I22 - 1 /\ I21 <= I23 /\ I22 <= I23 /\ 0 <= I25 - 1 /\ I21 <= I22 - 1 /\ 0 <= I26 - 1 /\ 0 <= I27 - 1 /\ 0 <= I21 - 1 /\ -1 <= I23 - 1 /\ I24 <= I20 /\ 0 <= I20 - 1 /\ 0 <= I24 - 1 /\ I28 - I29 * I30 <= I29 - 1 /\ 0 <= I28 - I29 * I30]
  5) f3#(I31, I32, I33, I34) -> f5#(I31, I32, I33, I34) [0 <= I33 - 1 /\ I32 <= I34 /\ I33 <= I34 /\ 0 <= I35 - 1 /\ I32 <= I33 - 1 /\ 0 <= I36 - 1 /\ 0 <= I37 - 1 /\ 0 <= I32 - 1 /\ -1 <= I34 - 1 /\ I38 <= I31 /\ 0 <= I31 - 1 /\ 0 <= I38 - 1]
  6) f5#(I39, I40, I41, I42) -> f3#(I43, I40, I41 + 1, I42) [I40 <= I42 /\ I41 <= I42 /\ 0 <= I40 - 1 /\ 0 <= I44 - 1 /\ I41 <= I40 /\ 1 <= I40 - I41 /\ 0 <= I45 - 1 /\ I41 <= 0 /\ -1 <= I42 - 1 /\ I43 <= I39 /\ 0 <= I39 - 1 /\ 0 <= I43 - 1 /\ I46 - I47 * I48 <= I47 - 1 /\ 0 <= I46 - I47 * I48]
  7) f3#(I49, I50, I51, I52) -> f5#(I49, I50, I51, I52) [I50 <= I52 /\ I51 <= I52 /\ 0 <= I50 - 1 /\ 0 <= I53 - 1 /\ I51 <= I50 /\ 1 <= I50 - I51 /\ 0 <= I54 - 1 /\ I51 <= 0 /\ -1 <= I52 - 1 /\ I55 <= I49 /\ 0 <= I49 - 1 /\ 0 <= I55 - 1]
  8) f5#(I56, I57, I58, I59) -> f3#(I60, 0, I58 + 1, I59) [I58 <= I59 /\ 0 <= I58 - 1 /\ -1 <= I59 - 1 /\ I58 <= 0 /\ 0 <= I61 - 1 /\ I60 <= I56 /\ 0 <= I56 - 1 /\ 0 <= I60 - 1 /\ 1 - I62 * I63 <= I62 - 1 /\ I62 * I63 <= 1 /\ 0 = I57]
  9) f3#(I64, I65, I66, I67) -> f5#(I64, 0, I66, I67) [I66 <= I67 /\ 0 <= I66 - 1 /\ -1 <= I67 - 1 /\ I66 <= 0 /\ 0 <= I68 - 1 /\ I69 <= I64 /\ 0 <= I64 - 1 /\ 0 <= I69 - 1 /\ 0 = I65]
  10) f5#(I70, I71, I72, I73) -> f3#(I74, 0, I72 + 1, I73) [0 <= I72 - 1 /\ -1 <= I73 - 1 /\ I72 <= I73 /\ 0 <= I75 - 1 /\ 0 <= I76 - 1 /\ I74 <= I70 /\ 0 <= I70 - 1 /\ 0 <= I74 - 1 /\ I77 - I78 * I79 <= I78 - 1 /\ 0 <= I77 - I78 * I79 /\ 0 = I71]
  11) f3#(I80, I81, I82, I83) -> f5#(I80, 0, I82, I83) [0 <= I82 - 1 /\ -1 <= I83 - 1 /\ I82 <= I83 /\ 0 <= I84 - 1 /\ 0 <= I85 - 1 /\ I86 <= I80 /\ 0 <= I80 - 1 /\ 0 <= I86 - 1 /\ 0 = I81]
  12) f5#(I87, I88, I89, I90) -> f3#(I91, 0, 1, I90) [-1 <= I90 - 1 /\ I91 <= I87 /\ 0 <= I87 - 1 /\ 0 <= I91 - 1 /\ 1 - I92 * I93 <= I92 - 1 /\ I92 * I93 <= 1 /\ 0 = I88 /\ 0 = I89]
  13) f3#(I94, I95, I96, I97) -> f5#(I94, 0, 0, I97) [-1 <= I97 - 1 /\ I98 <= I94 /\ 0 <= I94 - 1 /\ 0 <= I98 - 1 /\ 0 = I95 /\ 0 = I96]
  14) f5#(I99, I100, I101, I102) -> f3#(I103, 0, I101 + 1, I102) [-1 <= I102 - 1 /\ I101 <= I102 /\ I101 <= 0 /\ I103 <= I99 /\ 0 <= I99 - 1 /\ 0 <= I103 - 1 /\ 1 - I104 * I105 <= I104 - 1 /\ I104 * I105 <= 1 /\ 0 = I100]
  15) f3#(I106, I107, I108, I109) -> f5#(I106, 0, I108, I109) [-1 <= I109 - 1 /\ I108 <= I109 /\ I108 <= 0 /\ I110 <= I106 /\ 0 <= I106 - 1 /\ 0 <= I110 - 1 /\ 0 = I107]
  16) f3#(I111, I112, I113, I114) -> f4#(I112 - I113, I115, I116, I117) [I112 <= I114 /\ I113 <= I114 /\ 0 <= I112 - 1 /\ 0 <= I118 - 1 /\ I113 <= I112 /\ 0 <= I119 - 1 /\ 0 <= I120 - 1 /\ 0 <= I113 - 1 /\ 0 <= I111 - 1]
  17) f3#(I121, I122, I123, I124) -> f4#(I122 - I123, I125, I126, I127) [I122 <= I124 /\ I123 <= I124 /\ 0 <= I122 - 1 /\ 0 <= I128 - 1 /\ I123 <= I122 /\ 1 <= I122 - I123 /\ 0 <= I129 - 1 /\ I123 <= 0 /\ 0 <= I121 - 1]
  18) f3#(I130, I131, I132, I133) -> f4#(0 - I132, I134, I135, I136) [I132 <= I133 /\ 0 <= I132 - 1 /\ -1 <= I133 - 1 /\ I132 <= 0 /\ 0 <= I137 - 1 /\ 0 <= I130 - 1 /\ 0 = I131]
  19) f3#(I138, I139, I140, I141) -> f4#(0 - I140, I142, I143, I144) [0 = I139 /\ 0 <= I138 - 1 /\ I140 <= 0 /\ I140 <= I141 /\ -1 <= I141 - 1]
  20) f3#(I145, I146, I147, I148) -> f4#(I147 - I146, I149, I150, I151) [0 <= I147 - 1 /\ I146 <= I148 /\ I147 <= I148 /\ 0 <= I152 - 1 /\ I146 <= I147 - 1 /\ 0 <= I153 - 1 /\ 0 <= I154 - 1 /\ 0 <= I146 - 1 /\ 0 <= I145 - 1]
  21) f3#(I155, I156, I157, I158) -> f4#(I157, I159, I160, I161) [0 <= I157 - 1 /\ -1 <= I158 - 1 /\ I157 <= I158 /\ 0 <= I162 - 1 /\ 0 <= I163 - 1 /\ 0 <= I155 - 1 /\ 0 = I156]
  22) f3#(I164, I165, I166, I167) -> f4#(I166, I168, I169, I170) [I165 <= I167 /\ I166 <= I167 /\ 0 <= I165 - 1 /\ 0 <= I171 - 1 /\ I166 <= I165 /\ 0 <= I164 - 1]
  23) f3#(I172, I173, I174, I175) -> f4#(I174, I176, I177, I178) [0 = I173 /\ 0 <= I172 - 1 /\ I174 <= 0 /\ I174 <= I175 /\ -1 <= I175 - 1]
  24) f3#(I179, I180, I181, I182) -> f4#(I180, I183, I184, I185) [0 <= I181 - 1 /\ I180 <= I182 /\ I181 <= I182 /\ 0 <= I186 - 1 /\ I180 <= I181 - 1 /\ 0 <= I179 - 1]
  25) f3#(I187, I188, I189, I190) -> f4#(I188, I191, I192, I193) [0 <= I187 - 1 /\ I189 <= I188 /\ I189 <= I190 /\ I188 <= I190]
  26) f3#(I194, I195, I196, I197) -> f4#(I196, I198, I199, I200) [0 <= I194 - 1 /\ I195 <= I196 - 1 /\ I196 <= I197 /\ I195 <= I197 /\ 0 <= I196 - 1]
  27) f3#(I201, I202, I203, I204) -> f2#(I205, I202 + 1, I204, I206) [0 <= I205 - 1 /\ 0 <= I201 - 1 /\ I205 <= I201 /\ -1 <= I204 - 1 /\ I204 <= I203 - 1]
  28) f2#(I207, I208, I209, I210) -> f3#(I211, I208, 0, I209) [0 <= I211 - 1 /\ 0 <= I207 - 1 /\ I211 <= I207 /\ -1 <= I209 - 1 /\ I208 <= I209]
  29) f1#(I212, I213, I214, I215) -> f2#(I216, 0, I213, I217) [0 <= I216 - 1 /\ 0 <= I212 - 1 /\ -1 <= I213 - 1 /\ I216 <= I212]

We have the following SCCs.
  { 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 27, 28 }
  { 1 }

DP problem for innermost termination.
P =
  f4#(I0, I1, I2, I3) -> f4#(I0 - 1, I4, I5, I6) [I0 - 1 <= I0 - 1 /\ 0 <= I0 - 1]
R = 
  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
  f4(I0, I1, I2, I3) -> f4(I0 - 1, I4, I5, I6) [I0 - 1 <= I0 - 1 /\ 0 <= I0 - 1]
  f5(I7, I8, I9, I10) -> f3(I11, I8, I9 + 1, I10) [I8 <= I10 /\ I9 <= I10 /\ 0 <= I8 - 1 /\ 0 <= y1 - 1 /\ I9 <= I8 /\ 0 <= y2 - 1 /\ 0 <= y3 - 1 /\ 0 <= I9 - 1 /\ -1 <= I10 - 1 /\ I11 <= I7 /\ 0 <= I7 - 1 /\ 0 <= I11 - 1 /\ y5 - y4 * y6 <= y4 - 1 /\ 0 <= y5 - y4 * y6]
  f3(I12, I13, I14, I15) -> f5(I12, I13, I14, I15) [I13 <= I15 /\ I14 <= I15 /\ 0 <= I13 - 1 /\ 0 <= I16 - 1 /\ I14 <= I13 /\ 0 <= I17 - 1 /\ 0 <= I18 - 1 /\ 0 <= I14 - 1 /\ -1 <= I15 - 1 /\ I19 <= I12 /\ 0 <= I12 - 1 /\ 0 <= I19 - 1]
  f5(I20, I21, I22, I23) -> f3(I24, I21, I22 + 1, I23) [0 <= I22 - 1 /\ I21 <= I23 /\ I22 <= I23 /\ 0 <= I25 - 1 /\ I21 <= I22 - 1 /\ 0 <= I26 - 1 /\ 0 <= I27 - 1 /\ 0 <= I21 - 1 /\ -1 <= I23 - 1 /\ I24 <= I20 /\ 0 <= I20 - 1 /\ 0 <= I24 - 1 /\ I28 - I29 * I30 <= I29 - 1 /\ 0 <= I28 - I29 * I30]
  f3(I31, I32, I33, I34) -> f5(I31, I32, I33, I34) [0 <= I33 - 1 /\ I32 <= I34 /\ I33 <= I34 /\ 0 <= I35 - 1 /\ I32 <= I33 - 1 /\ 0 <= I36 - 1 /\ 0 <= I37 - 1 /\ 0 <= I32 - 1 /\ -1 <= I34 - 1 /\ I38 <= I31 /\ 0 <= I31 - 1 /\ 0 <= I38 - 1]
  f5(I39, I40, I41, I42) -> f3(I43, I40, I41 + 1, I42) [I40 <= I42 /\ I41 <= I42 /\ 0 <= I40 - 1 /\ 0 <= I44 - 1 /\ I41 <= I40 /\ 1 <= I40 - I41 /\ 0 <= I45 - 1 /\ I41 <= 0 /\ -1 <= I42 - 1 /\ I43 <= I39 /\ 0 <= I39 - 1 /\ 0 <= I43 - 1 /\ I46 - I47 * I48 <= I47 - 1 /\ 0 <= I46 - I47 * I48]
  f3(I49, I50, I51, I52) -> f5(I49, I50, I51, I52) [I50 <= I52 /\ I51 <= I52 /\ 0 <= I50 - 1 /\ 0 <= I53 - 1 /\ I51 <= I50 /\ 1 <= I50 - I51 /\ 0 <= I54 - 1 /\ I51 <= 0 /\ -1 <= I52 - 1 /\ I55 <= I49 /\ 0 <= I49 - 1 /\ 0 <= I55 - 1]
  f5(I56, I57, I58, I59) -> f3(I60, 0, I58 + 1, I59) [I58 <= I59 /\ 0 <= I58 - 1 /\ -1 <= I59 - 1 /\ I58 <= 0 /\ 0 <= I61 - 1 /\ I60 <= I56 /\ 0 <= I56 - 1 /\ 0 <= I60 - 1 /\ 1 - I62 * I63 <= I62 - 1 /\ I62 * I63 <= 1 /\ 0 = I57]
  f3(I64, I65, I66, I67) -> f5(I64, 0, I66, I67) [I66 <= I67 /\ 0 <= I66 - 1 /\ -1 <= I67 - 1 /\ I66 <= 0 /\ 0 <= I68 - 1 /\ I69 <= I64 /\ 0 <= I64 - 1 /\ 0 <= I69 - 1 /\ 0 = I65]
  f5(I70, I71, I72, I73) -> f3(I74, 0, I72 + 1, I73) [0 <= I72 - 1 /\ -1 <= I73 - 1 /\ I72 <= I73 /\ 0 <= I75 - 1 /\ 0 <= I76 - 1 /\ I74 <= I70 /\ 0 <= I70 - 1 /\ 0 <= I74 - 1 /\ I77 - I78 * I79 <= I78 - 1 /\ 0 <= I77 - I78 * I79 /\ 0 = I71]
  f3(I80, I81, I82, I83) -> f5(I80, 0, I82, I83) [0 <= I82 - 1 /\ -1 <= I83 - 1 /\ I82 <= I83 /\ 0 <= I84 - 1 /\ 0 <= I85 - 1 /\ I86 <= I80 /\ 0 <= I80 - 1 /\ 0 <= I86 - 1 /\ 0 = I81]
  f5(I87, I88, I89, I90) -> f3(I91, 0, 1, I90) [-1 <= I90 - 1 /\ I91 <= I87 /\ 0 <= I87 - 1 /\ 0 <= I91 - 1 /\ 1 - I92 * I93 <= I92 - 1 /\ I92 * I93 <= 1 /\ 0 = I88 /\ 0 = I89]
  f3(I94, I95, I96, I97) -> f5(I94, 0, 0, I97) [-1 <= I97 - 1 /\ I98 <= I94 /\ 0 <= I94 - 1 /\ 0 <= I98 - 1 /\ 0 = I95 /\ 0 = I96]
  f5(I99, I100, I101, I102) -> f3(I103, 0, I101 + 1, I102) [-1 <= I102 - 1 /\ I101 <= I102 /\ I101 <= 0 /\ I103 <= I99 /\ 0 <= I99 - 1 /\ 0 <= I103 - 1 /\ 1 - I104 * I105 <= I104 - 1 /\ I104 * I105 <= 1 /\ 0 = I100]
  f3(I106, I107, I108, I109) -> f5(I106, 0, I108, I109) [-1 <= I109 - 1 /\ I108 <= I109 /\ I108 <= 0 /\ I110 <= I106 /\ 0 <= I106 - 1 /\ 0 <= I110 - 1 /\ 0 = I107]
  f3(I111, I112, I113, I114) -> f4(I112 - I113, I115, I116, I117) [I112 <= I114 /\ I113 <= I114 /\ 0 <= I112 - 1 /\ 0 <= I118 - 1 /\ I113 <= I112 /\ 0 <= I119 - 1 /\ 0 <= I120 - 1 /\ 0 <= I113 - 1 /\ 0 <= I111 - 1]
  f3(I121, I122, I123, I124) -> f4(I122 - I123, I125, I126, I127) [I122 <= I124 /\ I123 <= I124 /\ 0 <= I122 - 1 /\ 0 <= I128 - 1 /\ I123 <= I122 /\ 1 <= I122 - I123 /\ 0 <= I129 - 1 /\ I123 <= 0 /\ 0 <= I121 - 1]
  f3(I130, I131, I132, I133) -> f4(0 - I132, I134, I135, I136) [I132 <= I133 /\ 0 <= I132 - 1 /\ -1 <= I133 - 1 /\ I132 <= 0 /\ 0 <= I137 - 1 /\ 0 <= I130 - 1 /\ 0 = I131]
  f3(I138, I139, I140, I141) -> f4(0 - I140, I142, I143, I144) [0 = I139 /\ 0 <= I138 - 1 /\ I140 <= 0 /\ I140 <= I141 /\ -1 <= I141 - 1]
  f3(I145, I146, I147, I148) -> f4(I147 - I146, I149, I150, I151) [0 <= I147 - 1 /\ I146 <= I148 /\ I147 <= I148 /\ 0 <= I152 - 1 /\ I146 <= I147 - 1 /\ 0 <= I153 - 1 /\ 0 <= I154 - 1 /\ 0 <= I146 - 1 /\ 0 <= I145 - 1]
  f3(I155, I156, I157, I158) -> f4(I157, I159, I160, I161) [0 <= I157 - 1 /\ -1 <= I158 - 1 /\ I157 <= I158 /\ 0 <= I162 - 1 /\ 0 <= I163 - 1 /\ 0 <= I155 - 1 /\ 0 = I156]
  f3(I164, I165, I166, I167) -> f4(I166, I168, I169, I170) [I165 <= I167 /\ I166 <= I167 /\ 0 <= I165 - 1 /\ 0 <= I171 - 1 /\ I166 <= I165 /\ 0 <= I164 - 1]
  f3(I172, I173, I174, I175) -> f4(I174, I176, I177, I178) [0 = I173 /\ 0 <= I172 - 1 /\ I174 <= 0 /\ I174 <= I175 /\ -1 <= I175 - 1]
  f3(I179, I180, I181, I182) -> f4(I180, I183, I184, I185) [0 <= I181 - 1 /\ I180 <= I182 /\ I181 <= I182 /\ 0 <= I186 - 1 /\ I180 <= I181 - 1 /\ 0 <= I179 - 1]
  f3(I187, I188, I189, I190) -> f4(I188, I191, I192, I193) [0 <= I187 - 1 /\ I189 <= I188 /\ I189 <= I190 /\ I188 <= I190]
  f3(I194, I195, I196, I197) -> f4(I196, I198, I199, I200) [0 <= I194 - 1 /\ I195 <= I196 - 1 /\ I196 <= I197 /\ I195 <= I197 /\ 0 <= I196 - 1]
  f3(I201, I202, I203, I204) -> f2(I205, I202 + 1, I204, I206) [0 <= I205 - 1 /\ 0 <= I201 - 1 /\ I205 <= I201 /\ -1 <= I204 - 1 /\ I204 <= I203 - 1]
  f2(I207, I208, I209, I210) -> f3(I211, I208, 0, I209) [0 <= I211 - 1 /\ 0 <= I207 - 1 /\ I211 <= I207 /\ -1 <= I209 - 1 /\ I208 <= I209]
  f1(I212, I213, I214, I215) -> f2(I216, 0, I213, I217) [0 <= I216 - 1 /\ 0 <= I212 - 1 /\ -1 <= I213 - 1 /\ I216 <= I212]

We use the basic value criterion with the projection function NU:
  NU[f4#(z1,z2,z3,z4)] = z1

This gives the following inequalities:
  I0 - 1 <= I0 - 1 /\ 0 <= I0 - 1  ==>  I0 >! I0 - 1

All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed.

