/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) -> f13#(x1, x2, x3, x4, x5, x6) 
  f13#(I0, I1, I2, I3, I4, I5) -> f12#(I0, I1, I2, I3, I4, I5) 
  f13#(I6, I7, I8, I9, I10, I11) -> f11#(I6, I7, I8, I9, I10, I11) 
  f13#(I12, I13, I14, I15, I16, I17) -> f10#(I12, I13, I14, I15, I16, I17) 
  f13#(I18, I19, I20, I21, I22, I23) -> f8#(I18, I19, I20, I21, I22, I23) 
  f13#(I30, I31, I32, I33, I34, I35) -> f7#(I30, I31, I32, I33, I34, I35) 
  f13#(I36, I37, I38, I39, I40, I41) -> f6#(I36, I37, I38, I39, I40, I41) 
  f13#(I42, I43, I44, I45, I46, I47) -> f5#(I42, I43, I44, I45, I46, I47) 
  f13#(I48, I49, I50, I51, I52, I53) -> f4#(I48, I49, I50, I51, I52, I53) 
  f13#(I54, I55, I56, I57, I58, I59) -> f3#(I54, I55, I56, I57, I58, I59) 
  f13#(I60, I61, I62, I63, I64, I65) -> f1#(I60, I61, I62, I63, I64, I65) 
  f13#(I72, I73, I74, I75, I76, I77) -> f7#(I76, I77, rnd3, rnd4, rnd5, rnd6) [rnd6 = rnd4 /\ rnd5 = rnd3 /\ rnd4 = rnd4 /\ rnd3 = rnd3]
  f13#(I78, I79, I80, I81, I82, I83) -> f12#(I82, I83, I84, I85, I86, I87) [I87 = I85 /\ I86 = I84 /\ I85 = I85 /\ I84 = I84]
  f12#(I88, I89, I90, I91, I92, I93) -> f11#(I92, I93, I90, I91, 0, 0) 
  f11#(I94, I95, I96, I97, I98, I99) -> f10#(I98, I99, I96, I97, I98, I99) [I98 <= 63]
  f11#(I100, I101, I102, I103, I104, I105) -> f8#(I104, I105, I102, I103, I104, I105) [64 <= I104]
  f10#(I106, I107, I108, I109, I110, I111) -> f11#(I110, I111, I112, I109, 1 + I110, I113) [I113 = I112 /\ I112 = I112]
  f7#(I124, I125, I126, I127, I128, I129) -> f6#(I128, I129, I130, I127, 7, I131) [I131 = I130 /\ I130 = I130]
  f6#(I132, I133, I134, I135, I136, I137) -> f5#(I136, I137, I138, I135, I136, I139) [I139 = I138 /\ 0 <= I136 /\ I138 = I138]
  f6#(I140, I141, I142, I143, I144, I145) -> f4#(I144, I145, I142, I143, I144, 7) [1 + I144 <= 0]
  f5#(I146, I147, I148, I149, I150, I151) -> f6#(I150, I151, I152, I149, -1 + I150, I153) [I153 = I152 /\ I152 = I152]
  f4#(I154, I155, I156, I157, I158, I159) -> f3#(I158, I159, I156, I157, I158, I159) [0 <= I159]
  f4#(I160, I161, I162, I163, I164, I165) -> f1#(I164, I165, I162, I163, I164, I165) [1 + I165 <= 0]
  f3#(I166, I167, I168, I169, I170, I171) -> f4#(I170, I171, I168, I169, I170, -1 + I171) 
R = 
  f14(x1, x2, x3, x4, x5, x6) -> f13(x1, x2, x3, x4, x5, x6) 
  f13(I0, I1, I2, I3, I4, I5) -> f12(I0, I1, I2, I3, I4, I5) 
  f13(I6, I7, I8, I9, I10, I11) -> f11(I6, I7, I8, I9, I10, I11) 
  f13(I12, I13, I14, I15, I16, I17) -> f10(I12, I13, I14, I15, I16, I17) 
  f13(I18, I19, I20, I21, I22, I23) -> f8(I18, I19, I20, I21, I22, I23) 
  f13(I24, I25, I26, I27, I28, I29) -> f9(I24, I25, I26, I27, I28, I29) 
  f13(I30, I31, I32, I33, I34, I35) -> f7(I30, I31, I32, I33, I34, I35) 
  f13(I36, I37, I38, I39, I40, I41) -> f6(I36, I37, I38, I39, I40, I41) 
  f13(I42, I43, I44, I45, I46, I47) -> f5(I42, I43, I44, I45, I46, I47) 
  f13(I48, I49, I50, I51, I52, I53) -> f4(I48, I49, I50, I51, I52, I53) 
  f13(I54, I55, I56, I57, I58, I59) -> f3(I54, I55, I56, I57, I58, I59) 
  f13(I60, I61, I62, I63, I64, I65) -> f1(I60, I61, I62, I63, I64, I65) 
  f13(I66, I67, I68, I69, I70, I71) -> f2(I66, I67, I68, I69, I70, I71) 
  f13(I72, I73, I74, I75, I76, I77) -> f7(I76, I77, rnd3, rnd4, rnd5, rnd6) [rnd6 = rnd4 /\ rnd5 = rnd3 /\ rnd4 = rnd4 /\ rnd3 = rnd3]
  f13(I78, I79, I80, I81, I82, I83) -> f12(I82, I83, I84, I85, I86, I87) [I87 = I85 /\ I86 = I84 /\ I85 = I85 /\ I84 = I84]
  f12(I88, I89, I90, I91, I92, I93) -> f11(I92, I93, I90, I91, 0, 0) 
  f11(I94, I95, I96, I97, I98, I99) -> f10(I98, I99, I96, I97, I98, I99) [I98 <= 63]
  f11(I100, I101, I102, I103, I104, I105) -> f8(I104, I105, I102, I103, I104, I105) [64 <= I104]
  f10(I106, I107, I108, I109, I110, I111) -> f11(I110, I111, I112, I109, 1 + I110, I113) [I113 = I112 /\ I112 = I112]
  f8(I114, I115, I116, I117, I118, I119) -> f9(I118, I119, I120, I121, I122, I123) [I123 = I121 /\ I122 = I120 /\ I121 = I121 /\ I120 = I120]
  f7(I124, I125, I126, I127, I128, I129) -> f6(I128, I129, I130, I127, 7, I131) [I131 = I130 /\ I130 = I130]
  f6(I132, I133, I134, I135, I136, I137) -> f5(I136, I137, I138, I135, I136, I139) [I139 = I138 /\ 0 <= I136 /\ I138 = I138]
  f6(I140, I141, I142, I143, I144, I145) -> f4(I144, I145, I142, I143, I144, 7) [1 + I144 <= 0]
  f5(I146, I147, I148, I149, I150, I151) -> f6(I150, I151, I152, I149, -1 + I150, I153) [I153 = I152 /\ I152 = I152]
  f4(I154, I155, I156, I157, I158, I159) -> f3(I158, I159, I156, I157, I158, I159) [0 <= I159]
  f4(I160, I161, I162, I163, I164, I165) -> f1(I164, I165, I162, I163, I164, I165) [1 + I165 <= 0]
  f3(I166, I167, I168, I169, I170, I171) -> f4(I170, I171, I168, I169, I170, -1 + I171) 
  f1(I172, I173, I174, I175, I176, I177) -> f2(I176, I177, I178, I179, I180, I181) [I181 = I179 /\ I180 = I178 /\ I179 = I179 /\ I178 = I178]

