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

The dependency graph for this problem is:
  0 -> 1
  1 -> 15
  2 -> 13
  3 -> 15
  4 -> 11
  5 -> 14
  6 -> 8, 9, 10
  7 -> 13
  8 -> 12
  9 -> 
  10 -> 12
  11 -> 6, 7
  12 -> 11
  13 -> 4, 5
  14 -> 2, 3
  15 -> 16, 17
  16 -> 14
  17 -> 
Where:
  0) f14#(x1, x2, x3, x4, x5, x6, x7) -> f13#(x1, x2, x3, x4, x5, x6, x7) 
  1) f13#(I0, I1, I2, I3, I4, I5, I6) -> f4#(I0, I1, 0, I3, I4, I5, I0) 
  2) f5#(I7, I8, I9, I10, I11, I12, I13) -> f7#(I7, I8, I9, I10, 0, I12, I13) [1 + I10 <= I8]
  3) f5#(I14, I15, I16, I17, I18, I19, I20) -> f4#(I14, I15, 1 + I16, I17, I18, I19, I20) [I15 <= I17]
  4) f8#(I21, I22, I23, I24, I25, I26, I27) -> f10#(I21, I22, I23, I24, I25, 0, I27) [1 + I25 <= I22]
  5) f8#(I28, I29, I30, I31, I32, I33, I34) -> f3#(I28, I29, I30, 1 + I31, I32, I33, I34) [I29 <= I32]
  6) f11#(I35, I36, I37, I38, I39, I40, I41) -> f12#(I35, I36, I37, I38, I39, I40, I41) [1 + I40 <= I36]
  7) f11#(I42, I43, I44, I45, I46, I47, I48) -> f7#(I42, I43, I44, I45, 1 + I46, I47, I48) [I43 <= I47]
  8) f12#(I49, I50, I51, I52, I53, I54, I55) -> f9#(I49, I50, I51, I52, I53, I54, I55) 
  9) f12#(I56, I57, I58, I59, I60, I61, I62) -> f2#(I56, I57, I58, I59, I60, I61, I62) 
  10) f12#(I63, I64, I65, I66, I67, I68, I69) -> f9#(I63, I64, I65, I66, I67, I68, I69) 
  11) f10#(I70, I71, I72, I73, I74, I75, I76) -> f11#(I70, I71, I72, I73, I74, I75, I76) 
  12) f9#(I77, I78, I79, I80, I81, I82, I83) -> f10#(I77, I78, I79, I80, I81, 1 + I82, I83) 
  13) f7#(I84, I85, I86, I87, I88, I89, I90) -> f8#(I84, I85, I86, I87, I88, I89, I90) 
  14) f3#(I98, I99, I100, I101, I102, I103, I104) -> f5#(I98, I99, I100, I101, I102, I103, I104) 
  15) f4#(I105, I106, I107, I108, I109, I110, I111) -> f1#(I105, I106, I107, I108, I109, I110, I111) 
  16) f1#(I112, I113, I114, I115, I116, I117, I118) -> f3#(I112, I113, I114, 0, I116, I117, I118) [1 + I114 <= I113]
  17) f1#(I119, I120, I121, I122, I123, I124, I125) -> f2#(I119, I120, I121, I122, I123, I124, I125) [I120 <= I121]

We have the following SCCs.
  { 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16 }

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

We use the extended value criterion with the projection function NU:
  NU[f1#(x0,x1,x2,x3,x4,x5,x6)] = x1 - x2
  NU[f9#(x0,x1,x2,x3,x4,x5,x6)] = x1 - x2 - 1
  NU[f12#(x0,x1,x2,x3,x4,x5,x6)] = x1 - x2 - 1
  NU[f11#(x0,x1,x2,x3,x4,x5,x6)] = x1 - x2 - 1
  NU[f3#(x0,x1,x2,x3,x4,x5,x6)] = x1 - x2 - 1
  NU[f10#(x0,x1,x2,x3,x4,x5,x6)] = x1 - x2 - 1
  NU[f8#(x0,x1,x2,x3,x4,x5,x6)] = x1 - x2 - 1
  NU[f4#(x0,x1,x2,x3,x4,x5,x6)] = x1 - x2
  NU[f7#(x0,x1,x2,x3,x4,x5,x6)] = x1 - x2 - 1
  NU[f5#(x0,x1,x2,x3,x4,x5,x6)] = x1 - x2 - 1