DP problem for innermost termination.
P =
  f5#(I7, I8, I9, I10) -> f3#(I11, I8, I9 + 1, I10) [I8 <= I10 /\ I9 <= I10 /\ 0 <= I8 - 1 /\ 0 <= y1 - 1 /\ I9 <= I8 /\ 0 <= y2 - 1 /\ 0 <= y3 - 1 /\ 0 <= I9 - 1 /\ -1 <= I10 - 1 /\ I11 <= I7 /\ 0 <= I7 - 1 /\ 0 <= I11 - 1 /\ y5 - y4 * y6 <= y4 - 1 /\ 0 <= y5 - y4 * y6]
  f3#(I12, I13, I14, I15) -> f5#(I12, I13, I14, I15) [I13 <= I15 /\ I14 <= I15 /\ 0 <= I13 - 1 /\ 0 <= I16 - 1 /\ I14 <= I13 /\ 0 <= I17 - 1 /\ 0 <= I18 - 1 /\ 0 <= I14 - 1 /\ -1 <= I15 - 1 /\ I19 <= I12 /\ 0 <= I12 - 1 /\ 0 <= I19 - 1]
  f5#(I20, I21, I22, I23) -> f3#(I24, I21, I22 + 1, I23) [0 <= I22 - 1 /\ I21 <= I23 /\ I22 <= I23 /\ 0 <= I25 - 1 /\ I21 <= I22 - 1 /\ 0 <= I26 - 1 /\ 0 <= I27 - 1 /\ 0 <= I21 - 1 /\ -1 <= I23 - 1 /\ I24 <= I20 /\ 0 <= I20 - 1 /\ 0 <= I24 - 1 /\ I28 - I29 * I30 <= I29 - 1 /\ 0 <= I28 - I29 * I30]
  f3#(I31, I32, I33, I34) -> f5#(I31, I32, I33, I34) [0 <= I33 - 1 /\ I32 <= I34 /\ I33 <= I34 /\ 0 <= I35 - 1 /\ I32 <= I33 - 1 /\ 0 <= I36 - 1 /\ 0 <= I37 - 1 /\ 0 <= I32 - 1 /\ -1 <= I34 - 1 /\ I38 <= I31 /\ 0 <= I31 - 1 /\ 0 <= I38 - 1]
  f5#(I39, I40, I41, I42) -> f3#(I43, I40, I41 + 1, I42) [I40 <= I42 /\ I41 <= I42 /\ 0 <= I40 - 1 /\ 0 <= I44 - 1 /\ I41 <= I40 /\ 1 <= I40 - I41 /\ 0 <= I45 - 1 /\ I41 <= 0 /\ -1 <= I42 - 1 /\ I43 <= I39 /\ 0 <= I39 - 1 /\ 0 <= I43 - 1 /\ I46 - I47 * I48 <= I47 - 1 /\ 0 <= I46 - I47 * I48]
  f3#(I49, I50, I51, I52) -> f5#(I49, I50, I51, I52) [I50 <= I52 /\ I51 <= I52 /\ 0 <= I50 - 1 /\ 0 <= I53 - 1 /\ I51 <= I50 /\ 1 <= I50 - I51 /\ 0 <= I54 - 1 /\ I51 <= 0 /\ -1 <= I52 - 1 /\ I55 <= I49 /\ 0 <= I49 - 1 /\ 0 <= I55 - 1]
  f5#(I70, I71, I72, I73) -> f3#(I74, 0, I72 + 1, I73) [0 <= I72 - 1 /\ -1 <= I73 - 1 /\ I72 <= I73 /\ 0 <= I75 - 1 /\ 0 <= I76 - 1 /\ I74 <= I70 /\ 0 <= I70 - 1 /\ 0 <= I74 - 1 /\ I77 - I78 * I79 <= I78 - 1 /\ 0 <= I77 - I78 * I79 /\ 0 = I71]
  f3#(I80, I81, I82, I83) -> f5#(I80, 0, I82, I83) [0 <= I82 - 1 /\ -1 <= I83 - 1 /\ I82 <= I83 /\ 0 <= I84 - 1 /\ 0 <= I85 - 1 /\ I86 <= I80 /\ 0 <= I80 - 1 /\ 0 <= I86 - 1 /\ 0 = I81]
  f5#(I87, I88, I89, I90) -> f3#(I91, 0, 1, I90) [-1 <= I90 - 1 /\ I91 <= I87 /\ 0 <= I87 - 1 /\ 0 <= I91 - 1 /\ 1 - I92 * I93 <= I92 - 1 /\ I92 * I93 <= 1 /\ 0 = I88 /\ 0 = I89]
  f3#(I94, I95, I96, I97) -> f5#(I94, 0, 0, I97) [-1 <= I97 - 1 /\ I98 <= I94 /\ 0 <= I94 - 1 /\ 0 <= I98 - 1 /\ 0 = I95 /\ 0 = I96]
  f5#(I99, I100, I101, I102) -> f3#(I103, 0, I101 + 1, I102) [-1 <= I102 - 1 /\ I101 <= I102 /\ I101 <= 0 /\ I103 <= I99 /\ 0 <= I99 - 1 /\ 0 <= I103 - 1 /\ 1 - I104 * I105 <= I104 - 1 /\ I104 * I105 <= 1 /\ 0 = I100]
  f3#(I106, I107, I108, I109) -> f5#(I106, 0, I108, I109) [-1 <= I109 - 1 /\ I108 <= I109 /\ I108 <= 0 /\ I110 <= I106 /\ 0 <= I106 - 1 /\ 0 <= I110 - 1 /\ 0 = I107]
  f3#(I201, I202, I203, I204) -> f2#(I205, I202 + 1, I204, I206) [0 <= I205 - 1 /\ 0 <= I201 - 1 /\ I205 <= I201 /\ -1 <= I204 - 1 /\ I204 <= I203 - 1]
  f2#(I207, I208, I209, I210) -> f3#(I211, I208, 0, I209) [0 <= I211 - 1 /\ 0 <= I207 - 1 /\ I211 <= I207 /\ -1 <= I209 - 1 /\ I208 <= I209]
R = 
  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
  f4(I0, I1, I2, I3) -> f4(I0 - 1, I4, I5, I6) [I0 - 1 <= I0 - 1 /\ 0 <= I0 - 1]
  f5(I7, I8, I9, I10) -> f3(I11, I8, I9 + 1, I10) [I8 <= I10 /\ I9 <= I10 /\ 0 <= I8 - 1 /\ 0 <= y1 - 1 /\ I9 <= I8 /\ 0 <= y2 - 1 /\ 0 <= y3 - 1 /\ 0 <= I9 - 1 /\ -1 <= I10 - 1 /\ I11 <= I7 /\ 0 <= I7 - 1 /\ 0 <= I11 - 1 /\ y5 - y4 * y6 <= y4 - 1 /\ 0 <= y5 - y4 * y6]
  f3(I12, I13, I14, I15) -> f5(I12, I13, I14, I15) [I13 <= I15 /\ I14 <= I15 /\ 0 <= I13 - 1 /\ 0 <= I16 - 1 /\ I14 <= I13 /\ 0 <= I17 - 1 /\ 0 <= I18 - 1 /\ 0 <= I14 - 1 /\ -1 <= I15 - 1 /\ I19 <= I12 /\ 0 <= I12 - 1 /\ 0 <= I19 - 1]
  f5(I20, I21, I22, I23) -> f3(I24, I21, I22 + 1, I23) [0 <= I22 - 1 /\ I21 <= I23 /\ I22 <= I23 /\ 0 <= I25 - 1 /\ I21 <= I22 - 1 /\ 0 <= I26 - 1 /\ 0 <= I27 - 1 /\ 0 <= I21 - 1 /\ -1 <= I23 - 1 /\ I24 <= I20 /\ 0 <= I20 - 1 /\ 0 <= I24 - 1 /\ I28 - I29 * I30 <= I29 - 1 /\ 0 <= I28 - I29 * I30]
  f3(I31, I32, I33, I34) -> f5(I31, I32, I33, I34) [0 <= I33 - 1 /\ I32 <= I34 /\ I33 <= I34 /\ 0 <= I35 - 1 /\ I32 <= I33 - 1 /\ 0 <= I36 - 1 /\ 0 <= I37 - 1 /\ 0 <= I32 - 1 /\ -1 <= I34 - 1 /\ I38 <= I31 /\ 0 <= I31 - 1 /\ 0 <= I38 - 1]
  f5(I39, I40, I41, I42) -> f3(I43, I40, I41 + 1, I42) [I40 <= I42 /\ I41 <= I42 /\ 0 <= I40 - 1 /\ 0 <= I44 - 1 /\ I41 <= I40 /\ 1 <= I40 - I41 /\ 0 <= I45 - 1 /\ I41 <= 0 /\ -1 <= I42 - 1 /\ I43 <= I39 /\ 0 <= I39 - 1 /\ 0 <= I43 - 1 /\ I46 - I47 * I48 <= I47 - 1 /\ 0 <= I46 - I47 * I48]
  f3(I49, I50, I51, I52) -> f5(I49, I50, I51, I52) [I50 <= I52 /\ I51 <= I52 /\ 0 <= I50 - 1 /\ 0 <= I53 - 1 /\ I51 <= I50 /\ 1 <= I50 - I51 /\ 0 <= I54 - 1 /\ I51 <= 0 /\ -1 <= I52 - 1 /\ I55 <= I49 /\ 0 <= I49 - 1 /\ 0 <= I55 - 1]
  f5(I56, I57, I58, I59) -> f3(I60, 0, I58 + 1, I59) [I58 <= I59 /\ 0 <= I58 - 1 /\ -1 <= I59 - 1 /\ I58 <= 0 /\ 0 <= I61 - 1 /\ I60 <= I56 /\ 0 <= I56 - 1 /\ 0 <= I60 - 1 /\ 1 - I62 * I63 <= I62 - 1 /\ I62 * I63 <= 1 /\ 0 = I57]
  f3(I64, I65, I66, I67) -> f5(I64, 0, I66, I67) [I66 <= I67 /\ 0 <= I66 - 1 /\ -1 <= I67 - 1 /\ I66 <= 0 /\ 0 <= I68 - 1 /\ I69 <= I64 /\ 0 <= I64 - 1 /\ 0 <= I69 - 1 /\ 0 = I65]
  f5(I70, I71, I72, I73) -> f3(I74, 0, I72 + 1, I73) [0 <= I72 - 1 /\ -1 <= I73 - 1 /\ I72 <= I73 /\ 0 <= I75 - 1 /\ 0 <= I76 - 1 /\ I74 <= I70 /\ 0 <= I70 - 1 /\ 0 <= I74 - 1 /\ I77 - I78 * I79 <= I78 - 1 /\ 0 <= I77 - I78 * I79 /\ 0 = I71]
  f3(I80, I81, I82, I83) -> f5(I80, 0, I82, I83) [0 <= I82 - 1 /\ -1 <= I83 - 1 /\ I82 <= I83 /\ 0 <= I84 - 1 /\ 0 <= I85 - 1 /\ I86 <= I80 /\ 0 <= I80 - 1 /\ 0 <= I86 - 1 /\ 0 = I81]
  f5(I87, I88, I89, I90) -> f3(I91, 0, 1, I90) [-1 <= I90 - 1 /\ I91 <= I87 /\ 0 <= I87 - 1 /\ 0 <= I91 - 1 /\ 1 - I92 * I93 <= I92 - 1 /\ I92 * I93 <= 1 /\ 0 = I88 /\ 0 = I89]
  f3(I94, I95, I96, I97) -> f5(I94, 0, 0, I97) [-1 <= I97 - 1 /\ I98 <= I94 /\ 0 <= I94 - 1 /\ 0 <= I98 - 1 /\ 0 = I95 /\ 0 = I96]
  f5(I99, I100, I101, I102) -> f3(I103, 0, I101 + 1, I102) [-1 <= I102 - 1 /\ I101 <= I102 /\ I101 <= 0 /\ I103 <= I99 /\ 0 <= I99 - 1 /\ 0 <= I103 - 1 /\ 1 - I104 * I105 <= I104 - 1 /\ I104 * I105 <= 1 /\ 0 = I100]
  f3(I106, I107, I108, I109) -> f5(I106, 0, I108, I109) [-1 <= I109 - 1 /\ I108 <= I109 /\ I108 <= 0 /\ I110 <= I106 /\ 0 <= I106 - 1 /\ 0 <= I110 - 1 /\ 0 = I107]
  f3(I111, I112, I113, I114) -> f4(I112 - I113, I115, I116, I117) [I112 <= I114 /\ I113 <= I114 /\ 0 <= I112 - 1 /\ 0 <= I118 - 1 /\ I113 <= I112 /\ 0 <= I119 - 1 /\ 0 <= I120 - 1 /\ 0 <= I113 - 1 /\ 0 <= I111 - 1]
  f3(I121, I122, I123, I124) -> f4(I122 - I123, I125, I126, I127) [I122 <= I124 /\ I123 <= I124 /\ 0 <= I122 - 1 /\ 0 <= I128 - 1 /\ I123 <= I122 /\ 1 <= I122 - I123 /\ 0 <= I129 - 1 /\ I123 <= 0 /\ 0 <= I121 - 1]
  f3(I130, I131, I132, I133) -> f4(0 - I132, I134, I135, I136) [I132 <= I133 /\ 0 <= I132 - 1 /\ -1 <= I133 - 1 /\ I132 <= 0 /\ 0 <= I137 - 1 /\ 0 <= I130 - 1 /\ 0 = I131]
  f3(I138, I139, I140, I141) -> f4(0 - I140, I142, I143, I144) [0 = I139 /\ 0 <= I138 - 1 /\ I140 <= 0 /\ I140 <= I141 /\ -1 <= I141 - 1]
  f3(I145, I146, I147, I148) -> f4(I147 - I146, I149, I150, I151) [0 <= I147 - 1 /\ I146 <= I148 /\ I147 <= I148 /\ 0 <= I152 - 1 /\ I146 <= I147 - 1 /\ 0 <= I153 - 1 /\ 0 <= I154 - 1 /\ 0 <= I146 - 1 /\ 0 <= I145 - 1]
  f3(I155, I156, I157, I158) -> f4(I157, I159, I160, I161) [0 <= I157 - 1 /\ -1 <= I158 - 1 /\ I157 <= I158 /\ 0 <= I162 - 1 /\ 0 <= I163 - 1 /\ 0 <= I155 - 1 /\ 0 = I156]
  f3(I164, I165, I166, I167) -> f4(I166, I168, I169, I170) [I165 <= I167 /\ I166 <= I167 /\ 0 <= I165 - 1 /\ 0 <= I171 - 1 /\ I166 <= I165 /\ 0 <= I164 - 1]
  f3(I172, I173, I174, I175) -> f4(I174, I176, I177, I178) [0 = I173 /\ 0 <= I172 - 1 /\ I174 <= 0 /\ I174 <= I175 /\ -1 <= I175 - 1]
  f3(I179, I180, I181, I182) -> f4(I180, I183, I184, I185) [0 <= I181 - 1 /\ I180 <= I182 /\ I181 <= I182 /\ 0 <= I186 - 1 /\ I180 <= I181 - 1 /\ 0 <= I179 - 1]
  f3(I187, I188, I189, I190) -> f4(I188, I191, I192, I193) [0 <= I187 - 1 /\ I189 <= I188 /\ I189 <= I190 /\ I188 <= I190]
  f3(I194, I195, I196, I197) -> f4(I196, I198, I199, I200) [0 <= I194 - 1 /\ I195 <= I196 - 1 /\ I196 <= I197 /\ I195 <= I197 /\ 0 <= I196 - 1]
  f3(I201, I202, I203, I204) -> f2(I205, I202 + 1, I204, I206) [0 <= I205 - 1 /\ 0 <= I201 - 1 /\ I205 <= I201 /\ -1 <= I204 - 1 /\ I204 <= I203 - 1]
  f2(I207, I208, I209, I210) -> f3(I211, I208, 0, I209) [0 <= I211 - 1 /\ 0 <= I207 - 1 /\ I211 <= I207 /\ -1 <= I209 - 1 /\ I208 <= I209]
  f1(I212, I213, I214, I215) -> f2(I216, 0, I213, I217) [0 <= I216 - 1 /\ 0 <= I212 - 1 /\ -1 <= I213 - 1 /\ I216 <= I212]

We use the extended value criterion with the projection function NU:
  NU[f2#(x0,x1,x2,x3)] = -x1 + x2 + 1
  NU[f3#(x0,x1,x2,x3)] = -x1 + x3
  NU[f5#(x0,x1,x2,x3)] = -x1 + x3

This gives the following inequalities:
  I8 <= I10 /\ I9 <= I10 /\ 0 <= I8 - 1 /\ 0 <= y1 - 1 /\ I9 <= I8 /\ 0 <= y2 - 1 /\ 0 <= y3 - 1 /\ 0 <= I9 - 1 /\ -1 <= I10 - 1 /\ I11 <= I7 /\ 0 <= I7 - 1 /\ 0 <= I11 - 1 /\ y5 - y4 * y6 <= y4 - 1 /\ 0 <= y5 - y4 * y6  ==>  -I8 + I10 >= -I8 + I10
  I13 <= I15 /\ I14 <= I15 /\ 0 <= I13 - 1 /\ 0 <= I16 - 1 /\ I14 <= I13 /\ 0 <= I17 - 1 /\ 0 <= I18 - 1 /\ 0 <= I14 - 1 /\ -1 <= I15 - 1 /\ I19 <= I12 /\ 0 <= I12 - 1 /\ 0 <= I19 - 1  ==>  -I13 + I15 >= -I13 + I15
  0 <= I22 - 1 /\ I21 <= I23 /\ I22 <= I23 /\ 0 <= I25 - 1 /\ I21 <= I22 - 1 /\ 0 <= I26 - 1 /\ 0 <= I27 - 1 /\ 0 <= I21 - 1 /\ -1 <= I23 - 1 /\ I24 <= I20 /\ 0 <= I20 - 1 /\ 0 <= I24 - 1 /\ I28 - I29 * I30 <= I29 - 1 /\ 0 <= I28 - I29 * I30  ==>  -I21 + I23 >= -I21 + I23
  0 <= I33 - 1 /\ I32 <= I34 /\ I33 <= I34 /\ 0 <= I35 - 1 /\ I32 <= I33 - 1 /\ 0 <= I36 - 1 /\ 0 <= I37 - 1 /\ 0 <= I32 - 1 /\ -1 <= I34 - 1 /\ I38 <= I31 /\ 0 <= I31 - 1 /\ 0 <= I38 - 1  ==>  -I32 + I34 >= -I32 + I34
  I40 <= I42 /\ I41 <= I42 /\ 0 <= I40 - 1 /\ 0 <= I44 - 1 /\ I41 <= I40 /\ 1 <= I40 - I41 /\ 0 <= I45 - 1 /\ I41 <= 0 /\ -1 <= I42 - 1 /\ I43 <= I39 /\ 0 <= I39 - 1 /\ 0 <= I43 - 1 /\ I46 - I47 * I48 <= I47 - 1 /\ 0 <= I46 - I47 * I48  ==>  -I40 + I42 >= -I40 + I42
  I50 <= I52 /\ I51 <= I52 /\ 0 <= I50 - 1 /\ 0 <= I53 - 1 /\ I51 <= I50 /\ 1 <= I50 - I51 /\ 0 <= I54 - 1 /\ I51 <= 0 /\ -1 <= I52 - 1 /\ I55 <= I49 /\ 0 <= I49 - 1 /\ 0 <= I55 - 1  ==>  -I50 + I52 >= -I50 + I52
  0 <= I72 - 1 /\ -1 <= I73 - 1 /\ I72 <= I73 /\ 0 <= I75 - 1 /\ 0 <= I76 - 1 /\ I74 <= I70 /\ 0 <= I70 - 1 /\ 0 <= I74 - 1 /\ I77 - I78 * I79 <= I78 - 1 /\ 0 <= I77 - I78 * I79 /\ 0 = I71  ==>  -I71 + I73 >= -0 + I73
  0 <= I82 - 1 /\ -1 <= I83 - 1 /\ I82 <= I83 /\ 0 <= I84 - 1 /\ 0 <= I85 - 1 /\ I86 <= I80 /\ 0 <= I80 - 1 /\ 0 <= I86 - 1 /\ 0 = I81  ==>  -I81 + I83 >= -0 + I83
  -1 <= I90 - 1 /\ I91 <= I87 /\ 0 <= I87 - 1 /\ 0 <= I91 - 1 /\ 1 - I92 * I93 <= I92 - 1 /\ I92 * I93 <= 1 /\ 0 = I88 /\ 0 = I89  ==>  -I88 + I90 >= -0 + I90
  -1 <= I97 - 1 /\ I98 <= I94 /\ 0 <= I94 - 1 /\ 0 <= I98 - 1 /\ 0 = I95 /\ 0 = I96  ==>  -I95 + I97 >= -0 + I97
  -1 <= I102 - 1 /\ I101 <= I102 /\ I101 <= 0 /\ I103 <= I99 /\ 0 <= I99 - 1 /\ 0 <= I103 - 1 /\ 1 - I104 * I105 <= I104 - 1 /\ I104 * I105 <= 1 /\ 0 = I100  ==>  -I100 + I102 >= -0 + I102
  -1 <= I109 - 1 /\ I108 <= I109 /\ I108 <= 0 /\ I110 <= I106 /\ 0 <= I106 - 1 /\ 0 <= I110 - 1 /\ 0 = I107  ==>  -I107 + I109 >= -0 + I109
  0 <= I205 - 1 /\ 0 <= I201 - 1 /\ I205 <= I201 /\ -1 <= I204 - 1 /\ I204 <= I203 - 1  ==>  -I202 + I204 >= -(I202 + 1) + I204 + 1
  0 <= I211 - 1 /\ 0 <= I207 - 1 /\ I211 <= I207 /\ -1 <= I209 - 1 /\ I208 <= I209  ==>  -I208 + I209 + 1 > -I208 + I209  with  -I208 + I209 + 1 >= 0