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
  14 -> 16
  15 -> 
  16 -> 14, 15
  17 -> 18
  18 -> 20
  19 -> 21
  20 -> 18, 19
  21 -> 23
  22 -> 
  23 -> 21, 22
Where:
  0) f14#(x1, x2, x3, x4, x5, x6) -> f13#(x1, x2, x3, x4, x5, x6) 
  1) f13#(I0, I1, I2, I3, I4, I5) -> f12#(I0, I1, I2, I3, I4, I5) 
  2) f13#(I6, I7, I8, I9, I10, I11) -> f11#(I6, I7, I8, I9, I10, I11) 
  3) f13#(I12, I13, I14, I15, I16, I17) -> f10#(I12, I13, I14, I15, I16, I17) 
  4) f13#(I18, I19, I20, I21, I22, I23) -> f8#(I18, I19, I20, I21, I22, I23) 
  5) f13#(I30, I31, I32, I33, I34, I35) -> f7#(I30, I31, I32, I33, I34, I35) 
  6) f13#(I36, I37, I38, I39, I40, I41) -> f6#(I36, I37, I38, I39, I40, I41) 
  7) f13#(I42, I43, I44, I45, I46, I47) -> f5#(I42, I43, I44, I45, I46, I47) 
  8) f13#(I48, I49, I50, I51, I52, I53) -> f4#(I48, I49, I50, I51, I52, I53) 
  9) f13#(I54, I55, I56, I57, I58, I59) -> f3#(I54, I55, I56, I57, I58, I59) 
  10) f13#(I60, I61, I62, I63, I64, I65) -> f1#(I60, I61, I62, I63, I64, I65) 
  11) f13#(I72, I73, I74, I75, I76, I77) -> f7#(I76, I77, rnd3, rnd4, rnd5, rnd6) [rnd6 = rnd4 /\ rnd5 = rnd3 /\ rnd4 = rnd4 /\ rnd3 = rnd3]
  12) f13#(I78, I79, I80, I81, I82, I83) -> f12#(I82, I83, I84, I85, I86, I87) [I87 = I85 /\ I86 = I84 /\ I85 = I85 /\ I84 = I84]
  13) f12#(I88, I89, I90, I91, I92, I93) -> f11#(I92, I93, I90, I91, 0, 0) 
  14) f11#(I94, I95, I96, I97, I98, I99) -> f10#(I98, I99, I96, I97, I98, I99) [I98 <= 63]
  15) f11#(I100, I101, I102, I103, I104, I105) -> f8#(I104, I105, I102, I103, I104, I105) [64 <= I104]
  16) f10#(I106, I107, I108, I109, I110, I111) -> f11#(I110, I111, I112, I109, 1 + I110, I113) [I113 = I112 /\ I112 = I112]
  17) f7#(I124, I125, I126, I127, I128, I129) -> f6#(I128, I129, I130, I127, 7, I131) [I131 = I130 /\ I130 = I130]
  18) f6#(I132, I133, I134, I135, I136, I137) -> f5#(I136, I137, I138, I135, I136, I139) [I139 = I138 /\ 0 <= I136 /\ I138 = I138]
  19) f6#(I140, I141, I142, I143, I144, I145) -> f4#(I144, I145, I142, I143, I144, 7) [1 + I144 <= 0]
  20) f5#(I146, I147, I148, I149, I150, I151) -> f6#(I150, I151, I152, I149, -1 + I150, I153) [I153 = I152 /\ I152 = I152]
  21) f4#(I154, I155, I156, I157, I158, I159) -> f3#(I158, I159, I156, I157, I158, I159) [0 <= I159]
  22) f4#(I160, I161, I162, I163, I164, I165) -> f1#(I164, I165, I162, I163, I164, I165) [1 + I165 <= 0]
  23) f3#(I166, I167, I168, I169, I170, I171) -> f4#(I170, I171, I168, I169, I170, -1 + I171) 

