/export/starexec/sandbox2/solver/bin/starexec_run_Transition /export/starexec/sandbox2/benchmark/theBenchmark.smt2 /export/starexec/sandbox2/output/output_files


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


YES

DP problem for innermost termination.
P =
  f19#(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f18#(x1, x2, x3, x4, x5, x6, x7, x8, x9) 
  f18#(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f1#(I0, I1, I2, I3, 0, I5, 0, rnd8, rnd9) [rnd8 = rnd8 /\ rnd9 = rnd9 /\ y1 = 0]
  f2#(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1#(I9, I10, I11, I12, 1 + I13, I14, I15, I16, I17) [1 + I13 <= 50]
  f2#(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6#(I18, I19, I20, I21, I22, 0, I24, I25, I26) [50 <= I22 /\ I27 = 0]
  f5#(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3#(I28, I29, I30, I31, I32, I33, I34, I35, I36) 
  f7#(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6#(I37, I38, I39, I40, I41, 1 + I42, I43, I44, I45) [1 + I42 <= 50]
  f7#(I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f10#(0, I47, I48, I49, I50, I51, I52, I53, I54) [50 <= I51 /\ I55 = 0]
  f9#(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8#(I56, I57, I58, I59, I60, I61, I62, I63, I64) 
  f11#(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f10#(1 + I65, I66, I67, I68, I69, I70, I71, I72, I73) [1 + I65 <= 50]
  f11#(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f14#(I74, I75, I76, I77, I78, I79, 0, I81, I82) [50 <= I74]
  f13#(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12#(I83, I84, I85, I86, I87, I88, I89, I90, I91) 
  f15#(I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f14#(I92, I93, I94, I95, I96, I97, 1 + I98, I99, I100) [1 + I98 <= 50]
  f15#(I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f17#(I101, 0, I103, I104, I105, I106, I107, I108, I109) [50 <= I107 /\ I110 = 0]
  f17#(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16#(I111, I112, I113, I114, I115, I116, I117, I118, I119) 
  f16#(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f17#(I120, 1 + I121, I122, I123, I124, I125, I126, I127, I128) [1 + I121 <= 50]
  f16#(I129, I130, I131, I132, I133, I134, I135, I136, I137) -> f13#(I129, I130, 0, I132, I133, I134, I135, I136, I137) [50 <= I130 /\ I138 = 0]
  f14#(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15#(I139, I140, I141, I142, I143, I144, I145, I146, I147) 
  f12#(I148, I149, I150, I151, I152, I153, I154, I155, I156) -> f13#(I148, I149, 1 + I150, I151, I152, I153, I154, I155, I156) [1 + I150 <= 50]
  f12#(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f9#(I157, I158, I159, 0, I161, I162, I163, I164, I165) [50 <= I159 /\ I166 = 0]
  f10#(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11#(I167, I168, I169, I170, I171, I172, I173, I174, I175) 
  f8#(I176, I177, I178, I179, I180, I181, I182, I183, I184) -> f9#(I176, I177, I178, 1 + I179, I180, I181, I182, I183, I184) [1 + I179 <= 50]
  f8#(I185, I186, I187, I188, I189, I190, I191, I192, I193) -> f5#(I185, I186, I187, I188, I189, I190, 0, I192, I193) [50 <= I188]
  f6#(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7#(I194, I195, I196, I197, I198, I199, I200, I201, I202) 
  f3#(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5#(I203, I204, I205, I206, I207, I208, 1 + I209, I210, I211) [1 + I209 <= 50]
  f1#(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2#(I221, I222, I223, I224, I225, I226, I227, I228, I229) 
R = 
  f19(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) 
  f18(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f1(I0, I1, I2, I3, 0, I5, 0, rnd8, rnd9) [rnd8 = rnd8 /\ rnd9 = rnd9 /\ y1 = 0]
  f2(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, 1 + I13, I14, I15, I16, I17) [1 + I13 <= 50]
  f2(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, 0, I24, I25, I26) [50 <= I22 /\ I27 = 0]
  f5(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3(I28, I29, I30, I31, I32, I33, I34, I35, I36) 
  f7(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6(I37, I38, I39, I40, I41, 1 + I42, I43, I44, I45) [1 + I42 <= 50]
  f7(I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f10(0, I47, I48, I49, I50, I51, I52, I53, I54) [50 <= I51 /\ I55 = 0]
  f9(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8(I56, I57, I58, I59, I60, I61, I62, I63, I64) 
  f11(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f10(1 + I65, I66, I67, I68, I69, I70, I71, I72, I73) [1 + I65 <= 50]
  f11(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f14(I74, I75, I76, I77, I78, I79, 0, I81, I82) [50 <= I74]
  f13(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12(I83, I84, I85, I86, I87, I88, I89, I90, I91) 
  f15(I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f14(I92, I93, I94, I95, I96, I97, 1 + I98, I99, I100) [1 + I98 <= 50]
  f15(I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f17(I101, 0, I103, I104, I105, I106, I107, I108, I109) [50 <= I107 /\ I110 = 0]
  f17(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16(I111, I112, I113, I114, I115, I116, I117, I118, I119) 
  f16(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f17(I120, 1 + I121, I122, I123, I124, I125, I126, I127, I128) [1 + I121 <= 50]
  f16(I129, I130, I131, I132, I133, I134, I135, I136, I137) -> f13(I129, I130, 0, I132, I133, I134, I135, I136, I137) [50 <= I130 /\ I138 = 0]
  f14(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15(I139, I140, I141, I142, I143, I144, I145, I146, I147) 
  f12(I148, I149, I150, I151, I152, I153, I154, I155, I156) -> f13(I148, I149, 1 + I150, I151, I152, I153, I154, I155, I156) [1 + I150 <= 50]
  f12(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f9(I157, I158, I159, 0, I161, I162, I163, I164, I165) [50 <= I159 /\ I166 = 0]
  f10(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11(I167, I168, I169, I170, I171, I172, I173, I174, I175) 
  f8(I176, I177, I178, I179, I180, I181, I182, I183, I184) -> f9(I176, I177, I178, 1 + I179, I180, I181, I182, I183, I184) [1 + I179 <= 50]
  f8(I185, I186, I187, I188, I189, I190, I191, I192, I193) -> f5(I185, I186, I187, I188, I189, I190, 0, I192, I193) [50 <= I188]
  f6(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7(I194, I195, I196, I197, I198, I199, I200, I201, I202) 
  f3(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5(I203, I204, I205, I206, I207, I208, 1 + I209, I210, I211) [1 + I209 <= 50]
  f3(I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f4(I212, I213, I214, I215, I216, I217, I218, I219, I220) [50 <= I218]
  f1(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2(I221, I222, I223, I224, I225, I226, I227, I228, I229) 

The dependency graph for this problem is:
  0 -> 1
  1 -> 24
  2 -> 24
  3 -> 22
  4 -> 23
  5 -> 22
  6 -> 19
  7 -> 20, 21
  8 -> 19
  9 -> 16
  10 -> 17, 18
  11 -> 16
  12 -> 13
  13 -> 14, 15
  14 -> 13
  15 -> 10
  16 -> 11, 12
  17 -> 10
  18 -> 7
  19 -> 8, 9
  20 -> 7
  21 -> 4
  22 -> 5, 6
  23 -> 4
  24 -> 2, 3
Where:
  0) f19#(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f18#(x1, x2, x3, x4, x5, x6, x7, x8, x9) 
  1) f18#(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f1#(I0, I1, I2, I3, 0, I5, 0, rnd8, rnd9) [rnd8 = rnd8 /\ rnd9 = rnd9 /\ y1 = 0]
  2) f2#(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1#(I9, I10, I11, I12, 1 + I13, I14, I15, I16, I17) [1 + I13 <= 50]
  3) f2#(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6#(I18, I19, I20, I21, I22, 0, I24, I25, I26) [50 <= I22 /\ I27 = 0]
  4) f5#(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3#(I28, I29, I30, I31, I32, I33, I34, I35, I36) 
  5) f7#(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6#(I37, I38, I39, I40, I41, 1 + I42, I43, I44, I45) [1 + I42 <= 50]
  6) f7#(I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f10#(0, I47, I48, I49, I50, I51, I52, I53, I54) [50 <= I51 /\ I55 = 0]
  7) f9#(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8#(I56, I57, I58, I59, I60, I61, I62, I63, I64) 
  8) f11#(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f10#(1 + I65, I66, I67, I68, I69, I70, I71, I72, I73) [1 + I65 <= 50]
  9) f11#(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f14#(I74, I75, I76, I77, I78, I79, 0, I81, I82) [50 <= I74]
  10) f13#(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12#(I83, I84, I85, I86, I87, I88, I89, I90, I91) 
  11) f15#(I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f14#(I92, I93, I94, I95, I96, I97, 1 + I98, I99, I100) [1 + I98 <= 50]
  12) f15#(I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f17#(I101, 0, I103, I104, I105, I106, I107, I108, I109) [50 <= I107 /\ I110 = 0]
  13) f17#(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16#(I111, I112, I113, I114, I115, I116, I117, I118, I119) 
  14) f16#(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f17#(I120, 1 + I121, I122, I123, I124, I125, I126, I127, I128) [1 + I121 <= 50]
  15) f16#(I129, I130, I131, I132, I133, I134, I135, I136, I137) -> f13#(I129, I130, 0, I132, I133, I134, I135, I136, I137) [50 <= I130 /\ I138 = 0]
  16) f14#(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15#(I139, I140, I141, I142, I143, I144, I145, I146, I147) 
  17) f12#(I148, I149, I150, I151, I152, I153, I154, I155, I156) -> f13#(I148, I149, 1 + I150, I151, I152, I153, I154, I155, I156) [1 + I150 <= 50]
  18) f12#(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f9#(I157, I158, I159, 0, I161, I162, I163, I164, I165) [50 <= I159 /\ I166 = 0]
  19) f10#(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11#(I167, I168, I169, I170, I171, I172, I173, I174, I175) 
  20) f8#(I176, I177, I178, I179, I180, I181, I182, I183, I184) -> f9#(I176, I177, I178, 1 + I179, I180, I181, I182, I183, I184) [1 + I179 <= 50]
  21) f8#(I185, I186, I187, I188, I189, I190, I191, I192, I193) -> f5#(I185, I186, I187, I188, I189, I190, 0, I192, I193) [50 <= I188]
  22) f6#(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7#(I194, I195, I196, I197, I198, I199, I200, I201, I202) 
  23) f3#(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5#(I203, I204, I205, I206, I207, I208, 1 + I209, I210, I211) [1 + I209 <= 50]
  24) f1#(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2#(I221, I222, I223, I224, I225, I226, I227, I228, I229) 

