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


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YES

DP problem for innermost termination.
P =
  f14#(x1, x2, x3, x4, x5, x6, x7, x8) -> f13#(x1, x2, x3, x4, x5, x6, x7, x8) 
  f13#(I0, I1, I2, I3, I4, I5, I6, I7) -> f12#(I0, I1, I2, I3, I4, I5, I6, I7) 
  f13#(I8, I9, I10, I11, I12, I13, I14, I15) -> f11#(I8, I9, I10, I11, I12, I13, I14, I15) 
  f13#(I16, I17, I18, I19, I20, I21, I22, I23) -> f10#(I16, I17, I18, I19, I20, I21, I22, I23) 
  f13#(I24, I25, I26, I27, I28, I29, I30, I31) -> f8#(I24, I25, I26, I27, I28, I29, I30, I31) 
  f13#(I40, I41, I42, I43, I44, I45, I46, I47) -> f7#(I40, I41, I42, I43, I44, I45, I46, I47) 
  f13#(I48, I49, I50, I51, I52, I53, I54, I55) -> f6#(I48, I49, I50, I51, I52, I53, I54, I55) 
  f13#(I56, I57, I58, I59, I60, I61, I62, I63) -> f5#(I56, I57, I58, I59, I60, I61, I62, I63) 
  f13#(I64, I65, I66, I67, I68, I69, I70, I71) -> f4#(I64, I65, I66, I67, I68, I69, I70, I71) 
  f13#(I72, I73, I74, I75, I76, I77, I78, I79) -> f3#(I72, I73, I74, I75, I76, I77, I78, I79) 
  f13#(I80, I81, I82, I83, I84, I85, I86, I87) -> f1#(I80, I81, I82, I83, I84, I85, I86, I87) 
  f13#(I96, I97, I98, I99, I100, I101, I102, I103) -> f7#(I96, I97, I102, I103, rnd5, rnd6, rnd7, rnd8) [rnd8 = rnd6 /\ rnd7 = rnd5 /\ rnd6 = rnd6 /\ rnd5 = rnd5]
  f13#(I104, I105, I106, I107, I108, I109, I110, I111) -> f12#(I104, I105, I110, I111, I112, I113, I114, I115) [I115 = I113 /\ I114 = I112 /\ I113 = I113 /\ I112 = I112]
  f12#(I116, I117, I118, I119, I120, I121, I122, I123) -> f11#(I116, I117, I122, I123, I120, I121, 0, 0) 
  f11#(I124, I125, I126, I127, I128, I129, I130, I131) -> f10#(I124, I125, I130, I131, I128, I129, I130, I131) [I130 <= I124]
  f11#(I132, I133, I134, I135, I136, I137, I138, I139) -> f8#(I132, I133, I138, I139, I136, I137, I138, I139) [1 + I132 <= I138]
  f10#(I140, I141, I142, I143, I144, I145, I146, I147) -> f11#(I140, I141, I146, I147, I148, I145, 1 + I146, I149) [I149 = I148 /\ I148 = I148]
  f7#(I162, I163, I164, I165, I166, I167, I168, I169) -> f6#(I162, I163, I168, I169, I170, I167, I163, I171) [I171 = I170 /\ I170 = I170]
  f6#(I172, I173, I174, I175, I176, I177, I178, I179) -> f5#(I172, I173, I178, I179, I180, I177, I178, I181) [I181 = I180 /\ 0 <= I178 /\ I180 = I180]
  f6#(I182, I183, I184, I185, I186, I187, I188, I189) -> f4#(I182, I183, I188, I189, I186, I187, I188, I183) [1 + I188 <= 0]
  f5#(I190, I191, I192, I193, I194, I195, I196, I197) -> f6#(I190, I191, I196, I197, I198, I195, -1 + I196, I199) [I199 = I198 /\ I198 = I198]
  f4#(I200, I201, I202, I203, I204, I205, I206, I207) -> f3#(I200, I201, I206, I207, I204, I205, I206, I207) [0 <= I207]
  f4#(I208, I209, I210, I211, I212, I213, I214, I215) -> f1#(I208, I209, I214, I215, I212, I213, I214, I215) [1 + I215 <= 0]
  f3#(I216, I217, I218, I219, I220, I221, I222, I223) -> f4#(I216, I217, I222, I223, I220, I221, I222, -1 + I223) 
R = 
  f14(x1, x2, x3, x4, x5, x6, x7, x8) -> f13(x1, x2, x3, x4, x5, x6, x7, x8) 
  f13(I0, I1, I2, I3, I4, I5, I6, I7) -> f12(I0, I1, I2, I3, I4, I5, I6, I7) 
  f13(I8, I9, I10, I11, I12, I13, I14, I15) -> f11(I8, I9, I10, I11, I12, I13, I14, I15) 
  f13(I16, I17, I18, I19, I20, I21, I22, I23) -> f10(I16, I17, I18, I19, I20, I21, I22, I23) 
  f13(I24, I25, I26, I27, I28, I29, I30, I31) -> f8(I24, I25, I26, I27, I28, I29, I30, I31) 
  f13(I32, I33, I34, I35, I36, I37, I38, I39) -> f9(I32, I33, I34, I35, I36, I37, I38, I39) 
  f13(I40, I41, I42, I43, I44, I45, I46, I47) -> f7(I40, I41, I42, I43, I44, I45, I46, I47) 
  f13(I48, I49, I50, I51, I52, I53, I54, I55) -> f6(I48, I49, I50, I51, I52, I53, I54, I55) 
  f13(I56, I57, I58, I59, I60, I61, I62, I63) -> f5(I56, I57, I58, I59, I60, I61, I62, I63) 
  f13(I64, I65, I66, I67, I68, I69, I70, I71) -> f4(I64, I65, I66, I67, I68, I69, I70, I71) 
  f13(I72, I73, I74, I75, I76, I77, I78, I79) -> f3(I72, I73, I74, I75, I76, I77, I78, I79) 
  f13(I80, I81, I82, I83, I84, I85, I86, I87) -> f1(I80, I81, I82, I83, I84, I85, I86, I87) 
  f13(I88, I89, I90, I91, I92, I93, I94, I95) -> f2(I88, I89, I90, I91, I92, I93, I94, I95) 
  f13(I96, I97, I98, I99, I100, I101, I102, I103) -> f7(I96, I97, I102, I103, rnd5, rnd6, rnd7, rnd8) [rnd8 = rnd6 /\ rnd7 = rnd5 /\ rnd6 = rnd6 /\ rnd5 = rnd5]
  f13(I104, I105, I106, I107, I108, I109, I110, I111) -> f12(I104, I105, I110, I111, I112, I113, I114, I115) [I115 = I113 /\ I114 = I112 /\ I113 = I113 /\ I112 = I112]
  f12(I116, I117, I118, I119, I120, I121, I122, I123) -> f11(I116, I117, I122, I123, I120, I121, 0, 0) 
  f11(I124, I125, I126, I127, I128, I129, I130, I131) -> f10(I124, I125, I130, I131, I128, I129, I130, I131) [I130 <= I124]
  f11(I132, I133, I134, I135, I136, I137, I138, I139) -> f8(I132, I133, I138, I139, I136, I137, I138, I139) [1 + I132 <= I138]
  f10(I140, I141, I142, I143, I144, I145, I146, I147) -> f11(I140, I141, I146, I147, I148, I145, 1 + I146, I149) [I149 = I148 /\ I148 = I148]
  f8(I150, I151, I152, I153, I154, I155, I156, I157) -> f9(I150, I151, I156, I157, I158, I159, I160, I161) [I161 = I159 /\ I160 = I158 /\ I159 = I159 /\ I158 = I158]
  f7(I162, I163, I164, I165, I166, I167, I168, I169) -> f6(I162, I163, I168, I169, I170, I167, I163, I171) [I171 = I170 /\ I170 = I170]
  f6(I172, I173, I174, I175, I176, I177, I178, I179) -> f5(I172, I173, I178, I179, I180, I177, I178, I181) [I181 = I180 /\ 0 <= I178 /\ I180 = I180]
  f6(I182, I183, I184, I185, I186, I187, I188, I189) -> f4(I182, I183, I188, I189, I186, I187, I188, I183) [1 + I188 <= 0]
  f5(I190, I191, I192, I193, I194, I195, I196, I197) -> f6(I190, I191, I196, I197, I198, I195, -1 + I196, I199) [I199 = I198 /\ I198 = I198]
  f4(I200, I201, I202, I203, I204, I205, I206, I207) -> f3(I200, I201, I206, I207, I204, I205, I206, I207) [0 <= I207]
  f4(I208, I209, I210, I211, I212, I213, I214, I215) -> f1(I208, I209, I214, I215, I212, I213, I214, I215) [1 + I215 <= 0]
  f3(I216, I217, I218, I219, I220, I221, I222, I223) -> f4(I216, I217, I222, I223, I220, I221, I222, -1 + I223) 
  f1(I224, I225, I226, I227, I228, I229, I230, I231) -> f2(I224, I225, I230, I231, I232, I233, I234, I235) [I235 = I233 /\ I234 = I232 /\ I233 = I233 /\ I232 = I232]