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

DP problem for innermost termination.
P =
  f4#(I154, I155, I156, I157, I158, I159) -> f3#(I158, I159, I156, I157, I158, I159) [0 <= I159]
  f3#(I166, I167, I168, I169, I170, I171) -> f4#(I170, I171, I168, I169, I170, -1 + I171) 
R = 
  f14(x1, x2, x3, x4, x5, x6) -> f13(x1, x2, x3, x4, x5, x6) 
  f13(I0, I1, I2, I3, I4, I5) -> f12(I0, I1, I2, I3, I4, I5) 
  f13(I6, I7, I8, I9, I10, I11) -> f11(I6, I7, I8, I9, I10, I11) 
  f13(I12, I13, I14, I15, I16, I17) -> f10(I12, I13, I14, I15, I16, I17) 
  f13(I18, I19, I20, I21, I22, I23) -> f8(I18, I19, I20, I21, I22, I23) 
  f13(I24, I25, I26, I27, I28, I29) -> f9(I24, I25, I26, I27, I28, I29) 
  f13(I30, I31, I32, I33, I34, I35) -> f7(I30, I31, I32, I33, I34, I35) 
  f13(I36, I37, I38, I39, I40, I41) -> f6(I36, I37, I38, I39, I40, I41) 
  f13(I42, I43, I44, I45, I46, I47) -> f5(I42, I43, I44, I45, I46, I47) 
  f13(I48, I49, I50, I51, I52, I53) -> f4(I48, I49, I50, I51, I52, I53) 
  f13(I54, I55, I56, I57, I58, I59) -> f3(I54, I55, I56, I57, I58, I59) 
  f13(I60, I61, I62, I63, I64, I65) -> f1(I60, I61, I62, I63, I64, I65) 
  f13(I66, I67, I68, I69, I70, I71) -> f2(I66, I67, I68, I69, I70, I71) 
  f13(I72, I73, I74, I75, I76, I77) -> f7(I76, I77, rnd3, rnd4, rnd5, rnd6) [rnd6 = rnd4 /\ rnd5 = rnd3 /\ rnd4 = rnd4 /\ rnd3 = rnd3]
  f13(I78, I79, I80, I81, I82, I83) -> f12(I82, I83, I84, I85, I86, I87) [I87 = I85 /\ I86 = I84 /\ I85 = I85 /\ I84 = I84]
  f12(I88, I89, I90, I91, I92, I93) -> f11(I92, I93, I90, I91, 0, 0) 
  f11(I94, I95, I96, I97, I98, I99) -> f10(I98, I99, I96, I97, I98, I99) [I98 <= 63]
  f11(I100, I101, I102, I103, I104, I105) -> f8(I104, I105, I102, I103, I104, I105) [64 <= I104]
  f10(I106, I107, I108, I109, I110, I111) -> f11(I110, I111, I112, I109, 1 + I110, I113) [I113 = I112 /\ I112 = I112]
  f8(I114, I115, I116, I117, I118, I119) -> f9(I118, I119, I120, I121, I122, I123) [I123 = I121 /\ I122 = I120 /\ I121 = I121 /\ I120 = I120]
  f7(I124, I125, I126, I127, I128, I129) -> f6(I128, I129, I130, I127, 7, I131) [I131 = I130 /\ I130 = I130]
  f6(I132, I133, I134, I135, I136, I137) -> f5(I136, I137, I138, I135, I136, I139) [I139 = I138 /\ 0 <= I136 /\ I138 = I138]
  f6(I140, I141, I142, I143, I144, I145) -> f4(I144, I145, I142, I143, I144, 7) [1 + I144 <= 0]
  f5(I146, I147, I148, I149, I150, I151) -> f6(I150, I151, I152, I149, -1 + I150, I153) [I153 = I152 /\ I152 = I152]
  f4(I154, I155, I156, I157, I158, I159) -> f3(I158, I159, I156, I157, I158, I159) [0 <= I159]
  f4(I160, I161, I162, I163, I164, I165) -> f1(I164, I165, I162, I163, I164, I165) [1 + I165 <= 0]
  f3(I166, I167, I168, I169, I170, I171) -> f4(I170, I171, I168, I169, I170, -1 + I171) 
  f1(I172, I173, I174, I175, I176, I177) -> f2(I176, I177, I178, I179, I180, I181) [I181 = I179 /\ I180 = I178 /\ I179 = I179 /\ I178 = I178]

