/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 =
  f15#(x1, x2, x3, x4, x5, x6, x7, x8) -> f14#(x1, x2, x3, x4, x5, x6, x7, x8) 
  f14#(I0, I1, I2, I3, I4, I5, I6, I7) -> f1#(I0, I1, I2, 0, I4, 0, rnd7, rnd8) [rnd7 = rnd7 /\ rnd8 = rnd8 /\ y1 = 0]
  f2#(I8, I9, I10, I11, I12, I13, I14, I15) -> f1#(I8, I9, I10, 1 + I11, I12, I13, I14, I15) [1 + I11 <= I8]
  f2#(I16, I17, I18, I19, I20, I21, I22, I23) -> f6#(I16, I17, I18, I19, 0, I21, I22, I23) [I16 <= I19 /\ I24 = 0]
  f5#(I25, I26, I27, I28, I29, I30, I31, I32) -> f3#(I25, I26, I27, I28, I29, I30, I31, I32) 
  f7#(I33, I34, I35, I36, I37, I38, I39, I40) -> f6#(I33, I34, I35, I36, 1 + I37, I38, I39, I40) [1 + I37 <= I33]
  f7#(I41, I42, I43, I44, I45, I46, I47, I48) -> f10#(I41, I42, I43, I44, I45, 0, I47, I48) [I41 <= I45]
  f9#(I49, I50, I51, I52, I53, I54, I55, I56) -> f8#(I49, I50, I51, I52, I53, I54, I55, I56) 
  f11#(I57, I58, I59, I60, I61, I62, I63, I64) -> f10#(I57, I58, I59, I60, I61, 1 + I62, I63, I64) [1 + I62 <= I57]
  f11#(I65, I66, I67, I68, I69, I70, I71, I72) -> f13#(I65, 0, I67, I68, I69, I70, I71, I72) [I65 <= I70 /\ I73 = 0]
  f13#(I74, I75, I76, I77, I78, I79, I80, I81) -> f12#(I74, I75, I76, I77, I78, I79, I80, I81) 
  f12#(I82, I83, I84, I85, I86, I87, I88, I89) -> f13#(I82, 1 + I83, I84, I85, I86, I87, I88, I89) [1 + I83 <= I82]
  f12#(I90, I91, I92, I93, I94, I95, I96, I97) -> f9#(I90, I91, 0, I93, I94, I95, I96, I97) [I90 <= I91 /\ I98 = 0]
  f10#(I99, I100, I101, I102, I103, I104, I105, I106) -> f11#(I99, I100, I101, I102, I103, I104, I105, I106) 
  f8#(I107, I108, I109, I110, I111, I112, I113, I114) -> f9#(I107, I108, 1 + I109, I110, I111, I112, I113, I114) [1 + I109 <= I107]
  f8#(I115, I116, I117, I118, I119, I120, I121, I122) -> f5#(I115, I116, I117, I118, I119, 0, I121, I122) [I115 <= I117]
  f6#(I123, I124, I125, I126, I127, I128, I129, I130) -> f7#(I123, I124, I125, I126, I127, I128, I129, I130) 
  f3#(I131, I132, I133, I134, I135, I136, I137, I138) -> f5#(I131, I132, I133, I134, I135, 1 + I136, I137, I138) [1 + I136 <= I131]
  f1#(I147, I148, I149, I150, I151, I152, I153, I154) -> f2#(I147, I148, I149, I150, I151, I152, I153, I154) 
R = 
  f15(x1, x2, x3, x4, x5, x6, x7, x8) -> f14(x1, x2, x3, x4, x5, x6, x7, x8) 
  f14(I0, I1, I2, I3, I4, I5, I6, I7) -> f1(I0, I1, I2, 0, I4, 0, rnd7, rnd8) [rnd7 = rnd7 /\ rnd8 = rnd8 /\ y1 = 0]
  f2(I8, I9, I10, I11, I12, I13, I14, I15) -> f1(I8, I9, I10, 1 + I11, I12, I13, I14, I15) [1 + I11 <= I8]
  f2(I16, I17, I18, I19, I20, I21, I22, I23) -> f6(I16, I17, I18, I19, 0, I21, I22, I23) [I16 <= I19 /\ I24 = 0]
  f5(I25, I26, I27, I28, I29, I30, I31, I32) -> f3(I25, I26, I27, I28, I29, I30, I31, I32) 
  f7(I33, I34, I35, I36, I37, I38, I39, I40) -> f6(I33, I34, I35, I36, 1 + I37, I38, I39, I40) [1 + I37 <= I33]
  f7(I41, I42, I43, I44, I45, I46, I47, I48) -> f10(I41, I42, I43, I44, I45, 0, I47, I48) [I41 <= I45]
  f9(I49, I50, I51, I52, I53, I54, I55, I56) -> f8(I49, I50, I51, I52, I53, I54, I55, I56) 
  f11(I57, I58, I59, I60, I61, I62, I63, I64) -> f10(I57, I58, I59, I60, I61, 1 + I62, I63, I64) [1 + I62 <= I57]
  f11(I65, I66, I67, I68, I69, I70, I71, I72) -> f13(I65, 0, I67, I68, I69, I70, I71, I72) [I65 <= I70 /\ I73 = 0]
  f13(I74, I75, I76, I77, I78, I79, I80, I81) -> f12(I74, I75, I76, I77, I78, I79, I80, I81) 
  f12(I82, I83, I84, I85, I86, I87, I88, I89) -> f13(I82, 1 + I83, I84, I85, I86, I87, I88, I89) [1 + I83 <= I82]
  f12(I90, I91, I92, I93, I94, I95, I96, I97) -> f9(I90, I91, 0, I93, I94, I95, I96, I97) [I90 <= I91 /\ I98 = 0]
  f10(I99, I100, I101, I102, I103, I104, I105, I106) -> f11(I99, I100, I101, I102, I103, I104, I105, I106) 
  f8(I107, I108, I109, I110, I111, I112, I113, I114) -> f9(I107, I108, 1 + I109, I110, I111, I112, I113, I114) [1 + I109 <= I107]
  f8(I115, I116, I117, I118, I119, I120, I121, I122) -> f5(I115, I116, I117, I118, I119, 0, I121, I122) [I115 <= I117]
  f6(I123, I124, I125, I126, I127, I128, I129, I130) -> f7(I123, I124, I125, I126, I127, I128, I129, I130) 
  f3(I131, I132, I133, I134, I135, I136, I137, I138) -> f5(I131, I132, I133, I134, I135, 1 + I136, I137, I138) [1 + I136 <= I131]
  f3(I139, I140, I141, I142, I143, I144, I145, I146) -> f4(I139, I140, I141, I142, I143, I144, I145, I146) [I139 <= I144]
  f1(I147, I148, I149, I150, I151, I152, I153, I154) -> f2(I147, I148, I149, I150, I151, I152, I153, I154) 