This gives the following inequalities:
  1 + I10 <= I8  ==>  I8 - I9 - 1 >= I8 - I9 - 1
  I15 <= I17  ==>  I15 - I16 - 1 >= I15 - (1 + I16)
  1 + I25 <= I22  ==>  I22 - I23 - 1 >= I22 - I23 - 1
  I29 <= I32  ==>  I29 - I30 - 1 >= I29 - I30 - 1
  1 + I40 <= I36  ==>  I36 - I37 - 1 >= I36 - I37 - 1
  I43 <= I47  ==>  I43 - I44 - 1 >= I43 - I44 - 1
    ==>  I50 - I51 - 1 >= I50 - I51 - 1
    ==>  I64 - I65 - 1 >= I64 - I65 - 1
    ==>  I71 - I72 - 1 >= I71 - I72 - 1
    ==>  I78 - I79 - 1 >= I78 - I79 - 1
    ==>  I85 - I86 - 1 >= I85 - I86 - 1
    ==>  I99 - I100 - 1 >= I99 - I100 - 1
    ==>  I106 - I107 >= I106 - I107
  1 + I114 <= I113  ==>  I113 - I114 > I113 - I114 - 1  with  I113 - I114 >= 0

We remove all the strictly oriented dependency pairs.

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

The dependency graph for this problem is:
  2 -> 13
  3 -> 15
  4 -> 11
  5 -> 14
  6 -> 8, 10
  7 -> 13
  8 -> 12
  10 -> 12
  11 -> 6, 7
  12 -> 11
  13 -> 4, 5
  14 -> 2, 3
  15 -> 
Where:
  2) f5#(I7, I8, I9, I10, I11, I12, I13) -> f7#(I7, I8, I9, I10, 0, I12, I13) [1 + I10 <= I8]
  3) f5#(I14, I15, I16, I17, I18, I19, I20) -> f4#(I14, I15, 1 + I16, I17, I18, I19, I20) [I15 <= I17]
  4) f8#(I21, I22, I23, I24, I25, I26, I27) -> f10#(I21, I22, I23, I24, I25, 0, I27) [1 + I25 <= I22]
  5) f8#(I28, I29, I30, I31, I32, I33, I34) -> f3#(I28, I29, I30, 1 + I31, I32, I33, I34) [I29 <= I32]
  6) f11#(I35, I36, I37, I38, I39, I40, I41) -> f12#(I35, I36, I37, I38, I39, I40, I41) [1 + I40 <= I36]
  7) f11#(I42, I43, I44, I45, I46, I47, I48) -> f7#(I42, I43, I44, I45, 1 + I46, I47, I48) [I43 <= I47]
  8) f12#(I49, I50, I51, I52, I53, I54, I55) -> f9#(I49, I50, I51, I52, I53, I54, I55) 
  10) f12#(I63, I64, I65, I66, I67, I68, I69) -> f9#(I63, I64, I65, I66, I67, I68, I69) 
  11) f10#(I70, I71, I72, I73, I74, I75, I76) -> f11#(I70, I71, I72, I73, I74, I75, I76) 
  12) f9#(I77, I78, I79, I80, I81, I82, I83) -> f10#(I77, I78, I79, I80, I81, 1 + I82, I83) 
  13) f7#(I84, I85, I86, I87, I88, I89, I90) -> f8#(I84, I85, I86, I87, I88, I89, I90) 
  14) f3#(I98, I99, I100, I101, I102, I103, I104) -> f5#(I98, I99, I100, I101, I102, I103, I104) 
  15) f4#(I105, I106, I107, I108, I109, I110, I111) -> f1#(I105, I106, I107, I108, I109, I110, I111) 

We have the following SCCs.
  { 2, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14 }