The dependency graph for this problem is:
  0 -> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
  1 -> 13
  2 -> 14, 15
  3 -> 16
  4 -> 
  5 -> 17
  6 -> 18, 19
  7 -> 20
  8 -> 21, 22
  9 -> 23
  10 -> 
  11 -> 17
  12 -> 13
  13 -> 14, 15
  14 -> 16
  15 -> 
  16 -> 14, 15
  17 -> 18, 19
  18 -> 20
  19 -> 21, 22
  20 -> 18, 19
  21 -> 23
  22 -> 
  23 -> 21, 22
Where:
  0) f14#(x1, x2, x3, x4, x5, x6, x7, x8) -> f13#(x1, x2, x3, x4, x5, x6, x7, x8) 
  1) f13#(I0, I1, I2, I3, I4, I5, I6, I7) -> f12#(I0, I1, I2, I3, I4, I5, I6, I7) 
  2) f13#(I8, I9, I10, I11, I12, I13, I14, I15) -> f11#(I8, I9, I10, I11, I12, I13, I14, I15) 
  3) f13#(I16, I17, I18, I19, I20, I21, I22, I23) -> f10#(I16, I17, I18, I19, I20, I21, I22, I23) 
  4) f13#(I24, I25, I26, I27, I28, I29, I30, I31) -> f8#(I24, I25, I26, I27, I28, I29, I30, I31) 
  5) f13#(I40, I41, I42, I43, I44, I45, I46, I47) -> f7#(I40, I41, I42, I43, I44, I45, I46, I47) 
  6) f13#(I48, I49, I50, I51, I52, I53, I54, I55) -> f6#(I48, I49, I50, I51, I52, I53, I54, I55) 
  7) f13#(I56, I57, I58, I59, I60, I61, I62, I63) -> f5#(I56, I57, I58, I59, I60, I61, I62, I63) 
  8) f13#(I64, I65, I66, I67, I68, I69, I70, I71) -> f4#(I64, I65, I66, I67, I68, I69, I70, I71) 
  9) f13#(I72, I73, I74, I75, I76, I77, I78, I79) -> f3#(I72, I73, I74, I75, I76, I77, I78, I79) 
  10) f13#(I80, I81, I82, I83, I84, I85, I86, I87) -> f1#(I80, I81, I82, I83, I84, I85, I86, I87) 
  11) f13#(I96, I97, I98, I99, I100, I101, I102, I103) -> f7#(I96, I97, I102, I103, rnd5, rnd6, rnd7, rnd8) [rnd8 = rnd6 /\ rnd7 = rnd5 /\ rnd6 = rnd6 /\ rnd5 = rnd5]
  12) f13#(I104, I105, I106, I107, I108, I109, I110, I111) -> f12#(I104, I105, I110, I111, I112, I113, I114, I115) [I115 = I113 /\ I114 = I112 /\ I113 = I113 /\ I112 = I112]
  13) f12#(I116, I117, I118, I119, I120, I121, I122, I123) -> f11#(I116, I117, I122, I123, I120, I121, 0, 0) 
  14) f11#(I124, I125, I126, I127, I128, I129, I130, I131) -> f10#(I124, I125, I130, I131, I128, I129, I130, I131) [I130 <= I124]
  15) f11#(I132, I133, I134, I135, I136, I137, I138, I139) -> f8#(I132, I133, I138, I139, I136, I137, I138, I139) [1 + I132 <= I138]
  16) f10#(I140, I141, I142, I143, I144, I145, I146, I147) -> f11#(I140, I141, I146, I147, I148, I145, 1 + I146, I149) [I149 = I148 /\ I148 = I148]
  17) f7#(I162, I163, I164, I165, I166, I167, I168, I169) -> f6#(I162, I163, I168, I169, I170, I167, I163, I171) [I171 = I170 /\ I170 = I170]
  18) f6#(I172, I173, I174, I175, I176, I177, I178, I179) -> f5#(I172, I173, I178, I179, I180, I177, I178, I181) [I181 = I180 /\ 0 <= I178 /\ I180 = I180]
  19) f6#(I182, I183, I184, I185, I186, I187, I188, I189) -> f4#(I182, I183, I188, I189, I186, I187, I188, I183) [1 + I188 <= 0]
  20) f5#(I190, I191, I192, I193, I194, I195, I196, I197) -> f6#(I190, I191, I196, I197, I198, I195, -1 + I196, I199) [I199 = I198 /\ I198 = I198]
  21) f4#(I200, I201, I202, I203, I204, I205, I206, I207) -> f3#(I200, I201, I206, I207, I204, I205, I206, I207) [0 <= I207]
  22) f4#(I208, I209, I210, I211, I212, I213, I214, I215) -> f1#(I208, I209, I214, I215, I212, I213, I214, I215) [1 + I215 <= 0]
  23) f3#(I216, I217, I218, I219, I220, I221, I222, I223) -> f4#(I216, I217, I222, I223, I220, I221, I222, -1 + I223) 