The dependency graph for this problem is:
  0 -> 1
  1 -> 18
  2 -> 18
  3 -> 16
  4 -> 17
  5 -> 16
  6 -> 13
  7 -> 14, 15
  8 -> 13
  9 -> 10
  10 -> 11, 12
  11 -> 10
  12 -> 7
  13 -> 8, 9
  14 -> 7
  15 -> 4
  16 -> 5, 6
  17 -> 4
  18 -> 2, 3
Where:
  0) f15#(x1, x2, x3, x4, x5, x6, x7, x8) -> f14#(x1, x2, x3, x4, x5, x6, x7, x8) 
  1) f14#(I0, I1, I2, I3, I4, I5, I6, I7) -> f1#(I0, I1, I2, 0, I4, 0, rnd7, rnd8) [rnd7 = rnd7 /\ rnd8 = rnd8 /\ y1 = 0]
  2) f2#(I8, I9, I10, I11, I12, I13, I14, I15) -> f1#(I8, I9, I10, 1 + I11, I12, I13, I14, I15) [1 + I11 <= I8]
  3) f2#(I16, I17, I18, I19, I20, I21, I22, I23) -> f6#(I16, I17, I18, I19, 0, I21, I22, I23) [I16 <= I19 /\ I24 = 0]
  4) f5#(I25, I26, I27, I28, I29, I30, I31, I32) -> f3#(I25, I26, I27, I28, I29, I30, I31, I32) 
  5) f7#(I33, I34, I35, I36, I37, I38, I39, I40) -> f6#(I33, I34, I35, I36, 1 + I37, I38, I39, I40) [1 + I37 <= I33]
  6) f7#(I41, I42, I43, I44, I45, I46, I47, I48) -> f10#(I41, I42, I43, I44, I45, 0, I47, I48) [I41 <= I45]
  7) f9#(I49, I50, I51, I52, I53, I54, I55, I56) -> f8#(I49, I50, I51, I52, I53, I54, I55, I56) 
  8) f11#(I57, I58, I59, I60, I61, I62, I63, I64) -> f10#(I57, I58, I59, I60, I61, 1 + I62, I63, I64) [1 + I62 <= I57]
  9) f11#(I65, I66, I67, I68, I69, I70, I71, I72) -> f13#(I65, 0, I67, I68, I69, I70, I71, I72) [I65 <= I70 /\ I73 = 0]
  10) f13#(I74, I75, I76, I77, I78, I79, I80, I81) -> f12#(I74, I75, I76, I77, I78, I79, I80, I81) 
  11) f12#(I82, I83, I84, I85, I86, I87, I88, I89) -> f13#(I82, 1 + I83, I84, I85, I86, I87, I88, I89) [1 + I83 <= I82]
  12) f12#(I90, I91, I92, I93, I94, I95, I96, I97) -> f9#(I90, I91, 0, I93, I94, I95, I96, I97) [I90 <= I91 /\ I98 = 0]
  13) f10#(I99, I100, I101, I102, I103, I104, I105, I106) -> f11#(I99, I100, I101, I102, I103, I104, I105, I106) 
  14) f8#(I107, I108, I109, I110, I111, I112, I113, I114) -> f9#(I107, I108, 1 + I109, I110, I111, I112, I113, I114) [1 + I109 <= I107]
  15) f8#(I115, I116, I117, I118, I119, I120, I121, I122) -> f5#(I115, I116, I117, I118, I119, 0, I121, I122) [I115 <= I117]
  16) f6#(I123, I124, I125, I126, I127, I128, I129, I130) -> f7#(I123, I124, I125, I126, I127, I128, I129, I130) 
  17) f3#(I131, I132, I133, I134, I135, I136, I137, I138) -> f5#(I131, I132, I133, I134, I135, 1 + I136, I137, I138) [1 + I136 <= I131]
  18) f1#(I147, I148, I149, I150, I151, I152, I153, I154) -> f2#(I147, I148, I149, I150, I151, I152, I153, I154) 

We have the following SCCs.
  { 2, 18 }
  { 5, 16 }
  { 8, 13 }
  { 10, 11 }
  { 7, 14 }
  { 4, 17 }

DP problem for innermost termination.
P =
  f5#(I25, I26, I27, I28, I29, I30, I31, I32) -> f3#(I25, I26, I27, I28, I29, I30, I31, I32) 
  f3#(I131, I132, I133, I134, I135, I136, I137, I138) -> f5#(I131, I132, I133, I134, I135, 1 + I136, I137, I138) [1 + I136 <= I131]
R = 
  f15(x1, x2, x3, x4, x5, x6, x7, x8) -> f14(x1, x2, x3, x4, x5, x6, x7, x8) 
  f14(I0, I1, I2, I3, I4, I5, I6, I7) -> f1(I0, I1, I2, 0, I4, 0, rnd7, rnd8) [rnd7 = rnd7 /\ rnd8 = rnd8 /\ y1 = 0]
  f2(I8, I9, I10, I11, I12, I13, I14, I15) -> f1(I8, I9, I10, 1 + I11, I12, I13, I14, I15) [1 + I11 <= I8]
  f2(I16, I17, I18, I19, I20, I21, I22, I23) -> f6(I16, I17, I18, I19, 0, I21, I22, I23) [I16 <= I19 /\ I24 = 0]
  f5(I25, I26, I27, I28, I29, I30, I31, I32) -> f3(I25, I26, I27, I28, I29, I30, I31, I32) 
  f7(I33, I34, I35, I36, I37, I38, I39, I40) -> f6(I33, I34, I35, I36, 1 + I37, I38, I39, I40) [1 + I37 <= I33]
  f7(I41, I42, I43, I44, I45, I46, I47, I48) -> f10(I41, I42, I43, I44, I45, 0, I47, I48) [I41 <= I45]
  f9(I49, I50, I51, I52, I53, I54, I55, I56) -> f8(I49, I50, I51, I52, I53, I54, I55, I56) 
  f11(I57, I58, I59, I60, I61, I62, I63, I64) -> f10(I57, I58, I59, I60, I61, 1 + I62, I63, I64) [1 + I62 <= I57]
  f11(I65, I66, I67, I68, I69, I70, I71, I72) -> f13(I65, 0, I67, I68, I69, I70, I71, I72) [I65 <= I70 /\ I73 = 0]
  f13(I74, I75, I76, I77, I78, I79, I80, I81) -> f12(I74, I75, I76, I77, I78, I79, I80, I81) 
  f12(I82, I83, I84, I85, I86, I87, I88, I89) -> f13(I82, 1 + I83, I84, I85, I86, I87, I88, I89) [1 + I83 <= I82]
  f12(I90, I91, I92, I93, I94, I95, I96, I97) -> f9(I90, I91, 0, I93, I94, I95, I96, I97) [I90 <= I91 /\ I98 = 0]
  f10(I99, I100, I101, I102, I103, I104, I105, I106) -> f11(I99, I100, I101, I102, I103, I104, I105, I106) 
  f8(I107, I108, I109, I110, I111, I112, I113, I114) -> f9(I107, I108, 1 + I109, I110, I111, I112, I113, I114) [1 + I109 <= I107]
  f8(I115, I116, I117, I118, I119, I120, I121, I122) -> f5(I115, I116, I117, I118, I119, 0, I121, I122) [I115 <= I117]
  f6(I123, I124, I125, I126, I127, I128, I129, I130) -> f7(I123, I124, I125, I126, I127, I128, I129, I130) 
  f3(I131, I132, I133, I134, I135, I136, I137, I138) -> f5(I131, I132, I133, I134, I135, 1 + I136, I137, I138) [1 + I136 <= I131]
  f3(I139, I140, I141, I142, I143, I144, I145, I146) -> f4(I139, I140, I141, I142, I143, I144, I145, I146) [I139 <= I144]
  f1(I147, I148, I149, I150, I151, I152, I153, I154) -> f2(I147, I148, I149, I150, I151, I152, I153, I154) 

We use the reverse value criterion with the projection function NU:
  NU[f3#(z1,z2,z3,z4,z5,z6,z7,z8)] = z1 + -1 * (1 + z6)
  NU[f5#(z1,z2,z3,z4,z5,z6,z7,z8)] = z1 + -1 * (1 + z6)

