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


--------------------------------------------------------------------------------


YES

DP problem for innermost termination.
P =
  f18#(x1, x2, x3, x4, x5, x6, x7) -> f17#(x1, x2, x3, x4, x5, x6, x7) 
  f17#(I0, I1, I2, I3, I4, I5, I6) -> f1#(5, 0, I2, 5, 0, I5, I6) 
  f5#(I7, I8, I9, I10, I11, I12, I13) -> f3#(I7, I8, I9, I10, I11, I12, I13) 
  f2#(I14, I15, I16, I17, I18, I19, I20) -> f16#(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17]
  f2#(I21, I22, I23, I24, I25, I26, I27) -> f8#(I21, 0, I23, I24, I25, I26, I27) [I24 <= I22]
  f16#(I28, I29, I30, I31, I32, I33, I34) -> f15#(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32]
  f16#(I35, I36, I37, I38, I39, I40, I41) -> f14#(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39]
  f16#(I42, I43, I44, I45, I46, I47, I48) -> f14#(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43]
  f15#(I49, I50, I51, I52, I53, I54, I55) -> f1#(I49, 1 + I50, I51, I52, I53, I54, I55) 
  f7#(I56, I57, I58, I59, I60, I61, I62) -> f10#(I56, I57, I58, I59, I60, I61, I62) 
  f14#(I63, I64, I65, I66, I67, I68, I69) -> f15#(I63, I64, I65, I66, I67, I68, I69) 
  f9#(I70, I71, I72, I73, I74, I75, I76) -> f12#(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73]
  f9#(I77, I78, I79, I80, I81, I82, I83) -> f7#(I77, 0, I79, I80, I81, I82, I83) [I80 <= I78]
  f13#(I84, I85, I86, I87, I88, I89, I90) -> f11#(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84]
  f13#(I91, I92, I93, I94, I95, I96, I97) -> f8#(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93]
  f12#(I98, I99, I100, I101, I102, I103, I104) -> f13#(I98, I99, I100, I101, I102, I103, I104) 
  f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, I106, 1 + I107, I108, I109, I110, I111) 
  f10#(I112, I113, I114, I115, I116, I117, I118) -> f6#(I112, I113, I114, I115, I116, I119, I120) [I120 = I120 /\ I119 = I119 /\ 1 + I113 <= I112]
  f10#(I121, I122, I123, I124, I125, I126, I127) -> f5#(I121, 0, I123, I124, I125, I126, I127) [I121 <= I122]
  f8#(I128, I129, I130, I131, I132, I133, I134) -> f9#(I128, I129, I130, I131, I132, I133, I134) 
  f6#(I142, I143, I144, I145, I146, I147, I148) -> f7#(I142, 1 + I143, I144, I145, I146, I147, I148) 
  f3#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, 1 + I150, I151, I152, I153, I154, I155) [1 + I150 <= I152]
  f1#(I163, I164, I165, I166, I167, I168, I169) -> f2#(I163, I164, I165, I166, I167, I168, I169) 
R = 
  f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 
  f17(I0, I1, I2, I3, I4, I5, I6) -> f1(5, 0, I2, 5, 0, I5, I6) 
  f5(I7, I8, I9, I10, I11, I12, I13) -> f3(I7, I8, I9, I10, I11, I12, I13) 
  f2(I14, I15, I16, I17, I18, I19, I20) -> f16(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17]
  f2(I21, I22, I23, I24, I25, I26, I27) -> f8(I21, 0, I23, I24, I25, I26, I27) [I24 <= I22]
  f16(I28, I29, I30, I31, I32, I33, I34) -> f15(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32]
  f16(I35, I36, I37, I38, I39, I40, I41) -> f14(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39]
  f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43]
  f15(I49, I50, I51, I52, I53, I54, I55) -> f1(I49, 1 + I50, I51, I52, I53, I54, I55) 
  f7(I56, I57, I58, I59, I60, I61, I62) -> f10(I56, I57, I58, I59, I60, I61, I62) 
  f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 
  f9(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73]
  f9(I77, I78, I79, I80, I81, I82, I83) -> f7(I77, 0, I79, I80, I81, I82, I83) [I80 <= I78]
  f13(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84]
  f13(I91, I92, I93, I94, I95, I96, I97) -> f8(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93]
  f12(I98, I99, I100, I101, I102, I103, I104) -> f13(I98, I99, I100, I101, I102, I103, I104) 
  f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 
  f10(I112, I113, I114, I115, I116, I117, I118) -> f6(I112, I113, I114, I115, I116, I119, I120) [I120 = I120 /\ I119 = I119 /\ 1 + I113 <= I112]
  f10(I121, I122, I123, I124, I125, I126, I127) -> f5(I121, 0, I123, I124, I125, I126, I127) [I121 <= I122]
  f8(I128, I129, I130, I131, I132, I133, I134) -> f9(I128, I129, I130, I131, I132, I133, I134) 
  f6(I135, I136, I137, I138, I139, I140, I141) -> f4(I135, I136, I137, I138, I139, I140, I141) 
  f6(I142, I143, I144, I145, I146, I147, I148) -> f7(I142, 1 + I143, I144, I145, I146, I147, I148) 
  f3(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) [1 + I150 <= I152]
  f3(I156, I157, I158, I159, I160, I161, I162) -> f4(I156, I157, I158, I159, I160, I161, I162) [I159 <= I157]
  f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) 