We have the following SCCs.
  { 14, 16 }
  { 18, 20 }
  { 21, 23 }

DP problem for innermost termination.
P =
  f4#(I200, I201, I202, I203, I204, I205, I206, I207) -> f3#(I200, I201, I206, I207, I204, I205, I206, I207) [0 <= I207]
  f3#(I216, I217, I218, I219, I220, I221, I222, I223) -> f4#(I216, I217, I222, I223, I220, I221, I222, -1 + I223) 
R = 
  f14(x1, x2, x3, x4, x5, x6, x7, x8) -> f13(x1, x2, x3, x4, x5, x6, x7, x8) 
  f13(I0, I1, I2, I3, I4, I5, I6, I7) -> f12(I0, I1, I2, I3, I4, I5, I6, I7) 
  f13(I8, I9, I10, I11, I12, I13, I14, I15) -> f11(I8, I9, I10, I11, I12, I13, I14, I15) 
  f13(I16, I17, I18, I19, I20, I21, I22, I23) -> f10(I16, I17, I18, I19, I20, I21, I22, I23) 
  f13(I24, I25, I26, I27, I28, I29, I30, I31) -> f8(I24, I25, I26, I27, I28, I29, I30, I31) 
  f13(I32, I33, I34, I35, I36, I37, I38, I39) -> f9(I32, I33, I34, I35, I36, I37, I38, I39) 
  f13(I40, I41, I42, I43, I44, I45, I46, I47) -> f7(I40, I41, I42, I43, I44, I45, I46, I47) 
  f13(I48, I49, I50, I51, I52, I53, I54, I55) -> f6(I48, I49, I50, I51, I52, I53, I54, I55) 
  f13(I56, I57, I58, I59, I60, I61, I62, I63) -> f5(I56, I57, I58, I59, I60, I61, I62, I63) 
  f13(I64, I65, I66, I67, I68, I69, I70, I71) -> f4(I64, I65, I66, I67, I68, I69, I70, I71) 
  f13(I72, I73, I74, I75, I76, I77, I78, I79) -> f3(I72, I73, I74, I75, I76, I77, I78, I79) 
  f13(I80, I81, I82, I83, I84, I85, I86, I87) -> f1(I80, I81, I82, I83, I84, I85, I86, I87) 
  f13(I88, I89, I90, I91, I92, I93, I94, I95) -> f2(I88, I89, I90, I91, I92, I93, I94, I95) 
  f13(I96, I97, I98, I99, I100, I101, I102, I103) -> f7(I96, I97, I102, I103, rnd5, rnd6, rnd7, rnd8) [rnd8 = rnd6 /\ rnd7 = rnd5 /\ rnd6 = rnd6 /\ rnd5 = rnd5]
  f13(I104, I105, I106, I107, I108, I109, I110, I111) -> f12(I104, I105, I110, I111, I112, I113, I114, I115) [I115 = I113 /\ I114 = I112 /\ I113 = I113 /\ I112 = I112]
  f12(I116, I117, I118, I119, I120, I121, I122, I123) -> f11(I116, I117, I122, I123, I120, I121, 0, 0) 
  f11(I124, I125, I126, I127, I128, I129, I130, I131) -> f10(I124, I125, I130, I131, I128, I129, I130, I131) [I130 <= I124]
  f11(I132, I133, I134, I135, I136, I137, I138, I139) -> f8(I132, I133, I138, I139, I136, I137, I138, I139) [1 + I132 <= I138]
  f10(I140, I141, I142, I143, I144, I145, I146, I147) -> f11(I140, I141, I146, I147, I148, I145, 1 + I146, I149) [I149 = I148 /\ I148 = I148]
  f8(I150, I151, I152, I153, I154, I155, I156, I157) -> f9(I150, I151, I156, I157, I158, I159, I160, I161) [I161 = I159 /\ I160 = I158 /\ I159 = I159 /\ I158 = I158]
  f7(I162, I163, I164, I165, I166, I167, I168, I169) -> f6(I162, I163, I168, I169, I170, I167, I163, I171) [I171 = I170 /\ I170 = I170]
  f6(I172, I173, I174, I175, I176, I177, I178, I179) -> f5(I172, I173, I178, I179, I180, I177, I178, I181) [I181 = I180 /\ 0 <= I178 /\ I180 = I180]
  f6(I182, I183, I184, I185, I186, I187, I188, I189) -> f4(I182, I183, I188, I189, I186, I187, I188, I183) [1 + I188 <= 0]
  f5(I190, I191, I192, I193, I194, I195, I196, I197) -> f6(I190, I191, I196, I197, I198, I195, -1 + I196, I199) [I199 = I198 /\ I198 = I198]
  f4(I200, I201, I202, I203, I204, I205, I206, I207) -> f3(I200, I201, I206, I207, I204, I205, I206, I207) [0 <= I207]
  f4(I208, I209, I210, I211, I212, I213, I214, I215) -> f1(I208, I209, I214, I215, I212, I213, I214, I215) [1 + I215 <= 0]
  f3(I216, I217, I218, I219, I220, I221, I222, I223) -> f4(I216, I217, I222, I223, I220, I221, I222, -1 + I223) 
  f1(I224, I225, I226, I227, I228, I229, I230, I231) -> f2(I224, I225, I230, I231, I232, I233, I234, I235) [I235 = I233 /\ I234 = I232 /\ I233 = I233 /\ I232 = I232]