This gives the following inequalities:
    ==>  I25 + -1 * (1 + I30) >= I25 + -1 * (1 + I30)
  1 + I136 <= I131  ==>  I131 + -1 * (1 + I136) > I131 + -1 * (1 + (1 + I136))  with  I131 + -1 * (1 + I136) >= 0

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f5#(I25, I26, I27, I28, I29, I30, I31, I32) -> f3#(I25, I26, I27, I28, I29, I30, I31, I32) 
R = 
  f15(x1, x2, x3, x4, x5, x6, x7, x8) -> f14(x1, x2, x3, x4, x5, x6, x7, x8) 
  f14(I0, I1, I2, I3, I4, I5, I6, I7) -> f1(I0, I1, I2, 0, I4, 0, rnd7, rnd8) [rnd7 = rnd7 /\ rnd8 = rnd8 /\ y1 = 0]
  f2(I8, I9, I10, I11, I12, I13, I14, I15) -> f1(I8, I9, I10, 1 + I11, I12, I13, I14, I15) [1 + I11 <= I8]
  f2(I16, I17, I18, I19, I20, I21, I22, I23) -> f6(I16, I17, I18, I19, 0, I21, I22, I23) [I16 <= I19 /\ I24 = 0]
  f5(I25, I26, I27, I28, I29, I30, I31, I32) -> f3(I25, I26, I27, I28, I29, I30, I31, I32) 
  f7(I33, I34, I35, I36, I37, I38, I39, I40) -> f6(I33, I34, I35, I36, 1 + I37, I38, I39, I40) [1 + I37 <= I33]
  f7(I41, I42, I43, I44, I45, I46, I47, I48) -> f10(I41, I42, I43, I44, I45, 0, I47, I48) [I41 <= I45]
  f9(I49, I50, I51, I52, I53, I54, I55, I56) -> f8(I49, I50, I51, I52, I53, I54, I55, I56) 
  f11(I57, I58, I59, I60, I61, I62, I63, I64) -> f10(I57, I58, I59, I60, I61, 1 + I62, I63, I64) [1 + I62 <= I57]
  f11(I65, I66, I67, I68, I69, I70, I71, I72) -> f13(I65, 0, I67, I68, I69, I70, I71, I72) [I65 <= I70 /\ I73 = 0]
  f13(I74, I75, I76, I77, I78, I79, I80, I81) -> f12(I74, I75, I76, I77, I78, I79, I80, I81) 
  f12(I82, I83, I84, I85, I86, I87, I88, I89) -> f13(I82, 1 + I83, I84, I85, I86, I87, I88, I89) [1 + I83 <= I82]
  f12(I90, I91, I92, I93, I94, I95, I96, I97) -> f9(I90, I91, 0, I93, I94, I95, I96, I97) [I90 <= I91 /\ I98 = 0]
  f10(I99, I100, I101, I102, I103, I104, I105, I106) -> f11(I99, I100, I101, I102, I103, I104, I105, I106) 
  f8(I107, I108, I109, I110, I111, I112, I113, I114) -> f9(I107, I108, 1 + I109, I110, I111, I112, I113, I114) [1 + I109 <= I107]
  f8(I115, I116, I117, I118, I119, I120, I121, I122) -> f5(I115, I116, I117, I118, I119, 0, I121, I122) [I115 <= I117]
  f6(I123, I124, I125, I126, I127, I128, I129, I130) -> f7(I123, I124, I125, I126, I127, I128, I129, I130) 
  f3(I131, I132, I133, I134, I135, I136, I137, I138) -> f5(I131, I132, I133, I134, I135, 1 + I136, I137, I138) [1 + I136 <= I131]
  f3(I139, I140, I141, I142, I143, I144, I145, I146) -> f4(I139, I140, I141, I142, I143, I144, I145, I146) [I139 <= I144]
  f1(I147, I148, I149, I150, I151, I152, I153, I154) -> f2(I147, I148, I149, I150, I151, I152, I153, I154) 

The dependency graph for this problem is:
  4 -> 
Where:
  4) f5#(I25, I26, I27, I28, I29, I30, I31, I32) -> f3#(I25, I26, I27, I28, I29, I30, I31, I32) 

We have the following SCCs.
  

DP problem for innermost termination.
P =
  f9#(I49, I50, I51, I52, I53, I54, I55, I56) -> f8#(I49, I50, I51, I52, I53, I54, I55, I56) 
  f8#(I107, I108, I109, I110, I111, I112, I113, I114) -> f9#(I107, I108, 1 + I109, I110, I111, I112, I113, I114) [1 + I109 <= I107]
R = 
  f15(x1, x2, x3, x4, x5, x6, x7, x8) -> f14(x1, x2, x3, x4, x5, x6, x7, x8) 
  f14(I0, I1, I2, I3, I4, I5, I6, I7) -> f1(I0, I1, I2, 0, I4, 0, rnd7, rnd8) [rnd7 = rnd7 /\ rnd8 = rnd8 /\ y1 = 0]
  f2(I8, I9, I10, I11, I12, I13, I14, I15) -> f1(I8, I9, I10, 1 + I11, I12, I13, I14, I15) [1 + I11 <= I8]
  f2(I16, I17, I18, I19, I20, I21, I22, I23) -> f6(I16, I17, I18, I19, 0, I21, I22, I23) [I16 <= I19 /\ I24 = 0]
  f5(I25, I26, I27, I28, I29, I30, I31, I32) -> f3(I25, I26, I27, I28, I29, I30, I31, I32) 
  f7(I33, I34, I35, I36, I37, I38, I39, I40) -> f6(I33, I34, I35, I36, 1 + I37, I38, I39, I40) [1 + I37 <= I33]
  f7(I41, I42, I43, I44, I45, I46, I47, I48) -> f10(I41, I42, I43, I44, I45, 0, I47, I48) [I41 <= I45]
  f9(I49, I50, I51, I52, I53, I54, I55, I56) -> f8(I49, I50, I51, I52, I53, I54, I55, I56) 
  f11(I57, I58, I59, I60, I61, I62, I63, I64) -> f10(I57, I58, I59, I60, I61, 1 + I62, I63, I64) [1 + I62 <= I57]
  f11(I65, I66, I67, I68, I69, I70, I71, I72) -> f13(I65, 0, I67, I68, I69, I70, I71, I72) [I65 <= I70 /\ I73 = 0]
  f13(I74, I75, I76, I77, I78, I79, I80, I81) -> f12(I74, I75, I76, I77, I78, I79, I80, I81) 
  f12(I82, I83, I84, I85, I86, I87, I88, I89) -> f13(I82, 1 + I83, I84, I85, I86, I87, I88, I89) [1 + I83 <= I82]
  f12(I90, I91, I92, I93, I94, I95, I96, I97) -> f9(I90, I91, 0, I93, I94, I95, I96, I97) [I90 <= I91 /\ I98 = 0]
  f10(I99, I100, I101, I102, I103, I104, I105, I106) -> f11(I99, I100, I101, I102, I103, I104, I105, I106) 
  f8(I107, I108, I109, I110, I111, I112, I113, I114) -> f9(I107, I108, 1 + I109, I110, I111, I112, I113, I114) [1 + I109 <= I107]
  f8(I115, I116, I117, I118, I119, I120, I121, I122) -> f5(I115, I116, I117, I118, I119, 0, I121, I122) [I115 <= I117]
  f6(I123, I124, I125, I126, I127, I128, I129, I130) -> f7(I123, I124, I125, I126, I127, I128, I129, I130) 
  f3(I131, I132, I133, I134, I135, I136, I137, I138) -> f5(I131, I132, I133, I134, I135, 1 + I136, I137, I138) [1 + I136 <= I131]
  f3(I139, I140, I141, I142, I143, I144, I145, I146) -> f4(I139, I140, I141, I142, I143, I144, I145, I146) [I139 <= I144]
  f1(I147, I148, I149, I150, I151, I152, I153, I154) -> f2(I147, I148, I149, I150, I151, I152, I153, I154) 