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

This gives the following inequalities:
  0 <= I159  ==>  I159 > -1 + I159 + -1 * 0  with  I159 >= 0
    ==>  -1 + I171 + -1 * 0 >= -1 + I171

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f3#(I166, I167, I168, I169, I170, I171) -> f4#(I170, I171, I168, I169, I170, -1 + I171) 
R = 
  f14(x1, x2, x3, x4, x5, x6) -> f13(x1, x2, x3, x4, x5, x6) 
  f13(I0, I1, I2, I3, I4, I5) -> f12(I0, I1, I2, I3, I4, I5) 
  f13(I6, I7, I8, I9, I10, I11) -> f11(I6, I7, I8, I9, I10, I11) 
  f13(I12, I13, I14, I15, I16, I17) -> f10(I12, I13, I14, I15, I16, I17) 
  f13(I18, I19, I20, I21, I22, I23) -> f8(I18, I19, I20, I21, I22, I23) 
  f13(I24, I25, I26, I27, I28, I29) -> f9(I24, I25, I26, I27, I28, I29) 
  f13(I30, I31, I32, I33, I34, I35) -> f7(I30, I31, I32, I33, I34, I35) 
  f13(I36, I37, I38, I39, I40, I41) -> f6(I36, I37, I38, I39, I40, I41) 
  f13(I42, I43, I44, I45, I46, I47) -> f5(I42, I43, I44, I45, I46, I47) 
  f13(I48, I49, I50, I51, I52, I53) -> f4(I48, I49, I50, I51, I52, I53) 
  f13(I54, I55, I56, I57, I58, I59) -> f3(I54, I55, I56, I57, I58, I59) 
  f13(I60, I61, I62, I63, I64, I65) -> f1(I60, I61, I62, I63, I64, I65) 
  f13(I66, I67, I68, I69, I70, I71) -> f2(I66, I67, I68, I69, I70, I71) 
  f13(I72, I73, I74, I75, I76, I77) -> f7(I76, I77, rnd3, rnd4, rnd5, rnd6) [rnd6 = rnd4 /\ rnd5 = rnd3 /\ rnd4 = rnd4 /\ rnd3 = rnd3]
  f13(I78, I79, I80, I81, I82, I83) -> f12(I82, I83, I84, I85, I86, I87) [I87 = I85 /\ I86 = I84 /\ I85 = I85 /\ I84 = I84]
  f12(I88, I89, I90, I91, I92, I93) -> f11(I92, I93, I90, I91, 0, 0) 
  f11(I94, I95, I96, I97, I98, I99) -> f10(I98, I99, I96, I97, I98, I99) [I98 <= 63]
  f11(I100, I101, I102, I103, I104, I105) -> f8(I104, I105, I102, I103, I104, I105) [64 <= I104]
  f10(I106, I107, I108, I109, I110, I111) -> f11(I110, I111, I112, I109, 1 + I110, I113) [I113 = I112 /\ I112 = I112]
  f8(I114, I115, I116, I117, I118, I119) -> f9(I118, I119, I120, I121, I122, I123) [I123 = I121 /\ I122 = I120 /\ I121 = I121 /\ I120 = I120]
  f7(I124, I125, I126, I127, I128, I129) -> f6(I128, I129, I130, I127, 7, I131) [I131 = I130 /\ I130 = I130]
  f6(I132, I133, I134, I135, I136, I137) -> f5(I136, I137, I138, I135, I136, I139) [I139 = I138 /\ 0 <= I136 /\ I138 = I138]
  f6(I140, I141, I142, I143, I144, I145) -> f4(I144, I145, I142, I143, I144, 7) [1 + I144 <= 0]
  f5(I146, I147, I148, I149, I150, I151) -> f6(I150, I151, I152, I149, -1 + I150, I153) [I153 = I152 /\ I152 = I152]
  f4(I154, I155, I156, I157, I158, I159) -> f3(I158, I159, I156, I157, I158, I159) [0 <= I159]
  f4(I160, I161, I162, I163, I164, I165) -> f1(I164, I165, I162, I163, I164, I165) [1 + I165 <= 0]
  f3(I166, I167, I168, I169, I170, I171) -> f4(I170, I171, I168, I169, I170, -1 + I171) 
  f1(I172, I173, I174, I175, I176, I177) -> f2(I176, I177, I178, I179, I180, I181) [I181 = I179 /\ I180 = I178 /\ I179 = I179 /\ I178 = I178]