We use the reverse value criterion with the projection function NU:
  NU[f3#(z1,z2,z3,z4,z5,z6,z7,z8)] = -1 + z8 + -1 * 0
  NU[f4#(z1,z2,z3,z4,z5,z6,z7,z8)] = z8 + -1 * 0

This gives the following inequalities:
  0 <= I207  ==>  I207 + -1 * 0 > -1 + I207 + -1 * 0  with  I207 + -1 * 0 >= 0
    ==>  -1 + I223 + -1 * 0 >= -1 + I223 + -1 * 0

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f3#(I216, I217, I218, I219, I220, I221, I222, I223) -> f4#(I216, I217, I222, I223, I220, I221, I222, -1 + I223) 
R = 
  f14(x1, x2, x3, x4, x5, x6, x7, x8) -> f13(x1, x2, x3, x4, x5, x6, x7, x8) 
  f13(I0, I1, I2, I3, I4, I5, I6, I7) -> f12(I0, I1, I2, I3, I4, I5, I6, I7) 
  f13(I8, I9, I10, I11, I12, I13, I14, I15) -> f11(I8, I9, I10, I11, I12, I13, I14, I15) 
  f13(I16, I17, I18, I19, I20, I21, I22, I23) -> f10(I16, I17, I18, I19, I20, I21, I22, I23) 
  f13(I24, I25, I26, I27, I28, I29, I30, I31) -> f8(I24, I25, I26, I27, I28, I29, I30, I31) 
  f13(I32, I33, I34, I35, I36, I37, I38, I39) -> f9(I32, I33, I34, I35, I36, I37, I38, I39) 
  f13(I40, I41, I42, I43, I44, I45, I46, I47) -> f7(I40, I41, I42, I43, I44, I45, I46, I47) 
  f13(I48, I49, I50, I51, I52, I53, I54, I55) -> f6(I48, I49, I50, I51, I52, I53, I54, I55) 
  f13(I56, I57, I58, I59, I60, I61, I62, I63) -> f5(I56, I57, I58, I59, I60, I61, I62, I63) 
  f13(I64, I65, I66, I67, I68, I69, I70, I71) -> f4(I64, I65, I66, I67, I68, I69, I70, I71) 
  f13(I72, I73, I74, I75, I76, I77, I78, I79) -> f3(I72, I73, I74, I75, I76, I77, I78, I79) 
  f13(I80, I81, I82, I83, I84, I85, I86, I87) -> f1(I80, I81, I82, I83, I84, I85, I86, I87) 
  f13(I88, I89, I90, I91, I92, I93, I94, I95) -> f2(I88, I89, I90, I91, I92, I93, I94, I95) 
  f13(I96, I97, I98, I99, I100, I101, I102, I103) -> f7(I96, I97, I102, I103, rnd5, rnd6, rnd7, rnd8) [rnd8 = rnd6 /\ rnd7 = rnd5 /\ rnd6 = rnd6 /\ rnd5 = rnd5]
  f13(I104, I105, I106, I107, I108, I109, I110, I111) -> f12(I104, I105, I110, I111, I112, I113, I114, I115) [I115 = I113 /\ I114 = I112 /\ I113 = I113 /\ I112 = I112]
  f12(I116, I117, I118, I119, I120, I121, I122, I123) -> f11(I116, I117, I122, I123, I120, I121, 0, 0) 
  f11(I124, I125, I126, I127, I128, I129, I130, I131) -> f10(I124, I125, I130, I131, I128, I129, I130, I131) [I130 <= I124]
  f11(I132, I133, I134, I135, I136, I137, I138, I139) -> f8(I132, I133, I138, I139, I136, I137, I138, I139) [1 + I132 <= I138]
  f10(I140, I141, I142, I143, I144, I145, I146, I147) -> f11(I140, I141, I146, I147, I148, I145, 1 + I146, I149) [I149 = I148 /\ I148 = I148]
  f8(I150, I151, I152, I153, I154, I155, I156, I157) -> f9(I150, I151, I156, I157, I158, I159, I160, I161) [I161 = I159 /\ I160 = I158 /\ I159 = I159 /\ I158 = I158]
  f7(I162, I163, I164, I165, I166, I167, I168, I169) -> f6(I162, I163, I168, I169, I170, I167, I163, I171) [I171 = I170 /\ I170 = I170]
  f6(I172, I173, I174, I175, I176, I177, I178, I179) -> f5(I172, I173, I178, I179, I180, I177, I178, I181) [I181 = I180 /\ 0 <= I178 /\ I180 = I180]
  f6(I182, I183, I184, I185, I186, I187, I188, I189) -> f4(I182, I183, I188, I189, I186, I187, I188, I183) [1 + I188 <= 0]
  f5(I190, I191, I192, I193, I194, I195, I196, I197) -> f6(I190, I191, I196, I197, I198, I195, -1 + I196, I199) [I199 = I198 /\ I198 = I198]
  f4(I200, I201, I202, I203, I204, I205, I206, I207) -> f3(I200, I201, I206, I207, I204, I205, I206, I207) [0 <= I207]
  f4(I208, I209, I210, I211, I212, I213, I214, I215) -> f1(I208, I209, I214, I215, I212, I213, I214, I215) [1 + I215 <= 0]
  f3(I216, I217, I218, I219, I220, I221, I222, I223) -> f4(I216, I217, I222, I223, I220, I221, I222, -1 + I223) 
  f1(I224, I225, I226, I227, I228, I229, I230, I231) -> f2(I224, I225, I230, I231, I232, I233, I234, I235) [I235 = I233 /\ I234 = I232 /\ I233 = I233 /\ I232 = I232]