We use the reverse value criterion with the projection function NU:
  NU[f8#(z1,z2,z3,z4,z5,z6,z7,z8)] = z1 + -1 * (1 + z3)
  NU[f9#(z1,z2,z3,z4,z5,z6,z7,z8)] = z1 + -1 * (1 + z3)

This gives the following inequalities:
    ==>  I49 + -1 * (1 + I51) >= I49 + -1 * (1 + I51)
  1 + I109 <= I107  ==>  I107 + -1 * (1 + I109) > I107 + -1 * (1 + (1 + I109))  with  I107 + -1 * (1 + I109) >= 0

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f9#(I49, I50, I51, I52, I53, I54, I55, I56) -> f8#(I49, I50, I51, I52, I53, I54, I55, I56) 
R = 
  f15(x1, x2, x3, x4, x5, x6, x7, x8) -> f14(x1, x2, x3, x4, x5, x6, x7, x8) 
  f14(I0, I1, I2, I3, I4, I5, I6, I7) -> f1(I0, I1, I2, 0, I4, 0, rnd7, rnd8) [rnd7 = rnd7 /\ rnd8 = rnd8 /\ y1 = 0]
  f2(I8, I9, I10, I11, I12, I13, I14, I15) -> f1(I8, I9, I10, 1 + I11, I12, I13, I14, I15) [1 + I11 <= I8]
  f2(I16, I17, I18, I19, I20, I21, I22, I23) -> f6(I16, I17, I18, I19, 0, I21, I22, I23) [I16 <= I19 /\ I24 = 0]
  f5(I25, I26, I27, I28, I29, I30, I31, I32) -> f3(I25, I26, I27, I28, I29, I30, I31, I32) 
  f7(I33, I34, I35, I36, I37, I38, I39, I40) -> f6(I33, I34, I35, I36, 1 + I37, I38, I39, I40) [1 + I37 <= I33]
  f7(I41, I42, I43, I44, I45, I46, I47, I48) -> f10(I41, I42, I43, I44, I45, 0, I47, I48) [I41 <= I45]
  f9(I49, I50, I51, I52, I53, I54, I55, I56) -> f8(I49, I50, I51, I52, I53, I54, I55, I56) 
  f11(I57, I58, I59, I60, I61, I62, I63, I64) -> f10(I57, I58, I59, I60, I61, 1 + I62, I63, I64) [1 + I62 <= I57]
  f11(I65, I66, I67, I68, I69, I70, I71, I72) -> f13(I65, 0, I67, I68, I69, I70, I71, I72) [I65 <= I70 /\ I73 = 0]
  f13(I74, I75, I76, I77, I78, I79, I80, I81) -> f12(I74, I75, I76, I77, I78, I79, I80, I81) 
  f12(I82, I83, I84, I85, I86, I87, I88, I89) -> f13(I82, 1 + I83, I84, I85, I86, I87, I88, I89) [1 + I83 <= I82]
  f12(I90, I91, I92, I93, I94, I95, I96, I97) -> f9(I90, I91, 0, I93, I94, I95, I96, I97) [I90 <= I91 /\ I98 = 0]
  f10(I99, I100, I101, I102, I103, I104, I105, I106) -> f11(I99, I100, I101, I102, I103, I104, I105, I106) 
  f8(I107, I108, I109, I110, I111, I112, I113, I114) -> f9(I107, I108, 1 + I109, I110, I111, I112, I113, I114) [1 + I109 <= I107]
  f8(I115, I116, I117, I118, I119, I120, I121, I122) -> f5(I115, I116, I117, I118, I119, 0, I121, I122) [I115 <= I117]
  f6(I123, I124, I125, I126, I127, I128, I129, I130) -> f7(I123, I124, I125, I126, I127, I128, I129, I130) 
  f3(I131, I132, I133, I134, I135, I136, I137, I138) -> f5(I131, I132, I133, I134, I135, 1 + I136, I137, I138) [1 + I136 <= I131]
  f3(I139, I140, I141, I142, I143, I144, I145, I146) -> f4(I139, I140, I141, I142, I143, I144, I145, I146) [I139 <= I144]
  f1(I147, I148, I149, I150, I151, I152, I153, I154) -> f2(I147, I148, I149, I150, I151, I152, I153, I154) 

The dependency graph for this problem is:
  7 -> 
Where:
  7) f9#(I49, I50, I51, I52, I53, I54, I55, I56) -> f8#(I49, I50, I51, I52, I53, I54, I55, I56) 

We have the following SCCs.
  

DP problem for innermost termination.
P =
  f13#(I74, I75, I76, I77, I78, I79, I80, I81) -> f12#(I74, I75, I76, I77, I78, I79, I80, I81) 
  f12#(I82, I83, I84, I85, I86, I87, I88, I89) -> f13#(I82, 1 + I83, I84, I85, I86, I87, I88, I89) [1 + I83 <= I82]
R = 
  f15(x1, x2, x3, x4, x5, x6, x7, x8) -> f14(x1, x2, x3, x4, x5, x6, x7, x8) 
  f14(I0, I1, I2, I3, I4, I5, I6, I7) -> f1(I0, I1, I2, 0, I4, 0, rnd7, rnd8) [rnd7 = rnd7 /\ rnd8 = rnd8 /\ y1 = 0]
  f2(I8, I9, I10, I11, I12, I13, I14, I15) -> f1(I8, I9, I10, 1 + I11, I12, I13, I14, I15) [1 + I11 <= I8]
  f2(I16, I17, I18, I19, I20, I21, I22, I23) -> f6(I16, I17, I18, I19, 0, I21, I22, I23) [I16 <= I19 /\ I24 = 0]
  f5(I25, I26, I27, I28, I29, I30, I31, I32) -> f3(I25, I26, I27, I28, I29, I30, I31, I32) 
  f7(I33, I34, I35, I36, I37, I38, I39, I40) -> f6(I33, I34, I35, I36, 1 + I37, I38, I39, I40) [1 + I37 <= I33]
  f7(I41, I42, I43, I44, I45, I46, I47, I48) -> f10(I41, I42, I43, I44, I45, 0, I47, I48) [I41 <= I45]
  f9(I49, I50, I51, I52, I53, I54, I55, I56) -> f8(I49, I50, I51, I52, I53, I54, I55, I56) 
  f11(I57, I58, I59, I60, I61, I62, I63, I64) -> f10(I57, I58, I59, I60, I61, 1 + I62, I63, I64) [1 + I62 <= I57]
  f11(I65, I66, I67, I68, I69, I70, I71, I72) -> f13(I65, 0, I67, I68, I69, I70, I71, I72) [I65 <= I70 /\ I73 = 0]
  f13(I74, I75, I76, I77, I78, I79, I80, I81) -> f12(I74, I75, I76, I77, I78, I79, I80, I81) 
  f12(I82, I83, I84, I85, I86, I87, I88, I89) -> f13(I82, 1 + I83, I84, I85, I86, I87, I88, I89) [1 + I83 <= I82]
  f12(I90, I91, I92, I93, I94, I95, I96, I97) -> f9(I90, I91, 0, I93, I94, I95, I96, I97) [I90 <= I91 /\ I98 = 0]
  f10(I99, I100, I101, I102, I103, I104, I105, I106) -> f11(I99, I100, I101, I102, I103, I104, I105, I106) 
  f8(I107, I108, I109, I110, I111, I112, I113, I114) -> f9(I107, I108, 1 + I109, I110, I111, I112, I113, I114) [1 + I109 <= I107]
  f8(I115, I116, I117, I118, I119, I120, I121, I122) -> f5(I115, I116, I117, I118, I119, 0, I121, I122) [I115 <= I117]
  f6(I123, I124, I125, I126, I127, I128, I129, I130) -> f7(I123, I124, I125, I126, I127, I128, I129, I130) 
  f3(I131, I132, I133, I134, I135, I136, I137, I138) -> f5(I131, I132, I133, I134, I135, 1 + I136, I137, I138) [1 + I136 <= I131]
  f3(I139, I140, I141, I142, I143, I144, I145, I146) -> f4(I139, I140, I141, I142, I143, I144, I145, I146) [I139 <= I144]
  f1(I147, I148, I149, I150, I151, I152, I153, I154) -> f2(I147, I148, I149, I150, I151, I152, I153, I154) 