The dependency graph for this problem is:
  0 -> 1
  1 -> 22
  2 -> 21
  3 -> 5, 6, 7
  4 -> 19
  5 -> 8
  6 -> 10
  7 -> 10
  8 -> 22
  9 -> 17, 18
  10 -> 8
  11 -> 15
  12 -> 9
  13 -> 16
  14 -> 19
  15 -> 13, 14
  16 -> 15
  17 -> 20
  18 -> 2
  19 -> 11, 12
  20 -> 9
  21 -> 2
  22 -> 3, 4
Where:
  0) f18#(x1, x2, x3, x4, x5, x6, x7) -> f17#(x1, x2, x3, x4, x5, x6, x7) 
  1) f17#(I0, I1, I2, I3, I4, I5, I6) -> f1#(5, 0, I2, 5, 0, I5, I6) 
  2) f5#(I7, I8, I9, I10, I11, I12, I13) -> f3#(I7, I8, I9, I10, I11, I12, I13) 
  3) f2#(I14, I15, I16, I17, I18, I19, I20) -> f16#(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17]
  4) f2#(I21, I22, I23, I24, I25, I26, I27) -> f8#(I21, 0, I23, I24, I25, I26, I27) [I24 <= I22]
  5) f16#(I28, I29, I30, I31, I32, I33, I34) -> f15#(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32]
  6) f16#(I35, I36, I37, I38, I39, I40, I41) -> f14#(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39]
  7) f16#(I42, I43, I44, I45, I46, I47, I48) -> f14#(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43]
  8) f15#(I49, I50, I51, I52, I53, I54, I55) -> f1#(I49, 1 + I50, I51, I52, I53, I54, I55) 
  9) f7#(I56, I57, I58, I59, I60, I61, I62) -> f10#(I56, I57, I58, I59, I60, I61, I62) 
  10) f14#(I63, I64, I65, I66, I67, I68, I69) -> f15#(I63, I64, I65, I66, I67, I68, I69) 
  11) f9#(I70, I71, I72, I73, I74, I75, I76) -> f12#(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73]
  12) f9#(I77, I78, I79, I80, I81, I82, I83) -> f7#(I77, 0, I79, I80, I81, I82, I83) [I80 <= I78]
  13) f13#(I84, I85, I86, I87, I88, I89, I90) -> f11#(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84]
  14) f13#(I91, I92, I93, I94, I95, I96, I97) -> f8#(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93]
  15) f12#(I98, I99, I100, I101, I102, I103, I104) -> f13#(I98, I99, I100, I101, I102, I103, I104) 
  16) f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, I106, 1 + I107, I108, I109, I110, I111) 
  17) f10#(I112, I113, I114, I115, I116, I117, I118) -> f6#(I112, I113, I114, I115, I116, I119, I120) [I120 = I120 /\ I119 = I119 /\ 1 + I113 <= I112]
  18) f10#(I121, I122, I123, I124, I125, I126, I127) -> f5#(I121, 0, I123, I124, I125, I126, I127) [I121 <= I122]
  19) f8#(I128, I129, I130, I131, I132, I133, I134) -> f9#(I128, I129, I130, I131, I132, I133, I134) 
  20) f6#(I142, I143, I144, I145, I146, I147, I148) -> f7#(I142, 1 + I143, I144, I145, I146, I147, I148) 
  21) f3#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, 1 + I150, I151, I152, I153, I154, I155) [1 + I150 <= I152]
  22) f1#(I163, I164, I165, I166, I167, I168, I169) -> f2#(I163, I164, I165, I166, I167, I168, I169) 

We have the following SCCs.
  { 3, 5, 6, 7, 8, 10, 22 }
  { 11, 13, 14, 15, 16, 19 }
  { 9, 17, 20 }
  { 2, 21 }

DP problem for innermost termination.
P =
  f5#(I7, I8, I9, I10, I11, I12, I13) -> f3#(I7, I8, I9, I10, I11, I12, I13) 
  f3#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, 1 + I150, I151, I152, I153, I154, I155) [1 + I150 <= I152]
R = 
  f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 
  f17(I0, I1, I2, I3, I4, I5, I6) -> f1(5, 0, I2, 5, 0, I5, I6) 
  f5(I7, I8, I9, I10, I11, I12, I13) -> f3(I7, I8, I9, I10, I11, I12, I13) 
  f2(I14, I15, I16, I17, I18, I19, I20) -> f16(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17]
  f2(I21, I22, I23, I24, I25, I26, I27) -> f8(I21, 0, I23, I24, I25, I26, I27) [I24 <= I22]
  f16(I28, I29, I30, I31, I32, I33, I34) -> f15(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32]
  f16(I35, I36, I37, I38, I39, I40, I41) -> f14(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39]
  f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43]
  f15(I49, I50, I51, I52, I53, I54, I55) -> f1(I49, 1 + I50, I51, I52, I53, I54, I55) 
  f7(I56, I57, I58, I59, I60, I61, I62) -> f10(I56, I57, I58, I59, I60, I61, I62) 
  f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 
  f9(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73]
  f9(I77, I78, I79, I80, I81, I82, I83) -> f7(I77, 0, I79, I80, I81, I82, I83) [I80 <= I78]
  f13(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84]
  f13(I91, I92, I93, I94, I95, I96, I97) -> f8(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93]
  f12(I98, I99, I100, I101, I102, I103, I104) -> f13(I98, I99, I100, I101, I102, I103, I104) 
  f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 
  f10(I112, I113, I114, I115, I116, I117, I118) -> f6(I112, I113, I114, I115, I116, I119, I120) [I120 = I120 /\ I119 = I119 /\ 1 + I113 <= I112]
  f10(I121, I122, I123, I124, I125, I126, I127) -> f5(I121, 0, I123, I124, I125, I126, I127) [I121 <= I122]
  f8(I128, I129, I130, I131, I132, I133, I134) -> f9(I128, I129, I130, I131, I132, I133, I134) 
  f6(I135, I136, I137, I138, I139, I140, I141) -> f4(I135, I136, I137, I138, I139, I140, I141) 
  f6(I142, I143, I144, I145, I146, I147, I148) -> f7(I142, 1 + I143, I144, I145, I146, I147, I148) 
  f3(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) [1 + I150 <= I152]
  f3(I156, I157, I158, I159, I160, I161, I162) -> f4(I156, I157, I158, I159, I160, I161, I162) [I159 <= I157]
  f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) 