The dependency graph for this problem is:
  23 -> 
Where:
  23) f3#(I216, I217, I218, I219, I220, I221, I222, I223) -> f4#(I216, I217, I222, I223, I220, I221, I222, -1 + I223) 

We have the following SCCs.
  

DP problem for innermost termination.
P =
  f6#(I172, I173, I174, I175, I176, I177, I178, I179) -> f5#(I172, I173, I178, I179, I180, I177, I178, I181) [I181 = I180 /\ 0 <= I178 /\ I180 = I180]
  f5#(I190, I191, I192, I193, I194, I195, I196, I197) -> f6#(I190, I191, I196, I197, I198, I195, -1 + I196, I199) [I199 = I198 /\ I198 = I198]
R = 
  f14(x1, x2, x3, x4, x5, x6, x7, x8) -> f13(x1, x2, x3, x4, x5, x6, x7, x8) 
  f13(I0, I1, I2, I3, I4, I5, I6, I7) -> f12(I0, I1, I2, I3, I4, I5, I6, I7) 
  f13(I8, I9, I10, I11, I12, I13, I14, I15) -> f11(I8, I9, I10, I11, I12, I13, I14, I15) 
  f13(I16, I17, I18, I19, I20, I21, I22, I23) -> f10(I16, I17, I18, I19, I20, I21, I22, I23) 
  f13(I24, I25, I26, I27, I28, I29, I30, I31) -> f8(I24, I25, I26, I27, I28, I29, I30, I31) 
  f13(I32, I33, I34, I35, I36, I37, I38, I39) -> f9(I32, I33, I34, I35, I36, I37, I38, I39) 
  f13(I40, I41, I42, I43, I44, I45, I46, I47) -> f7(I40, I41, I42, I43, I44, I45, I46, I47) 
  f13(I48, I49, I50, I51, I52, I53, I54, I55) -> f6(I48, I49, I50, I51, I52, I53, I54, I55) 
  f13(I56, I57, I58, I59, I60, I61, I62, I63) -> f5(I56, I57, I58, I59, I60, I61, I62, I63) 
  f13(I64, I65, I66, I67, I68, I69, I70, I71) -> f4(I64, I65, I66, I67, I68, I69, I70, I71) 
  f13(I72, I73, I74, I75, I76, I77, I78, I79) -> f3(I72, I73, I74, I75, I76, I77, I78, I79) 
  f13(I80, I81, I82, I83, I84, I85, I86, I87) -> f1(I80, I81, I82, I83, I84, I85, I86, I87) 
  f13(I88, I89, I90, I91, I92, I93, I94, I95) -> f2(I88, I89, I90, I91, I92, I93, I94, I95) 
  f13(I96, I97, I98, I99, I100, I101, I102, I103) -> f7(I96, I97, I102, I103, rnd5, rnd6, rnd7, rnd8) [rnd8 = rnd6 /\ rnd7 = rnd5 /\ rnd6 = rnd6 /\ rnd5 = rnd5]
  f13(I104, I105, I106, I107, I108, I109, I110, I111) -> f12(I104, I105, I110, I111, I112, I113, I114, I115) [I115 = I113 /\ I114 = I112 /\ I113 = I113 /\ I112 = I112]
  f12(I116, I117, I118, I119, I120, I121, I122, I123) -> f11(I116, I117, I122, I123, I120, I121, 0, 0) 
  f11(I124, I125, I126, I127, I128, I129, I130, I131) -> f10(I124, I125, I130, I131, I128, I129, I130, I131) [I130 <= I124]
  f11(I132, I133, I134, I135, I136, I137, I138, I139) -> f8(I132, I133, I138, I139, I136, I137, I138, I139) [1 + I132 <= I138]
  f10(I140, I141, I142, I143, I144, I145, I146, I147) -> f11(I140, I141, I146, I147, I148, I145, 1 + I146, I149) [I149 = I148 /\ I148 = I148]
  f8(I150, I151, I152, I153, I154, I155, I156, I157) -> f9(I150, I151, I156, I157, I158, I159, I160, I161) [I161 = I159 /\ I160 = I158 /\ I159 = I159 /\ I158 = I158]
  f7(I162, I163, I164, I165, I166, I167, I168, I169) -> f6(I162, I163, I168, I169, I170, I167, I163, I171) [I171 = I170 /\ I170 = I170]
  f6(I172, I173, I174, I175, I176, I177, I178, I179) -> f5(I172, I173, I178, I179, I180, I177, I178, I181) [I181 = I180 /\ 0 <= I178 /\ I180 = I180]
  f6(I182, I183, I184, I185, I186, I187, I188, I189) -> f4(I182, I183, I188, I189, I186, I187, I188, I183) [1 + I188 <= 0]
  f5(I190, I191, I192, I193, I194, I195, I196, I197) -> f6(I190, I191, I196, I197, I198, I195, -1 + I196, I199) [I199 = I198 /\ I198 = I198]
  f4(I200, I201, I202, I203, I204, I205, I206, I207) -> f3(I200, I201, I206, I207, I204, I205, I206, I207) [0 <= I207]
  f4(I208, I209, I210, I211, I212, I213, I214, I215) -> f1(I208, I209, I214, I215, I212, I213, I214, I215) [1 + I215 <= 0]
  f3(I216, I217, I218, I219, I220, I221, I222, I223) -> f4(I216, I217, I222, I223, I220, I221, I222, -1 + I223) 
  f1(I224, I225, I226, I227, I228, I229, I230, I231) -> f2(I224, I225, I230, I231, I232, I233, I234, I235) [I235 = I233 /\ I234 = I232 /\ I233 = I233 /\ I232 = I232]