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f5#(I7, I8, I9, I10) -> f3#(I11, I8, I9 + 1, I10) [I8 <= I10 /\ I9 <= I10 /\ 0 <= I8 - 1 /\ 0 <= y1 - 1 /\ I9 <= I8 /\ 0 <= y2 - 1 /\ 0 <= y3 - 1 /\ 0 <= I9 - 1 /\ -1 <= I10 - 1 /\ I11 <= I7 /\ 0 <= I7 - 1 /\ 0 <= I11 - 1 /\ y5 - y4 * y6 <= y4 - 1 /\ 0 <= y5 - y4 * y6]
  f3#(I12, I13, I14, I15) -> f5#(I12, I13, I14, I15) [I13 <= I15 /\ I14 <= I15 /\ 0 <= I13 - 1 /\ 0 <= I16 - 1 /\ I14 <= I13 /\ 0 <= I17 - 1 /\ 0 <= I18 - 1 /\ 0 <= I14 - 1 /\ -1 <= I15 - 1 /\ I19 <= I12 /\ 0 <= I12 - 1 /\ 0 <= I19 - 1]
  f5#(I20, I21, I22, I23) -> f3#(I24, I21, I22 + 1, I23) [0 <= I22 - 1 /\ I21 <= I23 /\ I22 <= I23 /\ 0 <= I25 - 1 /\ I21 <= I22 - 1 /\ 0 <= I26 - 1 /\ 0 <= I27 - 1 /\ 0 <= I21 - 1 /\ -1 <= I23 - 1 /\ I24 <= I20 /\ 0 <= I20 - 1 /\ 0 <= I24 - 1 /\ I28 - I29 * I30 <= I29 - 1 /\ 0 <= I28 - I29 * I30]
  f3#(I31, I32, I33, I34) -> f5#(I31, I32, I33, I34) [0 <= I33 - 1 /\ I32 <= I34 /\ I33 <= I34 /\ 0 <= I35 - 1 /\ I32 <= I33 - 1 /\ 0 <= I36 - 1 /\ 0 <= I37 - 1 /\ 0 <= I32 - 1 /\ -1 <= I34 - 1 /\ I38 <= I31 /\ 0 <= I31 - 1 /\ 0 <= I38 - 1]
  f5#(I39, I40, I41, I42) -> f3#(I43, I40, I41 + 1, I42) [I40 <= I42 /\ I41 <= I42 /\ 0 <= I40 - 1 /\ 0 <= I44 - 1 /\ I41 <= I40 /\ 1 <= I40 - I41 /\ 0 <= I45 - 1 /\ I41 <= 0 /\ -1 <= I42 - 1 /\ I43 <= I39 /\ 0 <= I39 - 1 /\ 0 <= I43 - 1 /\ I46 - I47 * I48 <= I47 - 1 /\ 0 <= I46 - I47 * I48]
  f3#(I49, I50, I51, I52) -> f5#(I49, I50, I51, I52) [I50 <= I52 /\ I51 <= I52 /\ 0 <= I50 - 1 /\ 0 <= I53 - 1 /\ I51 <= I50 /\ 1 <= I50 - I51 /\ 0 <= I54 - 1 /\ I51 <= 0 /\ -1 <= I52 - 1 /\ I55 <= I49 /\ 0 <= I49 - 1 /\ 0 <= I55 - 1]
  f5#(I70, I71, I72, I73) -> f3#(I74, 0, I72 + 1, I73) [0 <= I72 - 1 /\ -1 <= I73 - 1 /\ I72 <= I73 /\ 0 <= I75 - 1 /\ 0 <= I76 - 1 /\ I74 <= I70 /\ 0 <= I70 - 1 /\ 0 <= I74 - 1 /\ I77 - I78 * I79 <= I78 - 1 /\ 0 <= I77 - I78 * I79 /\ 0 = I71]
  f3#(I80, I81, I82, I83) -> f5#(I80, 0, I82, I83) [0 <= I82 - 1 /\ -1 <= I83 - 1 /\ I82 <= I83 /\ 0 <= I84 - 1 /\ 0 <= I85 - 1 /\ I86 <= I80 /\ 0 <= I80 - 1 /\ 0 <= I86 - 1 /\ 0 = I81]
  f5#(I87, I88, I89, I90) -> f3#(I91, 0, 1, I90) [-1 <= I90 - 1 /\ I91 <= I87 /\ 0 <= I87 - 1 /\ 0 <= I91 - 1 /\ 1 - I92 * I93 <= I92 - 1 /\ I92 * I93 <= 1 /\ 0 = I88 /\ 0 = I89]
  f3#(I94, I95, I96, I97) -> f5#(I94, 0, 0, I97) [-1 <= I97 - 1 /\ I98 <= I94 /\ 0 <= I94 - 1 /\ 0 <= I98 - 1 /\ 0 = I95 /\ 0 = I96]
  f5#(I99, I100, I101, I102) -> f3#(I103, 0, I101 + 1, I102) [-1 <= I102 - 1 /\ I101 <= I102 /\ I101 <= 0 /\ I103 <= I99 /\ 0 <= I99 - 1 /\ 0 <= I103 - 1 /\ 1 - I104 * I105 <= I104 - 1 /\ I104 * I105 <= 1 /\ 0 = I100]
  f3#(I106, I107, I108, I109) -> f5#(I106, 0, I108, I109) [-1 <= I109 - 1 /\ I108 <= I109 /\ I108 <= 0 /\ I110 <= I106 /\ 0 <= I106 - 1 /\ 0 <= I110 - 1 /\ 0 = I107]
  f3#(I201, I202, I203, I204) -> f2#(I205, I202 + 1, I204, I206) [0 <= I205 - 1 /\ 0 <= I201 - 1 /\ I205 <= I201 /\ -1 <= I204 - 1 /\ I204 <= I203 - 1]
R = 
  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
  f4(I0, I1, I2, I3) -> f4(I0 - 1, I4, I5, I6) [I0 - 1 <= I0 - 1 /\ 0 <= I0 - 1]
  f5(I7, I8, I9, I10) -> f3(I11, I8, I9 + 1, I10) [I8 <= I10 /\ I9 <= I10 /\ 0 <= I8 - 1 /\ 0 <= y1 - 1 /\ I9 <= I8 /\ 0 <= y2 - 1 /\ 0 <= y3 - 1 /\ 0 <= I9 - 1 /\ -1 <= I10 - 1 /\ I11 <= I7 /\ 0 <= I7 - 1 /\ 0 <= I11 - 1 /\ y5 - y4 * y6 <= y4 - 1 /\ 0 <= y5 - y4 * y6]
  f3(I12, I13, I14, I15) -> f5(I12, I13, I14, I15) [I13 <= I15 /\ I14 <= I15 /\ 0 <= I13 - 1 /\ 0 <= I16 - 1 /\ I14 <= I13 /\ 0 <= I17 - 1 /\ 0 <= I18 - 1 /\ 0 <= I14 - 1 /\ -1 <= I15 - 1 /\ I19 <= I12 /\ 0 <= I12 - 1 /\ 0 <= I19 - 1]
  f5(I20, I21, I22, I23) -> f3(I24, I21, I22 + 1, I23) [0 <= I22 - 1 /\ I21 <= I23 /\ I22 <= I23 /\ 0 <= I25 - 1 /\ I21 <= I22 - 1 /\ 0 <= I26 - 1 /\ 0 <= I27 - 1 /\ 0 <= I21 - 1 /\ -1 <= I23 - 1 /\ I24 <= I20 /\ 0 <= I20 - 1 /\ 0 <= I24 - 1 /\ I28 - I29 * I30 <= I29 - 1 /\ 0 <= I28 - I29 * I30]
  f3(I31, I32, I33, I34) -> f5(I31, I32, I33, I34) [0 <= I33 - 1 /\ I32 <= I34 /\ I33 <= I34 /\ 0 <= I35 - 1 /\ I32 <= I33 - 1 /\ 0 <= I36 - 1 /\ 0 <= I37 - 1 /\ 0 <= I32 - 1 /\ -1 <= I34 - 1 /\ I38 <= I31 /\ 0 <= I31 - 1 /\ 0 <= I38 - 1]
  f5(I39, I40, I41, I42) -> f3(I43, I40, I41 + 1, I42) [I40 <= I42 /\ I41 <= I42 /\ 0 <= I40 - 1 /\ 0 <= I44 - 1 /\ I41 <= I40 /\ 1 <= I40 - I41 /\ 0 <= I45 - 1 /\ I41 <= 0 /\ -1 <= I42 - 1 /\ I43 <= I39 /\ 0 <= I39 - 1 /\ 0 <= I43 - 1 /\ I46 - I47 * I48 <= I47 - 1 /\ 0 <= I46 - I47 * I48]
  f3(I49, I50, I51, I52) -> f5(I49, I50, I51, I52) [I50 <= I52 /\ I51 <= I52 /\ 0 <= I50 - 1 /\ 0 <= I53 - 1 /\ I51 <= I50 /\ 1 <= I50 - I51 /\ 0 <= I54 - 1 /\ I51 <= 0 /\ -1 <= I52 - 1 /\ I55 <= I49 /\ 0 <= I49 - 1 /\ 0 <= I55 - 1]
  f5(I56, I57, I58, I59) -> f3(I60, 0, I58 + 1, I59) [I58 <= I59 /\ 0 <= I58 - 1 /\ -1 <= I59 - 1 /\ I58 <= 0 /\ 0 <= I61 - 1 /\ I60 <= I56 /\ 0 <= I56 - 1 /\ 0 <= I60 - 1 /\ 1 - I62 * I63 <= I62 - 1 /\ I62 * I63 <= 1 /\ 0 = I57]
  f3(I64, I65, I66, I67) -> f5(I64, 0, I66, I67) [I66 <= I67 /\ 0 <= I66 - 1 /\ -1 <= I67 - 1 /\ I66 <= 0 /\ 0 <= I68 - 1 /\ I69 <= I64 /\ 0 <= I64 - 1 /\ 0 <= I69 - 1 /\ 0 = I65]
  f5(I70, I71, I72, I73) -> f3(I74, 0, I72 + 1, I73) [0 <= I72 - 1 /\ -1 <= I73 - 1 /\ I72 <= I73 /\ 0 <= I75 - 1 /\ 0 <= I76 - 1 /\ I74 <= I70 /\ 0 <= I70 - 1 /\ 0 <= I74 - 1 /\ I77 - I78 * I79 <= I78 - 1 /\ 0 <= I77 - I78 * I79 /\ 0 = I71]
  f3(I80, I81, I82, I83) -> f5(I80, 0, I82, I83) [0 <= I82 - 1 /\ -1 <= I83 - 1 /\ I82 <= I83 /\ 0 <= I84 - 1 /\ 0 <= I85 - 1 /\ I86 <= I80 /\ 0 <= I80 - 1 /\ 0 <= I86 - 1 /\ 0 = I81]
  f5(I87, I88, I89, I90) -> f3(I91, 0, 1, I90) [-1 <= I90 - 1 /\ I91 <= I87 /\ 0 <= I87 - 1 /\ 0 <= I91 - 1 /\ 1 - I92 * I93 <= I92 - 1 /\ I92 * I93 <= 1 /\ 0 = I88 /\ 0 = I89]
  f3(I94, I95, I96, I97) -> f5(I94, 0, 0, I97) [-1 <= I97 - 1 /\ I98 <= I94 /\ 0 <= I94 - 1 /\ 0 <= I98 - 1 /\ 0 = I95 /\ 0 = I96]
  f5(I99, I100, I101, I102) -> f3(I103, 0, I101 + 1, I102) [-1 <= I102 - 1 /\ I101 <= I102 /\ I101 <= 0 /\ I103 <= I99 /\ 0 <= I99 - 1 /\ 0 <= I103 - 1 /\ 1 - I104 * I105 <= I104 - 1 /\ I104 * I105 <= 1 /\ 0 = I100]
  f3(I106, I107, I108, I109) -> f5(I106, 0, I108, I109) [-1 <= I109 - 1 /\ I108 <= I109 /\ I108 <= 0 /\ I110 <= I106 /\ 0 <= I106 - 1 /\ 0 <= I110 - 1 /\ 0 = I107]
  f3(I111, I112, I113, I114) -> f4(I112 - I113, I115, I116, I117) [I112 <= I114 /\ I113 <= I114 /\ 0 <= I112 - 1 /\ 0 <= I118 - 1 /\ I113 <= I112 /\ 0 <= I119 - 1 /\ 0 <= I120 - 1 /\ 0 <= I113 - 1 /\ 0 <= I111 - 1]
  f3(I121, I122, I123, I124) -> f4(I122 - I123, I125, I126, I127) [I122 <= I124 /\ I123 <= I124 /\ 0 <= I122 - 1 /\ 0 <= I128 - 1 /\ I123 <= I122 /\ 1 <= I122 - I123 /\ 0 <= I129 - 1 /\ I123 <= 0 /\ 0 <= I121 - 1]
  f3(I130, I131, I132, I133) -> f4(0 - I132, I134, I135, I136) [I132 <= I133 /\ 0 <= I132 - 1 /\ -1 <= I133 - 1 /\ I132 <= 0 /\ 0 <= I137 - 1 /\ 0 <= I130 - 1 /\ 0 = I131]
  f3(I138, I139, I140, I141) -> f4(0 - I140, I142, I143, I144) [0 = I139 /\ 0 <= I138 - 1 /\ I140 <= 0 /\ I140 <= I141 /\ -1 <= I141 - 1]
  f3(I145, I146, I147, I148) -> f4(I147 - I146, I149, I150, I151) [0 <= I147 - 1 /\ I146 <= I148 /\ I147 <= I148 /\ 0 <= I152 - 1 /\ I146 <= I147 - 1 /\ 0 <= I153 - 1 /\ 0 <= I154 - 1 /\ 0 <= I146 - 1 /\ 0 <= I145 - 1]
  f3(I155, I156, I157, I158) -> f4(I157, I159, I160, I161) [0 <= I157 - 1 /\ -1 <= I158 - 1 /\ I157 <= I158 /\ 0 <= I162 - 1 /\ 0 <= I163 - 1 /\ 0 <= I155 - 1 /\ 0 = I156]
  f3(I164, I165, I166, I167) -> f4(I166, I168, I169, I170) [I165 <= I167 /\ I166 <= I167 /\ 0 <= I165 - 1 /\ 0 <= I171 - 1 /\ I166 <= I165 /\ 0 <= I164 - 1]
  f3(I172, I173, I174, I175) -> f4(I174, I176, I177, I178) [0 = I173 /\ 0 <= I172 - 1 /\ I174 <= 0 /\ I174 <= I175 /\ -1 <= I175 - 1]
  f3(I179, I180, I181, I182) -> f4(I180, I183, I184, I185) [0 <= I181 - 1 /\ I180 <= I182 /\ I181 <= I182 /\ 0 <= I186 - 1 /\ I180 <= I181 - 1 /\ 0 <= I179 - 1]
  f3(I187, I188, I189, I190) -> f4(I188, I191, I192, I193) [0 <= I187 - 1 /\ I189 <= I188 /\ I189 <= I190 /\ I188 <= I190]
  f3(I194, I195, I196, I197) -> f4(I196, I198, I199, I200) [0 <= I194 - 1 /\ I195 <= I196 - 1 /\ I196 <= I197 /\ I195 <= I197 /\ 0 <= I196 - 1]
  f3(I201, I202, I203, I204) -> f2(I205, I202 + 1, I204, I206) [0 <= I205 - 1 /\ 0 <= I201 - 1 /\ I205 <= I201 /\ -1 <= I204 - 1 /\ I204 <= I203 - 1]
  f2(I207, I208, I209, I210) -> f3(I211, I208, 0, I209) [0 <= I211 - 1 /\ 0 <= I207 - 1 /\ I211 <= I207 /\ -1 <= I209 - 1 /\ I208 <= I209]
  f1(I212, I213, I214, I215) -> f2(I216, 0, I213, I217) [0 <= I216 - 1 /\ 0 <= I212 - 1 /\ -1 <= I213 - 1 /\ I216 <= I212]

The dependency graph for this problem is:
  2 -> 3, 5, 27
  3 -> 2
  4 -> 5, 27
  5 -> 4
  6 -> 3, 7
  7 -> 6
  10 -> 11, 27
  11 -> 10
  12 -> 11, 27
  13 -> 12, 14
  14 -> 11, 13, 15, 27
  15 -> 12, 14
  27 -> 
Where:
  2) f5#(I7, I8, I9, I10) -> f3#(I11, I8, I9 + 1, I10) [I8 <= I10 /\ I9 <= I10 /\ 0 <= I8 - 1 /\ 0 <= y1 - 1 /\ I9 <= I8 /\ 0 <= y2 - 1 /\ 0 <= y3 - 1 /\ 0 <= I9 - 1 /\ -1 <= I10 - 1 /\ I11 <= I7 /\ 0 <= I7 - 1 /\ 0 <= I11 - 1 /\ y5 - y4 * y6 <= y4 - 1 /\ 0 <= y5 - y4 * y6]
  3) f3#(I12, I13, I14, I15) -> f5#(I12, I13, I14, I15) [I13 <= I15 /\ I14 <= I15 /\ 0 <= I13 - 1 /\ 0 <= I16 - 1 /\ I14 <= I13 /\ 0 <= I17 - 1 /\ 0 <= I18 - 1 /\ 0 <= I14 - 1 /\ -1 <= I15 - 1 /\ I19 <= I12 /\ 0 <= I12 - 1 /\ 0 <= I19 - 1]
  4) f5#(I20, I21, I22, I23) -> f3#(I24, I21, I22 + 1, I23) [0 <= I22 - 1 /\ I21 <= I23 /\ I22 <= I23 /\ 0 <= I25 - 1 /\ I21 <= I22 - 1 /\ 0 <= I26 - 1 /\ 0 <= I27 - 1 /\ 0 <= I21 - 1 /\ -1 <= I23 - 1 /\ I24 <= I20 /\ 0 <= I20 - 1 /\ 0 <= I24 - 1 /\ I28 - I29 * I30 <= I29 - 1 /\ 0 <= I28 - I29 * I30]
  5) f3#(I31, I32, I33, I34) -> f5#(I31, I32, I33, I34) [0 <= I33 - 1 /\ I32 <= I34 /\ I33 <= I34 /\ 0 <= I35 - 1 /\ I32 <= I33 - 1 /\ 0 <= I36 - 1 /\ 0 <= I37 - 1 /\ 0 <= I32 - 1 /\ -1 <= I34 - 1 /\ I38 <= I31 /\ 0 <= I31 - 1 /\ 0 <= I38 - 1]
  6) f5#(I39, I40, I41, I42) -> f3#(I43, I40, I41 + 1, I42) [I40 <= I42 /\ I41 <= I42 /\ 0 <= I40 - 1 /\ 0 <= I44 - 1 /\ I41 <= I40 /\ 1 <= I40 - I41 /\ 0 <= I45 - 1 /\ I41 <= 0 /\ -1 <= I42 - 1 /\ I43 <= I39 /\ 0 <= I39 - 1 /\ 0 <= I43 - 1 /\ I46 - I47 * I48 <= I47 - 1 /\ 0 <= I46 - I47 * I48]
  7) f3#(I49, I50, I51, I52) -> f5#(I49, I50, I51, I52) [I50 <= I52 /\ I51 <= I52 /\ 0 <= I50 - 1 /\ 0 <= I53 - 1 /\ I51 <= I50 /\ 1 <= I50 - I51 /\ 0 <= I54 - 1 /\ I51 <= 0 /\ -1 <= I52 - 1 /\ I55 <= I49 /\ 0 <= I49 - 1 /\ 0 <= I55 - 1]
  10) f5#(I70, I71, I72, I73) -> f3#(I74, 0, I72 + 1, I73) [0 <= I72 - 1 /\ -1 <= I73 - 1 /\ I72 <= I73 /\ 0 <= I75 - 1 /\ 0 <= I76 - 1 /\ I74 <= I70 /\ 0 <= I70 - 1 /\ 0 <= I74 - 1 /\ I77 - I78 * I79 <= I78 - 1 /\ 0 <= I77 - I78 * I79 /\ 0 = I71]
  11) f3#(I80, I81, I82, I83) -> f5#(I80, 0, I82, I83) [0 <= I82 - 1 /\ -1 <= I83 - 1 /\ I82 <= I83 /\ 0 <= I84 - 1 /\ 0 <= I85 - 1 /\ I86 <= I80 /\ 0 <= I80 - 1 /\ 0 <= I86 - 1 /\ 0 = I81]
  12) f5#(I87, I88, I89, I90) -> f3#(I91, 0, 1, I90) [-1 <= I90 - 1 /\ I91 <= I87 /\ 0 <= I87 - 1 /\ 0 <= I91 - 1 /\ 1 - I92 * I93 <= I92 - 1 /\ I92 * I93 <= 1 /\ 0 = I88 /\ 0 = I89]
  13) f3#(I94, I95, I96, I97) -> f5#(I94, 0, 0, I97) [-1 <= I97 - 1 /\ I98 <= I94 /\ 0 <= I94 - 1 /\ 0 <= I98 - 1 /\ 0 = I95 /\ 0 = I96]
  14) f5#(I99, I100, I101, I102) -> f3#(I103, 0, I101 + 1, I102) [-1 <= I102 - 1 /\ I101 <= I102 /\ I101 <= 0 /\ I103 <= I99 /\ 0 <= I99 - 1 /\ 0 <= I103 - 1 /\ 1 - I104 * I105 <= I104 - 1 /\ I104 * I105 <= 1 /\ 0 = I100]
  15) f3#(I106, I107, I108, I109) -> f5#(I106, 0, I108, I109) [-1 <= I109 - 1 /\ I108 <= I109 /\ I108 <= 0 /\ I110 <= I106 /\ 0 <= I106 - 1 /\ 0 <= I110 - 1 /\ 0 = I107]
  27) f3#(I201, I202, I203, I204) -> f2#(I205, I202 + 1, I204, I206) [0 <= I205 - 1 /\ 0 <= I201 - 1 /\ I205 <= I201 /\ -1 <= I204 - 1 /\ I204 <= I203 - 1]

We have the following SCCs.
  { 6, 7 }
  { 2, 3 }
  { 4, 5 }
  { 13, 14, 15 }
  { 10, 11 }