The dependency graph for this problem is:
  23 -> 
Where:
  23) f3#(I166, I167, I168, I169, I170, I171) -> f4#(I170, I171, I168, I169, I170, -1 + I171) 

We have the following SCCs.
  

DP problem for innermost termination.
P =
  f6#(I132, I133, I134, I135, I136, I137) -> f5#(I136, I137, I138, I135, I136, I139) [I139 = I138 /\ 0 <= I136 /\ I138 = I138]
  f5#(I146, I147, I148, I149, I150, I151) -> f6#(I150, I151, I152, I149, -1 + I150, I153) [I153 = I152 /\ I152 = I152]
R = 
  f14(x1, x2, x3, x4, x5, x6) -> f13(x1, x2, x3, x4, x5, x6) 
  f13(I0, I1, I2, I3, I4, I5) -> f12(I0, I1, I2, I3, I4, I5) 
  f13(I6, I7, I8, I9, I10, I11) -> f11(I6, I7, I8, I9, I10, I11) 
  f13(I12, I13, I14, I15, I16, I17) -> f10(I12, I13, I14, I15, I16, I17) 
  f13(I18, I19, I20, I21, I22, I23) -> f8(I18, I19, I20, I21, I22, I23) 
  f13(I24, I25, I26, I27, I28, I29) -> f9(I24, I25, I26, I27, I28, I29) 
  f13(I30, I31, I32, I33, I34, I35) -> f7(I30, I31, I32, I33, I34, I35) 
  f13(I36, I37, I38, I39, I40, I41) -> f6(I36, I37, I38, I39, I40, I41) 
  f13(I42, I43, I44, I45, I46, I47) -> f5(I42, I43, I44, I45, I46, I47) 
  f13(I48, I49, I50, I51, I52, I53) -> f4(I48, I49, I50, I51, I52, I53) 
  f13(I54, I55, I56, I57, I58, I59) -> f3(I54, I55, I56, I57, I58, I59) 
  f13(I60, I61, I62, I63, I64, I65) -> f1(I60, I61, I62, I63, I64, I65) 
  f13(I66, I67, I68, I69, I70, I71) -> f2(I66, I67, I68, I69, I70, I71) 
  f13(I72, I73, I74, I75, I76, I77) -> f7(I76, I77, rnd3, rnd4, rnd5, rnd6) [rnd6 = rnd4 /\ rnd5 = rnd3 /\ rnd4 = rnd4 /\ rnd3 = rnd3]
  f13(I78, I79, I80, I81, I82, I83) -> f12(I82, I83, I84, I85, I86, I87) [I87 = I85 /\ I86 = I84 /\ I85 = I85 /\ I84 = I84]
  f12(I88, I89, I90, I91, I92, I93) -> f11(I92, I93, I90, I91, 0, 0) 
  f11(I94, I95, I96, I97, I98, I99) -> f10(I98, I99, I96, I97, I98, I99) [I98 <= 63]
  f11(I100, I101, I102, I103, I104, I105) -> f8(I104, I105, I102, I103, I104, I105) [64 <= I104]
  f10(I106, I107, I108, I109, I110, I111) -> f11(I110, I111, I112, I109, 1 + I110, I113) [I113 = I112 /\ I112 = I112]
  f8(I114, I115, I116, I117, I118, I119) -> f9(I118, I119, I120, I121, I122, I123) [I123 = I121 /\ I122 = I120 /\ I121 = I121 /\ I120 = I120]
  f7(I124, I125, I126, I127, I128, I129) -> f6(I128, I129, I130, I127, 7, I131) [I131 = I130 /\ I130 = I130]
  f6(I132, I133, I134, I135, I136, I137) -> f5(I136, I137, I138, I135, I136, I139) [I139 = I138 /\ 0 <= I136 /\ I138 = I138]
  f6(I140, I141, I142, I143, I144, I145) -> f4(I144, I145, I142, I143, I144, 7) [1 + I144 <= 0]
  f5(I146, I147, I148, I149, I150, I151) -> f6(I150, I151, I152, I149, -1 + I150, I153) [I153 = I152 /\ I152 = I152]
  f4(I154, I155, I156, I157, I158, I159) -> f3(I158, I159, I156, I157, I158, I159) [0 <= I159]
  f4(I160, I161, I162, I163, I164, I165) -> f1(I164, I165, I162, I163, I164, I165) [1 + I165 <= 0]
  f3(I166, I167, I168, I169, I170, I171) -> f4(I170, I171, I168, I169, I170, -1 + I171) 
  f1(I172, I173, I174, I175, I176, I177) -> f2(I176, I177, I178, I179, I180, I181) [I181 = I179 /\ I180 = I178 /\ I179 = I179 /\ I178 = I178]