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

This gives the following inequalities:
    ==>  I10 + -1 * (1 + I8) >= I10 + -1 * (1 + I8)
  1 + I150 <= I152  ==>  I152 + -1 * (1 + I150) > I152 + -1 * (1 + (1 + I150))  with  I152 + -1 * (1 + I150) >= 0

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f5#(I7, I8, I9, I10, I11, I12, I13) -> f3#(I7, I8, I9, I10, I11, I12, I13) 
R = 
  f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 
  f17(I0, I1, I2, I3, I4, I5, I6) -> f1(5, 0, I2, 5, 0, I5, I6) 
  f5(I7, I8, I9, I10, I11, I12, I13) -> f3(I7, I8, I9, I10, I11, I12, I13) 
  f2(I14, I15, I16, I17, I18, I19, I20) -> f16(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17]
  f2(I21, I22, I23, I24, I25, I26, I27) -> f8(I21, 0, I23, I24, I25, I26, I27) [I24 <= I22]
  f16(I28, I29, I30, I31, I32, I33, I34) -> f15(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32]
  f16(I35, I36, I37, I38, I39, I40, I41) -> f14(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39]
  f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43]
  f15(I49, I50, I51, I52, I53, I54, I55) -> f1(I49, 1 + I50, I51, I52, I53, I54, I55) 
  f7(I56, I57, I58, I59, I60, I61, I62) -> f10(I56, I57, I58, I59, I60, I61, I62) 
  f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 
  f9(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73]
  f9(I77, I78, I79, I80, I81, I82, I83) -> f7(I77, 0, I79, I80, I81, I82, I83) [I80 <= I78]
  f13(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84]
  f13(I91, I92, I93, I94, I95, I96, I97) -> f8(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93]
  f12(I98, I99, I100, I101, I102, I103, I104) -> f13(I98, I99, I100, I101, I102, I103, I104) 
  f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 
  f10(I112, I113, I114, I115, I116, I117, I118) -> f6(I112, I113, I114, I115, I116, I119, I120) [I120 = I120 /\ I119 = I119 /\ 1 + I113 <= I112]
  f10(I121, I122, I123, I124, I125, I126, I127) -> f5(I121, 0, I123, I124, I125, I126, I127) [I121 <= I122]
  f8(I128, I129, I130, I131, I132, I133, I134) -> f9(I128, I129, I130, I131, I132, I133, I134) 
  f6(I135, I136, I137, I138, I139, I140, I141) -> f4(I135, I136, I137, I138, I139, I140, I141) 
  f6(I142, I143, I144, I145, I146, I147, I148) -> f7(I142, 1 + I143, I144, I145, I146, I147, I148) 
  f3(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) [1 + I150 <= I152]
  f3(I156, I157, I158, I159, I160, I161, I162) -> f4(I156, I157, I158, I159, I160, I161, I162) [I159 <= I157]
  f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) 

The dependency graph for this problem is:
  2 -> 
Where:
  2) f5#(I7, I8, I9, I10, I11, I12, I13) -> f3#(I7, I8, I9, I10, I11, I12, I13) 

We have the following SCCs.
  

DP problem for innermost termination.
P =
  f7#(I56, I57, I58, I59, I60, I61, I62) -> f10#(I56, I57, I58, I59, I60, I61, I62) 
  f10#(I112, I113, I114, I115, I116, I117, I118) -> f6#(I112, I113, I114, I115, I116, I119, I120) [I120 = I120 /\ I119 = I119 /\ 1 + I113 <= I112]
  f6#(I142, I143, I144, I145, I146, I147, I148) -> f7#(I142, 1 + I143, I144, I145, I146, I147, I148) 
R = 
  f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 
  f17(I0, I1, I2, I3, I4, I5, I6) -> f1(5, 0, I2, 5, 0, I5, I6) 
  f5(I7, I8, I9, I10, I11, I12, I13) -> f3(I7, I8, I9, I10, I11, I12, I13) 
  f2(I14, I15, I16, I17, I18, I19, I20) -> f16(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17]
  f2(I21, I22, I23, I24, I25, I26, I27) -> f8(I21, 0, I23, I24, I25, I26, I27) [I24 <= I22]
  f16(I28, I29, I30, I31, I32, I33, I34) -> f15(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32]
  f16(I35, I36, I37, I38, I39, I40, I41) -> f14(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39]
  f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43]
  f15(I49, I50, I51, I52, I53, I54, I55) -> f1(I49, 1 + I50, I51, I52, I53, I54, I55) 
  f7(I56, I57, I58, I59, I60, I61, I62) -> f10(I56, I57, I58, I59, I60, I61, I62) 
  f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 
  f9(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73]
  f9(I77, I78, I79, I80, I81, I82, I83) -> f7(I77, 0, I79, I80, I81, I82, I83) [I80 <= I78]
  f13(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84]
  f13(I91, I92, I93, I94, I95, I96, I97) -> f8(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93]
  f12(I98, I99, I100, I101, I102, I103, I104) -> f13(I98, I99, I100, I101, I102, I103, I104) 
  f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 
  f10(I112, I113, I114, I115, I116, I117, I118) -> f6(I112, I113, I114, I115, I116, I119, I120) [I120 = I120 /\ I119 = I119 /\ 1 + I113 <= I112]
  f10(I121, I122, I123, I124, I125, I126, I127) -> f5(I121, 0, I123, I124, I125, I126, I127) [I121 <= I122]
  f8(I128, I129, I130, I131, I132, I133, I134) -> f9(I128, I129, I130, I131, I132, I133, I134) 
  f6(I135, I136, I137, I138, I139, I140, I141) -> f4(I135, I136, I137, I138, I139, I140, I141) 
  f6(I142, I143, I144, I145, I146, I147, I148) -> f7(I142, 1 + I143, I144, I145, I146, I147, I148) 
  f3(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) [1 + I150 <= I152]
  f3(I156, I157, I158, I159, I160, I161, I162) -> f4(I156, I157, I158, I159, I160, I161, I162) [I159 <= I157]
  f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) 