We have the following SCCs.
  { 2, 24 }
  { 5, 22 }
  { 8, 19 }
  { 11, 16 }
  { 13, 14 }
  { 10, 17 }
  { 7, 20 }
  { 4, 23 }

DP problem for innermost termination.
P =
  f5#(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3#(I28, I29, I30, I31, I32, I33, I34, I35, I36) 
  f3#(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5#(I203, I204, I205, I206, I207, I208, 1 + I209, I210, I211) [1 + I209 <= 50]
R = 
  f19(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) 
  f18(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f1(I0, I1, I2, I3, 0, I5, 0, rnd8, rnd9) [rnd8 = rnd8 /\ rnd9 = rnd9 /\ y1 = 0]
  f2(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, 1 + I13, I14, I15, I16, I17) [1 + I13 <= 50]
  f2(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, 0, I24, I25, I26) [50 <= I22 /\ I27 = 0]
  f5(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3(I28, I29, I30, I31, I32, I33, I34, I35, I36) 
  f7(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6(I37, I38, I39, I40, I41, 1 + I42, I43, I44, I45) [1 + I42 <= 50]
  f7(I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f10(0, I47, I48, I49, I50, I51, I52, I53, I54) [50 <= I51 /\ I55 = 0]
  f9(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8(I56, I57, I58, I59, I60, I61, I62, I63, I64) 
  f11(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f10(1 + I65, I66, I67, I68, I69, I70, I71, I72, I73) [1 + I65 <= 50]
  f11(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f14(I74, I75, I76, I77, I78, I79, 0, I81, I82) [50 <= I74]
  f13(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12(I83, I84, I85, I86, I87, I88, I89, I90, I91) 
  f15(I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f14(I92, I93, I94, I95, I96, I97, 1 + I98, I99, I100) [1 + I98 <= 50]
  f15(I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f17(I101, 0, I103, I104, I105, I106, I107, I108, I109) [50 <= I107 /\ I110 = 0]
  f17(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16(I111, I112, I113, I114, I115, I116, I117, I118, I119) 
  f16(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f17(I120, 1 + I121, I122, I123, I124, I125, I126, I127, I128) [1 + I121 <= 50]
  f16(I129, I130, I131, I132, I133, I134, I135, I136, I137) -> f13(I129, I130, 0, I132, I133, I134, I135, I136, I137) [50 <= I130 /\ I138 = 0]
  f14(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15(I139, I140, I141, I142, I143, I144, I145, I146, I147) 
  f12(I148, I149, I150, I151, I152, I153, I154, I155, I156) -> f13(I148, I149, 1 + I150, I151, I152, I153, I154, I155, I156) [1 + I150 <= 50]
  f12(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f9(I157, I158, I159, 0, I161, I162, I163, I164, I165) [50 <= I159 /\ I166 = 0]
  f10(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11(I167, I168, I169, I170, I171, I172, I173, I174, I175) 
  f8(I176, I177, I178, I179, I180, I181, I182, I183, I184) -> f9(I176, I177, I178, 1 + I179, I180, I181, I182, I183, I184) [1 + I179 <= 50]
  f8(I185, I186, I187, I188, I189, I190, I191, I192, I193) -> f5(I185, I186, I187, I188, I189, I190, 0, I192, I193) [50 <= I188]
  f6(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7(I194, I195, I196, I197, I198, I199, I200, I201, I202) 
  f3(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5(I203, I204, I205, I206, I207, I208, 1 + I209, I210, I211) [1 + I209 <= 50]
  f3(I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f4(I212, I213, I214, I215, I216, I217, I218, I219, I220) [50 <= I218]
  f1(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2(I221, I222, I223, I224, I225, I226, I227, I228, I229) 

We use the reverse value criterion with the projection function NU:
  NU[f3#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = 50 + -1 * (1 + z7)
  NU[f5#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = 50 + -1 * (1 + z7)

This gives the following inequalities:
    ==>  50 + -1 * (1 + I34) >= 50 + -1 * (1 + I34)
  1 + I209 <= 50  ==>  50 + -1 * (1 + I209) > 50 + -1 * (1 + (1 + I209))  with  50 + -1 * (1 + I209) >= 0

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f5#(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3#(I28, I29, I30, I31, I32, I33, I34, I35, I36) 
R = 
  f19(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) 
  f18(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f1(I0, I1, I2, I3, 0, I5, 0, rnd8, rnd9) [rnd8 = rnd8 /\ rnd9 = rnd9 /\ y1 = 0]
  f2(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, 1 + I13, I14, I15, I16, I17) [1 + I13 <= 50]
  f2(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, 0, I24, I25, I26) [50 <= I22 /\ I27 = 0]
  f5(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3(I28, I29, I30, I31, I32, I33, I34, I35, I36) 
  f7(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6(I37, I38, I39, I40, I41, 1 + I42, I43, I44, I45) [1 + I42 <= 50]
  f7(I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f10(0, I47, I48, I49, I50, I51, I52, I53, I54) [50 <= I51 /\ I55 = 0]
  f9(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8(I56, I57, I58, I59, I60, I61, I62, I63, I64) 
  f11(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f10(1 + I65, I66, I67, I68, I69, I70, I71, I72, I73) [1 + I65 <= 50]
  f11(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f14(I74, I75, I76, I77, I78, I79, 0, I81, I82) [50 <= I74]
  f13(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12(I83, I84, I85, I86, I87, I88, I89, I90, I91) 
  f15(I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f14(I92, I93, I94, I95, I96, I97, 1 + I98, I99, I100) [1 + I98 <= 50]
  f15(I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f17(I101, 0, I103, I104, I105, I106, I107, I108, I109) [50 <= I107 /\ I110 = 0]
  f17(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16(I111, I112, I113, I114, I115, I116, I117, I118, I119) 
  f16(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f17(I120, 1 + I121, I122, I123, I124, I125, I126, I127, I128) [1 + I121 <= 50]
  f16(I129, I130, I131, I132, I133, I134, I135, I136, I137) -> f13(I129, I130, 0, I132, I133, I134, I135, I136, I137) [50 <= I130 /\ I138 = 0]
  f14(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15(I139, I140, I141, I142, I143, I144, I145, I146, I147) 
  f12(I148, I149, I150, I151, I152, I153, I154, I155, I156) -> f13(I148, I149, 1 + I150, I151, I152, I153, I154, I155, I156) [1 + I150 <= 50]
  f12(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f9(I157, I158, I159, 0, I161, I162, I163, I164, I165) [50 <= I159 /\ I166 = 0]
  f10(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11(I167, I168, I169, I170, I171, I172, I173, I174, I175) 
  f8(I176, I177, I178, I179, I180, I181, I182, I183, I184) -> f9(I176, I177, I178, 1 + I179, I180, I181, I182, I183, I184) [1 + I179 <= 50]
  f8(I185, I186, I187, I188, I189, I190, I191, I192, I193) -> f5(I185, I186, I187, I188, I189, I190, 0, I192, I193) [50 <= I188]
  f6(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7(I194, I195, I196, I197, I198, I199, I200, I201, I202) 
  f3(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5(I203, I204, I205, I206, I207, I208, 1 + I209, I210, I211) [1 + I209 <= 50]
  f3(I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f4(I212, I213, I214, I215, I216, I217, I218, I219, I220) [50 <= I218]
  f1(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2(I221, I222, I223, I224, I225, I226, I227, I228, I229) 

The dependency graph for this problem is:
  4 -> 
Where:
  4) f5#(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3#(I28, I29, I30, I31, I32, I33, I34, I35, I36) 

We have the following SCCs.
  