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

This gives the following inequalities:
  I139 = I138 /\ 0 <= I136 /\ I138 = I138  ==>  I136 > -1 + I136 + -1 * 0  with  I136 >= 0
  I153 = I152 /\ I152 = I152  ==>  -1 + I150 + -1 * 0 >= -1 + I150

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f5#(I146, I147, I148, I149, I150, I151) -> f6#(I150, I151, I152, I149, -1 + I150, I153) [I153 = I152 /\ I152 = I152]
R = 
  f14(x1, x2, x3, x4, x5, x6) -> f13(x1, x2, x3, x4, x5, x6) 
  f13(I0, I1, I2, I3, I4, I5) -> f12(I0, I1, I2, I3, I4, I5) 
  f13(I6, I7, I8, I9, I10, I11) -> f11(I6, I7, I8, I9, I10, I11) 
  f13(I12, I13, I14, I15, I16, I17) -> f10(I12, I13, I14, I15, I16, I17) 
  f13(I18, I19, I20, I21, I22, I23) -> f8(I18, I19, I20, I21, I22, I23) 
  f13(I24, I25, I26, I27, I28, I29) -> f9(I24, I25, I26, I27, I28, I29) 
  f13(I30, I31, I32, I33, I34, I35) -> f7(I30, I31, I32, I33, I34, I35) 
  f13(I36, I37, I38, I39, I40, I41) -> f6(I36, I37, I38, I39, I40, I41) 
  f13(I42, I43, I44, I45, I46, I47) -> f5(I42, I43, I44, I45, I46, I47) 
  f13(I48, I49, I50, I51, I52, I53) -> f4(I48, I49, I50, I51, I52, I53) 
  f13(I54, I55, I56, I57, I58, I59) -> f3(I54, I55, I56, I57, I58, I59) 
  f13(I60, I61, I62, I63, I64, I65) -> f1(I60, I61, I62, I63, I64, I65) 
  f13(I66, I67, I68, I69, I70, I71) -> f2(I66, I67, I68, I69, I70, I71) 
  f13(I72, I73, I74, I75, I76, I77) -> f7(I76, I77, rnd3, rnd4, rnd5, rnd6) [rnd6 = rnd4 /\ rnd5 = rnd3 /\ rnd4 = rnd4 /\ rnd3 = rnd3]
  f13(I78, I79, I80, I81, I82, I83) -> f12(I82, I83, I84, I85, I86, I87) [I87 = I85 /\ I86 = I84 /\ I85 = I85 /\ I84 = I84]
  f12(I88, I89, I90, I91, I92, I93) -> f11(I92, I93, I90, I91, 0, 0) 
  f11(I94, I95, I96, I97, I98, I99) -> f10(I98, I99, I96, I97, I98, I99) [I98 <= 63]
  f11(I100, I101, I102, I103, I104, I105) -> f8(I104, I105, I102, I103, I104, I105) [64 <= I104]
  f10(I106, I107, I108, I109, I110, I111) -> f11(I110, I111, I112, I109, 1 + I110, I113) [I113 = I112 /\ I112 = I112]
  f8(I114, I115, I116, I117, I118, I119) -> f9(I118, I119, I120, I121, I122, I123) [I123 = I121 /\ I122 = I120 /\ I121 = I121 /\ I120 = I120]
  f7(I124, I125, I126, I127, I128, I129) -> f6(I128, I129, I130, I127, 7, I131) [I131 = I130 /\ I130 = I130]
  f6(I132, I133, I134, I135, I136, I137) -> f5(I136, I137, I138, I135, I136, I139) [I139 = I138 /\ 0 <= I136 /\ I138 = I138]
  f6(I140, I141, I142, I143, I144, I145) -> f4(I144, I145, I142, I143, I144, 7) [1 + I144 <= 0]
  f5(I146, I147, I148, I149, I150, I151) -> f6(I150, I151, I152, I149, -1 + I150, I153) [I153 = I152 /\ I152 = I152]
  f4(I154, I155, I156, I157, I158, I159) -> f3(I158, I159, I156, I157, I158, I159) [0 <= I159]
  f4(I160, I161, I162, I163, I164, I165) -> f1(I164, I165, I162, I163, I164, I165) [1 + I165 <= 0]
  f3(I166, I167, I168, I169, I170, I171) -> f4(I170, I171, I168, I169, I170, -1 + I171) 
  f1(I172, I173, I174, I175, I176, I177) -> f2(I176, I177, I178, I179, I180, I181) [I181 = I179 /\ I180 = I178 /\ I179 = I179 /\ I178 = I178]

The dependency graph for this problem is:
  20 -> 
Where:
  20) f5#(I146, I147, I148, I149, I150, I151) -> f6#(I150, I151, I152, I149, -1 + I150, I153) [I153 = I152 /\ I152 = I152]

We have the following SCCs.
  