We use the extended value criterion with the projection function NU:
  NU[f6#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x1 - 2
  NU[f10#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x1 - 1
  NU[f7#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x1 - 1

This gives the following inequalities:
    ==>  I56 - I57 - 1 >= I56 - I57 - 1
  I120 = I120 /\ I119 = I119 /\ 1 + I113 <= I112  ==>  I112 - I113 - 1 > I112 - I113 - 2  with  I112 - I113 - 1 >= 0
    ==>  I142 - I143 - 2 >= I142 - (1 + I143) - 1

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f7#(I56, I57, I58, I59, I60, I61, I62) -> f10#(I56, I57, I58, I59, I60, I61, I62) 
  f6#(I142, I143, I144, I145, I146, I147, I148) -> f7#(I142, 1 + I143, I144, I145, I146, I147, I148) 
R = 
  f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 
  f17(I0, I1, I2, I3, I4, I5, I6) -> f1(5, 0, I2, 5, 0, I5, I6) 
  f5(I7, I8, I9, I10, I11, I12, I13) -> f3(I7, I8, I9, I10, I11, I12, I13) 
  f2(I14, I15, I16, I17, I18, I19, I20) -> f16(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17]
  f2(I21, I22, I23, I24, I25, I26, I27) -> f8(I21, 0, I23, I24, I25, I26, I27) [I24 <= I22]
  f16(I28, I29, I30, I31, I32, I33, I34) -> f15(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32]
  f16(I35, I36, I37, I38, I39, I40, I41) -> f14(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39]
  f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43]
  f15(I49, I50, I51, I52, I53, I54, I55) -> f1(I49, 1 + I50, I51, I52, I53, I54, I55) 
  f7(I56, I57, I58, I59, I60, I61, I62) -> f10(I56, I57, I58, I59, I60, I61, I62) 
  f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 
  f9(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73]
  f9(I77, I78, I79, I80, I81, I82, I83) -> f7(I77, 0, I79, I80, I81, I82, I83) [I80 <= I78]
  f13(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84]
  f13(I91, I92, I93, I94, I95, I96, I97) -> f8(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93]
  f12(I98, I99, I100, I101, I102, I103, I104) -> f13(I98, I99, I100, I101, I102, I103, I104) 
  f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 
  f10(I112, I113, I114, I115, I116, I117, I118) -> f6(I112, I113, I114, I115, I116, I119, I120) [I120 = I120 /\ I119 = I119 /\ 1 + I113 <= I112]
  f10(I121, I122, I123, I124, I125, I126, I127) -> f5(I121, 0, I123, I124, I125, I126, I127) [I121 <= I122]
  f8(I128, I129, I130, I131, I132, I133, I134) -> f9(I128, I129, I130, I131, I132, I133, I134) 
  f6(I135, I136, I137, I138, I139, I140, I141) -> f4(I135, I136, I137, I138, I139, I140, I141) 
  f6(I142, I143, I144, I145, I146, I147, I148) -> f7(I142, 1 + I143, I144, I145, I146, I147, I148) 
  f3(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) [1 + I150 <= I152]
  f3(I156, I157, I158, I159, I160, I161, I162) -> f4(I156, I157, I158, I159, I160, I161, I162) [I159 <= I157]
  f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) 

The dependency graph for this problem is:
  9 -> 
  20 -> 9
Where:
  9) f7#(I56, I57, I58, I59, I60, I61, I62) -> f10#(I56, I57, I58, I59, I60, I61, I62) 
  20) f6#(I142, I143, I144, I145, I146, I147, I148) -> f7#(I142, 1 + I143, I144, I145, I146, I147, I148) 

We have the following SCCs.
  

DP problem for innermost termination.
P =
  f9#(I70, I71, I72, I73, I74, I75, I76) -> f12#(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73]
  f13#(I84, I85, I86, I87, I88, I89, I90) -> f11#(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84]
  f13#(I91, I92, I93, I94, I95, I96, I97) -> f8#(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93]
  f12#(I98, I99, I100, I101, I102, I103, I104) -> f13#(I98, I99, I100, I101, I102, I103, I104) 
  f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, I106, 1 + I107, I108, I109, I110, I111) 
  f8#(I128, I129, I130, I131, I132, I133, I134) -> f9#(I128, I129, I130, I131, I132, I133, I134) 
R = 
  f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 
  f17(I0, I1, I2, I3, I4, I5, I6) -> f1(5, 0, I2, 5, 0, I5, I6) 
  f5(I7, I8, I9, I10, I11, I12, I13) -> f3(I7, I8, I9, I10, I11, I12, I13) 
  f2(I14, I15, I16, I17, I18, I19, I20) -> f16(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17]
  f2(I21, I22, I23, I24, I25, I26, I27) -> f8(I21, 0, I23, I24, I25, I26, I27) [I24 <= I22]
  f16(I28, I29, I30, I31, I32, I33, I34) -> f15(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32]
  f16(I35, I36, I37, I38, I39, I40, I41) -> f14(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39]
  f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43]
  f15(I49, I50, I51, I52, I53, I54, I55) -> f1(I49, 1 + I50, I51, I52, I53, I54, I55) 
  f7(I56, I57, I58, I59, I60, I61, I62) -> f10(I56, I57, I58, I59, I60, I61, I62) 
  f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 
  f9(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73]
  f9(I77, I78, I79, I80, I81, I82, I83) -> f7(I77, 0, I79, I80, I81, I82, I83) [I80 <= I78]
  f13(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84]
  f13(I91, I92, I93, I94, I95, I96, I97) -> f8(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93]
  f12(I98, I99, I100, I101, I102, I103, I104) -> f13(I98, I99, I100, I101, I102, I103, I104) 
  f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 
  f10(I112, I113, I114, I115, I116, I117, I118) -> f6(I112, I113, I114, I115, I116, I119, I120) [I120 = I120 /\ I119 = I119 /\ 1 + I113 <= I112]
  f10(I121, I122, I123, I124, I125, I126, I127) -> f5(I121, 0, I123, I124, I125, I126, I127) [I121 <= I122]
  f8(I128, I129, I130, I131, I132, I133, I134) -> f9(I128, I129, I130, I131, I132, I133, I134) 
  f6(I135, I136, I137, I138, I139, I140, I141) -> f4(I135, I136, I137, I138, I139, I140, I141) 
  f6(I142, I143, I144, I145, I146, I147, I148) -> f7(I142, 1 + I143, I144, I145, I146, I147, I148) 
  f3(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) [1 + I150 <= I152]
  f3(I156, I157, I158, I159, I160, I161, I162) -> f4(I156, I157, I158, I159, I160, I161, I162) [I159 <= I157]
  f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) 