DP problem for innermost termination.
P =
  f9#(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8#(I56, I57, I58, I59, I60, I61, I62, I63, I64) 
  f8#(I176, I177, I178, I179, I180, I181, I182, I183, I184) -> f9#(I176, I177, I178, 1 + I179, I180, I181, I182, I183, I184) [1 + I179 <= 50]
R = 
  f19(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) 
  f18(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f1(I0, I1, I2, I3, 0, I5, 0, rnd8, rnd9) [rnd8 = rnd8 /\ rnd9 = rnd9 /\ y1 = 0]
  f2(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, 1 + I13, I14, I15, I16, I17) [1 + I13 <= 50]
  f2(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, 0, I24, I25, I26) [50 <= I22 /\ I27 = 0]
  f5(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3(I28, I29, I30, I31, I32, I33, I34, I35, I36) 
  f7(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6(I37, I38, I39, I40, I41, 1 + I42, I43, I44, I45) [1 + I42 <= 50]
  f7(I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f10(0, I47, I48, I49, I50, I51, I52, I53, I54) [50 <= I51 /\ I55 = 0]
  f9(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8(I56, I57, I58, I59, I60, I61, I62, I63, I64) 
  f11(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f10(1 + I65, I66, I67, I68, I69, I70, I71, I72, I73) [1 + I65 <= 50]
  f11(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f14(I74, I75, I76, I77, I78, I79, 0, I81, I82) [50 <= I74]
  f13(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12(I83, I84, I85, I86, I87, I88, I89, I90, I91) 
  f15(I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f14(I92, I93, I94, I95, I96, I97, 1 + I98, I99, I100) [1 + I98 <= 50]
  f15(I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f17(I101, 0, I103, I104, I105, I106, I107, I108, I109) [50 <= I107 /\ I110 = 0]
  f17(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16(I111, I112, I113, I114, I115, I116, I117, I118, I119) 
  f16(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f17(I120, 1 + I121, I122, I123, I124, I125, I126, I127, I128) [1 + I121 <= 50]
  f16(I129, I130, I131, I132, I133, I134, I135, I136, I137) -> f13(I129, I130, 0, I132, I133, I134, I135, I136, I137) [50 <= I130 /\ I138 = 0]
  f14(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15(I139, I140, I141, I142, I143, I144, I145, I146, I147) 
  f12(I148, I149, I150, I151, I152, I153, I154, I155, I156) -> f13(I148, I149, 1 + I150, I151, I152, I153, I154, I155, I156) [1 + I150 <= 50]
  f12(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f9(I157, I158, I159, 0, I161, I162, I163, I164, I165) [50 <= I159 /\ I166 = 0]
  f10(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11(I167, I168, I169, I170, I171, I172, I173, I174, I175) 
  f8(I176, I177, I178, I179, I180, I181, I182, I183, I184) -> f9(I176, I177, I178, 1 + I179, I180, I181, I182, I183, I184) [1 + I179 <= 50]
  f8(I185, I186, I187, I188, I189, I190, I191, I192, I193) -> f5(I185, I186, I187, I188, I189, I190, 0, I192, I193) [50 <= I188]
  f6(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7(I194, I195, I196, I197, I198, I199, I200, I201, I202) 
  f3(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5(I203, I204, I205, I206, I207, I208, 1 + I209, I210, I211) [1 + I209 <= 50]
  f3(I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f4(I212, I213, I214, I215, I216, I217, I218, I219, I220) [50 <= I218]
  f1(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2(I221, I222, I223, I224, I225, I226, I227, I228, I229) 

We use the reverse value criterion with the projection function NU:
  NU[f8#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = 50 + -1 * (1 + z4)
  NU[f9#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = 50 + -1 * (1 + z4)

This gives the following inequalities:
    ==>  50 + -1 * (1 + I59) >= 50 + -1 * (1 + I59)
  1 + I179 <= 50  ==>  50 + -1 * (1 + I179) > 50 + -1 * (1 + (1 + I179))  with  50 + -1 * (1 + I179) >= 0

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f9#(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8#(I56, I57, I58, I59, I60, I61, I62, I63, I64) 
R = 
  f19(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) 
  f18(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f1(I0, I1, I2, I3, 0, I5, 0, rnd8, rnd9) [rnd8 = rnd8 /\ rnd9 = rnd9 /\ y1 = 0]
  f2(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, 1 + I13, I14, I15, I16, I17) [1 + I13 <= 50]
  f2(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, 0, I24, I25, I26) [50 <= I22 /\ I27 = 0]
  f5(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3(I28, I29, I30, I31, I32, I33, I34, I35, I36) 
  f7(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6(I37, I38, I39, I40, I41, 1 + I42, I43, I44, I45) [1 + I42 <= 50]
  f7(I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f10(0, I47, I48, I49, I50, I51, I52, I53, I54) [50 <= I51 /\ I55 = 0]
  f9(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8(I56, I57, I58, I59, I60, I61, I62, I63, I64) 
  f11(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f10(1 + I65, I66, I67, I68, I69, I70, I71, I72, I73) [1 + I65 <= 50]
  f11(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f14(I74, I75, I76, I77, I78, I79, 0, I81, I82) [50 <= I74]
  f13(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12(I83, I84, I85, I86, I87, I88, I89, I90, I91) 
  f15(I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f14(I92, I93, I94, I95, I96, I97, 1 + I98, I99, I100) [1 + I98 <= 50]
  f15(I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f17(I101, 0, I103, I104, I105, I106, I107, I108, I109) [50 <= I107 /\ I110 = 0]
  f17(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16(I111, I112, I113, I114, I115, I116, I117, I118, I119) 
  f16(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f17(I120, 1 + I121, I122, I123, I124, I125, I126, I127, I128) [1 + I121 <= 50]
  f16(I129, I130, I131, I132, I133, I134, I135, I136, I137) -> f13(I129, I130, 0, I132, I133, I134, I135, I136, I137) [50 <= I130 /\ I138 = 0]
  f14(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15(I139, I140, I141, I142, I143, I144, I145, I146, I147) 
  f12(I148, I149, I150, I151, I152, I153, I154, I155, I156) -> f13(I148, I149, 1 + I150, I151, I152, I153, I154, I155, I156) [1 + I150 <= 50]
  f12(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f9(I157, I158, I159, 0, I161, I162, I163, I164, I165) [50 <= I159 /\ I166 = 0]
  f10(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11(I167, I168, I169, I170, I171, I172, I173, I174, I175) 
  f8(I176, I177, I178, I179, I180, I181, I182, I183, I184) -> f9(I176, I177, I178, 1 + I179, I180, I181, I182, I183, I184) [1 + I179 <= 50]
  f8(I185, I186, I187, I188, I189, I190, I191, I192, I193) -> f5(I185, I186, I187, I188, I189, I190, 0, I192, I193) [50 <= I188]
  f6(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7(I194, I195, I196, I197, I198, I199, I200, I201, I202) 
  f3(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5(I203, I204, I205, I206, I207, I208, 1 + I209, I210, I211) [1 + I209 <= 50]
  f3(I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f4(I212, I213, I214, I215, I216, I217, I218, I219, I220) [50 <= I218]
  f1(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2(I221, I222, I223, I224, I225, I226, I227, I228, I229) 

The dependency graph for this problem is:
  7 -> 
Where:
  7) f9#(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8#(I56, I57, I58, I59, I60, I61, I62, I63, I64) 

We have the following SCCs.
  