We use the reverse value criterion with the projection function NU:
  NU[f5#(z1,z2,z3,z4,z5,z6,z7,z8)] = -1 + z7 + -1 * 0
  NU[f6#(z1,z2,z3,z4,z5,z6,z7,z8)] = z7 + -1 * 0

This gives the following inequalities:
  I181 = I180 /\ 0 <= I178 /\ I180 = I180  ==>  I178 + -1 * 0 > -1 + I178 + -1 * 0  with  I178 + -1 * 0 >= 0
  I199 = I198 /\ I198 = I198  ==>  -1 + I196 + -1 * 0 >= -1 + I196 + -1 * 0

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f5#(I190, I191, I192, I193, I194, I195, I196, I197) -> f6#(I190, I191, I196, I197, I198, I195, -1 + I196, I199) [I199 = I198 /\ I198 = I198]
R = 
  f14(x1, x2, x3, x4, x5, x6, x7, x8) -> f13(x1, x2, x3, x4, x5, x6, x7, x8) 
  f13(I0, I1, I2, I3, I4, I5, I6, I7) -> f12(I0, I1, I2, I3, I4, I5, I6, I7) 
  f13(I8, I9, I10, I11, I12, I13, I14, I15) -> f11(I8, I9, I10, I11, I12, I13, I14, I15) 
  f13(I16, I17, I18, I19, I20, I21, I22, I23) -> f10(I16, I17, I18, I19, I20, I21, I22, I23) 
  f13(I24, I25, I26, I27, I28, I29, I30, I31) -> f8(I24, I25, I26, I27, I28, I29, I30, I31) 
  f13(I32, I33, I34, I35, I36, I37, I38, I39) -> f9(I32, I33, I34, I35, I36, I37, I38, I39) 
  f13(I40, I41, I42, I43, I44, I45, I46, I47) -> f7(I40, I41, I42, I43, I44, I45, I46, I47) 
  f13(I48, I49, I50, I51, I52, I53, I54, I55) -> f6(I48, I49, I50, I51, I52, I53, I54, I55) 
  f13(I56, I57, I58, I59, I60, I61, I62, I63) -> f5(I56, I57, I58, I59, I60, I61, I62, I63) 
  f13(I64, I65, I66, I67, I68, I69, I70, I71) -> f4(I64, I65, I66, I67, I68, I69, I70, I71) 
  f13(I72, I73, I74, I75, I76, I77, I78, I79) -> f3(I72, I73, I74, I75, I76, I77, I78, I79) 
  f13(I80, I81, I82, I83, I84, I85, I86, I87) -> f1(I80, I81, I82, I83, I84, I85, I86, I87) 
  f13(I88, I89, I90, I91, I92, I93, I94, I95) -> f2(I88, I89, I90, I91, I92, I93, I94, I95) 
  f13(I96, I97, I98, I99, I100, I101, I102, I103) -> f7(I96, I97, I102, I103, rnd5, rnd6, rnd7, rnd8) [rnd8 = rnd6 /\ rnd7 = rnd5 /\ rnd6 = rnd6 /\ rnd5 = rnd5]
  f13(I104, I105, I106, I107, I108, I109, I110, I111) -> f12(I104, I105, I110, I111, I112, I113, I114, I115) [I115 = I113 /\ I114 = I112 /\ I113 = I113 /\ I112 = I112]
  f12(I116, I117, I118, I119, I120, I121, I122, I123) -> f11(I116, I117, I122, I123, I120, I121, 0, 0) 
  f11(I124, I125, I126, I127, I128, I129, I130, I131) -> f10(I124, I125, I130, I131, I128, I129, I130, I131) [I130 <= I124]
  f11(I132, I133, I134, I135, I136, I137, I138, I139) -> f8(I132, I133, I138, I139, I136, I137, I138, I139) [1 + I132 <= I138]
  f10(I140, I141, I142, I143, I144, I145, I146, I147) -> f11(I140, I141, I146, I147, I148, I145, 1 + I146, I149) [I149 = I148 /\ I148 = I148]
  f8(I150, I151, I152, I153, I154, I155, I156, I157) -> f9(I150, I151, I156, I157, I158, I159, I160, I161) [I161 = I159 /\ I160 = I158 /\ I159 = I159 /\ I158 = I158]
  f7(I162, I163, I164, I165, I166, I167, I168, I169) -> f6(I162, I163, I168, I169, I170, I167, I163, I171) [I171 = I170 /\ I170 = I170]
  f6(I172, I173, I174, I175, I176, I177, I178, I179) -> f5(I172, I173, I178, I179, I180, I177, I178, I181) [I181 = I180 /\ 0 <= I178 /\ I180 = I180]
  f6(I182, I183, I184, I185, I186, I187, I188, I189) -> f4(I182, I183, I188, I189, I186, I187, I188, I183) [1 + I188 <= 0]
  f5(I190, I191, I192, I193, I194, I195, I196, I197) -> f6(I190, I191, I196, I197, I198, I195, -1 + I196, I199) [I199 = I198 /\ I198 = I198]
  f4(I200, I201, I202, I203, I204, I205, I206, I207) -> f3(I200, I201, I206, I207, I204, I205, I206, I207) [0 <= I207]
  f4(I208, I209, I210, I211, I212, I213, I214, I215) -> f1(I208, I209, I214, I215, I212, I213, I214, I215) [1 + I215 <= 0]
  f3(I216, I217, I218, I219, I220, I221, I222, I223) -> f4(I216, I217, I222, I223, I220, I221, I222, -1 + I223) 
  f1(I224, I225, I226, I227, I228, I229, I230, I231) -> f2(I224, I225, I230, I231, I232, I233, I234, I235) [I235 = I233 /\ I234 = I232 /\ I233 = I233 /\ I232 = I232]