DP problem for innermost termination.
P =
  f11#(I94, I95, I96, I97, I98, I99) -> f10#(I98, I99, I96, I97, I98, I99) [I98 <= 63]
  f10#(I106, I107, I108, I109, I110, I111) -> f11#(I110, I111, I112, I109, 1 + I110, I113) [I113 = I112 /\ I112 = I112]
R = 
  f14(x1, x2, x3, x4, x5, x6) -> f13(x1, x2, x3, x4, x5, x6) 
  f13(I0, I1, I2, I3, I4, I5) -> f12(I0, I1, I2, I3, I4, I5) 
  f13(I6, I7, I8, I9, I10, I11) -> f11(I6, I7, I8, I9, I10, I11) 
  f13(I12, I13, I14, I15, I16, I17) -> f10(I12, I13, I14, I15, I16, I17) 
  f13(I18, I19, I20, I21, I22, I23) -> f8(I18, I19, I20, I21, I22, I23) 
  f13(I24, I25, I26, I27, I28, I29) -> f9(I24, I25, I26, I27, I28, I29) 
  f13(I30, I31, I32, I33, I34, I35) -> f7(I30, I31, I32, I33, I34, I35) 
  f13(I36, I37, I38, I39, I40, I41) -> f6(I36, I37, I38, I39, I40, I41) 
  f13(I42, I43, I44, I45, I46, I47) -> f5(I42, I43, I44, I45, I46, I47) 
  f13(I48, I49, I50, I51, I52, I53) -> f4(I48, I49, I50, I51, I52, I53) 
  f13(I54, I55, I56, I57, I58, I59) -> f3(I54, I55, I56, I57, I58, I59) 
  f13(I60, I61, I62, I63, I64, I65) -> f1(I60, I61, I62, I63, I64, I65) 
  f13(I66, I67, I68, I69, I70, I71) -> f2(I66, I67, I68, I69, I70, I71) 
  f13(I72, I73, I74, I75, I76, I77) -> f7(I76, I77, rnd3, rnd4, rnd5, rnd6) [rnd6 = rnd4 /\ rnd5 = rnd3 /\ rnd4 = rnd4 /\ rnd3 = rnd3]
  f13(I78, I79, I80, I81, I82, I83) -> f12(I82, I83, I84, I85, I86, I87) [I87 = I85 /\ I86 = I84 /\ I85 = I85 /\ I84 = I84]
  f12(I88, I89, I90, I91, I92, I93) -> f11(I92, I93, I90, I91, 0, 0) 
  f11(I94, I95, I96, I97, I98, I99) -> f10(I98, I99, I96, I97, I98, I99) [I98 <= 63]
  f11(I100, I101, I102, I103, I104, I105) -> f8(I104, I105, I102, I103, I104, I105) [64 <= I104]
  f10(I106, I107, I108, I109, I110, I111) -> f11(I110, I111, I112, I109, 1 + I110, I113) [I113 = I112 /\ I112 = I112]
  f8(I114, I115, I116, I117, I118, I119) -> f9(I118, I119, I120, I121, I122, I123) [I123 = I121 /\ I122 = I120 /\ I121 = I121 /\ I120 = I120]
  f7(I124, I125, I126, I127, I128, I129) -> f6(I128, I129, I130, I127, 7, I131) [I131 = I130 /\ I130 = I130]
  f6(I132, I133, I134, I135, I136, I137) -> f5(I136, I137, I138, I135, I136, I139) [I139 = I138 /\ 0 <= I136 /\ I138 = I138]
  f6(I140, I141, I142, I143, I144, I145) -> f4(I144, I145, I142, I143, I144, 7) [1 + I144 <= 0]
  f5(I146, I147, I148, I149, I150, I151) -> f6(I150, I151, I152, I149, -1 + I150, I153) [I153 = I152 /\ I152 = I152]
  f4(I154, I155, I156, I157, I158, I159) -> f3(I158, I159, I156, I157, I158, I159) [0 <= I159]
  f4(I160, I161, I162, I163, I164, I165) -> f1(I164, I165, I162, I163, I164, I165) [1 + I165 <= 0]
  f3(I166, I167, I168, I169, I170, I171) -> f4(I170, I171, I168, I169, I170, -1 + I171) 
  f1(I172, I173, I174, I175, I176, I177) -> f2(I176, I177, I178, I179, I180, I181) [I181 = I179 /\ I180 = I178 /\ I179 = I179 /\ I178 = I178]

We use the reverse value criterion with the projection function NU:
  NU[f10#(z1,z2,z3,z4,z5,z6)] = 63 + -1 * (1 + z5)
  NU[f11#(z1,z2,z3,z4,z5,z6)] = 63 + -1 * z5