DP problem for innermost termination.
P =
  f13#(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12#(I83, I84, I85, I86, I87, I88, I89, I90, I91) 
  f12#(I148, I149, I150, I151, I152, I153, I154, I155, I156) -> f13#(I148, I149, 1 + I150, I151, I152, I153, I154, I155, I156) [1 + I150 <= 50]
R = 
  f19(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) 
  f18(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f1(I0, I1, I2, I3, 0, I5, 0, rnd8, rnd9) [rnd8 = rnd8 /\ rnd9 = rnd9 /\ y1 = 0]
  f2(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, 1 + I13, I14, I15, I16, I17) [1 + I13 <= 50]
  f2(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, 0, I24, I25, I26) [50 <= I22 /\ I27 = 0]
  f5(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3(I28, I29, I30, I31, I32, I33, I34, I35, I36) 
  f7(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6(I37, I38, I39, I40, I41, 1 + I42, I43, I44, I45) [1 + I42 <= 50]
  f7(I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f10(0, I47, I48, I49, I50, I51, I52, I53, I54) [50 <= I51 /\ I55 = 0]
  f9(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8(I56, I57, I58, I59, I60, I61, I62, I63, I64) 
  f11(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f10(1 + I65, I66, I67, I68, I69, I70, I71, I72, I73) [1 + I65 <= 50]
  f11(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f14(I74, I75, I76, I77, I78, I79, 0, I81, I82) [50 <= I74]
  f13(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12(I83, I84, I85, I86, I87, I88, I89, I90, I91) 
  f15(I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f14(I92, I93, I94, I95, I96, I97, 1 + I98, I99, I100) [1 + I98 <= 50]
  f15(I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f17(I101, 0, I103, I104, I105, I106, I107, I108, I109) [50 <= I107 /\ I110 = 0]
  f17(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16(I111, I112, I113, I114, I115, I116, I117, I118, I119) 
  f16(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f17(I120, 1 + I121, I122, I123, I124, I125, I126, I127, I128) [1 + I121 <= 50]
  f16(I129, I130, I131, I132, I133, I134, I135, I136, I137) -> f13(I129, I130, 0, I132, I133, I134, I135, I136, I137) [50 <= I130 /\ I138 = 0]
  f14(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15(I139, I140, I141, I142, I143, I144, I145, I146, I147) 
  f12(I148, I149, I150, I151, I152, I153, I154, I155, I156) -> f13(I148, I149, 1 + I150, I151, I152, I153, I154, I155, I156) [1 + I150 <= 50]
  f12(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f9(I157, I158, I159, 0, I161, I162, I163, I164, I165) [50 <= I159 /\ I166 = 0]
  f10(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11(I167, I168, I169, I170, I171, I172, I173, I174, I175) 
  f8(I176, I177, I178, I179, I180, I181, I182, I183, I184) -> f9(I176, I177, I178, 1 + I179, I180, I181, I182, I183, I184) [1 + I179 <= 50]
  f8(I185, I186, I187, I188, I189, I190, I191, I192, I193) -> f5(I185, I186, I187, I188, I189, I190, 0, I192, I193) [50 <= I188]
  f6(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7(I194, I195, I196, I197, I198, I199, I200, I201, I202) 
  f3(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5(I203, I204, I205, I206, I207, I208, 1 + I209, I210, I211) [1 + I209 <= 50]
  f3(I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f4(I212, I213, I214, I215, I216, I217, I218, I219, I220) [50 <= I218]
  f1(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2(I221, I222, I223, I224, I225, I226, I227, I228, I229) 

We use the reverse value criterion with the projection function NU:
  NU[f12#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = 50 + -1 * (1 + z3)
  NU[f13#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = 50 + -1 * (1 + z3)

This gives the following inequalities:
    ==>  50 + -1 * (1 + I85) >= 50 + -1 * (1 + I85)
  1 + I150 <= 50  ==>  50 + -1 * (1 + I150) > 50 + -1 * (1 + (1 + I150))  with  50 + -1 * (1 + I150) >= 0

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f13#(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12#(I83, I84, I85, I86, I87, I88, I89, I90, I91) 
R = 
  f19(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) 
  f18(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f1(I0, I1, I2, I3, 0, I5, 0, rnd8, rnd9) [rnd8 = rnd8 /\ rnd9 = rnd9 /\ y1 = 0]
  f2(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, 1 + I13, I14, I15, I16, I17) [1 + I13 <= 50]
  f2(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, 0, I24, I25, I26) [50 <= I22 /\ I27 = 0]
  f5(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3(I28, I29, I30, I31, I32, I33, I34, I35, I36) 
  f7(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6(I37, I38, I39, I40, I41, 1 + I42, I43, I44, I45) [1 + I42 <= 50]
  f7(I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f10(0, I47, I48, I49, I50, I51, I52, I53, I54) [50 <= I51 /\ I55 = 0]
  f9(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8(I56, I57, I58, I59, I60, I61, I62, I63, I64) 
  f11(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f10(1 + I65, I66, I67, I68, I69, I70, I71, I72, I73) [1 + I65 <= 50]
  f11(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f14(I74, I75, I76, I77, I78, I79, 0, I81, I82) [50 <= I74]
  f13(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12(I83, I84, I85, I86, I87, I88, I89, I90, I91) 
  f15(I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f14(I92, I93, I94, I95, I96, I97, 1 + I98, I99, I100) [1 + I98 <= 50]
  f15(I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f17(I101, 0, I103, I104, I105, I106, I107, I108, I109) [50 <= I107 /\ I110 = 0]
  f17(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16(I111, I112, I113, I114, I115, I116, I117, I118, I119) 
  f16(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f17(I120, 1 + I121, I122, I123, I124, I125, I126, I127, I128) [1 + I121 <= 50]
  f16(I129, I130, I131, I132, I133, I134, I135, I136, I137) -> f13(I129, I130, 0, I132, I133, I134, I135, I136, I137) [50 <= I130 /\ I138 = 0]
  f14(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15(I139, I140, I141, I142, I143, I144, I145, I146, I147) 
  f12(I148, I149, I150, I151, I152, I153, I154, I155, I156) -> f13(I148, I149, 1 + I150, I151, I152, I153, I154, I155, I156) [1 + I150 <= 50]
  f12(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f9(I157, I158, I159, 0, I161, I162, I163, I164, I165) [50 <= I159 /\ I166 = 0]
  f10(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11(I167, I168, I169, I170, I171, I172, I173, I174, I175) 
  f8(I176, I177, I178, I179, I180, I181, I182, I183, I184) -> f9(I176, I177, I178, 1 + I179, I180, I181, I182, I183, I184) [1 + I179 <= 50]
  f8(I185, I186, I187, I188, I189, I190, I191, I192, I193) -> f5(I185, I186, I187, I188, I189, I190, 0, I192, I193) [50 <= I188]
  f6(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7(I194, I195, I196, I197, I198, I199, I200, I201, I202) 
  f3(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5(I203, I204, I205, I206, I207, I208, 1 + I209, I210, I211) [1 + I209 <= 50]
  f3(I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f4(I212, I213, I214, I215, I216, I217, I218, I219, I220) [50 <= I218]
  f1(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2(I221, I222, I223, I224, I225, I226, I227, I228, I229) 

The dependency graph for this problem is:
  10 -> 
Where:
  10) f13#(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12#(I83, I84, I85, I86, I87, I88, I89, I90, I91) 

We have the following SCCs.
  

DP problem for innermost termination.
P =
  f17#(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16#(I111, I112, I113, I114, I115, I116, I117, I118, I119) 
  f16#(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f17#(I120, 1 + I121, I122, I123, I124, I125, I126, I127, I128) [1 + I121 <= 50]
R = 
  f19(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) 
  f18(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f1(I0, I1, I2, I3, 0, I5, 0, rnd8, rnd9) [rnd8 = rnd8 /\ rnd9 = rnd9 /\ y1 = 0]
  f2(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, 1 + I13, I14, I15, I16, I17) [1 + I13 <= 50]
  f2(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, 0, I24, I25, I26) [50 <= I22 /\ I27 = 0]
  f5(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3(I28, I29, I30, I31, I32, I33, I34, I35, I36) 
  f7(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6(I37, I38, I39, I40, I41, 1 + I42, I43, I44, I45) [1 + I42 <= 50]
  f7(I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f10(0, I47, I48, I49, I50, I51, I52, I53, I54) [50 <= I51 /\ I55 = 0]
  f9(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8(I56, I57, I58, I59, I60, I61, I62, I63, I64) 
  f11(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f10(1 + I65, I66, I67, I68, I69, I70, I71, I72, I73) [1 + I65 <= 50]
  f11(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f14(I74, I75, I76, I77, I78, I79, 0, I81, I82) [50 <= I74]
  f13(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12(I83, I84, I85, I86, I87, I88, I89, I90, I91) 
  f15(I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f14(I92, I93, I94, I95, I96, I97, 1 + I98, I99, I100) [1 + I98 <= 50]
  f15(I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f17(I101, 0, I103, I104, I105, I106, I107, I108, I109) [50 <= I107 /\ I110 = 0]
  f17(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16(I111, I112, I113, I114, I115, I116, I117, I118, I119) 
  f16(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f17(I120, 1 + I121, I122, I123, I124, I125, I126, I127, I128) [1 + I121 <= 50]
  f16(I129, I130, I131, I132, I133, I134, I135, I136, I137) -> f13(I129, I130, 0, I132, I133, I134, I135, I136, I137) [50 <= I130 /\ I138 = 0]
  f14(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15(I139, I140, I141, I142, I143, I144, I145, I146, I147) 
  f12(I148, I149, I150, I151, I152, I153, I154, I155, I156) -> f13(I148, I149, 1 + I150, I151, I152, I153, I154, I155, I156) [1 + I150 <= 50]
  f12(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f9(I157, I158, I159, 0, I161, I162, I163, I164, I165) [50 <= I159 /\ I166 = 0]
  f10(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11(I167, I168, I169, I170, I171, I172, I173, I174, I175) 
  f8(I176, I177, I178, I179, I180, I181, I182, I183, I184) -> f9(I176, I177, I178, 1 + I179, I180, I181, I182, I183, I184) [1 + I179 <= 50]
  f8(I185, I186, I187, I188, I189, I190, I191, I192, I193) -> f5(I185, I186, I187, I188, I189, I190, 0, I192, I193) [50 <= I188]
  f6(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7(I194, I195, I196, I197, I198, I199, I200, I201, I202) 
  f3(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5(I203, I204, I205, I206, I207, I208, 1 + I209, I210, I211) [1 + I209 <= 50]
  f3(I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f4(I212, I213, I214, I215, I216, I217, I218, I219, I220) [50 <= I218]
  f1(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2(I221, I222, I223, I224, I225, I226, I227, I228, I229) 