We use the reverse value criterion with the projection function NU:
  NU[f12#(z1,z2,z3,z4,z5,z6,z7,z8)] = z1 + -1 * (1 + z2)
  NU[f13#(z1,z2,z3,z4,z5,z6,z7,z8)] = z1 + -1 * (1 + z2)

This gives the following inequalities:
    ==>  I74 + -1 * (1 + I75) >= I74 + -1 * (1 + I75)
  1 + I83 <= I82  ==>  I82 + -1 * (1 + I83) > I82 + -1 * (1 + (1 + I83))  with  I82 + -1 * (1 + I83) >= 0

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f13#(I74, I75, I76, I77, I78, I79, I80, I81) -> f12#(I74, I75, I76, I77, I78, I79, I80, I81) 
R = 
  f15(x1, x2, x3, x4, x5, x6, x7, x8) -> f14(x1, x2, x3, x4, x5, x6, x7, x8) 
  f14(I0, I1, I2, I3, I4, I5, I6, I7) -> f1(I0, I1, I2, 0, I4, 0, rnd7, rnd8) [rnd7 = rnd7 /\ rnd8 = rnd8 /\ y1 = 0]
  f2(I8, I9, I10, I11, I12, I13, I14, I15) -> f1(I8, I9, I10, 1 + I11, I12, I13, I14, I15) [1 + I11 <= I8]
  f2(I16, I17, I18, I19, I20, I21, I22, I23) -> f6(I16, I17, I18, I19, 0, I21, I22, I23) [I16 <= I19 /\ I24 = 0]
  f5(I25, I26, I27, I28, I29, I30, I31, I32) -> f3(I25, I26, I27, I28, I29, I30, I31, I32) 
  f7(I33, I34, I35, I36, I37, I38, I39, I40) -> f6(I33, I34, I35, I36, 1 + I37, I38, I39, I40) [1 + I37 <= I33]
  f7(I41, I42, I43, I44, I45, I46, I47, I48) -> f10(I41, I42, I43, I44, I45, 0, I47, I48) [I41 <= I45]
  f9(I49, I50, I51, I52, I53, I54, I55, I56) -> f8(I49, I50, I51, I52, I53, I54, I55, I56) 
  f11(I57, I58, I59, I60, I61, I62, I63, I64) -> f10(I57, I58, I59, I60, I61, 1 + I62, I63, I64) [1 + I62 <= I57]
  f11(I65, I66, I67, I68, I69, I70, I71, I72) -> f13(I65, 0, I67, I68, I69, I70, I71, I72) [I65 <= I70 /\ I73 = 0]
  f13(I74, I75, I76, I77, I78, I79, I80, I81) -> f12(I74, I75, I76, I77, I78, I79, I80, I81) 
  f12(I82, I83, I84, I85, I86, I87, I88, I89) -> f13(I82, 1 + I83, I84, I85, I86, I87, I88, I89) [1 + I83 <= I82]
  f12(I90, I91, I92, I93, I94, I95, I96, I97) -> f9(I90, I91, 0, I93, I94, I95, I96, I97) [I90 <= I91 /\ I98 = 0]
  f10(I99, I100, I101, I102, I103, I104, I105, I106) -> f11(I99, I100, I101, I102, I103, I104, I105, I106) 
  f8(I107, I108, I109, I110, I111, I112, I113, I114) -> f9(I107, I108, 1 + I109, I110, I111, I112, I113, I114) [1 + I109 <= I107]
  f8(I115, I116, I117, I118, I119, I120, I121, I122) -> f5(I115, I116, I117, I118, I119, 0, I121, I122) [I115 <= I117]
  f6(I123, I124, I125, I126, I127, I128, I129, I130) -> f7(I123, I124, I125, I126, I127, I128, I129, I130) 
  f3(I131, I132, I133, I134, I135, I136, I137, I138) -> f5(I131, I132, I133, I134, I135, 1 + I136, I137, I138) [1 + I136 <= I131]
  f3(I139, I140, I141, I142, I143, I144, I145, I146) -> f4(I139, I140, I141, I142, I143, I144, I145, I146) [I139 <= I144]
  f1(I147, I148, I149, I150, I151, I152, I153, I154) -> f2(I147, I148, I149, I150, I151, I152, I153, I154) 

The dependency graph for this problem is:
  10 -> 
Where:
  10) f13#(I74, I75, I76, I77, I78, I79, I80, I81) -> f12#(I74, I75, I76, I77, I78, I79, I80, I81) 

We have the following SCCs.
  

DP problem for innermost termination.
P =
  f11#(I57, I58, I59, I60, I61, I62, I63, I64) -> f10#(I57, I58, I59, I60, I61, 1 + I62, I63, I64) [1 + I62 <= I57]
  f10#(I99, I100, I101, I102, I103, I104, I105, I106) -> f11#(I99, I100, I101, I102, I103, I104, I105, I106) 
R = 
  f15(x1, x2, x3, x4, x5, x6, x7, x8) -> f14(x1, x2, x3, x4, x5, x6, x7, x8) 
  f14(I0, I1, I2, I3, I4, I5, I6, I7) -> f1(I0, I1, I2, 0, I4, 0, rnd7, rnd8) [rnd7 = rnd7 /\ rnd8 = rnd8 /\ y1 = 0]
  f2(I8, I9, I10, I11, I12, I13, I14, I15) -> f1(I8, I9, I10, 1 + I11, I12, I13, I14, I15) [1 + I11 <= I8]
  f2(I16, I17, I18, I19, I20, I21, I22, I23) -> f6(I16, I17, I18, I19, 0, I21, I22, I23) [I16 <= I19 /\ I24 = 0]
  f5(I25, I26, I27, I28, I29, I30, I31, I32) -> f3(I25, I26, I27, I28, I29, I30, I31, I32) 
  f7(I33, I34, I35, I36, I37, I38, I39, I40) -> f6(I33, I34, I35, I36, 1 + I37, I38, I39, I40) [1 + I37 <= I33]
  f7(I41, I42, I43, I44, I45, I46, I47, I48) -> f10(I41, I42, I43, I44, I45, 0, I47, I48) [I41 <= I45]
  f9(I49, I50, I51, I52, I53, I54, I55, I56) -> f8(I49, I50, I51, I52, I53, I54, I55, I56) 
  f11(I57, I58, I59, I60, I61, I62, I63, I64) -> f10(I57, I58, I59, I60, I61, 1 + I62, I63, I64) [1 + I62 <= I57]
  f11(I65, I66, I67, I68, I69, I70, I71, I72) -> f13(I65, 0, I67, I68, I69, I70, I71, I72) [I65 <= I70 /\ I73 = 0]
  f13(I74, I75, I76, I77, I78, I79, I80, I81) -> f12(I74, I75, I76, I77, I78, I79, I80, I81) 
  f12(I82, I83, I84, I85, I86, I87, I88, I89) -> f13(I82, 1 + I83, I84, I85, I86, I87, I88, I89) [1 + I83 <= I82]
  f12(I90, I91, I92, I93, I94, I95, I96, I97) -> f9(I90, I91, 0, I93, I94, I95, I96, I97) [I90 <= I91 /\ I98 = 0]
  f10(I99, I100, I101, I102, I103, I104, I105, I106) -> f11(I99, I100, I101, I102, I103, I104, I105, I106) 
  f8(I107, I108, I109, I110, I111, I112, I113, I114) -> f9(I107, I108, 1 + I109, I110, I111, I112, I113, I114) [1 + I109 <= I107]
  f8(I115, I116, I117, I118, I119, I120, I121, I122) -> f5(I115, I116, I117, I118, I119, 0, I121, I122) [I115 <= I117]
  f6(I123, I124, I125, I126, I127, I128, I129, I130) -> f7(I123, I124, I125, I126, I127, I128, I129, I130) 
  f3(I131, I132, I133, I134, I135, I136, I137, I138) -> f5(I131, I132, I133, I134, I135, 1 + I136, I137, I138) [1 + I136 <= I131]
  f3(I139, I140, I141, I142, I143, I144, I145, I146) -> f4(I139, I140, I141, I142, I143, I144, I145, I146) [I139 <= I144]
  f1(I147, I148, I149, I150, I151, I152, I153, I154) -> f2(I147, I148, I149, I150, I151, I152, I153, I154) 