We use the extended value criterion with the projection function NU:
  NU[f8#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 1
  NU[f11#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2
  NU[f13#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2
  NU[f12#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2
  NU[f9#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 1

This gives the following inequalities:
  1 + I71 <= I73  ==>  -I71 + I73 - 1 > -I71 + I73 - 2  with  -I71 + I73 - 1 >= 0
  rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84  ==>  -I85 + I87 - 2 >= -I85 + I87 - 2
  I91 <= I93  ==>  -I92 + I94 - 2 >= -(1 + I92) + I94 - 1
    ==>  -I99 + I101 - 2 >= -I99 + I101 - 2
    ==>  -I106 + I108 - 2 >= -I106 + I108 - 2
    ==>  -I129 + I131 - 1 >= -I129 + I131 - 1

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f13#(I84, I85, I86, I87, I88, I89, I90) -> f11#(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84]
  f13#(I91, I92, I93, I94, I95, I96, I97) -> f8#(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93]
  f12#(I98, I99, I100, I101, I102, I103, I104) -> f13#(I98, I99, I100, I101, I102, I103, I104) 
  f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, I106, 1 + I107, I108, I109, I110, I111) 
  f8#(I128, I129, I130, I131, I132, I133, I134) -> f9#(I128, I129, I130, I131, I132, I133, I134) 
R = 
  f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 
  f17(I0, I1, I2, I3, I4, I5, I6) -> f1(5, 0, I2, 5, 0, I5, I6) 
  f5(I7, I8, I9, I10, I11, I12, I13) -> f3(I7, I8, I9, I10, I11, I12, I13) 
  f2(I14, I15, I16, I17, I18, I19, I20) -> f16(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17]
  f2(I21, I22, I23, I24, I25, I26, I27) -> f8(I21, 0, I23, I24, I25, I26, I27) [I24 <= I22]
  f16(I28, I29, I30, I31, I32, I33, I34) -> f15(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32]
  f16(I35, I36, I37, I38, I39, I40, I41) -> f14(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39]
  f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43]
  f15(I49, I50, I51, I52, I53, I54, I55) -> f1(I49, 1 + I50, I51, I52, I53, I54, I55) 
  f7(I56, I57, I58, I59, I60, I61, I62) -> f10(I56, I57, I58, I59, I60, I61, I62) 
  f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 
  f9(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73]
  f9(I77, I78, I79, I80, I81, I82, I83) -> f7(I77, 0, I79, I80, I81, I82, I83) [I80 <= I78]
  f13(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84]
  f13(I91, I92, I93, I94, I95, I96, I97) -> f8(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93]
  f12(I98, I99, I100, I101, I102, I103, I104) -> f13(I98, I99, I100, I101, I102, I103, I104) 
  f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 
  f10(I112, I113, I114, I115, I116, I117, I118) -> f6(I112, I113, I114, I115, I116, I119, I120) [I120 = I120 /\ I119 = I119 /\ 1 + I113 <= I112]
  f10(I121, I122, I123, I124, I125, I126, I127) -> f5(I121, 0, I123, I124, I125, I126, I127) [I121 <= I122]
  f8(I128, I129, I130, I131, I132, I133, I134) -> f9(I128, I129, I130, I131, I132, I133, I134) 
  f6(I135, I136, I137, I138, I139, I140, I141) -> f4(I135, I136, I137, I138, I139, I140, I141) 
  f6(I142, I143, I144, I145, I146, I147, I148) -> f7(I142, 1 + I143, I144, I145, I146, I147, I148) 
  f3(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) [1 + I150 <= I152]
  f3(I156, I157, I158, I159, I160, I161, I162) -> f4(I156, I157, I158, I159, I160, I161, I162) [I159 <= I157]
  f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) 

The dependency graph for this problem is:
  13 -> 16
  14 -> 19
  15 -> 13, 14
  16 -> 15
  19 -> 
Where:
  13) f13#(I84, I85, I86, I87, I88, I89, I90) -> f11#(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84]
  14) f13#(I91, I92, I93, I94, I95, I96, I97) -> f8#(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93]
  15) f12#(I98, I99, I100, I101, I102, I103, I104) -> f13#(I98, I99, I100, I101, I102, I103, I104) 
  16) f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, I106, 1 + I107, I108, I109, I110, I111) 
  19) f8#(I128, I129, I130, I131, I132, I133, I134) -> f9#(I128, I129, I130, I131, I132, I133, I134) 