We use the reverse value criterion with the projection function NU:
  NU[f16#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = 50 + -1 * (1 + z2)
  NU[f17#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = 50 + -1 * (1 + z2)

This gives the following inequalities:
    ==>  50 + -1 * (1 + I112) >= 50 + -1 * (1 + I112)
  1 + I121 <= 50  ==>  50 + -1 * (1 + I121) > 50 + -1 * (1 + (1 + I121))  with  50 + -1 * (1 + I121) >= 0

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f17#(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16#(I111, I112, I113, I114, I115, I116, I117, I118, I119) 
R = 
  f19(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) 
  f18(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f1(I0, I1, I2, I3, 0, I5, 0, rnd8, rnd9) [rnd8 = rnd8 /\ rnd9 = rnd9 /\ y1 = 0]
  f2(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, 1 + I13, I14, I15, I16, I17) [1 + I13 <= 50]
  f2(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, 0, I24, I25, I26) [50 <= I22 /\ I27 = 0]
  f5(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3(I28, I29, I30, I31, I32, I33, I34, I35, I36) 
  f7(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6(I37, I38, I39, I40, I41, 1 + I42, I43, I44, I45) [1 + I42 <= 50]
  f7(I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f10(0, I47, I48, I49, I50, I51, I52, I53, I54) [50 <= I51 /\ I55 = 0]
  f9(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8(I56, I57, I58, I59, I60, I61, I62, I63, I64) 
  f11(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f10(1 + I65, I66, I67, I68, I69, I70, I71, I72, I73) [1 + I65 <= 50]
  f11(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f14(I74, I75, I76, I77, I78, I79, 0, I81, I82) [50 <= I74]
  f13(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12(I83, I84, I85, I86, I87, I88, I89, I90, I91) 
  f15(I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f14(I92, I93, I94, I95, I96, I97, 1 + I98, I99, I100) [1 + I98 <= 50]
  f15(I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f17(I101, 0, I103, I104, I105, I106, I107, I108, I109) [50 <= I107 /\ I110 = 0]
  f17(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16(I111, I112, I113, I114, I115, I116, I117, I118, I119) 
  f16(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f17(I120, 1 + I121, I122, I123, I124, I125, I126, I127, I128) [1 + I121 <= 50]
  f16(I129, I130, I131, I132, I133, I134, I135, I136, I137) -> f13(I129, I130, 0, I132, I133, I134, I135, I136, I137) [50 <= I130 /\ I138 = 0]
  f14(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15(I139, I140, I141, I142, I143, I144, I145, I146, I147) 
  f12(I148, I149, I150, I151, I152, I153, I154, I155, I156) -> f13(I148, I149, 1 + I150, I151, I152, I153, I154, I155, I156) [1 + I150 <= 50]
  f12(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f9(I157, I158, I159, 0, I161, I162, I163, I164, I165) [50 <= I159 /\ I166 = 0]
  f10(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11(I167, I168, I169, I170, I171, I172, I173, I174, I175) 
  f8(I176, I177, I178, I179, I180, I181, I182, I183, I184) -> f9(I176, I177, I178, 1 + I179, I180, I181, I182, I183, I184) [1 + I179 <= 50]
  f8(I185, I186, I187, I188, I189, I190, I191, I192, I193) -> f5(I185, I186, I187, I188, I189, I190, 0, I192, I193) [50 <= I188]
  f6(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7(I194, I195, I196, I197, I198, I199, I200, I201, I202) 
  f3(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5(I203, I204, I205, I206, I207, I208, 1 + I209, I210, I211) [1 + I209 <= 50]
  f3(I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f4(I212, I213, I214, I215, I216, I217, I218, I219, I220) [50 <= I218]
  f1(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2(I221, I222, I223, I224, I225, I226, I227, I228, I229) 

The dependency graph for this problem is:
  13 -> 
Where:
  13) f17#(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16#(I111, I112, I113, I114, I115, I116, I117, I118, I119) 

We have the following SCCs.
  

DP problem for innermost termination.
P =
  f15#(I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f14#(I92, I93, I94, I95, I96, I97, 1 + I98, I99, I100) [1 + I98 <= 50]
  f14#(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15#(I139, I140, I141, I142, I143, I144, I145, I146, I147) 
R = 
  f19(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) 
  f18(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f1(I0, I1, I2, I3, 0, I5, 0, rnd8, rnd9) [rnd8 = rnd8 /\ rnd9 = rnd9 /\ y1 = 0]
  f2(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, 1 + I13, I14, I15, I16, I17) [1 + I13 <= 50]
  f2(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, 0, I24, I25, I26) [50 <= I22 /\ I27 = 0]
  f5(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3(I28, I29, I30, I31, I32, I33, I34, I35, I36) 
  f7(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6(I37, I38, I39, I40, I41, 1 + I42, I43, I44, I45) [1 + I42 <= 50]
  f7(I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f10(0, I47, I48, I49, I50, I51, I52, I53, I54) [50 <= I51 /\ I55 = 0]
  f9(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8(I56, I57, I58, I59, I60, I61, I62, I63, I64) 
  f11(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f10(1 + I65, I66, I67, I68, I69, I70, I71, I72, I73) [1 + I65 <= 50]
  f11(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f14(I74, I75, I76, I77, I78, I79, 0, I81, I82) [50 <= I74]
  f13(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12(I83, I84, I85, I86, I87, I88, I89, I90, I91) 
  f15(I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f14(I92, I93, I94, I95, I96, I97, 1 + I98, I99, I100) [1 + I98 <= 50]
  f15(I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f17(I101, 0, I103, I104, I105, I106, I107, I108, I109) [50 <= I107 /\ I110 = 0]
  f17(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16(I111, I112, I113, I114, I115, I116, I117, I118, I119) 
  f16(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f17(I120, 1 + I121, I122, I123, I124, I125, I126, I127, I128) [1 + I121 <= 50]
  f16(I129, I130, I131, I132, I133, I134, I135, I136, I137) -> f13(I129, I130, 0, I132, I133, I134, I135, I136, I137) [50 <= I130 /\ I138 = 0]
  f14(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15(I139, I140, I141, I142, I143, I144, I145, I146, I147) 
  f12(I148, I149, I150, I151, I152, I153, I154, I155, I156) -> f13(I148, I149, 1 + I150, I151, I152, I153, I154, I155, I156) [1 + I150 <= 50]
  f12(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f9(I157, I158, I159, 0, I161, I162, I163, I164, I165) [50 <= I159 /\ I166 = 0]
  f10(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11(I167, I168, I169, I170, I171, I172, I173, I174, I175) 
  f8(I176, I177, I178, I179, I180, I181, I182, I183, I184) -> f9(I176, I177, I178, 1 + I179, I180, I181, I182, I183, I184) [1 + I179 <= 50]
  f8(I185, I186, I187, I188, I189, I190, I191, I192, I193) -> f5(I185, I186, I187, I188, I189, I190, 0, I192, I193) [50 <= I188]
  f6(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7(I194, I195, I196, I197, I198, I199, I200, I201, I202) 
  f3(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5(I203, I204, I205, I206, I207, I208, 1 + I209, I210, I211) [1 + I209 <= 50]
  f3(I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f4(I212, I213, I214, I215, I216, I217, I218, I219, I220) [50 <= I218]
  f1(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2(I221, I222, I223, I224, I225, I226, I227, I228, I229) 