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

We use the extended value criterion with the projection function NU:
  NU[f9#(x0,x1,x2,x3,x4,x5,x6)] = x1 - x3
  NU[f12#(x0,x1,x2,x3,x4,x5,x6)] = x1 - x3
  NU[f11#(x0,x1,x2,x3,x4,x5,x6)] = x1 - x3
  NU[f3#(x0,x1,x2,x3,x4,x5,x6)] = x1 - x3 + 1
  NU[f10#(x0,x1,x2,x3,x4,x5,x6)] = x1 - x3
  NU[f8#(x0,x1,x2,x3,x4,x5,x6)] = x1 - x3
  NU[f7#(x0,x1,x2,x3,x4,x5,x6)] = x1 - x3
  NU[f5#(x0,x1,x2,x3,x4,x5,x6)] = x1 - x3 + 1

This gives the following inequalities:
  1 + I10 <= I8  ==>  I8 - I10 + 1 > I8 - I10  with  I8 - I10 + 1 >= 0
  1 + I25 <= I22  ==>  I22 - I24 >= I22 - I24
  I29 <= I32  ==>  I29 - I31 >= I29 - (1 + I31) + 1
  1 + I40 <= I36  ==>  I36 - I38 >= I36 - I38
  I43 <= I47  ==>  I43 - I45 >= I43 - I45
    ==>  I50 - I52 >= I50 - I52
    ==>  I64 - I66 >= I64 - I66
    ==>  I71 - I73 >= I71 - I73
    ==>  I78 - I80 >= I78 - I80
    ==>  I85 - I87 >= I85 - I87
    ==>  I99 - I101 + 1 >= I99 - I101 + 1

We remove all the strictly oriented dependency pairs.

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

The dependency graph for this problem is:
  4 -> 11
  5 -> 14
  6 -> 8, 10
  7 -> 13
  8 -> 12
  10 -> 12
  11 -> 6, 7
  12 -> 11
  13 -> 4, 5
  14 -> 
Where:
  4) f8#(I21, I22, I23, I24, I25, I26, I27) -> f10#(I21, I22, I23, I24, I25, 0, I27) [1 + I25 <= I22]
  5) f8#(I28, I29, I30, I31, I32, I33, I34) -> f3#(I28, I29, I30, 1 + I31, I32, I33, I34) [I29 <= I32]
  6) f11#(I35, I36, I37, I38, I39, I40, I41) -> f12#(I35, I36, I37, I38, I39, I40, I41) [1 + I40 <= I36]
  7) f11#(I42, I43, I44, I45, I46, I47, I48) -> f7#(I42, I43, I44, I45, 1 + I46, I47, I48) [I43 <= I47]
  8) f12#(I49, I50, I51, I52, I53, I54, I55) -> f9#(I49, I50, I51, I52, I53, I54, I55) 
  10) f12#(I63, I64, I65, I66, I67, I68, I69) -> f9#(I63, I64, I65, I66, I67, I68, I69) 
  11) f10#(I70, I71, I72, I73, I74, I75, I76) -> f11#(I70, I71, I72, I73, I74, I75, I76) 
  12) f9#(I77, I78, I79, I80, I81, I82, I83) -> f10#(I77, I78, I79, I80, I81, 1 + I82, I83) 
  13) f7#(I84, I85, I86, I87, I88, I89, I90) -> f8#(I84, I85, I86, I87, I88, I89, I90) 
  14) f3#(I98, I99, I100, I101, I102, I103, I104) -> f5#(I98, I99, I100, I101, I102, I103, I104) 

We have the following SCCs.
  { 4, 6, 7, 8, 10, 11, 12, 13 }

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

We use the extended value criterion with the projection function NU:
  NU[f9#(x0,x1,x2,x3,x4,x5,x6)] = x1 - x4 - 2
  NU[f7#(x0,x1,x2,x3,x4,x5,x6)] = x1 - x4 - 1
  NU[f12#(x0,x1,x2,x3,x4,x5,x6)] = x1 - x4 - 2
  NU[f11#(x0,x1,x2,x3,x4,x5,x6)] = x1 - x4 - 2
  NU[f10#(x0,x1,x2,x3,x4,x5,x6)] = x1 - x4 - 2
  NU[f8#(x0,x1,x2,x3,x4,x5,x6)] = x1 - x4 - 1