This gives the following inequalities:
  I98 <= 63  ==>  63 + -1 * I98 > 63 + -1 * (1 + I98)  with  63 + -1 * I98 >= 0
  I113 = I112 /\ I112 = I112  ==>  63 + -1 * (1 + I110) >= 63 + -1 * (1 + I110)

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f10#(I106, I107, I108, I109, I110, I111) -> f11#(I110, I111, I112, I109, 1 + I110, I113) [I113 = I112 /\ I112 = I112]
R = 
  f14(x1, x2, x3, x4, x5, x6) -> f13(x1, x2, x3, x4, x5, x6) 
  f13(I0, I1, I2, I3, I4, I5) -> f12(I0, I1, I2, I3, I4, I5) 
  f13(I6, I7, I8, I9, I10, I11) -> f11(I6, I7, I8, I9, I10, I11) 
  f13(I12, I13, I14, I15, I16, I17) -> f10(I12, I13, I14, I15, I16, I17) 
  f13(I18, I19, I20, I21, I22, I23) -> f8(I18, I19, I20, I21, I22, I23) 
  f13(I24, I25, I26, I27, I28, I29) -> f9(I24, I25, I26, I27, I28, I29) 
  f13(I30, I31, I32, I33, I34, I35) -> f7(I30, I31, I32, I33, I34, I35) 
  f13(I36, I37, I38, I39, I40, I41) -> f6(I36, I37, I38, I39, I40, I41) 
  f13(I42, I43, I44, I45, I46, I47) -> f5(I42, I43, I44, I45, I46, I47) 
  f13(I48, I49, I50, I51, I52, I53) -> f4(I48, I49, I50, I51, I52, I53) 
  f13(I54, I55, I56, I57, I58, I59) -> f3(I54, I55, I56, I57, I58, I59) 
  f13(I60, I61, I62, I63, I64, I65) -> f1(I60, I61, I62, I63, I64, I65) 
  f13(I66, I67, I68, I69, I70, I71) -> f2(I66, I67, I68, I69, I70, I71) 
  f13(I72, I73, I74, I75, I76, I77) -> f7(I76, I77, rnd3, rnd4, rnd5, rnd6) [rnd6 = rnd4 /\ rnd5 = rnd3 /\ rnd4 = rnd4 /\ rnd3 = rnd3]
  f13(I78, I79, I80, I81, I82, I83) -> f12(I82, I83, I84, I85, I86, I87) [I87 = I85 /\ I86 = I84 /\ I85 = I85 /\ I84 = I84]
  f12(I88, I89, I90, I91, I92, I93) -> f11(I92, I93, I90, I91, 0, 0) 
  f11(I94, I95, I96, I97, I98, I99) -> f10(I98, I99, I96, I97, I98, I99) [I98 <= 63]
  f11(I100, I101, I102, I103, I104, I105) -> f8(I104, I105, I102, I103, I104, I105) [64 <= I104]
  f10(I106, I107, I108, I109, I110, I111) -> f11(I110, I111, I112, I109, 1 + I110, I113) [I113 = I112 /\ I112 = I112]
  f8(I114, I115, I116, I117, I118, I119) -> f9(I118, I119, I120, I121, I122, I123) [I123 = I121 /\ I122 = I120 /\ I121 = I121 /\ I120 = I120]
  f7(I124, I125, I126, I127, I128, I129) -> f6(I128, I129, I130, I127, 7, I131) [I131 = I130 /\ I130 = I130]
  f6(I132, I133, I134, I135, I136, I137) -> f5(I136, I137, I138, I135, I136, I139) [I139 = I138 /\ 0 <= I136 /\ I138 = I138]
  f6(I140, I141, I142, I143, I144, I145) -> f4(I144, I145, I142, I143, I144, 7) [1 + I144 <= 0]
  f5(I146, I147, I148, I149, I150, I151) -> f6(I150, I151, I152, I149, -1 + I150, I153) [I153 = I152 /\ I152 = I152]
  f4(I154, I155, I156, I157, I158, I159) -> f3(I158, I159, I156, I157, I158, I159) [0 <= I159]
  f4(I160, I161, I162, I163, I164, I165) -> f1(I164, I165, I162, I163, I164, I165) [1 + I165 <= 0]
  f3(I166, I167, I168, I169, I170, I171) -> f4(I170, I171, I168, I169, I170, -1 + I171) 
  f1(I172, I173, I174, I175, I176, I177) -> f2(I176, I177, I178, I179, I180, I181) [I181 = I179 /\ I180 = I178 /\ I179 = I179 /\ I178 = I178]

The dependency graph for this problem is:
  16 -> 
Where:
  16) f10#(I106, I107, I108, I109, I110, I111) -> f11#(I110, I111, I112, I109, 1 + I110, I113) [I113 = I112 /\ I112 = I112]

We have the following SCCs.