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

This gives the following inequalities:
  1 + I62 <= I57  ==>  I57 + -1 * (1 + I62) > I57 + -1 * (1 + (1 + I62))  with  I57 + -1 * (1 + I62) >= 0
    ==>  I99 + -1 * (1 + I104) >= I99 + -1 * (1 + I104)

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f10#(I99, I100, I101, I102, I103, I104, I105, I106) -> f11#(I99, I100, I101, I102, I103, I104, I105, I106) 
R = 
  f15(x1, x2, x3, x4, x5, x6, x7, x8) -> f14(x1, x2, x3, x4, x5, x6, x7, x8) 
  f14(I0, I1, I2, I3, I4, I5, I6, I7) -> f1(I0, I1, I2, 0, I4, 0, rnd7, rnd8) [rnd7 = rnd7 /\ rnd8 = rnd8 /\ y1 = 0]
  f2(I8, I9, I10, I11, I12, I13, I14, I15) -> f1(I8, I9, I10, 1 + I11, I12, I13, I14, I15) [1 + I11 <= I8]
  f2(I16, I17, I18, I19, I20, I21, I22, I23) -> f6(I16, I17, I18, I19, 0, I21, I22, I23) [I16 <= I19 /\ I24 = 0]
  f5(I25, I26, I27, I28, I29, I30, I31, I32) -> f3(I25, I26, I27, I28, I29, I30, I31, I32) 
  f7(I33, I34, I35, I36, I37, I38, I39, I40) -> f6(I33, I34, I35, I36, 1 + I37, I38, I39, I40) [1 + I37 <= I33]
  f7(I41, I42, I43, I44, I45, I46, I47, I48) -> f10(I41, I42, I43, I44, I45, 0, I47, I48) [I41 <= I45]
  f9(I49, I50, I51, I52, I53, I54, I55, I56) -> f8(I49, I50, I51, I52, I53, I54, I55, I56) 
  f11(I57, I58, I59, I60, I61, I62, I63, I64) -> f10(I57, I58, I59, I60, I61, 1 + I62, I63, I64) [1 + I62 <= I57]
  f11(I65, I66, I67, I68, I69, I70, I71, I72) -> f13(I65, 0, I67, I68, I69, I70, I71, I72) [I65 <= I70 /\ I73 = 0]
  f13(I74, I75, I76, I77, I78, I79, I80, I81) -> f12(I74, I75, I76, I77, I78, I79, I80, I81) 
  f12(I82, I83, I84, I85, I86, I87, I88, I89) -> f13(I82, 1 + I83, I84, I85, I86, I87, I88, I89) [1 + I83 <= I82]
  f12(I90, I91, I92, I93, I94, I95, I96, I97) -> f9(I90, I91, 0, I93, I94, I95, I96, I97) [I90 <= I91 /\ I98 = 0]
  f10(I99, I100, I101, I102, I103, I104, I105, I106) -> f11(I99, I100, I101, I102, I103, I104, I105, I106) 
  f8(I107, I108, I109, I110, I111, I112, I113, I114) -> f9(I107, I108, 1 + I109, I110, I111, I112, I113, I114) [1 + I109 <= I107]
  f8(I115, I116, I117, I118, I119, I120, I121, I122) -> f5(I115, I116, I117, I118, I119, 0, I121, I122) [I115 <= I117]
  f6(I123, I124, I125, I126, I127, I128, I129, I130) -> f7(I123, I124, I125, I126, I127, I128, I129, I130) 
  f3(I131, I132, I133, I134, I135, I136, I137, I138) -> f5(I131, I132, I133, I134, I135, 1 + I136, I137, I138) [1 + I136 <= I131]
  f3(I139, I140, I141, I142, I143, I144, I145, I146) -> f4(I139, I140, I141, I142, I143, I144, I145, I146) [I139 <= I144]
  f1(I147, I148, I149, I150, I151, I152, I153, I154) -> f2(I147, I148, I149, I150, I151, I152, I153, I154) 

The dependency graph for this problem is:
  13 -> 
Where:
  13) f10#(I99, I100, I101, I102, I103, I104, I105, I106) -> f11#(I99, I100, I101, I102, I103, I104, I105, I106) 

We have the following SCCs.
  