DP problem for innermost termination.
P =
  f5#(I70, I71, I72, I73) -> f3#(I74, 0, I72 + 1, I73) [0 <= I72 - 1 /\ -1 <= I73 - 1 /\ I72 <= I73 /\ 0 <= I75 - 1 /\ 0 <= I76 - 1 /\ I74 <= I70 /\ 0 <= I70 - 1 /\ 0 <= I74 - 1 /\ I77 - I78 * I79 <= I78 - 1 /\ 0 <= I77 - I78 * I79 /\ 0 = I71]
  f3#(I80, I81, I82, I83) -> f5#(I80, 0, I82, I83) [0 <= I82 - 1 /\ -1 <= I83 - 1 /\ I82 <= I83 /\ 0 <= I84 - 1 /\ 0 <= I85 - 1 /\ I86 <= I80 /\ 0 <= I80 - 1 /\ 0 <= I86 - 1 /\ 0 = I81]
R = 
  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
  f4(I0, I1, I2, I3) -> f4(I0 - 1, I4, I5, I6) [I0 - 1 <= I0 - 1 /\ 0 <= I0 - 1]
  f5(I7, I8, I9, I10) -> f3(I11, I8, I9 + 1, I10) [I8 <= I10 /\ I9 <= I10 /\ 0 <= I8 - 1 /\ 0 <= y1 - 1 /\ I9 <= I8 /\ 0 <= y2 - 1 /\ 0 <= y3 - 1 /\ 0 <= I9 - 1 /\ -1 <= I10 - 1 /\ I11 <= I7 /\ 0 <= I7 - 1 /\ 0 <= I11 - 1 /\ y5 - y4 * y6 <= y4 - 1 /\ 0 <= y5 - y4 * y6]
  f3(I12, I13, I14, I15) -> f5(I12, I13, I14, I15) [I13 <= I15 /\ I14 <= I15 /\ 0 <= I13 - 1 /\ 0 <= I16 - 1 /\ I14 <= I13 /\ 0 <= I17 - 1 /\ 0 <= I18 - 1 /\ 0 <= I14 - 1 /\ -1 <= I15 - 1 /\ I19 <= I12 /\ 0 <= I12 - 1 /\ 0 <= I19 - 1]
  f5(I20, I21, I22, I23) -> f3(I24, I21, I22 + 1, I23) [0 <= I22 - 1 /\ I21 <= I23 /\ I22 <= I23 /\ 0 <= I25 - 1 /\ I21 <= I22 - 1 /\ 0 <= I26 - 1 /\ 0 <= I27 - 1 /\ 0 <= I21 - 1 /\ -1 <= I23 - 1 /\ I24 <= I20 /\ 0 <= I20 - 1 /\ 0 <= I24 - 1 /\ I28 - I29 * I30 <= I29 - 1 /\ 0 <= I28 - I29 * I30]
  f3(I31, I32, I33, I34) -> f5(I31, I32, I33, I34) [0 <= I33 - 1 /\ I32 <= I34 /\ I33 <= I34 /\ 0 <= I35 - 1 /\ I32 <= I33 - 1 /\ 0 <= I36 - 1 /\ 0 <= I37 - 1 /\ 0 <= I32 - 1 /\ -1 <= I34 - 1 /\ I38 <= I31 /\ 0 <= I31 - 1 /\ 0 <= I38 - 1]
  f5(I39, I40, I41, I42) -> f3(I43, I40, I41 + 1, I42) [I40 <= I42 /\ I41 <= I42 /\ 0 <= I40 - 1 /\ 0 <= I44 - 1 /\ I41 <= I40 /\ 1 <= I40 - I41 /\ 0 <= I45 - 1 /\ I41 <= 0 /\ -1 <= I42 - 1 /\ I43 <= I39 /\ 0 <= I39 - 1 /\ 0 <= I43 - 1 /\ I46 - I47 * I48 <= I47 - 1 /\ 0 <= I46 - I47 * I48]
  f3(I49, I50, I51, I52) -> f5(I49, I50, I51, I52) [I50 <= I52 /\ I51 <= I52 /\ 0 <= I50 - 1 /\ 0 <= I53 - 1 /\ I51 <= I50 /\ 1 <= I50 - I51 /\ 0 <= I54 - 1 /\ I51 <= 0 /\ -1 <= I52 - 1 /\ I55 <= I49 /\ 0 <= I49 - 1 /\ 0 <= I55 - 1]
  f5(I56, I57, I58, I59) -> f3(I60, 0, I58 + 1, I59) [I58 <= I59 /\ 0 <= I58 - 1 /\ -1 <= I59 - 1 /\ I58 <= 0 /\ 0 <= I61 - 1 /\ I60 <= I56 /\ 0 <= I56 - 1 /\ 0 <= I60 - 1 /\ 1 - I62 * I63 <= I62 - 1 /\ I62 * I63 <= 1 /\ 0 = I57]
  f3(I64, I65, I66, I67) -> f5(I64, 0, I66, I67) [I66 <= I67 /\ 0 <= I66 - 1 /\ -1 <= I67 - 1 /\ I66 <= 0 /\ 0 <= I68 - 1 /\ I69 <= I64 /\ 0 <= I64 - 1 /\ 0 <= I69 - 1 /\ 0 = I65]
  f5(I70, I71, I72, I73) -> f3(I74, 0, I72 + 1, I73) [0 <= I72 - 1 /\ -1 <= I73 - 1 /\ I72 <= I73 /\ 0 <= I75 - 1 /\ 0 <= I76 - 1 /\ I74 <= I70 /\ 0 <= I70 - 1 /\ 0 <= I74 - 1 /\ I77 - I78 * I79 <= I78 - 1 /\ 0 <= I77 - I78 * I79 /\ 0 = I71]
  f3(I80, I81, I82, I83) -> f5(I80, 0, I82, I83) [0 <= I82 - 1 /\ -1 <= I83 - 1 /\ I82 <= I83 /\ 0 <= I84 - 1 /\ 0 <= I85 - 1 /\ I86 <= I80 /\ 0 <= I80 - 1 /\ 0 <= I86 - 1 /\ 0 = I81]
  f5(I87, I88, I89, I90) -> f3(I91, 0, 1, I90) [-1 <= I90 - 1 /\ I91 <= I87 /\ 0 <= I87 - 1 /\ 0 <= I91 - 1 /\ 1 - I92 * I93 <= I92 - 1 /\ I92 * I93 <= 1 /\ 0 = I88 /\ 0 = I89]
  f3(I94, I95, I96, I97) -> f5(I94, 0, 0, I97) [-1 <= I97 - 1 /\ I98 <= I94 /\ 0 <= I94 - 1 /\ 0 <= I98 - 1 /\ 0 = I95 /\ 0 = I96]
  f5(I99, I100, I101, I102) -> f3(I103, 0, I101 + 1, I102) [-1 <= I102 - 1 /\ I101 <= I102 /\ I101 <= 0 /\ I103 <= I99 /\ 0 <= I99 - 1 /\ 0 <= I103 - 1 /\ 1 - I104 * I105 <= I104 - 1 /\ I104 * I105 <= 1 /\ 0 = I100]
  f3(I106, I107, I108, I109) -> f5(I106, 0, I108, I109) [-1 <= I109 - 1 /\ I108 <= I109 /\ I108 <= 0 /\ I110 <= I106 /\ 0 <= I106 - 1 /\ 0 <= I110 - 1 /\ 0 = I107]
  f3(I111, I112, I113, I114) -> f4(I112 - I113, I115, I116, I117) [I112 <= I114 /\ I113 <= I114 /\ 0 <= I112 - 1 /\ 0 <= I118 - 1 /\ I113 <= I112 /\ 0 <= I119 - 1 /\ 0 <= I120 - 1 /\ 0 <= I113 - 1 /\ 0 <= I111 - 1]
  f3(I121, I122, I123, I124) -> f4(I122 - I123, I125, I126, I127) [I122 <= I124 /\ I123 <= I124 /\ 0 <= I122 - 1 /\ 0 <= I128 - 1 /\ I123 <= I122 /\ 1 <= I122 - I123 /\ 0 <= I129 - 1 /\ I123 <= 0 /\ 0 <= I121 - 1]
  f3(I130, I131, I132, I133) -> f4(0 - I132, I134, I135, I136) [I132 <= I133 /\ 0 <= I132 - 1 /\ -1 <= I133 - 1 /\ I132 <= 0 /\ 0 <= I137 - 1 /\ 0 <= I130 - 1 /\ 0 = I131]
  f3(I138, I139, I140, I141) -> f4(0 - I140, I142, I143, I144) [0 = I139 /\ 0 <= I138 - 1 /\ I140 <= 0 /\ I140 <= I141 /\ -1 <= I141 - 1]
  f3(I145, I146, I147, I148) -> f4(I147 - I146, I149, I150, I151) [0 <= I147 - 1 /\ I146 <= I148 /\ I147 <= I148 /\ 0 <= I152 - 1 /\ I146 <= I147 - 1 /\ 0 <= I153 - 1 /\ 0 <= I154 - 1 /\ 0 <= I146 - 1 /\ 0 <= I145 - 1]
  f3(I155, I156, I157, I158) -> f4(I157, I159, I160, I161) [0 <= I157 - 1 /\ -1 <= I158 - 1 /\ I157 <= I158 /\ 0 <= I162 - 1 /\ 0 <= I163 - 1 /\ 0 <= I155 - 1 /\ 0 = I156]
  f3(I164, I165, I166, I167) -> f4(I166, I168, I169, I170) [I165 <= I167 /\ I166 <= I167 /\ 0 <= I165 - 1 /\ 0 <= I171 - 1 /\ I166 <= I165 /\ 0 <= I164 - 1]
  f3(I172, I173, I174, I175) -> f4(I174, I176, I177, I178) [0 = I173 /\ 0 <= I172 - 1 /\ I174 <= 0 /\ I174 <= I175 /\ -1 <= I175 - 1]
  f3(I179, I180, I181, I182) -> f4(I180, I183, I184, I185) [0 <= I181 - 1 /\ I180 <= I182 /\ I181 <= I182 /\ 0 <= I186 - 1 /\ I180 <= I181 - 1 /\ 0 <= I179 - 1]
  f3(I187, I188, I189, I190) -> f4(I188, I191, I192, I193) [0 <= I187 - 1 /\ I189 <= I188 /\ I189 <= I190 /\ I188 <= I190]
  f3(I194, I195, I196, I197) -> f4(I196, I198, I199, I200) [0 <= I194 - 1 /\ I195 <= I196 - 1 /\ I196 <= I197 /\ I195 <= I197 /\ 0 <= I196 - 1]
  f3(I201, I202, I203, I204) -> f2(I205, I202 + 1, I204, I206) [0 <= I205 - 1 /\ 0 <= I201 - 1 /\ I205 <= I201 /\ -1 <= I204 - 1 /\ I204 <= I203 - 1]
  f2(I207, I208, I209, I210) -> f3(I211, I208, 0, I209) [0 <= I211 - 1 /\ 0 <= I207 - 1 /\ I211 <= I207 /\ -1 <= I209 - 1 /\ I208 <= I209]
  f1(I212, I213, I214, I215) -> f2(I216, 0, I213, I217) [0 <= I216 - 1 /\ 0 <= I212 - 1 /\ -1 <= I213 - 1 /\ I216 <= I212]

We use the reverse value criterion with the projection function NU:
  NU[f3#(z1,z2,z3,z4)] = z4 + -1 * z3
  NU[f5#(z1,z2,z3,z4)] = z4 + -1 * (z3 + 1)

This gives the following inequalities:
  0 <= I72 - 1 /\ -1 <= I73 - 1 /\ I72 <= I73 /\ 0 <= I75 - 1 /\ 0 <= I76 - 1 /\ I74 <= I70 /\ 0 <= I70 - 1 /\ 0 <= I74 - 1 /\ I77 - I78 * I79 <= I78 - 1 /\ 0 <= I77 - I78 * I79 /\ 0 = I71  ==>  I73 + -1 * (I72 + 1) >= I73 + -1 * (I72 + 1)
  0 <= I82 - 1 /\ -1 <= I83 - 1 /\ I82 <= I83 /\ 0 <= I84 - 1 /\ 0 <= I85 - 1 /\ I86 <= I80 /\ 0 <= I80 - 1 /\ 0 <= I86 - 1 /\ 0 = I81  ==>  I83 + -1 * I82 > I83 + -1 * (I82 + 1)  with  I83 + -1 * I82 >= 0

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f5#(I70, I71, I72, I73) -> f3#(I74, 0, I72 + 1, I73) [0 <= I72 - 1 /\ -1 <= I73 - 1 /\ I72 <= I73 /\ 0 <= I75 - 1 /\ 0 <= I76 - 1 /\ I74 <= I70 /\ 0 <= I70 - 1 /\ 0 <= I74 - 1 /\ I77 - I78 * I79 <= I78 - 1 /\ 0 <= I77 - I78 * I79 /\ 0 = I71]
R = 
  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
  f4(I0, I1, I2, I3) -> f4(I0 - 1, I4, I5, I6) [I0 - 1 <= I0 - 1 /\ 0 <= I0 - 1]
  f5(I7, I8, I9, I10) -> f3(I11, I8, I9 + 1, I10) [I8 <= I10 /\ I9 <= I10 /\ 0 <= I8 - 1 /\ 0 <= y1 - 1 /\ I9 <= I8 /\ 0 <= y2 - 1 /\ 0 <= y3 - 1 /\ 0 <= I9 - 1 /\ -1 <= I10 - 1 /\ I11 <= I7 /\ 0 <= I7 - 1 /\ 0 <= I11 - 1 /\ y5 - y4 * y6 <= y4 - 1 /\ 0 <= y5 - y4 * y6]
  f3(I12, I13, I14, I15) -> f5(I12, I13, I14, I15) [I13 <= I15 /\ I14 <= I15 /\ 0 <= I13 - 1 /\ 0 <= I16 - 1 /\ I14 <= I13 /\ 0 <= I17 - 1 /\ 0 <= I18 - 1 /\ 0 <= I14 - 1 /\ -1 <= I15 - 1 /\ I19 <= I12 /\ 0 <= I12 - 1 /\ 0 <= I19 - 1]
  f5(I20, I21, I22, I23) -> f3(I24, I21, I22 + 1, I23) [0 <= I22 - 1 /\ I21 <= I23 /\ I22 <= I23 /\ 0 <= I25 - 1 /\ I21 <= I22 - 1 /\ 0 <= I26 - 1 /\ 0 <= I27 - 1 /\ 0 <= I21 - 1 /\ -1 <= I23 - 1 /\ I24 <= I20 /\ 0 <= I20 - 1 /\ 0 <= I24 - 1 /\ I28 - I29 * I30 <= I29 - 1 /\ 0 <= I28 - I29 * I30]
  f3(I31, I32, I33, I34) -> f5(I31, I32, I33, I34) [0 <= I33 - 1 /\ I32 <= I34 /\ I33 <= I34 /\ 0 <= I35 - 1 /\ I32 <= I33 - 1 /\ 0 <= I36 - 1 /\ 0 <= I37 - 1 /\ 0 <= I32 - 1 /\ -1 <= I34 - 1 /\ I38 <= I31 /\ 0 <= I31 - 1 /\ 0 <= I38 - 1]
  f5(I39, I40, I41, I42) -> f3(I43, I40, I41 + 1, I42) [I40 <= I42 /\ I41 <= I42 /\ 0 <= I40 - 1 /\ 0 <= I44 - 1 /\ I41 <= I40 /\ 1 <= I40 - I41 /\ 0 <= I45 - 1 /\ I41 <= 0 /\ -1 <= I42 - 1 /\ I43 <= I39 /\ 0 <= I39 - 1 /\ 0 <= I43 - 1 /\ I46 - I47 * I48 <= I47 - 1 /\ 0 <= I46 - I47 * I48]
  f3(I49, I50, I51, I52) -> f5(I49, I50, I51, I52) [I50 <= I52 /\ I51 <= I52 /\ 0 <= I50 - 1 /\ 0 <= I53 - 1 /\ I51 <= I50 /\ 1 <= I50 - I51 /\ 0 <= I54 - 1 /\ I51 <= 0 /\ -1 <= I52 - 1 /\ I55 <= I49 /\ 0 <= I49 - 1 /\ 0 <= I55 - 1]
  f5(I56, I57, I58, I59) -> f3(I60, 0, I58 + 1, I59) [I58 <= I59 /\ 0 <= I58 - 1 /\ -1 <= I59 - 1 /\ I58 <= 0 /\ 0 <= I61 - 1 /\ I60 <= I56 /\ 0 <= I56 - 1 /\ 0 <= I60 - 1 /\ 1 - I62 * I63 <= I62 - 1 /\ I62 * I63 <= 1 /\ 0 = I57]
  f3(I64, I65, I66, I67) -> f5(I64, 0, I66, I67) [I66 <= I67 /\ 0 <= I66 - 1 /\ -1 <= I67 - 1 /\ I66 <= 0 /\ 0 <= I68 - 1 /\ I69 <= I64 /\ 0 <= I64 - 1 /\ 0 <= I69 - 1 /\ 0 = I65]
  f5(I70, I71, I72, I73) -> f3(I74, 0, I72 + 1, I73) [0 <= I72 - 1 /\ -1 <= I73 - 1 /\ I72 <= I73 /\ 0 <= I75 - 1 /\ 0 <= I76 - 1 /\ I74 <= I70 /\ 0 <= I70 - 1 /\ 0 <= I74 - 1 /\ I77 - I78 * I79 <= I78 - 1 /\ 0 <= I77 - I78 * I79 /\ 0 = I71]
  f3(I80, I81, I82, I83) -> f5(I80, 0, I82, I83) [0 <= I82 - 1 /\ -1 <= I83 - 1 /\ I82 <= I83 /\ 0 <= I84 - 1 /\ 0 <= I85 - 1 /\ I86 <= I80 /\ 0 <= I80 - 1 /\ 0 <= I86 - 1 /\ 0 = I81]
  f5(I87, I88, I89, I90) -> f3(I91, 0, 1, I90) [-1 <= I90 - 1 /\ I91 <= I87 /\ 0 <= I87 - 1 /\ 0 <= I91 - 1 /\ 1 - I92 * I93 <= I92 - 1 /\ I92 * I93 <= 1 /\ 0 = I88 /\ 0 = I89]
  f3(I94, I95, I96, I97) -> f5(I94, 0, 0, I97) [-1 <= I97 - 1 /\ I98 <= I94 /\ 0 <= I94 - 1 /\ 0 <= I98 - 1 /\ 0 = I95 /\ 0 = I96]
  f5(I99, I100, I101, I102) -> f3(I103, 0, I101 + 1, I102) [-1 <= I102 - 1 /\ I101 <= I102 /\ I101 <= 0 /\ I103 <= I99 /\ 0 <= I99 - 1 /\ 0 <= I103 - 1 /\ 1 - I104 * I105 <= I104 - 1 /\ I104 * I105 <= 1 /\ 0 = I100]
  f3(I106, I107, I108, I109) -> f5(I106, 0, I108, I109) [-1 <= I109 - 1 /\ I108 <= I109 /\ I108 <= 0 /\ I110 <= I106 /\ 0 <= I106 - 1 /\ 0 <= I110 - 1 /\ 0 = I107]
  f3(I111, I112, I113, I114) -> f4(I112 - I113, I115, I116, I117) [I112 <= I114 /\ I113 <= I114 /\ 0 <= I112 - 1 /\ 0 <= I118 - 1 /\ I113 <= I112 /\ 0 <= I119 - 1 /\ 0 <= I120 - 1 /\ 0 <= I113 - 1 /\ 0 <= I111 - 1]
  f3(I121, I122, I123, I124) -> f4(I122 - I123, I125, I126, I127) [I122 <= I124 /\ I123 <= I124 /\ 0 <= I122 - 1 /\ 0 <= I128 - 1 /\ I123 <= I122 /\ 1 <= I122 - I123 /\ 0 <= I129 - 1 /\ I123 <= 0 /\ 0 <= I121 - 1]
  f3(I130, I131, I132, I133) -> f4(0 - I132, I134, I135, I136) [I132 <= I133 /\ 0 <= I132 - 1 /\ -1 <= I133 - 1 /\ I132 <= 0 /\ 0 <= I137 - 1 /\ 0 <= I130 - 1 /\ 0 = I131]
  f3(I138, I139, I140, I141) -> f4(0 - I140, I142, I143, I144) [0 = I139 /\ 0 <= I138 - 1 /\ I140 <= 0 /\ I140 <= I141 /\ -1 <= I141 - 1]
  f3(I145, I146, I147, I148) -> f4(I147 - I146, I149, I150, I151) [0 <= I147 - 1 /\ I146 <= I148 /\ I147 <= I148 /\ 0 <= I152 - 1 /\ I146 <= I147 - 1 /\ 0 <= I153 - 1 /\ 0 <= I154 - 1 /\ 0 <= I146 - 1 /\ 0 <= I145 - 1]
  f3(I155, I156, I157, I158) -> f4(I157, I159, I160, I161) [0 <= I157 - 1 /\ -1 <= I158 - 1 /\ I157 <= I158 /\ 0 <= I162 - 1 /\ 0 <= I163 - 1 /\ 0 <= I155 - 1 /\ 0 = I156]
  f3(I164, I165, I166, I167) -> f4(I166, I168, I169, I170) [I165 <= I167 /\ I166 <= I167 /\ 0 <= I165 - 1 /\ 0 <= I171 - 1 /\ I166 <= I165 /\ 0 <= I164 - 1]
  f3(I172, I173, I174, I175) -> f4(I174, I176, I177, I178) [0 = I173 /\ 0 <= I172 - 1 /\ I174 <= 0 /\ I174 <= I175 /\ -1 <= I175 - 1]
  f3(I179, I180, I181, I182) -> f4(I180, I183, I184, I185) [0 <= I181 - 1 /\ I180 <= I182 /\ I181 <= I182 /\ 0 <= I186 - 1 /\ I180 <= I181 - 1 /\ 0 <= I179 - 1]
  f3(I187, I188, I189, I190) -> f4(I188, I191, I192, I193) [0 <= I187 - 1 /\ I189 <= I188 /\ I189 <= I190 /\ I188 <= I190]
  f3(I194, I195, I196, I197) -> f4(I196, I198, I199, I200) [0 <= I194 - 1 /\ I195 <= I196 - 1 /\ I196 <= I197 /\ I195 <= I197 /\ 0 <= I196 - 1]
  f3(I201, I202, I203, I204) -> f2(I205, I202 + 1, I204, I206) [0 <= I205 - 1 /\ 0 <= I201 - 1 /\ I205 <= I201 /\ -1 <= I204 - 1 /\ I204 <= I203 - 1]
  f2(I207, I208, I209, I210) -> f3(I211, I208, 0, I209) [0 <= I211 - 1 /\ 0 <= I207 - 1 /\ I211 <= I207 /\ -1 <= I209 - 1 /\ I208 <= I209]
  f1(I212, I213, I214, I215) -> f2(I216, 0, I213, I217) [0 <= I216 - 1 /\ 0 <= I212 - 1 /\ -1 <= I213 - 1 /\ I216 <= I212]

The dependency graph for this problem is:
  10 -> 
Where:
  10) f5#(I70, I71, I72, I73) -> f3#(I74, 0, I72 + 1, I73) [0 <= I72 - 1 /\ -1 <= I73 - 1 /\ I72 <= I73 /\ 0 <= I75 - 1 /\ 0 <= I76 - 1 /\ I74 <= I70 /\ 0 <= I70 - 1 /\ 0 <= I74 - 1 /\ I77 - I78 * I79 <= I78 - 1 /\ 0 <= I77 - I78 * I79 /\ 0 = I71]

We have the following SCCs.
  