This gives the following inequalities:
  1 + I25 <= I22  ==>  I22 - I25 - 1 > I22 - I25 - 2  with  I22 - I25 - 1 >= 0
  1 + I40 <= I36  ==>  I36 - I39 - 2 >= I36 - I39 - 2
  I43 <= I47  ==>  I43 - I46 - 2 >= I43 - (1 + I46) - 1
    ==>  I50 - I53 - 2 >= I50 - I53 - 2
    ==>  I64 - I67 - 2 >= I64 - I67 - 2
    ==>  I71 - I74 - 2 >= I71 - I74 - 2
    ==>  I78 - I81 - 2 >= I78 - I81 - 2
    ==>  I85 - I88 - 1 >= I85 - I88 - 1

We remove all the strictly oriented dependency pairs.

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

The dependency graph for this problem is:
  6 -> 8, 10
  7 -> 13
  8 -> 12
  10 -> 12
  11 -> 6, 7
  12 -> 11
  13 -> 
Where:
  6) f11#(I35, I36, I37, I38, I39, I40, I41) -> f12#(I35, I36, I37, I38, I39, I40, I41) [1 + I40 <= I36]
  7) f11#(I42, I43, I44, I45, I46, I47, I48) -> f7#(I42, I43, I44, I45, 1 + I46, I47, I48) [I43 <= I47]
  8) f12#(I49, I50, I51, I52, I53, I54, I55) -> f9#(I49, I50, I51, I52, I53, I54, I55) 
  10) f12#(I63, I64, I65, I66, I67, I68, I69) -> f9#(I63, I64, I65, I66, I67, I68, I69) 
  11) f10#(I70, I71, I72, I73, I74, I75, I76) -> f11#(I70, I71, I72, I73, I74, I75, I76) 
  12) f9#(I77, I78, I79, I80, I81, I82, I83) -> f10#(I77, I78, I79, I80, I81, 1 + I82, I83) 
  13) f7#(I84, I85, I86, I87, I88, I89, I90) -> f8#(I84, I85, I86, I87, I88, I89, I90) 

We have the following SCCs.
  { 6, 8, 10, 11, 12 }

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

We use the extended value criterion with the projection function NU:
  NU[f10#(x0,x1,x2,x3,x4,x5,x6)] = x1 - x5
  NU[f9#(x0,x1,x2,x3,x4,x5,x6)] = x1 - x5 - 1
  NU[f12#(x0,x1,x2,x3,x4,x5,x6)] = x1 - x5 - 1
  NU[f11#(x0,x1,x2,x3,x4,x5,x6)] = x1 - x5

This gives the following inequalities:
  1 + I40 <= I36  ==>  I36 - I40 > I36 - I40 - 1  with  I36 - I40 >= 0
    ==>  I50 - I54 - 1 >= I50 - I54 - 1
    ==>  I64 - I68 - 1 >= I64 - I68 - 1
    ==>  I71 - I75 >= I71 - I75
    ==>  I78 - I82 - 1 >= I78 - (1 + I82)

We remove all the strictly oriented dependency pairs.

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

The dependency graph for this problem is:
  8 -> 12
  10 -> 12
  11 -> 
  12 -> 11
Where:
  8) f12#(I49, I50, I51, I52, I53, I54, I55) -> f9#(I49, I50, I51, I52, I53, I54, I55) 
  10) f12#(I63, I64, I65, I66, I67, I68, I69) -> f9#(I63, I64, I65, I66, I67, I68, I69) 
  11) f10#(I70, I71, I72, I73, I74, I75, I76) -> f11#(I70, I71, I72, I73, I74, I75, I76) 
  12) f9#(I77, I78, I79, I80, I81, I82, I83) -> f10#(I77, I78, I79, I80, I81, 1 + I82, I83) 

We have the following SCCs.