DP problem for innermost termination.
P =
  f7#(I33, I34, I35, I36, I37, I38, I39, I40) -> f6#(I33, I34, I35, I36, 1 + I37, I38, I39, I40) [1 + I37 <= I33]
  f6#(I123, I124, I125, I126, I127, I128, I129, I130) -> f7#(I123, I124, I125, I126, I127, I128, I129, I130) 
R = 
  f15(x1, x2, x3, x4, x5, x6, x7, x8) -> f14(x1, x2, x3, x4, x5, x6, x7, x8) 
  f14(I0, I1, I2, I3, I4, I5, I6, I7) -> f1(I0, I1, I2, 0, I4, 0, rnd7, rnd8) [rnd7 = rnd7 /\ rnd8 = rnd8 /\ y1 = 0]
  f2(I8, I9, I10, I11, I12, I13, I14, I15) -> f1(I8, I9, I10, 1 + I11, I12, I13, I14, I15) [1 + I11 <= I8]
  f2(I16, I17, I18, I19, I20, I21, I22, I23) -> f6(I16, I17, I18, I19, 0, I21, I22, I23) [I16 <= I19 /\ I24 = 0]
  f5(I25, I26, I27, I28, I29, I30, I31, I32) -> f3(I25, I26, I27, I28, I29, I30, I31, I32) 
  f7(I33, I34, I35, I36, I37, I38, I39, I40) -> f6(I33, I34, I35, I36, 1 + I37, I38, I39, I40) [1 + I37 <= I33]
  f7(I41, I42, I43, I44, I45, I46, I47, I48) -> f10(I41, I42, I43, I44, I45, 0, I47, I48) [I41 <= I45]
  f9(I49, I50, I51, I52, I53, I54, I55, I56) -> f8(I49, I50, I51, I52, I53, I54, I55, I56) 
  f11(I57, I58, I59, I60, I61, I62, I63, I64) -> f10(I57, I58, I59, I60, I61, 1 + I62, I63, I64) [1 + I62 <= I57]
  f11(I65, I66, I67, I68, I69, I70, I71, I72) -> f13(I65, 0, I67, I68, I69, I70, I71, I72) [I65 <= I70 /\ I73 = 0]
  f13(I74, I75, I76, I77, I78, I79, I80, I81) -> f12(I74, I75, I76, I77, I78, I79, I80, I81) 
  f12(I82, I83, I84, I85, I86, I87, I88, I89) -> f13(I82, 1 + I83, I84, I85, I86, I87, I88, I89) [1 + I83 <= I82]
  f12(I90, I91, I92, I93, I94, I95, I96, I97) -> f9(I90, I91, 0, I93, I94, I95, I96, I97) [I90 <= I91 /\ I98 = 0]
  f10(I99, I100, I101, I102, I103, I104, I105, I106) -> f11(I99, I100, I101, I102, I103, I104, I105, I106) 
  f8(I107, I108, I109, I110, I111, I112, I113, I114) -> f9(I107, I108, 1 + I109, I110, I111, I112, I113, I114) [1 + I109 <= I107]
  f8(I115, I116, I117, I118, I119, I120, I121, I122) -> f5(I115, I116, I117, I118, I119, 0, I121, I122) [I115 <= I117]
  f6(I123, I124, I125, I126, I127, I128, I129, I130) -> f7(I123, I124, I125, I126, I127, I128, I129, I130) 
  f3(I131, I132, I133, I134, I135, I136, I137, I138) -> f5(I131, I132, I133, I134, I135, 1 + I136, I137, I138) [1 + I136 <= I131]
  f3(I139, I140, I141, I142, I143, I144, I145, I146) -> f4(I139, I140, I141, I142, I143, I144, I145, I146) [I139 <= I144]
  f1(I147, I148, I149, I150, I151, I152, I153, I154) -> f2(I147, I148, I149, I150, I151, I152, I153, I154) 

We use the reverse value criterion with the projection function NU:
  NU[f6#(z1,z2,z3,z4,z5,z6,z7,z8)] = z1 + -1 * (1 + z5)
  NU[f7#(z1,z2,z3,z4,z5,z6,z7,z8)] = z1 + -1 * (1 + z5)

This gives the following inequalities:
  1 + I37 <= I33  ==>  I33 + -1 * (1 + I37) > I33 + -1 * (1 + (1 + I37))  with  I33 + -1 * (1 + I37) >= 0
    ==>  I123 + -1 * (1 + I127) >= I123 + -1 * (1 + I127)

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f6#(I123, I124, I125, I126, I127, I128, I129, I130) -> f7#(I123, I124, I125, I126, I127, I128, I129, I130) 
R = 
  f15(x1, x2, x3, x4, x5, x6, x7, x8) -> f14(x1, x2, x3, x4, x5, x6, x7, x8) 
  f14(I0, I1, I2, I3, I4, I5, I6, I7) -> f1(I0, I1, I2, 0, I4, 0, rnd7, rnd8) [rnd7 = rnd7 /\ rnd8 = rnd8 /\ y1 = 0]
  f2(I8, I9, I10, I11, I12, I13, I14, I15) -> f1(I8, I9, I10, 1 + I11, I12, I13, I14, I15) [1 + I11 <= I8]
  f2(I16, I17, I18, I19, I20, I21, I22, I23) -> f6(I16, I17, I18, I19, 0, I21, I22, I23) [I16 <= I19 /\ I24 = 0]
  f5(I25, I26, I27, I28, I29, I30, I31, I32) -> f3(I25, I26, I27, I28, I29, I30, I31, I32) 
  f7(I33, I34, I35, I36, I37, I38, I39, I40) -> f6(I33, I34, I35, I36, 1 + I37, I38, I39, I40) [1 + I37 <= I33]
  f7(I41, I42, I43, I44, I45, I46, I47, I48) -> f10(I41, I42, I43, I44, I45, 0, I47, I48) [I41 <= I45]
  f9(I49, I50, I51, I52, I53, I54, I55, I56) -> f8(I49, I50, I51, I52, I53, I54, I55, I56) 
  f11(I57, I58, I59, I60, I61, I62, I63, I64) -> f10(I57, I58, I59, I60, I61, 1 + I62, I63, I64) [1 + I62 <= I57]
  f11(I65, I66, I67, I68, I69, I70, I71, I72) -> f13(I65, 0, I67, I68, I69, I70, I71, I72) [I65 <= I70 /\ I73 = 0]
  f13(I74, I75, I76, I77, I78, I79, I80, I81) -> f12(I74, I75, I76, I77, I78, I79, I80, I81) 
  f12(I82, I83, I84, I85, I86, I87, I88, I89) -> f13(I82, 1 + I83, I84, I85, I86, I87, I88, I89) [1 + I83 <= I82]
  f12(I90, I91, I92, I93, I94, I95, I96, I97) -> f9(I90, I91, 0, I93, I94, I95, I96, I97) [I90 <= I91 /\ I98 = 0]
  f10(I99, I100, I101, I102, I103, I104, I105, I106) -> f11(I99, I100, I101, I102, I103, I104, I105, I106) 
  f8(I107, I108, I109, I110, I111, I112, I113, I114) -> f9(I107, I108, 1 + I109, I110, I111, I112, I113, I114) [1 + I109 <= I107]
  f8(I115, I116, I117, I118, I119, I120, I121, I122) -> f5(I115, I116, I117, I118, I119, 0, I121, I122) [I115 <= I117]
  f6(I123, I124, I125, I126, I127, I128, I129, I130) -> f7(I123, I124, I125, I126, I127, I128, I129, I130) 
  f3(I131, I132, I133, I134, I135, I136, I137, I138) -> f5(I131, I132, I133, I134, I135, 1 + I136, I137, I138) [1 + I136 <= I131]
  f3(I139, I140, I141, I142, I143, I144, I145, I146) -> f4(I139, I140, I141, I142, I143, I144, I145, I146) [I139 <= I144]
  f1(I147, I148, I149, I150, I151, I152, I153, I154) -> f2(I147, I148, I149, I150, I151, I152, I153, I154) 

The dependency graph for this problem is:
  16 -> 
Where:
  16) f6#(I123, I124, I125, I126, I127, I128, I129, I130) -> f7#(I123, I124, I125, I126, I127, I128, I129, I130) 

We have the following SCCs.
  