DP problem for innermost termination.
P =
  f3#(I94, I95, I96, I97) -> f5#(I94, 0, 0, I97) [-1 <= I97 - 1 /\ I98 <= I94 /\ 0 <= I94 - 1 /\ 0 <= I98 - 1 /\ 0 = I95 /\ 0 = I96]
  f5#(I99, I100, I101, I102) -> f3#(I103, 0, I101 + 1, I102) [-1 <= I102 - 1 /\ I101 <= I102 /\ I101 <= 0 /\ I103 <= I99 /\ 0 <= I99 - 1 /\ 0 <= I103 - 1 /\ 1 - I104 * I105 <= I104 - 1 /\ I104 * I105 <= 1 /\ 0 = I100]
  f3#(I106, I107, I108, I109) -> f5#(I106, 0, I108, I109) [-1 <= I109 - 1 /\ I108 <= I109 /\ I108 <= 0 /\ I110 <= I106 /\ 0 <= I106 - 1 /\ 0 <= I110 - 1 /\ 0 = I107]
R = 
  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
  f4(I0, I1, I2, I3) -> f4(I0 - 1, I4, I5, I6) [I0 - 1 <= I0 - 1 /\ 0 <= I0 - 1]
  f5(I7, I8, I9, I10) -> f3(I11, I8, I9 + 1, I10) [I8 <= I10 /\ I9 <= I10 /\ 0 <= I8 - 1 /\ 0 <= y1 - 1 /\ I9 <= I8 /\ 0 <= y2 - 1 /\ 0 <= y3 - 1 /\ 0 <= I9 - 1 /\ -1 <= I10 - 1 /\ I11 <= I7 /\ 0 <= I7 - 1 /\ 0 <= I11 - 1 /\ y5 - y4 * y6 <= y4 - 1 /\ 0 <= y5 - y4 * y6]
  f3(I12, I13, I14, I15) -> f5(I12, I13, I14, I15) [I13 <= I15 /\ I14 <= I15 /\ 0 <= I13 - 1 /\ 0 <= I16 - 1 /\ I14 <= I13 /\ 0 <= I17 - 1 /\ 0 <= I18 - 1 /\ 0 <= I14 - 1 /\ -1 <= I15 - 1 /\ I19 <= I12 /\ 0 <= I12 - 1 /\ 0 <= I19 - 1]
  f5(I20, I21, I22, I23) -> f3(I24, I21, I22 + 1, I23) [0 <= I22 - 1 /\ I21 <= I23 /\ I22 <= I23 /\ 0 <= I25 - 1 /\ I21 <= I22 - 1 /\ 0 <= I26 - 1 /\ 0 <= I27 - 1 /\ 0 <= I21 - 1 /\ -1 <= I23 - 1 /\ I24 <= I20 /\ 0 <= I20 - 1 /\ 0 <= I24 - 1 /\ I28 - I29 * I30 <= I29 - 1 /\ 0 <= I28 - I29 * I30]
  f3(I31, I32, I33, I34) -> f5(I31, I32, I33, I34) [0 <= I33 - 1 /\ I32 <= I34 /\ I33 <= I34 /\ 0 <= I35 - 1 /\ I32 <= I33 - 1 /\ 0 <= I36 - 1 /\ 0 <= I37 - 1 /\ 0 <= I32 - 1 /\ -1 <= I34 - 1 /\ I38 <= I31 /\ 0 <= I31 - 1 /\ 0 <= I38 - 1]
  f5(I39, I40, I41, I42) -> f3(I43, I40, I41 + 1, I42) [I40 <= I42 /\ I41 <= I42 /\ 0 <= I40 - 1 /\ 0 <= I44 - 1 /\ I41 <= I40 /\ 1 <= I40 - I41 /\ 0 <= I45 - 1 /\ I41 <= 0 /\ -1 <= I42 - 1 /\ I43 <= I39 /\ 0 <= I39 - 1 /\ 0 <= I43 - 1 /\ I46 - I47 * I48 <= I47 - 1 /\ 0 <= I46 - I47 * I48]
  f3(I49, I50, I51, I52) -> f5(I49, I50, I51, I52) [I50 <= I52 /\ I51 <= I52 /\ 0 <= I50 - 1 /\ 0 <= I53 - 1 /\ I51 <= I50 /\ 1 <= I50 - I51 /\ 0 <= I54 - 1 /\ I51 <= 0 /\ -1 <= I52 - 1 /\ I55 <= I49 /\ 0 <= I49 - 1 /\ 0 <= I55 - 1]
  f5(I56, I57, I58, I59) -> f3(I60, 0, I58 + 1, I59) [I58 <= I59 /\ 0 <= I58 - 1 /\ -1 <= I59 - 1 /\ I58 <= 0 /\ 0 <= I61 - 1 /\ I60 <= I56 /\ 0 <= I56 - 1 /\ 0 <= I60 - 1 /\ 1 - I62 * I63 <= I62 - 1 /\ I62 * I63 <= 1 /\ 0 = I57]
  f3(I64, I65, I66, I67) -> f5(I64, 0, I66, I67) [I66 <= I67 /\ 0 <= I66 - 1 /\ -1 <= I67 - 1 /\ I66 <= 0 /\ 0 <= I68 - 1 /\ I69 <= I64 /\ 0 <= I64 - 1 /\ 0 <= I69 - 1 /\ 0 = I65]
  f5(I70, I71, I72, I73) -> f3(I74, 0, I72 + 1, I73) [0 <= I72 - 1 /\ -1 <= I73 - 1 /\ I72 <= I73 /\ 0 <= I75 - 1 /\ 0 <= I76 - 1 /\ I74 <= I70 /\ 0 <= I70 - 1 /\ 0 <= I74 - 1 /\ I77 - I78 * I79 <= I78 - 1 /\ 0 <= I77 - I78 * I79 /\ 0 = I71]
  f3(I80, I81, I82, I83) -> f5(I80, 0, I82, I83) [0 <= I82 - 1 /\ -1 <= I83 - 1 /\ I82 <= I83 /\ 0 <= I84 - 1 /\ 0 <= I85 - 1 /\ I86 <= I80 /\ 0 <= I80 - 1 /\ 0 <= I86 - 1 /\ 0 = I81]
  f5(I87, I88, I89, I90) -> f3(I91, 0, 1, I90) [-1 <= I90 - 1 /\ I91 <= I87 /\ 0 <= I87 - 1 /\ 0 <= I91 - 1 /\ 1 - I92 * I93 <= I92 - 1 /\ I92 * I93 <= 1 /\ 0 = I88 /\ 0 = I89]
  f3(I94, I95, I96, I97) -> f5(I94, 0, 0, I97) [-1 <= I97 - 1 /\ I98 <= I94 /\ 0 <= I94 - 1 /\ 0 <= I98 - 1 /\ 0 = I95 /\ 0 = I96]
  f5(I99, I100, I101, I102) -> f3(I103, 0, I101 + 1, I102) [-1 <= I102 - 1 /\ I101 <= I102 /\ I101 <= 0 /\ I103 <= I99 /\ 0 <= I99 - 1 /\ 0 <= I103 - 1 /\ 1 - I104 * I105 <= I104 - 1 /\ I104 * I105 <= 1 /\ 0 = I100]
  f3(I106, I107, I108, I109) -> f5(I106, 0, I108, I109) [-1 <= I109 - 1 /\ I108 <= I109 /\ I108 <= 0 /\ I110 <= I106 /\ 0 <= I106 - 1 /\ 0 <= I110 - 1 /\ 0 = I107]
  f3(I111, I112, I113, I114) -> f4(I112 - I113, I115, I116, I117) [I112 <= I114 /\ I113 <= I114 /\ 0 <= I112 - 1 /\ 0 <= I118 - 1 /\ I113 <= I112 /\ 0 <= I119 - 1 /\ 0 <= I120 - 1 /\ 0 <= I113 - 1 /\ 0 <= I111 - 1]
  f3(I121, I122, I123, I124) -> f4(I122 - I123, I125, I126, I127) [I122 <= I124 /\ I123 <= I124 /\ 0 <= I122 - 1 /\ 0 <= I128 - 1 /\ I123 <= I122 /\ 1 <= I122 - I123 /\ 0 <= I129 - 1 /\ I123 <= 0 /\ 0 <= I121 - 1]
  f3(I130, I131, I132, I133) -> f4(0 - I132, I134, I135, I136) [I132 <= I133 /\ 0 <= I132 - 1 /\ -1 <= I133 - 1 /\ I132 <= 0 /\ 0 <= I137 - 1 /\ 0 <= I130 - 1 /\ 0 = I131]
  f3(I138, I139, I140, I141) -> f4(0 - I140, I142, I143, I144) [0 = I139 /\ 0 <= I138 - 1 /\ I140 <= 0 /\ I140 <= I141 /\ -1 <= I141 - 1]
  f3(I145, I146, I147, I148) -> f4(I147 - I146, I149, I150, I151) [0 <= I147 - 1 /\ I146 <= I148 /\ I147 <= I148 /\ 0 <= I152 - 1 /\ I146 <= I147 - 1 /\ 0 <= I153 - 1 /\ 0 <= I154 - 1 /\ 0 <= I146 - 1 /\ 0 <= I145 - 1]
  f3(I155, I156, I157, I158) -> f4(I157, I159, I160, I161) [0 <= I157 - 1 /\ -1 <= I158 - 1 /\ I157 <= I158 /\ 0 <= I162 - 1 /\ 0 <= I163 - 1 /\ 0 <= I155 - 1 /\ 0 = I156]
  f3(I164, I165, I166, I167) -> f4(I166, I168, I169, I170) [I165 <= I167 /\ I166 <= I167 /\ 0 <= I165 - 1 /\ 0 <= I171 - 1 /\ I166 <= I165 /\ 0 <= I164 - 1]
  f3(I172, I173, I174, I175) -> f4(I174, I176, I177, I178) [0 = I173 /\ 0 <= I172 - 1 /\ I174 <= 0 /\ I174 <= I175 /\ -1 <= I175 - 1]
  f3(I179, I180, I181, I182) -> f4(I180, I183, I184, I185) [0 <= I181 - 1 /\ I180 <= I182 /\ I181 <= I182 /\ 0 <= I186 - 1 /\ I180 <= I181 - 1 /\ 0 <= I179 - 1]
  f3(I187, I188, I189, I190) -> f4(I188, I191, I192, I193) [0 <= I187 - 1 /\ I189 <= I188 /\ I189 <= I190 /\ I188 <= I190]
  f3(I194, I195, I196, I197) -> f4(I196, I198, I199, I200) [0 <= I194 - 1 /\ I195 <= I196 - 1 /\ I196 <= I197 /\ I195 <= I197 /\ 0 <= I196 - 1]
  f3(I201, I202, I203, I204) -> f2(I205, I202 + 1, I204, I206) [0 <= I205 - 1 /\ 0 <= I201 - 1 /\ I205 <= I201 /\ -1 <= I204 - 1 /\ I204 <= I203 - 1]
  f2(I207, I208, I209, I210) -> f3(I211, I208, 0, I209) [0 <= I211 - 1 /\ 0 <= I207 - 1 /\ I211 <= I207 /\ -1 <= I209 - 1 /\ I208 <= I209]
  f1(I212, I213, I214, I215) -> f2(I216, 0, I213, I217) [0 <= I216 - 1 /\ 0 <= I212 - 1 /\ -1 <= I213 - 1 /\ I216 <= I212]

We use the reverse value criterion with the projection function NU:
  NU[f5#(z1,z2,z3,z4)] = 0 + -1 * (z3 + 1)
  NU[f3#(z1,z2,z3,z4)] = 0 + -1 * z3

This gives the following inequalities:
  -1 <= I97 - 1 /\ I98 <= I94 /\ 0 <= I94 - 1 /\ 0 <= I98 - 1 /\ 0 = I95 /\ 0 = I96  ==>  0 + -1 * I96 > 0 + -1 * (0 + 1)  with  0 + -1 * I96 >= 0
  -1 <= I102 - 1 /\ I101 <= I102 /\ I101 <= 0 /\ I103 <= I99 /\ 0 <= I99 - 1 /\ 0 <= I103 - 1 /\ 1 - I104 * I105 <= I104 - 1 /\ I104 * I105 <= 1 /\ 0 = I100  ==>  0 + -1 * (I101 + 1) >= 0 + -1 * (I101 + 1)
  -1 <= I109 - 1 /\ I108 <= I109 /\ I108 <= 0 /\ I110 <= I106 /\ 0 <= I106 - 1 /\ 0 <= I110 - 1 /\ 0 = I107  ==>  0 + -1 * I108 > 0 + -1 * (I108 + 1)  with  0 + -1 * I108 >= 0

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f5#(I99, I100, I101, I102) -> f3#(I103, 0, I101 + 1, I102) [-1 <= I102 - 1 /\ I101 <= I102 /\ I101 <= 0 /\ I103 <= I99 /\ 0 <= I99 - 1 /\ 0 <= I103 - 1 /\ 1 - I104 * I105 <= I104 - 1 /\ I104 * I105 <= 1 /\ 0 = I100]
R = 
  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
  f4(I0, I1, I2, I3) -> f4(I0 - 1, I4, I5, I6) [I0 - 1 <= I0 - 1 /\ 0 <= I0 - 1]
  f5(I7, I8, I9, I10) -> f3(I11, I8, I9 + 1, I10) [I8 <= I10 /\ I9 <= I10 /\ 0 <= I8 - 1 /\ 0 <= y1 - 1 /\ I9 <= I8 /\ 0 <= y2 - 1 /\ 0 <= y3 - 1 /\ 0 <= I9 - 1 /\ -1 <= I10 - 1 /\ I11 <= I7 /\ 0 <= I7 - 1 /\ 0 <= I11 - 1 /\ y5 - y4 * y6 <= y4 - 1 /\ 0 <= y5 - y4 * y6]
  f3(I12, I13, I14, I15) -> f5(I12, I13, I14, I15) [I13 <= I15 /\ I14 <= I15 /\ 0 <= I13 - 1 /\ 0 <= I16 - 1 /\ I14 <= I13 /\ 0 <= I17 - 1 /\ 0 <= I18 - 1 /\ 0 <= I14 - 1 /\ -1 <= I15 - 1 /\ I19 <= I12 /\ 0 <= I12 - 1 /\ 0 <= I19 - 1]
  f5(I20, I21, I22, I23) -> f3(I24, I21, I22 + 1, I23) [0 <= I22 - 1 /\ I21 <= I23 /\ I22 <= I23 /\ 0 <= I25 - 1 /\ I21 <= I22 - 1 /\ 0 <= I26 - 1 /\ 0 <= I27 - 1 /\ 0 <= I21 - 1 /\ -1 <= I23 - 1 /\ I24 <= I20 /\ 0 <= I20 - 1 /\ 0 <= I24 - 1 /\ I28 - I29 * I30 <= I29 - 1 /\ 0 <= I28 - I29 * I30]
  f3(I31, I32, I33, I34) -> f5(I31, I32, I33, I34) [0 <= I33 - 1 /\ I32 <= I34 /\ I33 <= I34 /\ 0 <= I35 - 1 /\ I32 <= I33 - 1 /\ 0 <= I36 - 1 /\ 0 <= I37 - 1 /\ 0 <= I32 - 1 /\ -1 <= I34 - 1 /\ I38 <= I31 /\ 0 <= I31 - 1 /\ 0 <= I38 - 1]
  f5(I39, I40, I41, I42) -> f3(I43, I40, I41 + 1, I42) [I40 <= I42 /\ I41 <= I42 /\ 0 <= I40 - 1 /\ 0 <= I44 - 1 /\ I41 <= I40 /\ 1 <= I40 - I41 /\ 0 <= I45 - 1 /\ I41 <= 0 /\ -1 <= I42 - 1 /\ I43 <= I39 /\ 0 <= I39 - 1 /\ 0 <= I43 - 1 /\ I46 - I47 * I48 <= I47 - 1 /\ 0 <= I46 - I47 * I48]
  f3(I49, I50, I51, I52) -> f5(I49, I50, I51, I52) [I50 <= I52 /\ I51 <= I52 /\ 0 <= I50 - 1 /\ 0 <= I53 - 1 /\ I51 <= I50 /\ 1 <= I50 - I51 /\ 0 <= I54 - 1 /\ I51 <= 0 /\ -1 <= I52 - 1 /\ I55 <= I49 /\ 0 <= I49 - 1 /\ 0 <= I55 - 1]
  f5(I56, I57, I58, I59) -> f3(I60, 0, I58 + 1, I59) [I58 <= I59 /\ 0 <= I58 - 1 /\ -1 <= I59 - 1 /\ I58 <= 0 /\ 0 <= I61 - 1 /\ I60 <= I56 /\ 0 <= I56 - 1 /\ 0 <= I60 - 1 /\ 1 - I62 * I63 <= I62 - 1 /\ I62 * I63 <= 1 /\ 0 = I57]
  f3(I64, I65, I66, I67) -> f5(I64, 0, I66, I67) [I66 <= I67 /\ 0 <= I66 - 1 /\ -1 <= I67 - 1 /\ I66 <= 0 /\ 0 <= I68 - 1 /\ I69 <= I64 /\ 0 <= I64 - 1 /\ 0 <= I69 - 1 /\ 0 = I65]
  f5(I70, I71, I72, I73) -> f3(I74, 0, I72 + 1, I73) [0 <= I72 - 1 /\ -1 <= I73 - 1 /\ I72 <= I73 /\ 0 <= I75 - 1 /\ 0 <= I76 - 1 /\ I74 <= I70 /\ 0 <= I70 - 1 /\ 0 <= I74 - 1 /\ I77 - I78 * I79 <= I78 - 1 /\ 0 <= I77 - I78 * I79 /\ 0 = I71]
  f3(I80, I81, I82, I83) -> f5(I80, 0, I82, I83) [0 <= I82 - 1 /\ -1 <= I83 - 1 /\ I82 <= I83 /\ 0 <= I84 - 1 /\ 0 <= I85 - 1 /\ I86 <= I80 /\ 0 <= I80 - 1 /\ 0 <= I86 - 1 /\ 0 = I81]
  f5(I87, I88, I89, I90) -> f3(I91, 0, 1, I90) [-1 <= I90 - 1 /\ I91 <= I87 /\ 0 <= I87 - 1 /\ 0 <= I91 - 1 /\ 1 - I92 * I93 <= I92 - 1 /\ I92 * I93 <= 1 /\ 0 = I88 /\ 0 = I89]
  f3(I94, I95, I96, I97) -> f5(I94, 0, 0, I97) [-1 <= I97 - 1 /\ I98 <= I94 /\ 0 <= I94 - 1 /\ 0 <= I98 - 1 /\ 0 = I95 /\ 0 = I96]
  f5(I99, I100, I101, I102) -> f3(I103, 0, I101 + 1, I102) [-1 <= I102 - 1 /\ I101 <= I102 /\ I101 <= 0 /\ I103 <= I99 /\ 0 <= I99 - 1 /\ 0 <= I103 - 1 /\ 1 - I104 * I105 <= I104 - 1 /\ I104 * I105 <= 1 /\ 0 = I100]
  f3(I106, I107, I108, I109) -> f5(I106, 0, I108, I109) [-1 <= I109 - 1 /\ I108 <= I109 /\ I108 <= 0 /\ I110 <= I106 /\ 0 <= I106 - 1 /\ 0 <= I110 - 1 /\ 0 = I107]
  f3(I111, I112, I113, I114) -> f4(I112 - I113, I115, I116, I117) [I112 <= I114 /\ I113 <= I114 /\ 0 <= I112 - 1 /\ 0 <= I118 - 1 /\ I113 <= I112 /\ 0 <= I119 - 1 /\ 0 <= I120 - 1 /\ 0 <= I113 - 1 /\ 0 <= I111 - 1]
  f3(I121, I122, I123, I124) -> f4(I122 - I123, I125, I126, I127) [I122 <= I124 /\ I123 <= I124 /\ 0 <= I122 - 1 /\ 0 <= I128 - 1 /\ I123 <= I122 /\ 1 <= I122 - I123 /\ 0 <= I129 - 1 /\ I123 <= 0 /\ 0 <= I121 - 1]
  f3(I130, I131, I132, I133) -> f4(0 - I132, I134, I135, I136) [I132 <= I133 /\ 0 <= I132 - 1 /\ -1 <= I133 - 1 /\ I132 <= 0 /\ 0 <= I137 - 1 /\ 0 <= I130 - 1 /\ 0 = I131]
  f3(I138, I139, I140, I141) -> f4(0 - I140, I142, I143, I144) [0 = I139 /\ 0 <= I138 - 1 /\ I140 <= 0 /\ I140 <= I141 /\ -1 <= I141 - 1]
  f3(I145, I146, I147, I148) -> f4(I147 - I146, I149, I150, I151) [0 <= I147 - 1 /\ I146 <= I148 /\ I147 <= I148 /\ 0 <= I152 - 1 /\ I146 <= I147 - 1 /\ 0 <= I153 - 1 /\ 0 <= I154 - 1 /\ 0 <= I146 - 1 /\ 0 <= I145 - 1]
  f3(I155, I156, I157, I158) -> f4(I157, I159, I160, I161) [0 <= I157 - 1 /\ -1 <= I158 - 1 /\ I157 <= I158 /\ 0 <= I162 - 1 /\ 0 <= I163 - 1 /\ 0 <= I155 - 1 /\ 0 = I156]
  f3(I164, I165, I166, I167) -> f4(I166, I168, I169, I170) [I165 <= I167 /\ I166 <= I167 /\ 0 <= I165 - 1 /\ 0 <= I171 - 1 /\ I166 <= I165 /\ 0 <= I164 - 1]
  f3(I172, I173, I174, I175) -> f4(I174, I176, I177, I178) [0 = I173 /\ 0 <= I172 - 1 /\ I174 <= 0 /\ I174 <= I175 /\ -1 <= I175 - 1]
  f3(I179, I180, I181, I182) -> f4(I180, I183, I184, I185) [0 <= I181 - 1 /\ I180 <= I182 /\ I181 <= I182 /\ 0 <= I186 - 1 /\ I180 <= I181 - 1 /\ 0 <= I179 - 1]
  f3(I187, I188, I189, I190) -> f4(I188, I191, I192, I193) [0 <= I187 - 1 /\ I189 <= I188 /\ I189 <= I190 /\ I188 <= I190]
  f3(I194, I195, I196, I197) -> f4(I196, I198, I199, I200) [0 <= I194 - 1 /\ I195 <= I196 - 1 /\ I196 <= I197 /\ I195 <= I197 /\ 0 <= I196 - 1]
  f3(I201, I202, I203, I204) -> f2(I205, I202 + 1, I204, I206) [0 <= I205 - 1 /\ 0 <= I201 - 1 /\ I205 <= I201 /\ -1 <= I204 - 1 /\ I204 <= I203 - 1]
  f2(I207, I208, I209, I210) -> f3(I211, I208, 0, I209) [0 <= I211 - 1 /\ 0 <= I207 - 1 /\ I211 <= I207 /\ -1 <= I209 - 1 /\ I208 <= I209]
  f1(I212, I213, I214, I215) -> f2(I216, 0, I213, I217) [0 <= I216 - 1 /\ 0 <= I212 - 1 /\ -1 <= I213 - 1 /\ I216 <= I212]

The dependency graph for this problem is:
  14 -> 
Where:
  14) f5#(I99, I100, I101, I102) -> f3#(I103, 0, I101 + 1, I102) [-1 <= I102 - 1 /\ I101 <= I102 /\ I101 <= 0 /\ I103 <= I99 /\ 0 <= I99 - 1 /\ 0 <= I103 - 1 /\ 1 - I104 * I105 <= I104 - 1 /\ I104 * I105 <= 1 /\ 0 = I100]

We have the following SCCs.
  