We have the following SCCs.
  { 13, 15, 16 }

DP problem for innermost termination.
P =
  f13#(I84, I85, I86, I87, I88, I89, I90) -> f11#(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84]
  f12#(I98, I99, I100, I101, I102, I103, I104) -> f13#(I98, I99, I100, I101, I102, I103, I104) 
  f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, I106, 1 + I107, I108, I109, I110, I111) 
R = 
  f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 
  f17(I0, I1, I2, I3, I4, I5, I6) -> f1(5, 0, I2, 5, 0, I5, I6) 
  f5(I7, I8, I9, I10, I11, I12, I13) -> f3(I7, I8, I9, I10, I11, I12, I13) 
  f2(I14, I15, I16, I17, I18, I19, I20) -> f16(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17]
  f2(I21, I22, I23, I24, I25, I26, I27) -> f8(I21, 0, I23, I24, I25, I26, I27) [I24 <= I22]
  f16(I28, I29, I30, I31, I32, I33, I34) -> f15(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32]
  f16(I35, I36, I37, I38, I39, I40, I41) -> f14(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39]
  f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43]
  f15(I49, I50, I51, I52, I53, I54, I55) -> f1(I49, 1 + I50, I51, I52, I53, I54, I55) 
  f7(I56, I57, I58, I59, I60, I61, I62) -> f10(I56, I57, I58, I59, I60, I61, I62) 
  f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 
  f9(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73]
  f9(I77, I78, I79, I80, I81, I82, I83) -> f7(I77, 0, I79, I80, I81, I82, I83) [I80 <= I78]
  f13(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84]
  f13(I91, I92, I93, I94, I95, I96, I97) -> f8(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93]
  f12(I98, I99, I100, I101, I102, I103, I104) -> f13(I98, I99, I100, I101, I102, I103, I104) 
  f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 
  f10(I112, I113, I114, I115, I116, I117, I118) -> f6(I112, I113, I114, I115, I116, I119, I120) [I120 = I120 /\ I119 = I119 /\ 1 + I113 <= I112]
  f10(I121, I122, I123, I124, I125, I126, I127) -> f5(I121, 0, I123, I124, I125, I126, I127) [I121 <= I122]
  f8(I128, I129, I130, I131, I132, I133, I134) -> f9(I128, I129, I130, I131, I132, I133, I134) 
  f6(I135, I136, I137, I138, I139, I140, I141) -> f4(I135, I136, I137, I138, I139, I140, I141) 
  f6(I142, I143, I144, I145, I146, I147, I148) -> f7(I142, 1 + I143, I144, I145, I146, I147, I148) 
  f3(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) [1 + I150 <= I152]
  f3(I156, I157, I158, I159, I160, I161, I162) -> f4(I156, I157, I158, I159, I160, I161, I162) [I159 <= I157]
  f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) 

We use the extended value criterion with the projection function NU:
  NU[f12#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x2 - 1
  NU[f11#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x2 - 2
  NU[f13#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x2 - 1

This gives the following inequalities:
  rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84  ==>  I84 - I86 - 1 > I84 - I86 - 2  with  I84 - I86 - 1 >= 0
    ==>  I98 - I100 - 1 >= I98 - I100 - 1
    ==>  I105 - I107 - 2 >= I105 - (1 + I107) - 1

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f12#(I98, I99, I100, I101, I102, I103, I104) -> f13#(I98, I99, I100, I101, I102, I103, I104) 
  f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, I106, 1 + I107, I108, I109, I110, I111) 
R = 
  f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 
  f17(I0, I1, I2, I3, I4, I5, I6) -> f1(5, 0, I2, 5, 0, I5, I6) 
  f5(I7, I8, I9, I10, I11, I12, I13) -> f3(I7, I8, I9, I10, I11, I12, I13) 
  f2(I14, I15, I16, I17, I18, I19, I20) -> f16(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17]
  f2(I21, I22, I23, I24, I25, I26, I27) -> f8(I21, 0, I23, I24, I25, I26, I27) [I24 <= I22]
  f16(I28, I29, I30, I31, I32, I33, I34) -> f15(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32]
  f16(I35, I36, I37, I38, I39, I40, I41) -> f14(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39]
  f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43]
  f15(I49, I50, I51, I52, I53, I54, I55) -> f1(I49, 1 + I50, I51, I52, I53, I54, I55) 
  f7(I56, I57, I58, I59, I60, I61, I62) -> f10(I56, I57, I58, I59, I60, I61, I62) 
  f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 
  f9(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73]
  f9(I77, I78, I79, I80, I81, I82, I83) -> f7(I77, 0, I79, I80, I81, I82, I83) [I80 <= I78]
  f13(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84]
  f13(I91, I92, I93, I94, I95, I96, I97) -> f8(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93]
  f12(I98, I99, I100, I101, I102, I103, I104) -> f13(I98, I99, I100, I101, I102, I103, I104) 
  f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 
  f10(I112, I113, I114, I115, I116, I117, I118) -> f6(I112, I113, I114, I115, I116, I119, I120) [I120 = I120 /\ I119 = I119 /\ 1 + I113 <= I112]
  f10(I121, I122, I123, I124, I125, I126, I127) -> f5(I121, 0, I123, I124, I125, I126, I127) [I121 <= I122]
  f8(I128, I129, I130, I131, I132, I133, I134) -> f9(I128, I129, I130, I131, I132, I133, I134) 
  f6(I135, I136, I137, I138, I139, I140, I141) -> f4(I135, I136, I137, I138, I139, I140, I141) 
  f6(I142, I143, I144, I145, I146, I147, I148) -> f7(I142, 1 + I143, I144, I145, I146, I147, I148) 
  f3(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) [1 + I150 <= I152]
  f3(I156, I157, I158, I159, I160, I161, I162) -> f4(I156, I157, I158, I159, I160, I161, I162) [I159 <= I157]
  f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) 

The dependency graph for this problem is:
  15 -> 
  16 -> 15
Where:
  15) f12#(I98, I99, I100, I101, I102, I103, I104) -> f13#(I98, I99, I100, I101, I102, I103, I104) 
  16) f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, I106, 1 + I107, I108, I109, I110, I111) 

We have the following SCCs.
  