The dependency graph for this problem is:
  20 -> 
Where:
  20) f5#(I190, I191, I192, I193, I194, I195, I196, I197) -> f6#(I190, I191, I196, I197, I198, I195, -1 + I196, I199) [I199 = I198 /\ I198 = I198]

We have the following SCCs.
  

DP problem for innermost termination.
P =
  f11#(I124, I125, I126, I127, I128, I129, I130, I131) -> f10#(I124, I125, I130, I131, I128, I129, I130, I131) [I130 <= I124]
  f10#(I140, I141, I142, I143, I144, I145, I146, I147) -> f11#(I140, I141, I146, I147, I148, I145, 1 + I146, I149) [I149 = I148 /\ I148 = I148]
R = 
  f14(x1, x2, x3, x4, x5, x6, x7, x8) -> f13(x1, x2, x3, x4, x5, x6, x7, x8) 
  f13(I0, I1, I2, I3, I4, I5, I6, I7) -> f12(I0, I1, I2, I3, I4, I5, I6, I7) 
  f13(I8, I9, I10, I11, I12, I13, I14, I15) -> f11(I8, I9, I10, I11, I12, I13, I14, I15) 
  f13(I16, I17, I18, I19, I20, I21, I22, I23) -> f10(I16, I17, I18, I19, I20, I21, I22, I23) 
  f13(I24, I25, I26, I27, I28, I29, I30, I31) -> f8(I24, I25, I26, I27, I28, I29, I30, I31) 
  f13(I32, I33, I34, I35, I36, I37, I38, I39) -> f9(I32, I33, I34, I35, I36, I37, I38, I39) 
  f13(I40, I41, I42, I43, I44, I45, I46, I47) -> f7(I40, I41, I42, I43, I44, I45, I46, I47) 
  f13(I48, I49, I50, I51, I52, I53, I54, I55) -> f6(I48, I49, I50, I51, I52, I53, I54, I55) 
  f13(I56, I57, I58, I59, I60, I61, I62, I63) -> f5(I56, I57, I58, I59, I60, I61, I62, I63) 
  f13(I64, I65, I66, I67, I68, I69, I70, I71) -> f4(I64, I65, I66, I67, I68, I69, I70, I71) 
  f13(I72, I73, I74, I75, I76, I77, I78, I79) -> f3(I72, I73, I74, I75, I76, I77, I78, I79) 
  f13(I80, I81, I82, I83, I84, I85, I86, I87) -> f1(I80, I81, I82, I83, I84, I85, I86, I87) 
  f13(I88, I89, I90, I91, I92, I93, I94, I95) -> f2(I88, I89, I90, I91, I92, I93, I94, I95) 
  f13(I96, I97, I98, I99, I100, I101, I102, I103) -> f7(I96, I97, I102, I103, rnd5, rnd6, rnd7, rnd8) [rnd8 = rnd6 /\ rnd7 = rnd5 /\ rnd6 = rnd6 /\ rnd5 = rnd5]
  f13(I104, I105, I106, I107, I108, I109, I110, I111) -> f12(I104, I105, I110, I111, I112, I113, I114, I115) [I115 = I113 /\ I114 = I112 /\ I113 = I113 /\ I112 = I112]
  f12(I116, I117, I118, I119, I120, I121, I122, I123) -> f11(I116, I117, I122, I123, I120, I121, 0, 0) 
  f11(I124, I125, I126, I127, I128, I129, I130, I131) -> f10(I124, I125, I130, I131, I128, I129, I130, I131) [I130 <= I124]
  f11(I132, I133, I134, I135, I136, I137, I138, I139) -> f8(I132, I133, I138, I139, I136, I137, I138, I139) [1 + I132 <= I138]
  f10(I140, I141, I142, I143, I144, I145, I146, I147) -> f11(I140, I141, I146, I147, I148, I145, 1 + I146, I149) [I149 = I148 /\ I148 = I148]
  f8(I150, I151, I152, I153, I154, I155, I156, I157) -> f9(I150, I151, I156, I157, I158, I159, I160, I161) [I161 = I159 /\ I160 = I158 /\ I159 = I159 /\ I158 = I158]
  f7(I162, I163, I164, I165, I166, I167, I168, I169) -> f6(I162, I163, I168, I169, I170, I167, I163, I171) [I171 = I170 /\ I170 = I170]
  f6(I172, I173, I174, I175, I176, I177, I178, I179) -> f5(I172, I173, I178, I179, I180, I177, I178, I181) [I181 = I180 /\ 0 <= I178 /\ I180 = I180]
  f6(I182, I183, I184, I185, I186, I187, I188, I189) -> f4(I182, I183, I188, I189, I186, I187, I188, I183) [1 + I188 <= 0]
  f5(I190, I191, I192, I193, I194, I195, I196, I197) -> f6(I190, I191, I196, I197, I198, I195, -1 + I196, I199) [I199 = I198 /\ I198 = I198]
  f4(I200, I201, I202, I203, I204, I205, I206, I207) -> f3(I200, I201, I206, I207, I204, I205, I206, I207) [0 <= I207]
  f4(I208, I209, I210, I211, I212, I213, I214, I215) -> f1(I208, I209, I214, I215, I212, I213, I214, I215) [1 + I215 <= 0]
  f3(I216, I217, I218, I219, I220, I221, I222, I223) -> f4(I216, I217, I222, I223, I220, I221, I222, -1 + I223) 
  f1(I224, I225, I226, I227, I228, I229, I230, I231) -> f2(I224, I225, I230, I231, I232, I233, I234, I235) [I235 = I233 /\ I234 = I232 /\ I233 = I233 /\ I232 = I232]