DP problem for innermost termination.
P =
  f5#(I20, I21, I22, I23) -> f3#(I24, I21, I22 + 1, I23) [0 <= I22 - 1 /\ I21 <= I23 /\ I22 <= I23 /\ 0 <= I25 - 1 /\ I21 <= I22 - 1 /\ 0 <= I26 - 1 /\ 0 <= I27 - 1 /\ 0 <= I21 - 1 /\ -1 <= I23 - 1 /\ I24 <= I20 /\ 0 <= I20 - 1 /\ 0 <= I24 - 1 /\ I28 - I29 * I30 <= I29 - 1 /\ 0 <= I28 - I29 * I30]
  f3#(I31, I32, I33, I34) -> f5#(I31, I32, I33, I34) [0 <= I33 - 1 /\ I32 <= I34 /\ I33 <= I34 /\ 0 <= I35 - 1 /\ I32 <= I33 - 1 /\ 0 <= I36 - 1 /\ 0 <= I37 - 1 /\ 0 <= I32 - 1 /\ -1 <= I34 - 1 /\ I38 <= I31 /\ 0 <= I31 - 1 /\ 0 <= I38 - 1]
R = 
  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
  f4(I0, I1, I2, I3) -> f4(I0 - 1, I4, I5, I6) [I0 - 1 <= I0 - 1 /\ 0 <= I0 - 1]
  f5(I7, I8, I9, I10) -> f3(I11, I8, I9 + 1, I10) [I8 <= I10 /\ I9 <= I10 /\ 0 <= I8 - 1 /\ 0 <= y1 - 1 /\ I9 <= I8 /\ 0 <= y2 - 1 /\ 0 <= y3 - 1 /\ 0 <= I9 - 1 /\ -1 <= I10 - 1 /\ I11 <= I7 /\ 0 <= I7 - 1 /\ 0 <= I11 - 1 /\ y5 - y4 * y6 <= y4 - 1 /\ 0 <= y5 - y4 * y6]
  f3(I12, I13, I14, I15) -> f5(I12, I13, I14, I15) [I13 <= I15 /\ I14 <= I15 /\ 0 <= I13 - 1 /\ 0 <= I16 - 1 /\ I14 <= I13 /\ 0 <= I17 - 1 /\ 0 <= I18 - 1 /\ 0 <= I14 - 1 /\ -1 <= I15 - 1 /\ I19 <= I12 /\ 0 <= I12 - 1 /\ 0 <= I19 - 1]
  f5(I20, I21, I22, I23) -> f3(I24, I21, I22 + 1, I23) [0 <= I22 - 1 /\ I21 <= I23 /\ I22 <= I23 /\ 0 <= I25 - 1 /\ I21 <= I22 - 1 /\ 0 <= I26 - 1 /\ 0 <= I27 - 1 /\ 0 <= I21 - 1 /\ -1 <= I23 - 1 /\ I24 <= I20 /\ 0 <= I20 - 1 /\ 0 <= I24 - 1 /\ I28 - I29 * I30 <= I29 - 1 /\ 0 <= I28 - I29 * I30]
  f3(I31, I32, I33, I34) -> f5(I31, I32, I33, I34) [0 <= I33 - 1 /\ I32 <= I34 /\ I33 <= I34 /\ 0 <= I35 - 1 /\ I32 <= I33 - 1 /\ 0 <= I36 - 1 /\ 0 <= I37 - 1 /\ 0 <= I32 - 1 /\ -1 <= I34 - 1 /\ I38 <= I31 /\ 0 <= I31 - 1 /\ 0 <= I38 - 1]
  f5(I39, I40, I41, I42) -> f3(I43, I40, I41 + 1, I42) [I40 <= I42 /\ I41 <= I42 /\ 0 <= I40 - 1 /\ 0 <= I44 - 1 /\ I41 <= I40 /\ 1 <= I40 - I41 /\ 0 <= I45 - 1 /\ I41 <= 0 /\ -1 <= I42 - 1 /\ I43 <= I39 /\ 0 <= I39 - 1 /\ 0 <= I43 - 1 /\ I46 - I47 * I48 <= I47 - 1 /\ 0 <= I46 - I47 * I48]
  f3(I49, I50, I51, I52) -> f5(I49, I50, I51, I52) [I50 <= I52 /\ I51 <= I52 /\ 0 <= I50 - 1 /\ 0 <= I53 - 1 /\ I51 <= I50 /\ 1 <= I50 - I51 /\ 0 <= I54 - 1 /\ I51 <= 0 /\ -1 <= I52 - 1 /\ I55 <= I49 /\ 0 <= I49 - 1 /\ 0 <= I55 - 1]
  f5(I56, I57, I58, I59) -> f3(I60, 0, I58 + 1, I59) [I58 <= I59 /\ 0 <= I58 - 1 /\ -1 <= I59 - 1 /\ I58 <= 0 /\ 0 <= I61 - 1 /\ I60 <= I56 /\ 0 <= I56 - 1 /\ 0 <= I60 - 1 /\ 1 - I62 * I63 <= I62 - 1 /\ I62 * I63 <= 1 /\ 0 = I57]
  f3(I64, I65, I66, I67) -> f5(I64, 0, I66, I67) [I66 <= I67 /\ 0 <= I66 - 1 /\ -1 <= I67 - 1 /\ I66 <= 0 /\ 0 <= I68 - 1 /\ I69 <= I64 /\ 0 <= I64 - 1 /\ 0 <= I69 - 1 /\ 0 = I65]
  f5(I70, I71, I72, I73) -> f3(I74, 0, I72 + 1, I73) [0 <= I72 - 1 /\ -1 <= I73 - 1 /\ I72 <= I73 /\ 0 <= I75 - 1 /\ 0 <= I76 - 1 /\ I74 <= I70 /\ 0 <= I70 - 1 /\ 0 <= I74 - 1 /\ I77 - I78 * I79 <= I78 - 1 /\ 0 <= I77 - I78 * I79 /\ 0 = I71]
  f3(I80, I81, I82, I83) -> f5(I80, 0, I82, I83) [0 <= I82 - 1 /\ -1 <= I83 - 1 /\ I82 <= I83 /\ 0 <= I84 - 1 /\ 0 <= I85 - 1 /\ I86 <= I80 /\ 0 <= I80 - 1 /\ 0 <= I86 - 1 /\ 0 = I81]
  f5(I87, I88, I89, I90) -> f3(I91, 0, 1, I90) [-1 <= I90 - 1 /\ I91 <= I87 /\ 0 <= I87 - 1 /\ 0 <= I91 - 1 /\ 1 - I92 * I93 <= I92 - 1 /\ I92 * I93 <= 1 /\ 0 = I88 /\ 0 = I89]
  f3(I94, I95, I96, I97) -> f5(I94, 0, 0, I97) [-1 <= I97 - 1 /\ I98 <= I94 /\ 0 <= I94 - 1 /\ 0 <= I98 - 1 /\ 0 = I95 /\ 0 = I96]
  f5(I99, I100, I101, I102) -> f3(I103, 0, I101 + 1, I102) [-1 <= I102 - 1 /\ I101 <= I102 /\ I101 <= 0 /\ I103 <= I99 /\ 0 <= I99 - 1 /\ 0 <= I103 - 1 /\ 1 - I104 * I105 <= I104 - 1 /\ I104 * I105 <= 1 /\ 0 = I100]
  f3(I106, I107, I108, I109) -> f5(I106, 0, I108, I109) [-1 <= I109 - 1 /\ I108 <= I109 /\ I108 <= 0 /\ I110 <= I106 /\ 0 <= I106 - 1 /\ 0 <= I110 - 1 /\ 0 = I107]
  f3(I111, I112, I113, I114) -> f4(I112 - I113, I115, I116, I117) [I112 <= I114 /\ I113 <= I114 /\ 0 <= I112 - 1 /\ 0 <= I118 - 1 /\ I113 <= I112 /\ 0 <= I119 - 1 /\ 0 <= I120 - 1 /\ 0 <= I113 - 1 /\ 0 <= I111 - 1]
  f3(I121, I122, I123, I124) -> f4(I122 - I123, I125, I126, I127) [I122 <= I124 /\ I123 <= I124 /\ 0 <= I122 - 1 /\ 0 <= I128 - 1 /\ I123 <= I122 /\ 1 <= I122 - I123 /\ 0 <= I129 - 1 /\ I123 <= 0 /\ 0 <= I121 - 1]
  f3(I130, I131, I132, I133) -> f4(0 - I132, I134, I135, I136) [I132 <= I133 /\ 0 <= I132 - 1 /\ -1 <= I133 - 1 /\ I132 <= 0 /\ 0 <= I137 - 1 /\ 0 <= I130 - 1 /\ 0 = I131]
  f3(I138, I139, I140, I141) -> f4(0 - I140, I142, I143, I144) [0 = I139 /\ 0 <= I138 - 1 /\ I140 <= 0 /\ I140 <= I141 /\ -1 <= I141 - 1]
  f3(I145, I146, I147, I148) -> f4(I147 - I146, I149, I150, I151) [0 <= I147 - 1 /\ I146 <= I148 /\ I147 <= I148 /\ 0 <= I152 - 1 /\ I146 <= I147 - 1 /\ 0 <= I153 - 1 /\ 0 <= I154 - 1 /\ 0 <= I146 - 1 /\ 0 <= I145 - 1]
  f3(I155, I156, I157, I158) -> f4(I157, I159, I160, I161) [0 <= I157 - 1 /\ -1 <= I158 - 1 /\ I157 <= I158 /\ 0 <= I162 - 1 /\ 0 <= I163 - 1 /\ 0 <= I155 - 1 /\ 0 = I156]
  f3(I164, I165, I166, I167) -> f4(I166, I168, I169, I170) [I165 <= I167 /\ I166 <= I167 /\ 0 <= I165 - 1 /\ 0 <= I171 - 1 /\ I166 <= I165 /\ 0 <= I164 - 1]
  f3(I172, I173, I174, I175) -> f4(I174, I176, I177, I178) [0 = I173 /\ 0 <= I172 - 1 /\ I174 <= 0 /\ I174 <= I175 /\ -1 <= I175 - 1]
  f3(I179, I180, I181, I182) -> f4(I180, I183, I184, I185) [0 <= I181 - 1 /\ I180 <= I182 /\ I181 <= I182 /\ 0 <= I186 - 1 /\ I180 <= I181 - 1 /\ 0 <= I179 - 1]
  f3(I187, I188, I189, I190) -> f4(I188, I191, I192, I193) [0 <= I187 - 1 /\ I189 <= I188 /\ I189 <= I190 /\ I188 <= I190]
  f3(I194, I195, I196, I197) -> f4(I196, I198, I199, I200) [0 <= I194 - 1 /\ I195 <= I196 - 1 /\ I196 <= I197 /\ I195 <= I197 /\ 0 <= I196 - 1]
  f3(I201, I202, I203, I204) -> f2(I205, I202 + 1, I204, I206) [0 <= I205 - 1 /\ 0 <= I201 - 1 /\ I205 <= I201 /\ -1 <= I204 - 1 /\ I204 <= I203 - 1]
  f2(I207, I208, I209, I210) -> f3(I211, I208, 0, I209) [0 <= I211 - 1 /\ 0 <= I207 - 1 /\ I211 <= I207 /\ -1 <= I209 - 1 /\ I208 <= I209]
  f1(I212, I213, I214, I215) -> f2(I216, 0, I213, I217) [0 <= I216 - 1 /\ 0 <= I212 - 1 /\ -1 <= I213 - 1 /\ I216 <= I212]

We use the reverse value criterion with the projection function NU:
  NU[f3#(z1,z2,z3,z4)] = z4 + -1 * z3
  NU[f5#(z1,z2,z3,z4)] = z4 + -1 * (z3 + 1)

This gives the following inequalities:
  0 <= I22 - 1 /\ I21 <= I23 /\ I22 <= I23 /\ 0 <= I25 - 1 /\ I21 <= I22 - 1 /\ 0 <= I26 - 1 /\ 0 <= I27 - 1 /\ 0 <= I21 - 1 /\ -1 <= I23 - 1 /\ I24 <= I20 /\ 0 <= I20 - 1 /\ 0 <= I24 - 1 /\ I28 - I29 * I30 <= I29 - 1 /\ 0 <= I28 - I29 * I30  ==>  I23 + -1 * (I22 + 1) >= I23 + -1 * (I22 + 1)
  0 <= I33 - 1 /\ I32 <= I34 /\ I33 <= I34 /\ 0 <= I35 - 1 /\ I32 <= I33 - 1 /\ 0 <= I36 - 1 /\ 0 <= I37 - 1 /\ 0 <= I32 - 1 /\ -1 <= I34 - 1 /\ I38 <= I31 /\ 0 <= I31 - 1 /\ 0 <= I38 - 1  ==>  I34 + -1 * I33 > I34 + -1 * (I33 + 1)  with  I34 + -1 * I33 >= 0

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f5#(I20, I21, I22, I23) -> f3#(I24, I21, I22 + 1, I23) [0 <= I22 - 1 /\ I21 <= I23 /\ I22 <= I23 /\ 0 <= I25 - 1 /\ I21 <= I22 - 1 /\ 0 <= I26 - 1 /\ 0 <= I27 - 1 /\ 0 <= I21 - 1 /\ -1 <= I23 - 1 /\ I24 <= I20 /\ 0 <= I20 - 1 /\ 0 <= I24 - 1 /\ I28 - I29 * I30 <= I29 - 1 /\ 0 <= I28 - I29 * I30]
R = 
  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
  f4(I0, I1, I2, I3) -> f4(I0 - 1, I4, I5, I6) [I0 - 1 <= I0 - 1 /\ 0 <= I0 - 1]
  f5(I7, I8, I9, I10) -> f3(I11, I8, I9 + 1, I10) [I8 <= I10 /\ I9 <= I10 /\ 0 <= I8 - 1 /\ 0 <= y1 - 1 /\ I9 <= I8 /\ 0 <= y2 - 1 /\ 0 <= y3 - 1 /\ 0 <= I9 - 1 /\ -1 <= I10 - 1 /\ I11 <= I7 /\ 0 <= I7 - 1 /\ 0 <= I11 - 1 /\ y5 - y4 * y6 <= y4 - 1 /\ 0 <= y5 - y4 * y6]
  f3(I12, I13, I14, I15) -> f5(I12, I13, I14, I15) [I13 <= I15 /\ I14 <= I15 /\ 0 <= I13 - 1 /\ 0 <= I16 - 1 /\ I14 <= I13 /\ 0 <= I17 - 1 /\ 0 <= I18 - 1 /\ 0 <= I14 - 1 /\ -1 <= I15 - 1 /\ I19 <= I12 /\ 0 <= I12 - 1 /\ 0 <= I19 - 1]
  f5(I20, I21, I22, I23) -> f3(I24, I21, I22 + 1, I23) [0 <= I22 - 1 /\ I21 <= I23 /\ I22 <= I23 /\ 0 <= I25 - 1 /\ I21 <= I22 - 1 /\ 0 <= I26 - 1 /\ 0 <= I27 - 1 /\ 0 <= I21 - 1 /\ -1 <= I23 - 1 /\ I24 <= I20 /\ 0 <= I20 - 1 /\ 0 <= I24 - 1 /\ I28 - I29 * I30 <= I29 - 1 /\ 0 <= I28 - I29 * I30]
  f3(I31, I32, I33, I34) -> f5(I31, I32, I33, I34) [0 <= I33 - 1 /\ I32 <= I34 /\ I33 <= I34 /\ 0 <= I35 - 1 /\ I32 <= I33 - 1 /\ 0 <= I36 - 1 /\ 0 <= I37 - 1 /\ 0 <= I32 - 1 /\ -1 <= I34 - 1 /\ I38 <= I31 /\ 0 <= I31 - 1 /\ 0 <= I38 - 1]
  f5(I39, I40, I41, I42) -> f3(I43, I40, I41 + 1, I42) [I40 <= I42 /\ I41 <= I42 /\ 0 <= I40 - 1 /\ 0 <= I44 - 1 /\ I41 <= I40 /\ 1 <= I40 - I41 /\ 0 <= I45 - 1 /\ I41 <= 0 /\ -1 <= I42 - 1 /\ I43 <= I39 /\ 0 <= I39 - 1 /\ 0 <= I43 - 1 /\ I46 - I47 * I48 <= I47 - 1 /\ 0 <= I46 - I47 * I48]
  f3(I49, I50, I51, I52) -> f5(I49, I50, I51, I52) [I50 <= I52 /\ I51 <= I52 /\ 0 <= I50 - 1 /\ 0 <= I53 - 1 /\ I51 <= I50 /\ 1 <= I50 - I51 /\ 0 <= I54 - 1 /\ I51 <= 0 /\ -1 <= I52 - 1 /\ I55 <= I49 /\ 0 <= I49 - 1 /\ 0 <= I55 - 1]
  f5(I56, I57, I58, I59) -> f3(I60, 0, I58 + 1, I59) [I58 <= I59 /\ 0 <= I58 - 1 /\ -1 <= I59 - 1 /\ I58 <= 0 /\ 0 <= I61 - 1 /\ I60 <= I56 /\ 0 <= I56 - 1 /\ 0 <= I60 - 1 /\ 1 - I62 * I63 <= I62 - 1 /\ I62 * I63 <= 1 /\ 0 = I57]
  f3(I64, I65, I66, I67) -> f5(I64, 0, I66, I67) [I66 <= I67 /\ 0 <= I66 - 1 /\ -1 <= I67 - 1 /\ I66 <= 0 /\ 0 <= I68 - 1 /\ I69 <= I64 /\ 0 <= I64 - 1 /\ 0 <= I69 - 1 /\ 0 = I65]
  f5(I70, I71, I72, I73) -> f3(I74, 0, I72 + 1, I73) [0 <= I72 - 1 /\ -1 <= I73 - 1 /\ I72 <= I73 /\ 0 <= I75 - 1 /\ 0 <= I76 - 1 /\ I74 <= I70 /\ 0 <= I70 - 1 /\ 0 <= I74 - 1 /\ I77 - I78 * I79 <= I78 - 1 /\ 0 <= I77 - I78 * I79 /\ 0 = I71]
  f3(I80, I81, I82, I83) -> f5(I80, 0, I82, I83) [0 <= I82 - 1 /\ -1 <= I83 - 1 /\ I82 <= I83 /\ 0 <= I84 - 1 /\ 0 <= I85 - 1 /\ I86 <= I80 /\ 0 <= I80 - 1 /\ 0 <= I86 - 1 /\ 0 = I81]
  f5(I87, I88, I89, I90) -> f3(I91, 0, 1, I90) [-1 <= I90 - 1 /\ I91 <= I87 /\ 0 <= I87 - 1 /\ 0 <= I91 - 1 /\ 1 - I92 * I93 <= I92 - 1 /\ I92 * I93 <= 1 /\ 0 = I88 /\ 0 = I89]
  f3(I94, I95, I96, I97) -> f5(I94, 0, 0, I97) [-1 <= I97 - 1 /\ I98 <= I94 /\ 0 <= I94 - 1 /\ 0 <= I98 - 1 /\ 0 = I95 /\ 0 = I96]
  f5(I99, I100, I101, I102) -> f3(I103, 0, I101 + 1, I102) [-1 <= I102 - 1 /\ I101 <= I102 /\ I101 <= 0 /\ I103 <= I99 /\ 0 <= I99 - 1 /\ 0 <= I103 - 1 /\ 1 - I104 * I105 <= I104 - 1 /\ I104 * I105 <= 1 /\ 0 = I100]
  f3(I106, I107, I108, I109) -> f5(I106, 0, I108, I109) [-1 <= I109 - 1 /\ I108 <= I109 /\ I108 <= 0 /\ I110 <= I106 /\ 0 <= I106 - 1 /\ 0 <= I110 - 1 /\ 0 = I107]
  f3(I111, I112, I113, I114) -> f4(I112 - I113, I115, I116, I117) [I112 <= I114 /\ I113 <= I114 /\ 0 <= I112 - 1 /\ 0 <= I118 - 1 /\ I113 <= I112 /\ 0 <= I119 - 1 /\ 0 <= I120 - 1 /\ 0 <= I113 - 1 /\ 0 <= I111 - 1]
  f3(I121, I122, I123, I124) -> f4(I122 - I123, I125, I126, I127) [I122 <= I124 /\ I123 <= I124 /\ 0 <= I122 - 1 /\ 0 <= I128 - 1 /\ I123 <= I122 /\ 1 <= I122 - I123 /\ 0 <= I129 - 1 /\ I123 <= 0 /\ 0 <= I121 - 1]
  f3(I130, I131, I132, I133) -> f4(0 - I132, I134, I135, I136) [I132 <= I133 /\ 0 <= I132 - 1 /\ -1 <= I133 - 1 /\ I132 <= 0 /\ 0 <= I137 - 1 /\ 0 <= I130 - 1 /\ 0 = I131]
  f3(I138, I139, I140, I141) -> f4(0 - I140, I142, I143, I144) [0 = I139 /\ 0 <= I138 - 1 /\ I140 <= 0 /\ I140 <= I141 /\ -1 <= I141 - 1]
  f3(I145, I146, I147, I148) -> f4(I147 - I146, I149, I150, I151) [0 <= I147 - 1 /\ I146 <= I148 /\ I147 <= I148 /\ 0 <= I152 - 1 /\ I146 <= I147 - 1 /\ 0 <= I153 - 1 /\ 0 <= I154 - 1 /\ 0 <= I146 - 1 /\ 0 <= I145 - 1]
  f3(I155, I156, I157, I158) -> f4(I157, I159, I160, I161) [0 <= I157 - 1 /\ -1 <= I158 - 1 /\ I157 <= I158 /\ 0 <= I162 - 1 /\ 0 <= I163 - 1 /\ 0 <= I155 - 1 /\ 0 = I156]
  f3(I164, I165, I166, I167) -> f4(I166, I168, I169, I170) [I165 <= I167 /\ I166 <= I167 /\ 0 <= I165 - 1 /\ 0 <= I171 - 1 /\ I166 <= I165 /\ 0 <= I164 - 1]
  f3(I172, I173, I174, I175) -> f4(I174, I176, I177, I178) [0 = I173 /\ 0 <= I172 - 1 /\ I174 <= 0 /\ I174 <= I175 /\ -1 <= I175 - 1]
  f3(I179, I180, I181, I182) -> f4(I180, I183, I184, I185) [0 <= I181 - 1 /\ I180 <= I182 /\ I181 <= I182 /\ 0 <= I186 - 1 /\ I180 <= I181 - 1 /\ 0 <= I179 - 1]
  f3(I187, I188, I189, I190) -> f4(I188, I191, I192, I193) [0 <= I187 - 1 /\ I189 <= I188 /\ I189 <= I190 /\ I188 <= I190]
  f3(I194, I195, I196, I197) -> f4(I196, I198, I199, I200) [0 <= I194 - 1 /\ I195 <= I196 - 1 /\ I196 <= I197 /\ I195 <= I197 /\ 0 <= I196 - 1]
  f3(I201, I202, I203, I204) -> f2(I205, I202 + 1, I204, I206) [0 <= I205 - 1 /\ 0 <= I201 - 1 /\ I205 <= I201 /\ -1 <= I204 - 1 /\ I204 <= I203 - 1]
  f2(I207, I208, I209, I210) -> f3(I211, I208, 0, I209) [0 <= I211 - 1 /\ 0 <= I207 - 1 /\ I211 <= I207 /\ -1 <= I209 - 1 /\ I208 <= I209]
  f1(I212, I213, I214, I215) -> f2(I216, 0, I213, I217) [0 <= I216 - 1 /\ 0 <= I212 - 1 /\ -1 <= I213 - 1 /\ I216 <= I212]

The dependency graph for this problem is:
  4 -> 
Where:
  4) f5#(I20, I21, I22, I23) -> f3#(I24, I21, I22 + 1, I23) [0 <= I22 - 1 /\ I21 <= I23 /\ I22 <= I23 /\ 0 <= I25 - 1 /\ I21 <= I22 - 1 /\ 0 <= I26 - 1 /\ 0 <= I27 - 1 /\ 0 <= I21 - 1 /\ -1 <= I23 - 1 /\ I24 <= I20 /\ 0 <= I20 - 1 /\ 0 <= I24 - 1 /\ I28 - I29 * I30 <= I29 - 1 /\ 0 <= I28 - I29 * I30]

We have the following SCCs.
  