DP problem for innermost termination.
P =
  f2#(I14, I15, I16, I17, I18, I19, I20) -> f16#(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17]
  f16#(I28, I29, I30, I31, I32, I33, I34) -> f15#(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32]
  f16#(I35, I36, I37, I38, I39, I40, I41) -> f14#(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39]
  f16#(I42, I43, I44, I45, I46, I47, I48) -> f14#(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43]
  f15#(I49, I50, I51, I52, I53, I54, I55) -> f1#(I49, 1 + I50, I51, I52, I53, I54, I55) 
  f14#(I63, I64, I65, I66, I67, I68, I69) -> f15#(I63, I64, I65, I66, I67, I68, I69) 
  f1#(I163, I164, I165, I166, I167, I168, I169) -> f2#(I163, I164, I165, I166, I167, I168, I169) 
R = 
  f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 
  f17(I0, I1, I2, I3, I4, I5, I6) -> f1(5, 0, I2, 5, 0, I5, I6) 
  f5(I7, I8, I9, I10, I11, I12, I13) -> f3(I7, I8, I9, I10, I11, I12, I13) 
  f2(I14, I15, I16, I17, I18, I19, I20) -> f16(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17]
  f2(I21, I22, I23, I24, I25, I26, I27) -> f8(I21, 0, I23, I24, I25, I26, I27) [I24 <= I22]
  f16(I28, I29, I30, I31, I32, I33, I34) -> f15(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32]
  f16(I35, I36, I37, I38, I39, I40, I41) -> f14(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39]
  f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43]
  f15(I49, I50, I51, I52, I53, I54, I55) -> f1(I49, 1 + I50, I51, I52, I53, I54, I55) 
  f7(I56, I57, I58, I59, I60, I61, I62) -> f10(I56, I57, I58, I59, I60, I61, I62) 
  f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 
  f9(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73]
  f9(I77, I78, I79, I80, I81, I82, I83) -> f7(I77, 0, I79, I80, I81, I82, I83) [I80 <= I78]
  f13(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84]
  f13(I91, I92, I93, I94, I95, I96, I97) -> f8(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93]
  f12(I98, I99, I100, I101, I102, I103, I104) -> f13(I98, I99, I100, I101, I102, I103, I104) 
  f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 
  f10(I112, I113, I114, I115, I116, I117, I118) -> f6(I112, I113, I114, I115, I116, I119, I120) [I120 = I120 /\ I119 = I119 /\ 1 + I113 <= I112]
  f10(I121, I122, I123, I124, I125, I126, I127) -> f5(I121, 0, I123, I124, I125, I126, I127) [I121 <= I122]
  f8(I128, I129, I130, I131, I132, I133, I134) -> f9(I128, I129, I130, I131, I132, I133, I134) 
  f6(I135, I136, I137, I138, I139, I140, I141) -> f4(I135, I136, I137, I138, I139, I140, I141) 
  f6(I142, I143, I144, I145, I146, I147, I148) -> f7(I142, 1 + I143, I144, I145, I146, I147, I148) 
  f3(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) [1 + I150 <= I152]
  f3(I156, I157, I158, I159, I160, I161, I162) -> f4(I156, I157, I158, I159, I160, I161, I162) [I159 <= I157]
  f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) 

We use the extended value criterion with the projection function NU:
  NU[f1#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x4
  NU[f14#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x4 - 1
  NU[f15#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x4 - 1
  NU[f16#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x4
  NU[f2#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x4

This gives the following inequalities:
  1 + I15 <= I17  ==>  -I15 + I18 >= -I15 + I18
  I32 <= I29 /\ I29 <= I32  ==>  -I29 + I32 > -I29 + I32 - 1  with  -I29 + I32 >= 0
  1 + I36 <= I39  ==>  -I36 + I39 > -I36 + I39 - 1  with  -I36 + I39 >= 0
  1 + I46 <= I43  ==>  -I43 + I46 >= -I43 + I46 - 1
    ==>  -I50 + I53 - 1 >= -(1 + I50) + I53
    ==>  -I64 + I67 - 1 >= -I64 + I67 - 1
    ==>  -I164 + I167 >= -I164 + I167