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

This gives the following inequalities:
  I130 <= I124  ==>  I124 + -1 * I130 > I124 + -1 * (1 + I130)  with  I124 + -1 * I130 >= 0
  I149 = I148 /\ I148 = I148  ==>  I140 + -1 * (1 + I146) >= I140 + -1 * (1 + I146)

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f10#(I140, I141, I142, I143, I144, I145, I146, I147) -> f11#(I140, I141, I146, I147, I148, I145, 1 + I146, I149) [I149 = I148 /\ I148 = I148]
R = 
  f14(x1, x2, x3, x4, x5, x6, x7, x8) -> f13(x1, x2, x3, x4, x5, x6, x7, x8) 
  f13(I0, I1, I2, I3, I4, I5, I6, I7) -> f12(I0, I1, I2, I3, I4, I5, I6, I7) 
  f13(I8, I9, I10, I11, I12, I13, I14, I15) -> f11(I8, I9, I10, I11, I12, I13, I14, I15) 
  f13(I16, I17, I18, I19, I20, I21, I22, I23) -> f10(I16, I17, I18, I19, I20, I21, I22, I23) 
  f13(I24, I25, I26, I27, I28, I29, I30, I31) -> f8(I24, I25, I26, I27, I28, I29, I30, I31) 
  f13(I32, I33, I34, I35, I36, I37, I38, I39) -> f9(I32, I33, I34, I35, I36, I37, I38, I39) 
  f13(I40, I41, I42, I43, I44, I45, I46, I47) -> f7(I40, I41, I42, I43, I44, I45, I46, I47) 
  f13(I48, I49, I50, I51, I52, I53, I54, I55) -> f6(I48, I49, I50, I51, I52, I53, I54, I55) 
  f13(I56, I57, I58, I59, I60, I61, I62, I63) -> f5(I56, I57, I58, I59, I60, I61, I62, I63) 
  f13(I64, I65, I66, I67, I68, I69, I70, I71) -> f4(I64, I65, I66, I67, I68, I69, I70, I71) 
  f13(I72, I73, I74, I75, I76, I77, I78, I79) -> f3(I72, I73, I74, I75, I76, I77, I78, I79) 
  f13(I80, I81, I82, I83, I84, I85, I86, I87) -> f1(I80, I81, I82, I83, I84, I85, I86, I87) 
  f13(I88, I89, I90, I91, I92, I93, I94, I95) -> f2(I88, I89, I90, I91, I92, I93, I94, I95) 
  f13(I96, I97, I98, I99, I100, I101, I102, I103) -> f7(I96, I97, I102, I103, rnd5, rnd6, rnd7, rnd8) [rnd8 = rnd6 /\ rnd7 = rnd5 /\ rnd6 = rnd6 /\ rnd5 = rnd5]
  f13(I104, I105, I106, I107, I108, I109, I110, I111) -> f12(I104, I105, I110, I111, I112, I113, I114, I115) [I115 = I113 /\ I114 = I112 /\ I113 = I113 /\ I112 = I112]
  f12(I116, I117, I118, I119, I120, I121, I122, I123) -> f11(I116, I117, I122, I123, I120, I121, 0, 0) 
  f11(I124, I125, I126, I127, I128, I129, I130, I131) -> f10(I124, I125, I130, I131, I128, I129, I130, I131) [I130 <= I124]
  f11(I132, I133, I134, I135, I136, I137, I138, I139) -> f8(I132, I133, I138, I139, I136, I137, I138, I139) [1 + I132 <= I138]
  f10(I140, I141, I142, I143, I144, I145, I146, I147) -> f11(I140, I141, I146, I147, I148, I145, 1 + I146, I149) [I149 = I148 /\ I148 = I148]
  f8(I150, I151, I152, I153, I154, I155, I156, I157) -> f9(I150, I151, I156, I157, I158, I159, I160, I161) [I161 = I159 /\ I160 = I158 /\ I159 = I159 /\ I158 = I158]
  f7(I162, I163, I164, I165, I166, I167, I168, I169) -> f6(I162, I163, I168, I169, I170, I167, I163, I171) [I171 = I170 /\ I170 = I170]
  f6(I172, I173, I174, I175, I176, I177, I178, I179) -> f5(I172, I173, I178, I179, I180, I177, I178, I181) [I181 = I180 /\ 0 <= I178 /\ I180 = I180]
  f6(I182, I183, I184, I185, I186, I187, I188, I189) -> f4(I182, I183, I188, I189, I186, I187, I188, I183) [1 + I188 <= 0]
  f5(I190, I191, I192, I193, I194, I195, I196, I197) -> f6(I190, I191, I196, I197, I198, I195, -1 + I196, I199) [I199 = I198 /\ I198 = I198]
  f4(I200, I201, I202, I203, I204, I205, I206, I207) -> f3(I200, I201, I206, I207, I204, I205, I206, I207) [0 <= I207]
  f4(I208, I209, I210, I211, I212, I213, I214, I215) -> f1(I208, I209, I214, I215, I212, I213, I214, I215) [1 + I215 <= 0]
  f3(I216, I217, I218, I219, I220, I221, I222, I223) -> f4(I216, I217, I222, I223, I220, I221, I222, -1 + I223) 
  f1(I224, I225, I226, I227, I228, I229, I230, I231) -> f2(I224, I225, I230, I231, I232, I233, I234, I235) [I235 = I233 /\ I234 = I232 /\ I233 = I233 /\ I232 = I232]

The dependency graph for this problem is:
  16 -> 
Where:
  16) f10#(I140, I141, I142, I143, I144, I145, I146, I147) -> f11#(I140, I141, I146, I147, I148, I145, 1 + I146, I149) [I149 = I148 /\ I148 = I148]

We have the following SCCs.