DP problem for innermost termination.
P =
  f5#(I7, I8, I9, I10) -> f3#(I11, I8, I9 + 1, I10) [I8 <= I10 /\ I9 <= I10 /\ 0 <= I8 - 1 /\ 0 <= y1 - 1 /\ I9 <= I8 /\ 0 <= y2 - 1 /\ 0 <= y3 - 1 /\ 0 <= I9 - 1 /\ -1 <= I10 - 1 /\ I11 <= I7 /\ 0 <= I7 - 1 /\ 0 <= I11 - 1 /\ y5 - y4 * y6 <= y4 - 1 /\ 0 <= y5 - y4 * y6]
  f3#(I12, I13, I14, I15) -> f5#(I12, I13, I14, I15) [I13 <= I15 /\ I14 <= I15 /\ 0 <= I13 - 1 /\ 0 <= I16 - 1 /\ I14 <= I13 /\ 0 <= I17 - 1 /\ 0 <= I18 - 1 /\ 0 <= I14 - 1 /\ -1 <= I15 - 1 /\ I19 <= I12 /\ 0 <= I12 - 1 /\ 0 <= I19 - 1]
R = 
  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
  f4(I0, I1, I2, I3) -> f4(I0 - 1, I4, I5, I6) [I0 - 1 <= I0 - 1 /\ 0 <= I0 - 1]
  f5(I7, I8, I9, I10) -> f3(I11, I8, I9 + 1, I10) [I8 <= I10 /\ I9 <= I10 /\ 0 <= I8 - 1 /\ 0 <= y1 - 1 /\ I9 <= I8 /\ 0 <= y2 - 1 /\ 0 <= y3 - 1 /\ 0 <= I9 - 1 /\ -1 <= I10 - 1 /\ I11 <= I7 /\ 0 <= I7 - 1 /\ 0 <= I11 - 1 /\ y5 - y4 * y6 <= y4 - 1 /\ 0 <= y5 - y4 * y6]
  f3(I12, I13, I14, I15) -> f5(I12, I13, I14, I15) [I13 <= I15 /\ I14 <= I15 /\ 0 <= I13 - 1 /\ 0 <= I16 - 1 /\ I14 <= I13 /\ 0 <= I17 - 1 /\ 0 <= I18 - 1 /\ 0 <= I14 - 1 /\ -1 <= I15 - 1 /\ I19 <= I12 /\ 0 <= I12 - 1 /\ 0 <= I19 - 1]
  f5(I20, I21, I22, I23) -> f3(I24, I21, I22 + 1, I23) [0 <= I22 - 1 /\ I21 <= I23 /\ I22 <= I23 /\ 0 <= I25 - 1 /\ I21 <= I22 - 1 /\ 0 <= I26 - 1 /\ 0 <= I27 - 1 /\ 0 <= I21 - 1 /\ -1 <= I23 - 1 /\ I24 <= I20 /\ 0 <= I20 - 1 /\ 0 <= I24 - 1 /\ I28 - I29 * I30 <= I29 - 1 /\ 0 <= I28 - I29 * I30]
  f3(I31, I32, I33, I34) -> f5(I31, I32, I33, I34) [0 <= I33 - 1 /\ I32 <= I34 /\ I33 <= I34 /\ 0 <= I35 - 1 /\ I32 <= I33 - 1 /\ 0 <= I36 - 1 /\ 0 <= I37 - 1 /\ 0 <= I32 - 1 /\ -1 <= I34 - 1 /\ I38 <= I31 /\ 0 <= I31 - 1 /\ 0 <= I38 - 1]
  f5(I39, I40, I41, I42) -> f3(I43, I40, I41 + 1, I42) [I40 <= I42 /\ I41 <= I42 /\ 0 <= I40 - 1 /\ 0 <= I44 - 1 /\ I41 <= I40 /\ 1 <= I40 - I41 /\ 0 <= I45 - 1 /\ I41 <= 0 /\ -1 <= I42 - 1 /\ I43 <= I39 /\ 0 <= I39 - 1 /\ 0 <= I43 - 1 /\ I46 - I47 * I48 <= I47 - 1 /\ 0 <= I46 - I47 * I48]
  f3(I49, I50, I51, I52) -> f5(I49, I50, I51, I52) [I50 <= I52 /\ I51 <= I52 /\ 0 <= I50 - 1 /\ 0 <= I53 - 1 /\ I51 <= I50 /\ 1 <= I50 - I51 /\ 0 <= I54 - 1 /\ I51 <= 0 /\ -1 <= I52 - 1 /\ I55 <= I49 /\ 0 <= I49 - 1 /\ 0 <= I55 - 1]
  f5(I56, I57, I58, I59) -> f3(I60, 0, I58 + 1, I59) [I58 <= I59 /\ 0 <= I58 - 1 /\ -1 <= I59 - 1 /\ I58 <= 0 /\ 0 <= I61 - 1 /\ I60 <= I56 /\ 0 <= I56 - 1 /\ 0 <= I60 - 1 /\ 1 - I62 * I63 <= I62 - 1 /\ I62 * I63 <= 1 /\ 0 = I57]
  f3(I64, I65, I66, I67) -> f5(I64, 0, I66, I67) [I66 <= I67 /\ 0 <= I66 - 1 /\ -1 <= I67 - 1 /\ I66 <= 0 /\ 0 <= I68 - 1 /\ I69 <= I64 /\ 0 <= I64 - 1 /\ 0 <= I69 - 1 /\ 0 = I65]
  f5(I70, I71, I72, I73) -> f3(I74, 0, I72 + 1, I73) [0 <= I72 - 1 /\ -1 <= I73 - 1 /\ I72 <= I73 /\ 0 <= I75 - 1 /\ 0 <= I76 - 1 /\ I74 <= I70 /\ 0 <= I70 - 1 /\ 0 <= I74 - 1 /\ I77 - I78 * I79 <= I78 - 1 /\ 0 <= I77 - I78 * I79 /\ 0 = I71]
  f3(I80, I81, I82, I83) -> f5(I80, 0, I82, I83) [0 <= I82 - 1 /\ -1 <= I83 - 1 /\ I82 <= I83 /\ 0 <= I84 - 1 /\ 0 <= I85 - 1 /\ I86 <= I80 /\ 0 <= I80 - 1 /\ 0 <= I86 - 1 /\ 0 = I81]
  f5(I87, I88, I89, I90) -> f3(I91, 0, 1, I90) [-1 <= I90 - 1 /\ I91 <= I87 /\ 0 <= I87 - 1 /\ 0 <= I91 - 1 /\ 1 - I92 * I93 <= I92 - 1 /\ I92 * I93 <= 1 /\ 0 = I88 /\ 0 = I89]
  f3(I94, I95, I96, I97) -> f5(I94, 0, 0, I97) [-1 <= I97 - 1 /\ I98 <= I94 /\ 0 <= I94 - 1 /\ 0 <= I98 - 1 /\ 0 = I95 /\ 0 = I96]
  f5(I99, I100, I101, I102) -> f3(I103, 0, I101 + 1, I102) [-1 <= I102 - 1 /\ I101 <= I102 /\ I101 <= 0 /\ I103 <= I99 /\ 0 <= I99 - 1 /\ 0 <= I103 - 1 /\ 1 - I104 * I105 <= I104 - 1 /\ I104 * I105 <= 1 /\ 0 = I100]
  f3(I106, I107, I108, I109) -> f5(I106, 0, I108, I109) [-1 <= I109 - 1 /\ I108 <= I109 /\ I108 <= 0 /\ I110 <= I106 /\ 0 <= I106 - 1 /\ 0 <= I110 - 1 /\ 0 = I107]
  f3(I111, I112, I113, I114) -> f4(I112 - I113, I115, I116, I117) [I112 <= I114 /\ I113 <= I114 /\ 0 <= I112 - 1 /\ 0 <= I118 - 1 /\ I113 <= I112 /\ 0 <= I119 - 1 /\ 0 <= I120 - 1 /\ 0 <= I113 - 1 /\ 0 <= I111 - 1]
  f3(I121, I122, I123, I124) -> f4(I122 - I123, I125, I126, I127) [I122 <= I124 /\ I123 <= I124 /\ 0 <= I122 - 1 /\ 0 <= I128 - 1 /\ I123 <= I122 /\ 1 <= I122 - I123 /\ 0 <= I129 - 1 /\ I123 <= 0 /\ 0 <= I121 - 1]
  f3(I130, I131, I132, I133) -> f4(0 - I132, I134, I135, I136) [I132 <= I133 /\ 0 <= I132 - 1 /\ -1 <= I133 - 1 /\ I132 <= 0 /\ 0 <= I137 - 1 /\ 0 <= I130 - 1 /\ 0 = I131]
  f3(I138, I139, I140, I141) -> f4(0 - I140, I142, I143, I144) [0 = I139 /\ 0 <= I138 - 1 /\ I140 <= 0 /\ I140 <= I141 /\ -1 <= I141 - 1]
  f3(I145, I146, I147, I148) -> f4(I147 - I146, I149, I150, I151) [0 <= I147 - 1 /\ I146 <= I148 /\ I147 <= I148 /\ 0 <= I152 - 1 /\ I146 <= I147 - 1 /\ 0 <= I153 - 1 /\ 0 <= I154 - 1 /\ 0 <= I146 - 1 /\ 0 <= I145 - 1]
  f3(I155, I156, I157, I158) -> f4(I157, I159, I160, I161) [0 <= I157 - 1 /\ -1 <= I158 - 1 /\ I157 <= I158 /\ 0 <= I162 - 1 /\ 0 <= I163 - 1 /\ 0 <= I155 - 1 /\ 0 = I156]
  f3(I164, I165, I166, I167) -> f4(I166, I168, I169, I170) [I165 <= I167 /\ I166 <= I167 /\ 0 <= I165 - 1 /\ 0 <= I171 - 1 /\ I166 <= I165 /\ 0 <= I164 - 1]
  f3(I172, I173, I174, I175) -> f4(I174, I176, I177, I178) [0 = I173 /\ 0 <= I172 - 1 /\ I174 <= 0 /\ I174 <= I175 /\ -1 <= I175 - 1]
  f3(I179, I180, I181, I182) -> f4(I180, I183, I184, I185) [0 <= I181 - 1 /\ I180 <= I182 /\ I181 <= I182 /\ 0 <= I186 - 1 /\ I180 <= I181 - 1 /\ 0 <= I179 - 1]
  f3(I187, I188, I189, I190) -> f4(I188, I191, I192, I193) [0 <= I187 - 1 /\ I189 <= I188 /\ I189 <= I190 /\ I188 <= I190]
  f3(I194, I195, I196, I197) -> f4(I196, I198, I199, I200) [0 <= I194 - 1 /\ I195 <= I196 - 1 /\ I196 <= I197 /\ I195 <= I197 /\ 0 <= I196 - 1]
  f3(I201, I202, I203, I204) -> f2(I205, I202 + 1, I204, I206) [0 <= I205 - 1 /\ 0 <= I201 - 1 /\ I205 <= I201 /\ -1 <= I204 - 1 /\ I204 <= I203 - 1]
  f2(I207, I208, I209, I210) -> f3(I211, I208, 0, I209) [0 <= I211 - 1 /\ 0 <= I207 - 1 /\ I211 <= I207 /\ -1 <= I209 - 1 /\ I208 <= I209]
  f1(I212, I213, I214, I215) -> f2(I216, 0, I213, I217) [0 <= I216 - 1 /\ 0 <= I212 - 1 /\ -1 <= I213 - 1 /\ I216 <= I212]

We use the reverse value criterion with the projection function NU:
  NU[f3#(z1,z2,z3,z4)] = z4 + -1 * z3
  NU[f5#(z1,z2,z3,z4)] = z4 + -1 * (z3 + 1)

This gives the following inequalities:
  I8 <= I10 /\ I9 <= I10 /\ 0 <= I8 - 1 /\ 0 <= y1 - 1 /\ I9 <= I8 /\ 0 <= y2 - 1 /\ 0 <= y3 - 1 /\ 0 <= I9 - 1 /\ -1 <= I10 - 1 /\ I11 <= I7 /\ 0 <= I7 - 1 /\ 0 <= I11 - 1 /\ y5 - y4 * y6 <= y4 - 1 /\ 0 <= y5 - y4 * y6  ==>  I10 + -1 * (I9 + 1) >= I10 + -1 * (I9 + 1)
  I13 <= I15 /\ I14 <= I15 /\ 0 <= I13 - 1 /\ 0 <= I16 - 1 /\ I14 <= I13 /\ 0 <= I17 - 1 /\ 0 <= I18 - 1 /\ 0 <= I14 - 1 /\ -1 <= I15 - 1 /\ I19 <= I12 /\ 0 <= I12 - 1 /\ 0 <= I19 - 1  ==>  I15 + -1 * I14 > I15 + -1 * (I14 + 1)  with  I15 + -1 * I14 >= 0

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f5#(I7, I8, I9, I10) -> f3#(I11, I8, I9 + 1, I10) [I8 <= I10 /\ I9 <= I10 /\ 0 <= I8 - 1 /\ 0 <= y1 - 1 /\ I9 <= I8 /\ 0 <= y2 - 1 /\ 0 <= y3 - 1 /\ 0 <= I9 - 1 /\ -1 <= I10 - 1 /\ I11 <= I7 /\ 0 <= I7 - 1 /\ 0 <= I11 - 1 /\ y5 - y4 * y6 <= y4 - 1 /\ 0 <= y5 - y4 * y6]
R = 
  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
  f4(I0, I1, I2, I3) -> f4(I0 - 1, I4, I5, I6) [I0 - 1 <= I0 - 1 /\ 0 <= I0 - 1]
  f5(I7, I8, I9, I10) -> f3(I11, I8, I9 + 1, I10) [I8 <= I10 /\ I9 <= I10 /\ 0 <= I8 - 1 /\ 0 <= y1 - 1 /\ I9 <= I8 /\ 0 <= y2 - 1 /\ 0 <= y3 - 1 /\ 0 <= I9 - 1 /\ -1 <= I10 - 1 /\ I11 <= I7 /\ 0 <= I7 - 1 /\ 0 <= I11 - 1 /\ y5 - y4 * y6 <= y4 - 1 /\ 0 <= y5 - y4 * y6]
  f3(I12, I13, I14, I15) -> f5(I12, I13, I14, I15) [I13 <= I15 /\ I14 <= I15 /\ 0 <= I13 - 1 /\ 0 <= I16 - 1 /\ I14 <= I13 /\ 0 <= I17 - 1 /\ 0 <= I18 - 1 /\ 0 <= I14 - 1 /\ -1 <= I15 - 1 /\ I19 <= I12 /\ 0 <= I12 - 1 /\ 0 <= I19 - 1]
  f5(I20, I21, I22, I23) -> f3(I24, I21, I22 + 1, I23) [0 <= I22 - 1 /\ I21 <= I23 /\ I22 <= I23 /\ 0 <= I25 - 1 /\ I21 <= I22 - 1 /\ 0 <= I26 - 1 /\ 0 <= I27 - 1 /\ 0 <= I21 - 1 /\ -1 <= I23 - 1 /\ I24 <= I20 /\ 0 <= I20 - 1 /\ 0 <= I24 - 1 /\ I28 - I29 * I30 <= I29 - 1 /\ 0 <= I28 - I29 * I30]
  f3(I31, I32, I33, I34) -> f5(I31, I32, I33, I34) [0 <= I33 - 1 /\ I32 <= I34 /\ I33 <= I34 /\ 0 <= I35 - 1 /\ I32 <= I33 - 1 /\ 0 <= I36 - 1 /\ 0 <= I37 - 1 /\ 0 <= I32 - 1 /\ -1 <= I34 - 1 /\ I38 <= I31 /\ 0 <= I31 - 1 /\ 0 <= I38 - 1]
  f5(I39, I40, I41, I42) -> f3(I43, I40, I41 + 1, I42) [I40 <= I42 /\ I41 <= I42 /\ 0 <= I40 - 1 /\ 0 <= I44 - 1 /\ I41 <= I40 /\ 1 <= I40 - I41 /\ 0 <= I45 - 1 /\ I41 <= 0 /\ -1 <= I42 - 1 /\ I43 <= I39 /\ 0 <= I39 - 1 /\ 0 <= I43 - 1 /\ I46 - I47 * I48 <= I47 - 1 /\ 0 <= I46 - I47 * I48]
  f3(I49, I50, I51, I52) -> f5(I49, I50, I51, I52) [I50 <= I52 /\ I51 <= I52 /\ 0 <= I50 - 1 /\ 0 <= I53 - 1 /\ I51 <= I50 /\ 1 <= I50 - I51 /\ 0 <= I54 - 1 /\ I51 <= 0 /\ -1 <= I52 - 1 /\ I55 <= I49 /\ 0 <= I49 - 1 /\ 0 <= I55 - 1]
  f5(I56, I57, I58, I59) -> f3(I60, 0, I58 + 1, I59) [I58 <= I59 /\ 0 <= I58 - 1 /\ -1 <= I59 - 1 /\ I58 <= 0 /\ 0 <= I61 - 1 /\ I60 <= I56 /\ 0 <= I56 - 1 /\ 0 <= I60 - 1 /\ 1 - I62 * I63 <= I62 - 1 /\ I62 * I63 <= 1 /\ 0 = I57]
  f3(I64, I65, I66, I67) -> f5(I64, 0, I66, I67) [I66 <= I67 /\ 0 <= I66 - 1 /\ -1 <= I67 - 1 /\ I66 <= 0 /\ 0 <= I68 - 1 /\ I69 <= I64 /\ 0 <= I64 - 1 /\ 0 <= I69 - 1 /\ 0 = I65]
  f5(I70, I71, I72, I73) -> f3(I74, 0, I72 + 1, I73) [0 <= I72 - 1 /\ -1 <= I73 - 1 /\ I72 <= I73 /\ 0 <= I75 - 1 /\ 0 <= I76 - 1 /\ I74 <= I70 /\ 0 <= I70 - 1 /\ 0 <= I74 - 1 /\ I77 - I78 * I79 <= I78 - 1 /\ 0 <= I77 - I78 * I79 /\ 0 = I71]
  f3(I80, I81, I82, I83) -> f5(I80, 0, I82, I83) [0 <= I82 - 1 /\ -1 <= I83 - 1 /\ I82 <= I83 /\ 0 <= I84 - 1 /\ 0 <= I85 - 1 /\ I86 <= I80 /\ 0 <= I80 - 1 /\ 0 <= I86 - 1 /\ 0 = I81]
  f5(I87, I88, I89, I90) -> f3(I91, 0, 1, I90) [-1 <= I90 - 1 /\ I91 <= I87 /\ 0 <= I87 - 1 /\ 0 <= I91 - 1 /\ 1 - I92 * I93 <= I92 - 1 /\ I92 * I93 <= 1 /\ 0 = I88 /\ 0 = I89]
  f3(I94, I95, I96, I97) -> f5(I94, 0, 0, I97) [-1 <= I97 - 1 /\ I98 <= I94 /\ 0 <= I94 - 1 /\ 0 <= I98 - 1 /\ 0 = I95 /\ 0 = I96]
  f5(I99, I100, I101, I102) -> f3(I103, 0, I101 + 1, I102) [-1 <= I102 - 1 /\ I101 <= I102 /\ I101 <= 0 /\ I103 <= I99 /\ 0 <= I99 - 1 /\ 0 <= I103 - 1 /\ 1 - I104 * I105 <= I104 - 1 /\ I104 * I105 <= 1 /\ 0 = I100]
  f3(I106, I107, I108, I109) -> f5(I106, 0, I108, I109) [-1 <= I109 - 1 /\ I108 <= I109 /\ I108 <= 0 /\ I110 <= I106 /\ 0 <= I106 - 1 /\ 0 <= I110 - 1 /\ 0 = I107]
  f3(I111, I112, I113, I114) -> f4(I112 - I113, I115, I116, I117) [I112 <= I114 /\ I113 <= I114 /\ 0 <= I112 - 1 /\ 0 <= I118 - 1 /\ I113 <= I112 /\ 0 <= I119 - 1 /\ 0 <= I120 - 1 /\ 0 <= I113 - 1 /\ 0 <= I111 - 1]
  f3(I121, I122, I123, I124) -> f4(I122 - I123, I125, I126, I127) [I122 <= I124 /\ I123 <= I124 /\ 0 <= I122 - 1 /\ 0 <= I128 - 1 /\ I123 <= I122 /\ 1 <= I122 - I123 /\ 0 <= I129 - 1 /\ I123 <= 0 /\ 0 <= I121 - 1]
  f3(I130, I131, I132, I133) -> f4(0 - I132, I134, I135, I136) [I132 <= I133 /\ 0 <= I132 - 1 /\ -1 <= I133 - 1 /\ I132 <= 0 /\ 0 <= I137 - 1 /\ 0 <= I130 - 1 /\ 0 = I131]
  f3(I138, I139, I140, I141) -> f4(0 - I140, I142, I143, I144) [0 = I139 /\ 0 <= I138 - 1 /\ I140 <= 0 /\ I140 <= I141 /\ -1 <= I141 - 1]
  f3(I145, I146, I147, I148) -> f4(I147 - I146, I149, I150, I151) [0 <= I147 - 1 /\ I146 <= I148 /\ I147 <= I148 /\ 0 <= I152 - 1 /\ I146 <= I147 - 1 /\ 0 <= I153 - 1 /\ 0 <= I154 - 1 /\ 0 <= I146 - 1 /\ 0 <= I145 - 1]
  f3(I155, I156, I157, I158) -> f4(I157, I159, I160, I161) [0 <= I157 - 1 /\ -1 <= I158 - 1 /\ I157 <= I158 /\ 0 <= I162 - 1 /\ 0 <= I163 - 1 /\ 0 <= I155 - 1 /\ 0 = I156]
  f3(I164, I165, I166, I167) -> f4(I166, I168, I169, I170) [I165 <= I167 /\ I166 <= I167 /\ 0 <= I165 - 1 /\ 0 <= I171 - 1 /\ I166 <= I165 /\ 0 <= I164 - 1]
  f3(I172, I173, I174, I175) -> f4(I174, I176, I177, I178) [0 = I173 /\ 0 <= I172 - 1 /\ I174 <= 0 /\ I174 <= I175 /\ -1 <= I175 - 1]
  f3(I179, I180, I181, I182) -> f4(I180, I183, I184, I185) [0 <= I181 - 1 /\ I180 <= I182 /\ I181 <= I182 /\ 0 <= I186 - 1 /\ I180 <= I181 - 1 /\ 0 <= I179 - 1]
  f3(I187, I188, I189, I190) -> f4(I188, I191, I192, I193) [0 <= I187 - 1 /\ I189 <= I188 /\ I189 <= I190 /\ I188 <= I190]
  f3(I194, I195, I196, I197) -> f4(I196, I198, I199, I200) [0 <= I194 - 1 /\ I195 <= I196 - 1 /\ I196 <= I197 /\ I195 <= I197 /\ 0 <= I196 - 1]
  f3(I201, I202, I203, I204) -> f2(I205, I202 + 1, I204, I206) [0 <= I205 - 1 /\ 0 <= I201 - 1 /\ I205 <= I201 /\ -1 <= I204 - 1 /\ I204 <= I203 - 1]
  f2(I207, I208, I209, I210) -> f3(I211, I208, 0, I209) [0 <= I211 - 1 /\ 0 <= I207 - 1 /\ I211 <= I207 /\ -1 <= I209 - 1 /\ I208 <= I209]
  f1(I212, I213, I214, I215) -> f2(I216, 0, I213, I217) [0 <= I216 - 1 /\ 0 <= I212 - 1 /\ -1 <= I213 - 1 /\ I216 <= I212]

The dependency graph for this problem is:
  2 -> 
Where:
  2) f5#(I7, I8, I9, I10) -> f3#(I11, I8, I9 + 1, I10) [I8 <= I10 /\ I9 <= I10 /\ 0 <= I8 - 1 /\ 0 <= y1 - 1 /\ I9 <= I8 /\ 0 <= y2 - 1 /\ 0 <= y3 - 1 /\ 0 <= I9 - 1 /\ -1 <= I10 - 1 /\ I11 <= I7 /\ 0 <= I7 - 1 /\ 0 <= I11 - 1 /\ y5 - y4 * y6 <= y4 - 1 /\ 0 <= y5 - y4 * y6]

We have the following SCCs.
  