DP problem for innermost termination.
P =
  f2#(I8, I9, I10, I11, I12, I13, I14, I15) -> f1#(I8, I9, I10, 1 + I11, I12, I13, I14, I15) [1 + I11 <= I8]
  f1#(I147, I148, I149, I150, I151, I152, I153, I154) -> f2#(I147, I148, I149, I150, I151, I152, I153, I154) 
R = 
  f15(x1, x2, x3, x4, x5, x6, x7, x8) -> f14(x1, x2, x3, x4, x5, x6, x7, x8) 
  f14(I0, I1, I2, I3, I4, I5, I6, I7) -> f1(I0, I1, I2, 0, I4, 0, rnd7, rnd8) [rnd7 = rnd7 /\ rnd8 = rnd8 /\ y1 = 0]
  f2(I8, I9, I10, I11, I12, I13, I14, I15) -> f1(I8, I9, I10, 1 + I11, I12, I13, I14, I15) [1 + I11 <= I8]
  f2(I16, I17, I18, I19, I20, I21, I22, I23) -> f6(I16, I17, I18, I19, 0, I21, I22, I23) [I16 <= I19 /\ I24 = 0]
  f5(I25, I26, I27, I28, I29, I30, I31, I32) -> f3(I25, I26, I27, I28, I29, I30, I31, I32) 
  f7(I33, I34, I35, I36, I37, I38, I39, I40) -> f6(I33, I34, I35, I36, 1 + I37, I38, I39, I40) [1 + I37 <= I33]
  f7(I41, I42, I43, I44, I45, I46, I47, I48) -> f10(I41, I42, I43, I44, I45, 0, I47, I48) [I41 <= I45]
  f9(I49, I50, I51, I52, I53, I54, I55, I56) -> f8(I49, I50, I51, I52, I53, I54, I55, I56) 
  f11(I57, I58, I59, I60, I61, I62, I63, I64) -> f10(I57, I58, I59, I60, I61, 1 + I62, I63, I64) [1 + I62 <= I57]
  f11(I65, I66, I67, I68, I69, I70, I71, I72) -> f13(I65, 0, I67, I68, I69, I70, I71, I72) [I65 <= I70 /\ I73 = 0]
  f13(I74, I75, I76, I77, I78, I79, I80, I81) -> f12(I74, I75, I76, I77, I78, I79, I80, I81) 
  f12(I82, I83, I84, I85, I86, I87, I88, I89) -> f13(I82, 1 + I83, I84, I85, I86, I87, I88, I89) [1 + I83 <= I82]
  f12(I90, I91, I92, I93, I94, I95, I96, I97) -> f9(I90, I91, 0, I93, I94, I95, I96, I97) [I90 <= I91 /\ I98 = 0]
  f10(I99, I100, I101, I102, I103, I104, I105, I106) -> f11(I99, I100, I101, I102, I103, I104, I105, I106) 
  f8(I107, I108, I109, I110, I111, I112, I113, I114) -> f9(I107, I108, 1 + I109, I110, I111, I112, I113, I114) [1 + I109 <= I107]
  f8(I115, I116, I117, I118, I119, I120, I121, I122) -> f5(I115, I116, I117, I118, I119, 0, I121, I122) [I115 <= I117]
  f6(I123, I124, I125, I126, I127, I128, I129, I130) -> f7(I123, I124, I125, I126, I127, I128, I129, I130) 
  f3(I131, I132, I133, I134, I135, I136, I137, I138) -> f5(I131, I132, I133, I134, I135, 1 + I136, I137, I138) [1 + I136 <= I131]
  f3(I139, I140, I141, I142, I143, I144, I145, I146) -> f4(I139, I140, I141, I142, I143, I144, I145, I146) [I139 <= I144]
  f1(I147, I148, I149, I150, I151, I152, I153, I154) -> f2(I147, I148, I149, I150, I151, I152, I153, I154) 

We use the reverse value criterion with the projection function NU:
  NU[f1#(z1,z2,z3,z4,z5,z6,z7,z8)] = z1 + -1 * (1 + z4)
  NU[f2#(z1,z2,z3,z4,z5,z6,z7,z8)] = z1 + -1 * (1 + z4)

This gives the following inequalities:
  1 + I11 <= I8  ==>  I8 + -1 * (1 + I11) > I8 + -1 * (1 + (1 + I11))  with  I8 + -1 * (1 + I11) >= 0
    ==>  I147 + -1 * (1 + I150) >= I147 + -1 * (1 + I150)

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f1#(I147, I148, I149, I150, I151, I152, I153, I154) -> f2#(I147, I148, I149, I150, I151, I152, I153, I154) 
R = 
  f15(x1, x2, x3, x4, x5, x6, x7, x8) -> f14(x1, x2, x3, x4, x5, x6, x7, x8) 
  f14(I0, I1, I2, I3, I4, I5, I6, I7) -> f1(I0, I1, I2, 0, I4, 0, rnd7, rnd8) [rnd7 = rnd7 /\ rnd8 = rnd8 /\ y1 = 0]
  f2(I8, I9, I10, I11, I12, I13, I14, I15) -> f1(I8, I9, I10, 1 + I11, I12, I13, I14, I15) [1 + I11 <= I8]
  f2(I16, I17, I18, I19, I20, I21, I22, I23) -> f6(I16, I17, I18, I19, 0, I21, I22, I23) [I16 <= I19 /\ I24 = 0]
  f5(I25, I26, I27, I28, I29, I30, I31, I32) -> f3(I25, I26, I27, I28, I29, I30, I31, I32) 
  f7(I33, I34, I35, I36, I37, I38, I39, I40) -> f6(I33, I34, I35, I36, 1 + I37, I38, I39, I40) [1 + I37 <= I33]
  f7(I41, I42, I43, I44, I45, I46, I47, I48) -> f10(I41, I42, I43, I44, I45, 0, I47, I48) [I41 <= I45]
  f9(I49, I50, I51, I52, I53, I54, I55, I56) -> f8(I49, I50, I51, I52, I53, I54, I55, I56) 
  f11(I57, I58, I59, I60, I61, I62, I63, I64) -> f10(I57, I58, I59, I60, I61, 1 + I62, I63, I64) [1 + I62 <= I57]
  f11(I65, I66, I67, I68, I69, I70, I71, I72) -> f13(I65, 0, I67, I68, I69, I70, I71, I72) [I65 <= I70 /\ I73 = 0]
  f13(I74, I75, I76, I77, I78, I79, I80, I81) -> f12(I74, I75, I76, I77, I78, I79, I80, I81) 
  f12(I82, I83, I84, I85, I86, I87, I88, I89) -> f13(I82, 1 + I83, I84, I85, I86, I87, I88, I89) [1 + I83 <= I82]
  f12(I90, I91, I92, I93, I94, I95, I96, I97) -> f9(I90, I91, 0, I93, I94, I95, I96, I97) [I90 <= I91 /\ I98 = 0]
  f10(I99, I100, I101, I102, I103, I104, I105, I106) -> f11(I99, I100, I101, I102, I103, I104, I105, I106) 
  f8(I107, I108, I109, I110, I111, I112, I113, I114) -> f9(I107, I108, 1 + I109, I110, I111, I112, I113, I114) [1 + I109 <= I107]
  f8(I115, I116, I117, I118, I119, I120, I121, I122) -> f5(I115, I116, I117, I118, I119, 0, I121, I122) [I115 <= I117]
  f6(I123, I124, I125, I126, I127, I128, I129, I130) -> f7(I123, I124, I125, I126, I127, I128, I129, I130) 
  f3(I131, I132, I133, I134, I135, I136, I137, I138) -> f5(I131, I132, I133, I134, I135, 1 + I136, I137, I138) [1 + I136 <= I131]
  f3(I139, I140, I141, I142, I143, I144, I145, I146) -> f4(I139, I140, I141, I142, I143, I144, I145, I146) [I139 <= I144]
  f1(I147, I148, I149, I150, I151, I152, I153, I154) -> f2(I147, I148, I149, I150, I151, I152, I153, I154) 

The dependency graph for this problem is:
  18 -> 
Where:
  18) f1#(I147, I148, I149, I150, I151, I152, I153, I154) -> f2#(I147, I148, I149, I150, I151, I152, I153, I154) 

We have the following SCCs.