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f2#(I14, I15, I16, I17, I18, I19, I20) -> f16#(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17]
  f16#(I42, I43, I44, I45, I46, I47, I48) -> f14#(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43]
  f15#(I49, I50, I51, I52, I53, I54, I55) -> f1#(I49, 1 + I50, I51, I52, I53, I54, I55) 
  f14#(I63, I64, I65, I66, I67, I68, I69) -> f15#(I63, I64, I65, I66, I67, I68, I69) 
  f1#(I163, I164, I165, I166, I167, I168, I169) -> f2#(I163, I164, I165, I166, I167, I168, I169) 
R = 
  f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 
  f17(I0, I1, I2, I3, I4, I5, I6) -> f1(5, 0, I2, 5, 0, I5, I6) 
  f5(I7, I8, I9, I10, I11, I12, I13) -> f3(I7, I8, I9, I10, I11, I12, I13) 
  f2(I14, I15, I16, I17, I18, I19, I20) -> f16(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17]
  f2(I21, I22, I23, I24, I25, I26, I27) -> f8(I21, 0, I23, I24, I25, I26, I27) [I24 <= I22]
  f16(I28, I29, I30, I31, I32, I33, I34) -> f15(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32]
  f16(I35, I36, I37, I38, I39, I40, I41) -> f14(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39]
  f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43]
  f15(I49, I50, I51, I52, I53, I54, I55) -> f1(I49, 1 + I50, I51, I52, I53, I54, I55) 
  f7(I56, I57, I58, I59, I60, I61, I62) -> f10(I56, I57, I58, I59, I60, I61, I62) 
  f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 
  f9(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73]
  f9(I77, I78, I79, I80, I81, I82, I83) -> f7(I77, 0, I79, I80, I81, I82, I83) [I80 <= I78]
  f13(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84]
  f13(I91, I92, I93, I94, I95, I96, I97) -> f8(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93]
  f12(I98, I99, I100, I101, I102, I103, I104) -> f13(I98, I99, I100, I101, I102, I103, I104) 
  f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 
  f10(I112, I113, I114, I115, I116, I117, I118) -> f6(I112, I113, I114, I115, I116, I119, I120) [I120 = I120 /\ I119 = I119 /\ 1 + I113 <= I112]
  f10(I121, I122, I123, I124, I125, I126, I127) -> f5(I121, 0, I123, I124, I125, I126, I127) [I121 <= I122]
  f8(I128, I129, I130, I131, I132, I133, I134) -> f9(I128, I129, I130, I131, I132, I133, I134) 
  f6(I135, I136, I137, I138, I139, I140, I141) -> f4(I135, I136, I137, I138, I139, I140, I141) 
  f6(I142, I143, I144, I145, I146, I147, I148) -> f7(I142, 1 + I143, I144, I145, I146, I147, I148) 
  f3(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) [1 + I150 <= I152]
  f3(I156, I157, I158, I159, I160, I161, I162) -> f4(I156, I157, I158, I159, I160, I161, I162) [I159 <= I157]
  f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) 

We use the extended value criterion with the projection function NU:
  NU[f1#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 1
  NU[f15#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2
  NU[f14#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2
  NU[f16#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2
  NU[f2#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 1

This gives the following inequalities:
  1 + I15 <= I17  ==>  -I15 + I17 - 1 > -I15 + I17 - 2  with  -I15 + I17 - 1 >= 0
  1 + I46 <= I43  ==>  -I43 + I45 - 2 >= -I43 + I45 - 2
    ==>  -I50 + I52 - 2 >= -(1 + I50) + I52 - 1
    ==>  -I64 + I66 - 2 >= -I64 + I66 - 2
    ==>  -I164 + I166 - 1 >= -I164 + I166 - 1

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f16#(I42, I43, I44, I45, I46, I47, I48) -> f14#(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43]
  f15#(I49, I50, I51, I52, I53, I54, I55) -> f1#(I49, 1 + I50, I51, I52, I53, I54, I55) 
  f14#(I63, I64, I65, I66, I67, I68, I69) -> f15#(I63, I64, I65, I66, I67, I68, I69) 
  f1#(I163, I164, I165, I166, I167, I168, I169) -> f2#(I163, I164, I165, I166, I167, I168, I169) 
R = 
  f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 
  f17(I0, I1, I2, I3, I4, I5, I6) -> f1(5, 0, I2, 5, 0, I5, I6) 
  f5(I7, I8, I9, I10, I11, I12, I13) -> f3(I7, I8, I9, I10, I11, I12, I13) 
  f2(I14, I15, I16, I17, I18, I19, I20) -> f16(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17]
  f2(I21, I22, I23, I24, I25, I26, I27) -> f8(I21, 0, I23, I24, I25, I26, I27) [I24 <= I22]
  f16(I28, I29, I30, I31, I32, I33, I34) -> f15(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32]
  f16(I35, I36, I37, I38, I39, I40, I41) -> f14(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39]
  f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43]
  f15(I49, I50, I51, I52, I53, I54, I55) -> f1(I49, 1 + I50, I51, I52, I53, I54, I55) 
  f7(I56, I57, I58, I59, I60, I61, I62) -> f10(I56, I57, I58, I59, I60, I61, I62) 
  f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 
  f9(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73]
  f9(I77, I78, I79, I80, I81, I82, I83) -> f7(I77, 0, I79, I80, I81, I82, I83) [I80 <= I78]
  f13(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84]
  f13(I91, I92, I93, I94, I95, I96, I97) -> f8(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93]
  f12(I98, I99, I100, I101, I102, I103, I104) -> f13(I98, I99, I100, I101, I102, I103, I104) 
  f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 
  f10(I112, I113, I114, I115, I116, I117, I118) -> f6(I112, I113, I114, I115, I116, I119, I120) [I120 = I120 /\ I119 = I119 /\ 1 + I113 <= I112]
  f10(I121, I122, I123, I124, I125, I126, I127) -> f5(I121, 0, I123, I124, I125, I126, I127) [I121 <= I122]
  f8(I128, I129, I130, I131, I132, I133, I134) -> f9(I128, I129, I130, I131, I132, I133, I134) 
  f6(I135, I136, I137, I138, I139, I140, I141) -> f4(I135, I136, I137, I138, I139, I140, I141) 
  f6(I142, I143, I144, I145, I146, I147, I148) -> f7(I142, 1 + I143, I144, I145, I146, I147, I148) 
  f3(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) [1 + I150 <= I152]
  f3(I156, I157, I158, I159, I160, I161, I162) -> f4(I156, I157, I158, I159, I160, I161, I162) [I159 <= I157]
  f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) 

The dependency graph for this problem is:
  7 -> 10
  8 -> 22
  10 -> 8
  22 -> 
Where:
  7) f16#(I42, I43, I44, I45, I46, I47, I48) -> f14#(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43]
  8) f15#(I49, I50, I51, I52, I53, I54, I55) -> f1#(I49, 1 + I50, I51, I52, I53, I54, I55) 
  10) f14#(I63, I64, I65, I66, I67, I68, I69) -> f15#(I63, I64, I65, I66, I67, I68, I69) 
  22) f1#(I163, I164, I165, I166, I167, I168, I169) -> f2#(I163, I164, I165, I166, I167, I168, I169) 

We have the following SCCs.