DP problem for innermost termination.
P =
  f5#(I39, I40, I41, I42) -> f3#(I43, I40, I41 + 1, I42) [I40 <= I42 /\ I41 <= I42 /\ 0 <= I40 - 1 /\ 0 <= I44 - 1 /\ I41 <= I40 /\ 1 <= I40 - I41 /\ 0 <= I45 - 1 /\ I41 <= 0 /\ -1 <= I42 - 1 /\ I43 <= I39 /\ 0 <= I39 - 1 /\ 0 <= I43 - 1 /\ I46 - I47 * I48 <= I47 - 1 /\ 0 <= I46 - I47 * I48]
  f3#(I49, I50, I51, I52) -> f5#(I49, I50, I51, I52) [I50 <= I52 /\ I51 <= I52 /\ 0 <= I50 - 1 /\ 0 <= I53 - 1 /\ I51 <= I50 /\ 1 <= I50 - I51 /\ 0 <= I54 - 1 /\ I51 <= 0 /\ -1 <= I52 - 1 /\ I55 <= I49 /\ 0 <= I49 - 1 /\ 0 <= I55 - 1]
R = 
  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
  f4(I0, I1, I2, I3) -> f4(I0 - 1, I4, I5, I6) [I0 - 1 <= I0 - 1 /\ 0 <= I0 - 1]
  f5(I7, I8, I9, I10) -> f3(I11, I8, I9 + 1, I10) [I8 <= I10 /\ I9 <= I10 /\ 0 <= I8 - 1 /\ 0 <= y1 - 1 /\ I9 <= I8 /\ 0 <= y2 - 1 /\ 0 <= y3 - 1 /\ 0 <= I9 - 1 /\ -1 <= I10 - 1 /\ I11 <= I7 /\ 0 <= I7 - 1 /\ 0 <= I11 - 1 /\ y5 - y4 * y6 <= y4 - 1 /\ 0 <= y5 - y4 * y6]
  f3(I12, I13, I14, I15) -> f5(I12, I13, I14, I15) [I13 <= I15 /\ I14 <= I15 /\ 0 <= I13 - 1 /\ 0 <= I16 - 1 /\ I14 <= I13 /\ 0 <= I17 - 1 /\ 0 <= I18 - 1 /\ 0 <= I14 - 1 /\ -1 <= I15 - 1 /\ I19 <= I12 /\ 0 <= I12 - 1 /\ 0 <= I19 - 1]
  f5(I20, I21, I22, I23) -> f3(I24, I21, I22 + 1, I23) [0 <= I22 - 1 /\ I21 <= I23 /\ I22 <= I23 /\ 0 <= I25 - 1 /\ I21 <= I22 - 1 /\ 0 <= I26 - 1 /\ 0 <= I27 - 1 /\ 0 <= I21 - 1 /\ -1 <= I23 - 1 /\ I24 <= I20 /\ 0 <= I20 - 1 /\ 0 <= I24 - 1 /\ I28 - I29 * I30 <= I29 - 1 /\ 0 <= I28 - I29 * I30]
  f3(I31, I32, I33, I34) -> f5(I31, I32, I33, I34) [0 <= I33 - 1 /\ I32 <= I34 /\ I33 <= I34 /\ 0 <= I35 - 1 /\ I32 <= I33 - 1 /\ 0 <= I36 - 1 /\ 0 <= I37 - 1 /\ 0 <= I32 - 1 /\ -1 <= I34 - 1 /\ I38 <= I31 /\ 0 <= I31 - 1 /\ 0 <= I38 - 1]
  f5(I39, I40, I41, I42) -> f3(I43, I40, I41 + 1, I42) [I40 <= I42 /\ I41 <= I42 /\ 0 <= I40 - 1 /\ 0 <= I44 - 1 /\ I41 <= I40 /\ 1 <= I40 - I41 /\ 0 <= I45 - 1 /\ I41 <= 0 /\ -1 <= I42 - 1 /\ I43 <= I39 /\ 0 <= I39 - 1 /\ 0 <= I43 - 1 /\ I46 - I47 * I48 <= I47 - 1 /\ 0 <= I46 - I47 * I48]
  f3(I49, I50, I51, I52) -> f5(I49, I50, I51, I52) [I50 <= I52 /\ I51 <= I52 /\ 0 <= I50 - 1 /\ 0 <= I53 - 1 /\ I51 <= I50 /\ 1 <= I50 - I51 /\ 0 <= I54 - 1 /\ I51 <= 0 /\ -1 <= I52 - 1 /\ I55 <= I49 /\ 0 <= I49 - 1 /\ 0 <= I55 - 1]
  f5(I56, I57, I58, I59) -> f3(I60, 0, I58 + 1, I59) [I58 <= I59 /\ 0 <= I58 - 1 /\ -1 <= I59 - 1 /\ I58 <= 0 /\ 0 <= I61 - 1 /\ I60 <= I56 /\ 0 <= I56 - 1 /\ 0 <= I60 - 1 /\ 1 - I62 * I63 <= I62 - 1 /\ I62 * I63 <= 1 /\ 0 = I57]
  f3(I64, I65, I66, I67) -> f5(I64, 0, I66, I67) [I66 <= I67 /\ 0 <= I66 - 1 /\ -1 <= I67 - 1 /\ I66 <= 0 /\ 0 <= I68 - 1 /\ I69 <= I64 /\ 0 <= I64 - 1 /\ 0 <= I69 - 1 /\ 0 = I65]
  f5(I70, I71, I72, I73) -> f3(I74, 0, I72 + 1, I73) [0 <= I72 - 1 /\ -1 <= I73 - 1 /\ I72 <= I73 /\ 0 <= I75 - 1 /\ 0 <= I76 - 1 /\ I74 <= I70 /\ 0 <= I70 - 1 /\ 0 <= I74 - 1 /\ I77 - I78 * I79 <= I78 - 1 /\ 0 <= I77 - I78 * I79 /\ 0 = I71]
  f3(I80, I81, I82, I83) -> f5(I80, 0, I82, I83) [0 <= I82 - 1 /\ -1 <= I83 - 1 /\ I82 <= I83 /\ 0 <= I84 - 1 /\ 0 <= I85 - 1 /\ I86 <= I80 /\ 0 <= I80 - 1 /\ 0 <= I86 - 1 /\ 0 = I81]
  f5(I87, I88, I89, I90) -> f3(I91, 0, 1, I90) [-1 <= I90 - 1 /\ I91 <= I87 /\ 0 <= I87 - 1 /\ 0 <= I91 - 1 /\ 1 - I92 * I93 <= I92 - 1 /\ I92 * I93 <= 1 /\ 0 = I88 /\ 0 = I89]
  f3(I94, I95, I96, I97) -> f5(I94, 0, 0, I97) [-1 <= I97 - 1 /\ I98 <= I94 /\ 0 <= I94 - 1 /\ 0 <= I98 - 1 /\ 0 = I95 /\ 0 = I96]
  f5(I99, I100, I101, I102) -> f3(I103, 0, I101 + 1, I102) [-1 <= I102 - 1 /\ I101 <= I102 /\ I101 <= 0 /\ I103 <= I99 /\ 0 <= I99 - 1 /\ 0 <= I103 - 1 /\ 1 - I104 * I105 <= I104 - 1 /\ I104 * I105 <= 1 /\ 0 = I100]
  f3(I106, I107, I108, I109) -> f5(I106, 0, I108, I109) [-1 <= I109 - 1 /\ I108 <= I109 /\ I108 <= 0 /\ I110 <= I106 /\ 0 <= I106 - 1 /\ 0 <= I110 - 1 /\ 0 = I107]
  f3(I111, I112, I113, I114) -> f4(I112 - I113, I115, I116, I117) [I112 <= I114 /\ I113 <= I114 /\ 0 <= I112 - 1 /\ 0 <= I118 - 1 /\ I113 <= I112 /\ 0 <= I119 - 1 /\ 0 <= I120 - 1 /\ 0 <= I113 - 1 /\ 0 <= I111 - 1]
  f3(I121, I122, I123, I124) -> f4(I122 - I123, I125, I126, I127) [I122 <= I124 /\ I123 <= I124 /\ 0 <= I122 - 1 /\ 0 <= I128 - 1 /\ I123 <= I122 /\ 1 <= I122 - I123 /\ 0 <= I129 - 1 /\ I123 <= 0 /\ 0 <= I121 - 1]
  f3(I130, I131, I132, I133) -> f4(0 - I132, I134, I135, I136) [I132 <= I133 /\ 0 <= I132 - 1 /\ -1 <= I133 - 1 /\ I132 <= 0 /\ 0 <= I137 - 1 /\ 0 <= I130 - 1 /\ 0 = I131]
  f3(I138, I139, I140, I141) -> f4(0 - I140, I142, I143, I144) [0 = I139 /\ 0 <= I138 - 1 /\ I140 <= 0 /\ I140 <= I141 /\ -1 <= I141 - 1]
  f3(I145, I146, I147, I148) -> f4(I147 - I146, I149, I150, I151) [0 <= I147 - 1 /\ I146 <= I148 /\ I147 <= I148 /\ 0 <= I152 - 1 /\ I146 <= I147 - 1 /\ 0 <= I153 - 1 /\ 0 <= I154 - 1 /\ 0 <= I146 - 1 /\ 0 <= I145 - 1]
  f3(I155, I156, I157, I158) -> f4(I157, I159, I160, I161) [0 <= I157 - 1 /\ -1 <= I158 - 1 /\ I157 <= I158 /\ 0 <= I162 - 1 /\ 0 <= I163 - 1 /\ 0 <= I155 - 1 /\ 0 = I156]
  f3(I164, I165, I166, I167) -> f4(I166, I168, I169, I170) [I165 <= I167 /\ I166 <= I167 /\ 0 <= I165 - 1 /\ 0 <= I171 - 1 /\ I166 <= I165 /\ 0 <= I164 - 1]
  f3(I172, I173, I174, I175) -> f4(I174, I176, I177, I178) [0 = I173 /\ 0 <= I172 - 1 /\ I174 <= 0 /\ I174 <= I175 /\ -1 <= I175 - 1]
  f3(I179, I180, I181, I182) -> f4(I180, I183, I184, I185) [0 <= I181 - 1 /\ I180 <= I182 /\ I181 <= I182 /\ 0 <= I186 - 1 /\ I180 <= I181 - 1 /\ 0 <= I179 - 1]
  f3(I187, I188, I189, I190) -> f4(I188, I191, I192, I193) [0 <= I187 - 1 /\ I189 <= I188 /\ I189 <= I190 /\ I188 <= I190]
  f3(I194, I195, I196, I197) -> f4(I196, I198, I199, I200) [0 <= I194 - 1 /\ I195 <= I196 - 1 /\ I196 <= I197 /\ I195 <= I197 /\ 0 <= I196 - 1]
  f3(I201, I202, I203, I204) -> f2(I205, I202 + 1, I204, I206) [0 <= I205 - 1 /\ 0 <= I201 - 1 /\ I205 <= I201 /\ -1 <= I204 - 1 /\ I204 <= I203 - 1]
  f2(I207, I208, I209, I210) -> f3(I211, I208, 0, I209) [0 <= I211 - 1 /\ 0 <= I207 - 1 /\ I211 <= I207 /\ -1 <= I209 - 1 /\ I208 <= I209]
  f1(I212, I213, I214, I215) -> f2(I216, 0, I213, I217) [0 <= I216 - 1 /\ 0 <= I212 - 1 /\ -1 <= I213 - 1 /\ I216 <= I212]

We use the reverse value criterion with the projection function NU:
  NU[f3#(z1,z2,z3,z4)] = 0 + -1 * z3
  NU[f5#(z1,z2,z3,z4)] = 0 + -1 * (z3 + 1)

This gives the following inequalities:
  I40 <= I42 /\ I41 <= I42 /\ 0 <= I40 - 1 /\ 0 <= I44 - 1 /\ I41 <= I40 /\ 1 <= I40 - I41 /\ 0 <= I45 - 1 /\ I41 <= 0 /\ -1 <= I42 - 1 /\ I43 <= I39 /\ 0 <= I39 - 1 /\ 0 <= I43 - 1 /\ I46 - I47 * I48 <= I47 - 1 /\ 0 <= I46 - I47 * I48  ==>  0 + -1 * (I41 + 1) >= 0 + -1 * (I41 + 1)
  I50 <= I52 /\ I51 <= I52 /\ 0 <= I50 - 1 /\ 0 <= I53 - 1 /\ I51 <= I50 /\ 1 <= I50 - I51 /\ 0 <= I54 - 1 /\ I51 <= 0 /\ -1 <= I52 - 1 /\ I55 <= I49 /\ 0 <= I49 - 1 /\ 0 <= I55 - 1  ==>  0 + -1 * I51 > 0 + -1 * (I51 + 1)  with  0 + -1 * I51 >= 0

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f5#(I39, I40, I41, I42) -> f3#(I43, I40, I41 + 1, I42) [I40 <= I42 /\ I41 <= I42 /\ 0 <= I40 - 1 /\ 0 <= I44 - 1 /\ I41 <= I40 /\ 1 <= I40 - I41 /\ 0 <= I45 - 1 /\ I41 <= 0 /\ -1 <= I42 - 1 /\ I43 <= I39 /\ 0 <= I39 - 1 /\ 0 <= I43 - 1 /\ I46 - I47 * I48 <= I47 - 1 /\ 0 <= I46 - I47 * I48]
R = 
  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
  f4(I0, I1, I2, I3) -> f4(I0 - 1, I4, I5, I6) [I0 - 1 <= I0 - 1 /\ 0 <= I0 - 1]
  f5(I7, I8, I9, I10) -> f3(I11, I8, I9 + 1, I10) [I8 <= I10 /\ I9 <= I10 /\ 0 <= I8 - 1 /\ 0 <= y1 - 1 /\ I9 <= I8 /\ 0 <= y2 - 1 /\ 0 <= y3 - 1 /\ 0 <= I9 - 1 /\ -1 <= I10 - 1 /\ I11 <= I7 /\ 0 <= I7 - 1 /\ 0 <= I11 - 1 /\ y5 - y4 * y6 <= y4 - 1 /\ 0 <= y5 - y4 * y6]
  f3(I12, I13, I14, I15) -> f5(I12, I13, I14, I15) [I13 <= I15 /\ I14 <= I15 /\ 0 <= I13 - 1 /\ 0 <= I16 - 1 /\ I14 <= I13 /\ 0 <= I17 - 1 /\ 0 <= I18 - 1 /\ 0 <= I14 - 1 /\ -1 <= I15 - 1 /\ I19 <= I12 /\ 0 <= I12 - 1 /\ 0 <= I19 - 1]
  f5(I20, I21, I22, I23) -> f3(I24, I21, I22 + 1, I23) [0 <= I22 - 1 /\ I21 <= I23 /\ I22 <= I23 /\ 0 <= I25 - 1 /\ I21 <= I22 - 1 /\ 0 <= I26 - 1 /\ 0 <= I27 - 1 /\ 0 <= I21 - 1 /\ -1 <= I23 - 1 /\ I24 <= I20 /\ 0 <= I20 - 1 /\ 0 <= I24 - 1 /\ I28 - I29 * I30 <= I29 - 1 /\ 0 <= I28 - I29 * I30]
  f3(I31, I32, I33, I34) -> f5(I31, I32, I33, I34) [0 <= I33 - 1 /\ I32 <= I34 /\ I33 <= I34 /\ 0 <= I35 - 1 /\ I32 <= I33 - 1 /\ 0 <= I36 - 1 /\ 0 <= I37 - 1 /\ 0 <= I32 - 1 /\ -1 <= I34 - 1 /\ I38 <= I31 /\ 0 <= I31 - 1 /\ 0 <= I38 - 1]
  f5(I39, I40, I41, I42) -> f3(I43, I40, I41 + 1, I42) [I40 <= I42 /\ I41 <= I42 /\ 0 <= I40 - 1 /\ 0 <= I44 - 1 /\ I41 <= I40 /\ 1 <= I40 - I41 /\ 0 <= I45 - 1 /\ I41 <= 0 /\ -1 <= I42 - 1 /\ I43 <= I39 /\ 0 <= I39 - 1 /\ 0 <= I43 - 1 /\ I46 - I47 * I48 <= I47 - 1 /\ 0 <= I46 - I47 * I48]
  f3(I49, I50, I51, I52) -> f5(I49, I50, I51, I52) [I50 <= I52 /\ I51 <= I52 /\ 0 <= I50 - 1 /\ 0 <= I53 - 1 /\ I51 <= I50 /\ 1 <= I50 - I51 /\ 0 <= I54 - 1 /\ I51 <= 0 /\ -1 <= I52 - 1 /\ I55 <= I49 /\ 0 <= I49 - 1 /\ 0 <= I55 - 1]
  f5(I56, I57, I58, I59) -> f3(I60, 0, I58 + 1, I59) [I58 <= I59 /\ 0 <= I58 - 1 /\ -1 <= I59 - 1 /\ I58 <= 0 /\ 0 <= I61 - 1 /\ I60 <= I56 /\ 0 <= I56 - 1 /\ 0 <= I60 - 1 /\ 1 - I62 * I63 <= I62 - 1 /\ I62 * I63 <= 1 /\ 0 = I57]
  f3(I64, I65, I66, I67) -> f5(I64, 0, I66, I67) [I66 <= I67 /\ 0 <= I66 - 1 /\ -1 <= I67 - 1 /\ I66 <= 0 /\ 0 <= I68 - 1 /\ I69 <= I64 /\ 0 <= I64 - 1 /\ 0 <= I69 - 1 /\ 0 = I65]
  f5(I70, I71, I72, I73) -> f3(I74, 0, I72 + 1, I73) [0 <= I72 - 1 /\ -1 <= I73 - 1 /\ I72 <= I73 /\ 0 <= I75 - 1 /\ 0 <= I76 - 1 /\ I74 <= I70 /\ 0 <= I70 - 1 /\ 0 <= I74 - 1 /\ I77 - I78 * I79 <= I78 - 1 /\ 0 <= I77 - I78 * I79 /\ 0 = I71]
  f3(I80, I81, I82, I83) -> f5(I80, 0, I82, I83) [0 <= I82 - 1 /\ -1 <= I83 - 1 /\ I82 <= I83 /\ 0 <= I84 - 1 /\ 0 <= I85 - 1 /\ I86 <= I80 /\ 0 <= I80 - 1 /\ 0 <= I86 - 1 /\ 0 = I81]
  f5(I87, I88, I89, I90) -> f3(I91, 0, 1, I90) [-1 <= I90 - 1 /\ I91 <= I87 /\ 0 <= I87 - 1 /\ 0 <= I91 - 1 /\ 1 - I92 * I93 <= I92 - 1 /\ I92 * I93 <= 1 /\ 0 = I88 /\ 0 = I89]
  f3(I94, I95, I96, I97) -> f5(I94, 0, 0, I97) [-1 <= I97 - 1 /\ I98 <= I94 /\ 0 <= I94 - 1 /\ 0 <= I98 - 1 /\ 0 = I95 /\ 0 = I96]
  f5(I99, I100, I101, I102) -> f3(I103, 0, I101 + 1, I102) [-1 <= I102 - 1 /\ I101 <= I102 /\ I101 <= 0 /\ I103 <= I99 /\ 0 <= I99 - 1 /\ 0 <= I103 - 1 /\ 1 - I104 * I105 <= I104 - 1 /\ I104 * I105 <= 1 /\ 0 = I100]
  f3(I106, I107, I108, I109) -> f5(I106, 0, I108, I109) [-1 <= I109 - 1 /\ I108 <= I109 /\ I108 <= 0 /\ I110 <= I106 /\ 0 <= I106 - 1 /\ 0 <= I110 - 1 /\ 0 = I107]
  f3(I111, I112, I113, I114) -> f4(I112 - I113, I115, I116, I117) [I112 <= I114 /\ I113 <= I114 /\ 0 <= I112 - 1 /\ 0 <= I118 - 1 /\ I113 <= I112 /\ 0 <= I119 - 1 /\ 0 <= I120 - 1 /\ 0 <= I113 - 1 /\ 0 <= I111 - 1]
  f3(I121, I122, I123, I124) -> f4(I122 - I123, I125, I126, I127) [I122 <= I124 /\ I123 <= I124 /\ 0 <= I122 - 1 /\ 0 <= I128 - 1 /\ I123 <= I122 /\ 1 <= I122 - I123 /\ 0 <= I129 - 1 /\ I123 <= 0 /\ 0 <= I121 - 1]
  f3(I130, I131, I132, I133) -> f4(0 - I132, I134, I135, I136) [I132 <= I133 /\ 0 <= I132 - 1 /\ -1 <= I133 - 1 /\ I132 <= 0 /\ 0 <= I137 - 1 /\ 0 <= I130 - 1 /\ 0 = I131]
  f3(I138, I139, I140, I141) -> f4(0 - I140, I142, I143, I144) [0 = I139 /\ 0 <= I138 - 1 /\ I140 <= 0 /\ I140 <= I141 /\ -1 <= I141 - 1]
  f3(I145, I146, I147, I148) -> f4(I147 - I146, I149, I150, I151) [0 <= I147 - 1 /\ I146 <= I148 /\ I147 <= I148 /\ 0 <= I152 - 1 /\ I146 <= I147 - 1 /\ 0 <= I153 - 1 /\ 0 <= I154 - 1 /\ 0 <= I146 - 1 /\ 0 <= I145 - 1]
  f3(I155, I156, I157, I158) -> f4(I157, I159, I160, I161) [0 <= I157 - 1 /\ -1 <= I158 - 1 /\ I157 <= I158 /\ 0 <= I162 - 1 /\ 0 <= I163 - 1 /\ 0 <= I155 - 1 /\ 0 = I156]
  f3(I164, I165, I166, I167) -> f4(I166, I168, I169, I170) [I165 <= I167 /\ I166 <= I167 /\ 0 <= I165 - 1 /\ 0 <= I171 - 1 /\ I166 <= I165 /\ 0 <= I164 - 1]
  f3(I172, I173, I174, I175) -> f4(I174, I176, I177, I178) [0 = I173 /\ 0 <= I172 - 1 /\ I174 <= 0 /\ I174 <= I175 /\ -1 <= I175 - 1]
  f3(I179, I180, I181, I182) -> f4(I180, I183, I184, I185) [0 <= I181 - 1 /\ I180 <= I182 /\ I181 <= I182 /\ 0 <= I186 - 1 /\ I180 <= I181 - 1 /\ 0 <= I179 - 1]
  f3(I187, I188, I189, I190) -> f4(I188, I191, I192, I193) [0 <= I187 - 1 /\ I189 <= I188 /\ I189 <= I190 /\ I188 <= I190]
  f3(I194, I195, I196, I197) -> f4(I196, I198, I199, I200) [0 <= I194 - 1 /\ I195 <= I196 - 1 /\ I196 <= I197 /\ I195 <= I197 /\ 0 <= I196 - 1]
  f3(I201, I202, I203, I204) -> f2(I205, I202 + 1, I204, I206) [0 <= I205 - 1 /\ 0 <= I201 - 1 /\ I205 <= I201 /\ -1 <= I204 - 1 /\ I204 <= I203 - 1]
  f2(I207, I208, I209, I210) -> f3(I211, I208, 0, I209) [0 <= I211 - 1 /\ 0 <= I207 - 1 /\ I211 <= I207 /\ -1 <= I209 - 1 /\ I208 <= I209]
  f1(I212, I213, I214, I215) -> f2(I216, 0, I213, I217) [0 <= I216 - 1 /\ 0 <= I212 - 1 /\ -1 <= I213 - 1 /\ I216 <= I212]

The dependency graph for this problem is:
  6 -> 
Where:
  6) f5#(I39, I40, I41, I42) -> f3#(I43, I40, I41 + 1, I42) [I40 <= I42 /\ I41 <= I42 /\ 0 <= I40 - 1 /\ 0 <= I44 - 1 /\ I41 <= I40 /\ 1 <= I40 - I41 /\ 0 <= I45 - 1 /\ I41 <= 0 /\ -1 <= I42 - 1 /\ I43 <= I39 /\ 0 <= I39 - 1 /\ 0 <= I43 - 1 /\ I46 - I47 * I48 <= I47 - 1 /\ 0 <= I46 - I47 * I48]

We have the following SCCs.