We use the reverse value criterion with the projection function NU:
  NU[f14#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = 50 + -1 * (1 + z7)
  NU[f15#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = 50 + -1 * (1 + z7)

This gives the following inequalities:
  1 + I98 <= 50  ==>  50 + -1 * (1 + I98) > 50 + -1 * (1 + (1 + I98))  with  50 + -1 * (1 + I98) >= 0
    ==>  50 + -1 * (1 + I145) >= 50 + -1 * (1 + I145)

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f14#(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15#(I139, I140, I141, I142, I143, I144, I145, I146, I147) 
R = 
  f19(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) 
  f18(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f1(I0, I1, I2, I3, 0, I5, 0, rnd8, rnd9) [rnd8 = rnd8 /\ rnd9 = rnd9 /\ y1 = 0]
  f2(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, 1 + I13, I14, I15, I16, I17) [1 + I13 <= 50]
  f2(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, 0, I24, I25, I26) [50 <= I22 /\ I27 = 0]
  f5(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3(I28, I29, I30, I31, I32, I33, I34, I35, I36) 
  f7(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6(I37, I38, I39, I40, I41, 1 + I42, I43, I44, I45) [1 + I42 <= 50]
  f7(I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f10(0, I47, I48, I49, I50, I51, I52, I53, I54) [50 <= I51 /\ I55 = 0]
  f9(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8(I56, I57, I58, I59, I60, I61, I62, I63, I64) 
  f11(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f10(1 + I65, I66, I67, I68, I69, I70, I71, I72, I73) [1 + I65 <= 50]
  f11(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f14(I74, I75, I76, I77, I78, I79, 0, I81, I82) [50 <= I74]
  f13(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12(I83, I84, I85, I86, I87, I88, I89, I90, I91) 
  f15(I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f14(I92, I93, I94, I95, I96, I97, 1 + I98, I99, I100) [1 + I98 <= 50]
  f15(I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f17(I101, 0, I103, I104, I105, I106, I107, I108, I109) [50 <= I107 /\ I110 = 0]
  f17(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16(I111, I112, I113, I114, I115, I116, I117, I118, I119) 
  f16(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f17(I120, 1 + I121, I122, I123, I124, I125, I126, I127, I128) [1 + I121 <= 50]
  f16(I129, I130, I131, I132, I133, I134, I135, I136, I137) -> f13(I129, I130, 0, I132, I133, I134, I135, I136, I137) [50 <= I130 /\ I138 = 0]
  f14(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15(I139, I140, I141, I142, I143, I144, I145, I146, I147) 
  f12(I148, I149, I150, I151, I152, I153, I154, I155, I156) -> f13(I148, I149, 1 + I150, I151, I152, I153, I154, I155, I156) [1 + I150 <= 50]
  f12(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f9(I157, I158, I159, 0, I161, I162, I163, I164, I165) [50 <= I159 /\ I166 = 0]
  f10(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11(I167, I168, I169, I170, I171, I172, I173, I174, I175) 
  f8(I176, I177, I178, I179, I180, I181, I182, I183, I184) -> f9(I176, I177, I178, 1 + I179, I180, I181, I182, I183, I184) [1 + I179 <= 50]
  f8(I185, I186, I187, I188, I189, I190, I191, I192, I193) -> f5(I185, I186, I187, I188, I189, I190, 0, I192, I193) [50 <= I188]
  f6(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7(I194, I195, I196, I197, I198, I199, I200, I201, I202) 
  f3(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5(I203, I204, I205, I206, I207, I208, 1 + I209, I210, I211) [1 + I209 <= 50]
  f3(I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f4(I212, I213, I214, I215, I216, I217, I218, I219, I220) [50 <= I218]
  f1(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2(I221, I222, I223, I224, I225, I226, I227, I228, I229) 

The dependency graph for this problem is:
  16 -> 
Where:
  16) f14#(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15#(I139, I140, I141, I142, I143, I144, I145, I146, I147) 

We have the following SCCs.
  

DP problem for innermost termination.
P =
  f11#(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f10#(1 + I65, I66, I67, I68, I69, I70, I71, I72, I73) [1 + I65 <= 50]
  f10#(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11#(I167, I168, I169, I170, I171, I172, I173, I174, I175) 
R = 
  f19(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) 
  f18(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f1(I0, I1, I2, I3, 0, I5, 0, rnd8, rnd9) [rnd8 = rnd8 /\ rnd9 = rnd9 /\ y1 = 0]
  f2(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, 1 + I13, I14, I15, I16, I17) [1 + I13 <= 50]
  f2(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, 0, I24, I25, I26) [50 <= I22 /\ I27 = 0]
  f5(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3(I28, I29, I30, I31, I32, I33, I34, I35, I36) 
  f7(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6(I37, I38, I39, I40, I41, 1 + I42, I43, I44, I45) [1 + I42 <= 50]
  f7(I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f10(0, I47, I48, I49, I50, I51, I52, I53, I54) [50 <= I51 /\ I55 = 0]
  f9(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8(I56, I57, I58, I59, I60, I61, I62, I63, I64) 
  f11(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f10(1 + I65, I66, I67, I68, I69, I70, I71, I72, I73) [1 + I65 <= 50]
  f11(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f14(I74, I75, I76, I77, I78, I79, 0, I81, I82) [50 <= I74]
  f13(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12(I83, I84, I85, I86, I87, I88, I89, I90, I91) 
  f15(I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f14(I92, I93, I94, I95, I96, I97, 1 + I98, I99, I100) [1 + I98 <= 50]
  f15(I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f17(I101, 0, I103, I104, I105, I106, I107, I108, I109) [50 <= I107 /\ I110 = 0]
  f17(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16(I111, I112, I113, I114, I115, I116, I117, I118, I119) 
  f16(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f17(I120, 1 + I121, I122, I123, I124, I125, I126, I127, I128) [1 + I121 <= 50]
  f16(I129, I130, I131, I132, I133, I134, I135, I136, I137) -> f13(I129, I130, 0, I132, I133, I134, I135, I136, I137) [50 <= I130 /\ I138 = 0]
  f14(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15(I139, I140, I141, I142, I143, I144, I145, I146, I147) 
  f12(I148, I149, I150, I151, I152, I153, I154, I155, I156) -> f13(I148, I149, 1 + I150, I151, I152, I153, I154, I155, I156) [1 + I150 <= 50]
  f12(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f9(I157, I158, I159, 0, I161, I162, I163, I164, I165) [50 <= I159 /\ I166 = 0]
  f10(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11(I167, I168, I169, I170, I171, I172, I173, I174, I175) 
  f8(I176, I177, I178, I179, I180, I181, I182, I183, I184) -> f9(I176, I177, I178, 1 + I179, I180, I181, I182, I183, I184) [1 + I179 <= 50]
  f8(I185, I186, I187, I188, I189, I190, I191, I192, I193) -> f5(I185, I186, I187, I188, I189, I190, 0, I192, I193) [50 <= I188]
  f6(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7(I194, I195, I196, I197, I198, I199, I200, I201, I202) 
  f3(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5(I203, I204, I205, I206, I207, I208, 1 + I209, I210, I211) [1 + I209 <= 50]
  f3(I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f4(I212, I213, I214, I215, I216, I217, I218, I219, I220) [50 <= I218]
  f1(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2(I221, I222, I223, I224, I225, I226, I227, I228, I229) 

We use the reverse value criterion with the projection function NU:
  NU[f10#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = 50 + -1 * (1 + z1)
  NU[f11#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = 50 + -1 * (1 + z1)

This gives the following inequalities:
  1 + I65 <= 50  ==>  50 + -1 * (1 + I65) > 50 + -1 * (1 + (1 + I65))  with  50 + -1 * (1 + I65) >= 0
    ==>  50 + -1 * (1 + I167) >= 50 + -1 * (1 + I167)

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f10#(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11#(I167, I168, I169, I170, I171, I172, I173, I174, I175) 
R = 
  f19(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) 
  f18(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f1(I0, I1, I2, I3, 0, I5, 0, rnd8, rnd9) [rnd8 = rnd8 /\ rnd9 = rnd9 /\ y1 = 0]
  f2(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, 1 + I13, I14, I15, I16, I17) [1 + I13 <= 50]
  f2(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, 0, I24, I25, I26) [50 <= I22 /\ I27 = 0]
  f5(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3(I28, I29, I30, I31, I32, I33, I34, I35, I36) 
  f7(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6(I37, I38, I39, I40, I41, 1 + I42, I43, I44, I45) [1 + I42 <= 50]
  f7(I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f10(0, I47, I48, I49, I50, I51, I52, I53, I54) [50 <= I51 /\ I55 = 0]
  f9(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8(I56, I57, I58, I59, I60, I61, I62, I63, I64) 
  f11(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f10(1 + I65, I66, I67, I68, I69, I70, I71, I72, I73) [1 + I65 <= 50]
  f11(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f14(I74, I75, I76, I77, I78, I79, 0, I81, I82) [50 <= I74]
  f13(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12(I83, I84, I85, I86, I87, I88, I89, I90, I91) 
  f15(I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f14(I92, I93, I94, I95, I96, I97, 1 + I98, I99, I100) [1 + I98 <= 50]
  f15(I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f17(I101, 0, I103, I104, I105, I106, I107, I108, I109) [50 <= I107 /\ I110 = 0]
  f17(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16(I111, I112, I113, I114, I115, I116, I117, I118, I119) 
  f16(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f17(I120, 1 + I121, I122, I123, I124, I125, I126, I127, I128) [1 + I121 <= 50]
  f16(I129, I130, I131, I132, I133, I134, I135, I136, I137) -> f13(I129, I130, 0, I132, I133, I134, I135, I136, I137) [50 <= I130 /\ I138 = 0]
  f14(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15(I139, I140, I141, I142, I143, I144, I145, I146, I147) 
  f12(I148, I149, I150, I151, I152, I153, I154, I155, I156) -> f13(I148, I149, 1 + I150, I151, I152, I153, I154, I155, I156) [1 + I150 <= 50]
  f12(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f9(I157, I158, I159, 0, I161, I162, I163, I164, I165) [50 <= I159 /\ I166 = 0]
  f10(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11(I167, I168, I169, I170, I171, I172, I173, I174, I175) 
  f8(I176, I177, I178, I179, I180, I181, I182, I183, I184) -> f9(I176, I177, I178, 1 + I179, I180, I181, I182, I183, I184) [1 + I179 <= 50]
  f8(I185, I186, I187, I188, I189, I190, I191, I192, I193) -> f5(I185, I186, I187, I188, I189, I190, 0, I192, I193) [50 <= I188]
  f6(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7(I194, I195, I196, I197, I198, I199, I200, I201, I202) 
  f3(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5(I203, I204, I205, I206, I207, I208, 1 + I209, I210, I211) [1 + I209 <= 50]
  f3(I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f4(I212, I213, I214, I215, I216, I217, I218, I219, I220) [50 <= I218]
  f1(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2(I221, I222, I223, I224, I225, I226, I227, I228, I229) 

The dependency graph for this problem is:
  19 -> 
Where:
  19) f10#(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11#(I167, I168, I169, I170, I171, I172, I173, I174, I175) 

We have the following SCCs.
  

DP problem for innermost termination.
P =
  f7#(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6#(I37, I38, I39, I40, I41, 1 + I42, I43, I44, I45) [1 + I42 <= 50]
  f6#(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7#(I194, I195, I196, I197, I198, I199, I200, I201, I202) 
R = 
  f19(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) 
  f18(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f1(I0, I1, I2, I3, 0, I5, 0, rnd8, rnd9) [rnd8 = rnd8 /\ rnd9 = rnd9 /\ y1 = 0]
  f2(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, 1 + I13, I14, I15, I16, I17) [1 + I13 <= 50]
  f2(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, 0, I24, I25, I26) [50 <= I22 /\ I27 = 0]
  f5(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3(I28, I29, I30, I31, I32, I33, I34, I35, I36) 
  f7(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6(I37, I38, I39, I40, I41, 1 + I42, I43, I44, I45) [1 + I42 <= 50]
  f7(I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f10(0, I47, I48, I49, I50, I51, I52, I53, I54) [50 <= I51 /\ I55 = 0]
  f9(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8(I56, I57, I58, I59, I60, I61, I62, I63, I64) 
  f11(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f10(1 + I65, I66, I67, I68, I69, I70, I71, I72, I73) [1 + I65 <= 50]
  f11(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f14(I74, I75, I76, I77, I78, I79, 0, I81, I82) [50 <= I74]
  f13(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12(I83, I84, I85, I86, I87, I88, I89, I90, I91) 
  f15(I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f14(I92, I93, I94, I95, I96, I97, 1 + I98, I99, I100) [1 + I98 <= 50]
  f15(I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f17(I101, 0, I103, I104, I105, I106, I107, I108, I109) [50 <= I107 /\ I110 = 0]
  f17(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16(I111, I112, I113, I114, I115, I116, I117, I118, I119) 
  f16(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f17(I120, 1 + I121, I122, I123, I124, I125, I126, I127, I128) [1 + I121 <= 50]
  f16(I129, I130, I131, I132, I133, I134, I135, I136, I137) -> f13(I129, I130, 0, I132, I133, I134, I135, I136, I137) [50 <= I130 /\ I138 = 0]
  f14(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15(I139, I140, I141, I142, I143, I144, I145, I146, I147) 
  f12(I148, I149, I150, I151, I152, I153, I154, I155, I156) -> f13(I148, I149, 1 + I150, I151, I152, I153, I154, I155, I156) [1 + I150 <= 50]
  f12(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f9(I157, I158, I159, 0, I161, I162, I163, I164, I165) [50 <= I159 /\ I166 = 0]
  f10(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11(I167, I168, I169, I170, I171, I172, I173, I174, I175) 
  f8(I176, I177, I178, I179, I180, I181, I182, I183, I184) -> f9(I176, I177, I178, 1 + I179, I180, I181, I182, I183, I184) [1 + I179 <= 50]
  f8(I185, I186, I187, I188, I189, I190, I191, I192, I193) -> f5(I185, I186, I187, I188, I189, I190, 0, I192, I193) [50 <= I188]
  f6(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7(I194, I195, I196, I197, I198, I199, I200, I201, I202) 
  f3(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5(I203, I204, I205, I206, I207, I208, 1 + I209, I210, I211) [1 + I209 <= 50]
  f3(I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f4(I212, I213, I214, I215, I216, I217, I218, I219, I220) [50 <= I218]
  f1(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2(I221, I222, I223, I224, I225, I226, I227, I228, I229) 

We use the reverse value criterion with the projection function NU:
  NU[f6#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = 50 + -1 * (1 + z6)
  NU[f7#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = 50 + -1 * (1 + z6)

This gives the following inequalities:
  1 + I42 <= 50  ==>  50 + -1 * (1 + I42) > 50 + -1 * (1 + (1 + I42))  with  50 + -1 * (1 + I42) >= 0
    ==>  50 + -1 * (1 + I199) >= 50 + -1 * (1 + I199)

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f6#(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7#(I194, I195, I196, I197, I198, I199, I200, I201, I202) 
R = 
  f19(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) 
  f18(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f1(I0, I1, I2, I3, 0, I5, 0, rnd8, rnd9) [rnd8 = rnd8 /\ rnd9 = rnd9 /\ y1 = 0]
  f2(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, 1 + I13, I14, I15, I16, I17) [1 + I13 <= 50]
  f2(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, 0, I24, I25, I26) [50 <= I22 /\ I27 = 0]
  f5(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3(I28, I29, I30, I31, I32, I33, I34, I35, I36) 
  f7(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6(I37, I38, I39, I40, I41, 1 + I42, I43, I44, I45) [1 + I42 <= 50]
  f7(I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f10(0, I47, I48, I49, I50, I51, I52, I53, I54) [50 <= I51 /\ I55 = 0]
  f9(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8(I56, I57, I58, I59, I60, I61, I62, I63, I64) 
  f11(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f10(1 + I65, I66, I67, I68, I69, I70, I71, I72, I73) [1 + I65 <= 50]
  f11(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f14(I74, I75, I76, I77, I78, I79, 0, I81, I82) [50 <= I74]
  f13(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12(I83, I84, I85, I86, I87, I88, I89, I90, I91) 
  f15(I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f14(I92, I93, I94, I95, I96, I97, 1 + I98, I99, I100) [1 + I98 <= 50]
  f15(I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f17(I101, 0, I103, I104, I105, I106, I107, I108, I109) [50 <= I107 /\ I110 = 0]
  f17(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16(I111, I112, I113, I114, I115, I116, I117, I118, I119) 
  f16(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f17(I120, 1 + I121, I122, I123, I124, I125, I126, I127, I128) [1 + I121 <= 50]
  f16(I129, I130, I131, I132, I133, I134, I135, I136, I137) -> f13(I129, I130, 0, I132, I133, I134, I135, I136, I137) [50 <= I130 /\ I138 = 0]
  f14(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15(I139, I140, I141, I142, I143, I144, I145, I146, I147) 
  f12(I148, I149, I150, I151, I152, I153, I154, I155, I156) -> f13(I148, I149, 1 + I150, I151, I152, I153, I154, I155, I156) [1 + I150 <= 50]
  f12(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f9(I157, I158, I159, 0, I161, I162, I163, I164, I165) [50 <= I159 /\ I166 = 0]
  f10(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11(I167, I168, I169, I170, I171, I172, I173, I174, I175) 
  f8(I176, I177, I178, I179, I180, I181, I182, I183, I184) -> f9(I176, I177, I178, 1 + I179, I180, I181, I182, I183, I184) [1 + I179 <= 50]
  f8(I185, I186, I187, I188, I189, I190, I191, I192, I193) -> f5(I185, I186, I187, I188, I189, I190, 0, I192, I193) [50 <= I188]
  f6(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7(I194, I195, I196, I197, I198, I199, I200, I201, I202) 
  f3(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5(I203, I204, I205, I206, I207, I208, 1 + I209, I210, I211) [1 + I209 <= 50]
  f3(I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f4(I212, I213, I214, I215, I216, I217, I218, I219, I220) [50 <= I218]
  f1(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2(I221, I222, I223, I224, I225, I226, I227, I228, I229) 

The dependency graph for this problem is:
  22 -> 
Where:
  22) f6#(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7#(I194, I195, I196, I197, I198, I199, I200, I201, I202) 

We have the following SCCs.
  

DP problem for innermost termination.
P =
  f2#(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1#(I9, I10, I11, I12, 1 + I13, I14, I15, I16, I17) [1 + I13 <= 50]
  f1#(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2#(I221, I222, I223, I224, I225, I226, I227, I228, I229) 
R = 
  f19(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) 
  f18(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f1(I0, I1, I2, I3, 0, I5, 0, rnd8, rnd9) [rnd8 = rnd8 /\ rnd9 = rnd9 /\ y1 = 0]
  f2(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, 1 + I13, I14, I15, I16, I17) [1 + I13 <= 50]
  f2(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, 0, I24, I25, I26) [50 <= I22 /\ I27 = 0]
  f5(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3(I28, I29, I30, I31, I32, I33, I34, I35, I36) 
  f7(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6(I37, I38, I39, I40, I41, 1 + I42, I43, I44, I45) [1 + I42 <= 50]
  f7(I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f10(0, I47, I48, I49, I50, I51, I52, I53, I54) [50 <= I51 /\ I55 = 0]
  f9(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8(I56, I57, I58, I59, I60, I61, I62, I63, I64) 
  f11(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f10(1 + I65, I66, I67, I68, I69, I70, I71, I72, I73) [1 + I65 <= 50]
  f11(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f14(I74, I75, I76, I77, I78, I79, 0, I81, I82) [50 <= I74]
  f13(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12(I83, I84, I85, I86, I87, I88, I89, I90, I91) 
  f15(I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f14(I92, I93, I94, I95, I96, I97, 1 + I98, I99, I100) [1 + I98 <= 50]
  f15(I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f17(I101, 0, I103, I104, I105, I106, I107, I108, I109) [50 <= I107 /\ I110 = 0]
  f17(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16(I111, I112, I113, I114, I115, I116, I117, I118, I119) 
  f16(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f17(I120, 1 + I121, I122, I123, I124, I125, I126, I127, I128) [1 + I121 <= 50]
  f16(I129, I130, I131, I132, I133, I134, I135, I136, I137) -> f13(I129, I130, 0, I132, I133, I134, I135, I136, I137) [50 <= I130 /\ I138 = 0]
  f14(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15(I139, I140, I141, I142, I143, I144, I145, I146, I147) 
  f12(I148, I149, I150, I151, I152, I153, I154, I155, I156) -> f13(I148, I149, 1 + I150, I151, I152, I153, I154, I155, I156) [1 + I150 <= 50]
  f12(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f9(I157, I158, I159, 0, I161, I162, I163, I164, I165) [50 <= I159 /\ I166 = 0]
  f10(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11(I167, I168, I169, I170, I171, I172, I173, I174, I175) 
  f8(I176, I177, I178, I179, I180, I181, I182, I183, I184) -> f9(I176, I177, I178, 1 + I179, I180, I181, I182, I183, I184) [1 + I179 <= 50]
  f8(I185, I186, I187, I188, I189, I190, I191, I192, I193) -> f5(I185, I186, I187, I188, I189, I190, 0, I192, I193) [50 <= I188]
  f6(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7(I194, I195, I196, I197, I198, I199, I200, I201, I202) 
  f3(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5(I203, I204, I205, I206, I207, I208, 1 + I209, I210, I211) [1 + I209 <= 50]
  f3(I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f4(I212, I213, I214, I215, I216, I217, I218, I219, I220) [50 <= I218]
  f1(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2(I221, I222, I223, I224, I225, I226, I227, I228, I229) 

We use the reverse value criterion with the projection function NU:
  NU[f1#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = 50 + -1 * (1 + z5)
  NU[f2#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = 50 + -1 * (1 + z5)

This gives the following inequalities:
  1 + I13 <= 50  ==>  50 + -1 * (1 + I13) > 50 + -1 * (1 + (1 + I13))  with  50 + -1 * (1 + I13) >= 0
    ==>  50 + -1 * (1 + I225) >= 50 + -1 * (1 + I225)

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f1#(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2#(I221, I222, I223, I224, I225, I226, I227, I228, I229) 
R = 
  f19(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) 
  f18(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f1(I0, I1, I2, I3, 0, I5, 0, rnd8, rnd9) [rnd8 = rnd8 /\ rnd9 = rnd9 /\ y1 = 0]
  f2(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, 1 + I13, I14, I15, I16, I17) [1 + I13 <= 50]
  f2(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, 0, I24, I25, I26) [50 <= I22 /\ I27 = 0]
  f5(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3(I28, I29, I30, I31, I32, I33, I34, I35, I36) 
  f7(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6(I37, I38, I39, I40, I41, 1 + I42, I43, I44, I45) [1 + I42 <= 50]
  f7(I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f10(0, I47, I48, I49, I50, I51, I52, I53, I54) [50 <= I51 /\ I55 = 0]
  f9(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8(I56, I57, I58, I59, I60, I61, I62, I63, I64) 
  f11(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f10(1 + I65, I66, I67, I68, I69, I70, I71, I72, I73) [1 + I65 <= 50]
  f11(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f14(I74, I75, I76, I77, I78, I79, 0, I81, I82) [50 <= I74]
  f13(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12(I83, I84, I85, I86, I87, I88, I89, I90, I91) 
  f15(I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f14(I92, I93, I94, I95, I96, I97, 1 + I98, I99, I100) [1 + I98 <= 50]
  f15(I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f17(I101, 0, I103, I104, I105, I106, I107, I108, I109) [50 <= I107 /\ I110 = 0]
  f17(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16(I111, I112, I113, I114, I115, I116, I117, I118, I119) 
  f16(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f17(I120, 1 + I121, I122, I123, I124, I125, I126, I127, I128) [1 + I121 <= 50]
  f16(I129, I130, I131, I132, I133, I134, I135, I136, I137) -> f13(I129, I130, 0, I132, I133, I134, I135, I136, I137) [50 <= I130 /\ I138 = 0]
  f14(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15(I139, I140, I141, I142, I143, I144, I145, I146, I147) 
  f12(I148, I149, I150, I151, I152, I153, I154, I155, I156) -> f13(I148, I149, 1 + I150, I151, I152, I153, I154, I155, I156) [1 + I150 <= 50]
  f12(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f9(I157, I158, I159, 0, I161, I162, I163, I164, I165) [50 <= I159 /\ I166 = 0]
  f10(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11(I167, I168, I169, I170, I171, I172, I173, I174, I175) 
  f8(I176, I177, I178, I179, I180, I181, I182, I183, I184) -> f9(I176, I177, I178, 1 + I179, I180, I181, I182, I183, I184) [1 + I179 <= 50]
  f8(I185, I186, I187, I188, I189, I190, I191, I192, I193) -> f5(I185, I186, I187, I188, I189, I190, 0, I192, I193) [50 <= I188]
  f6(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7(I194, I195, I196, I197, I198, I199, I200, I201, I202) 
  f3(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5(I203, I204, I205, I206, I207, I208, 1 + I209, I210, I211) [1 + I209 <= 50]
  f3(I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f4(I212, I213, I214, I215, I216, I217, I218, I219, I220) [50 <= I218]
  f1(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2(I221, I222, I223, I224, I225, I226, I227, I228, I229) 

The dependency graph for this problem is:
  24 -> 
Where:
  24) f1#(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2#(I221, I222, I223, I224, I225, I226, I227, I228, I229) 

We have the following SCCs.