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


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YES

DP problem for innermost termination.
P =
  f19#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f18#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 
  f18#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1#(I0, I1, I2, I3, I4, 0, I6, 0, rnd9, rnd10) [rnd9 = rnd9 /\ rnd10 = rnd10 /\ y1 = 0]
  f2#(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1#(I10, I11, I12, I13, I14, 1 + I15, I16, I17, I18, I19) [1 + I15 <= I10]
  f2#(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f6#(I20, I21, I22, I23, I24, I25, -1 + I20, I27, I28, I29) [I20 <= I25 /\ I30 = 0]
  f5#(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3#(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 
  f7#(I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f6#(I41, I42, I43, I44, I45, I46, -1 + I47, I48, I49, I50) [0 <= I47]
  f7#(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60) -> f10#(I51, 0, I53, I54, I55, I56, I57, I58, I59, I60) [1 + I57 <= 0 /\ I61 = 0]
  f9#(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8#(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 
  f11#(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81) -> f10#(I72, 1 + I73, I74, I75, I76, I77, I78, I79, I80, I81) [1 + I73 <= I72]
  f11#(I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f14#(I82, I83, I84, I85, I86, I87, I88, 0, I90, I91) [I82 <= I83]
  f13#(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12#(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 
  f15#(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14#(I102, I103, I104, I105, I106, I107, I108, 1 + I109, I110, I111) [1 + I109 <= I102]
  f15#(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f17#(I112, I113, 0, I115, I116, I117, I118, I119, I120, I121) [I112 <= I119 /\ I122 = 0]
  f17#(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16#(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 
  f16#(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f17#(I133, I134, 1 + I135, I136, I137, I138, I139, I140, I141, I142) [1 + I135 <= I133]
  f16#(I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f13#(I143, I144, I145, -1 + I143, I147, I148, I149, I150, I151, I152) [I143 <= I145 /\ I153 = 0]
  f14#(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15#(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 
  f12#(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f13#(I164, I165, I166, -1 + I167, I168, I169, I170, I171, I172, I173) [0 <= I167]
  f12#(I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f9#(I174, I175, I176, I177, 0, I179, I180, I181, I182, I183) [1 + I177 <= 0 /\ I184 = 0]
  f10#(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11#(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 
  f8#(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204) -> f9#(I195, I196, I197, I198, 1 + I199, I200, I201, I202, I203, I204) [1 + I199 <= I195]
  f8#(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214) -> f5#(I205, I206, I207, I208, I209, I210, I211, -1 + I205, I213, I214) [I205 <= I209]
  f6#(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7#(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 
  f3#(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234) -> f5#(I225, I226, I227, I228, I229, I230, I231, -1 + I232, I233, I234) [0 <= I232]
  f1#(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2#(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 
R = 
  f19(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 
  f18(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, rnd9, rnd10) [rnd9 = rnd9 /\ rnd10 = rnd10 /\ y1 = 0]
  f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1(I10, I11, I12, I13, I14, 1 + I15, I16, I17, I18, I19) [1 + I15 <= I10]
  f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f6(I20, I21, I22, I23, I24, I25, -1 + I20, I27, I28, I29) [I20 <= I25 /\ I30 = 0]
  f5(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 
  f7(I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f6(I41, I42, I43, I44, I45, I46, -1 + I47, I48, I49, I50) [0 <= I47]
  f7(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60) -> f10(I51, 0, I53, I54, I55, I56, I57, I58, I59, I60) [1 + I57 <= 0 /\ I61 = 0]
  f9(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 
  f11(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81) -> f10(I72, 1 + I73, I74, I75, I76, I77, I78, I79, I80, I81) [1 + I73 <= I72]
  f11(I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f14(I82, I83, I84, I85, I86, I87, I88, 0, I90, I91) [I82 <= I83]
  f13(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 
  f15(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14(I102, I103, I104, I105, I106, I107, I108, 1 + I109, I110, I111) [1 + I109 <= I102]
  f15(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f17(I112, I113, 0, I115, I116, I117, I118, I119, I120, I121) [I112 <= I119 /\ I122 = 0]
  f17(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 
  f16(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f17(I133, I134, 1 + I135, I136, I137, I138, I139, I140, I141, I142) [1 + I135 <= I133]
  f16(I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f13(I143, I144, I145, -1 + I143, I147, I148, I149, I150, I151, I152) [I143 <= I145 /\ I153 = 0]
  f14(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 
  f12(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f13(I164, I165, I166, -1 + I167, I168, I169, I170, I171, I172, I173) [0 <= I167]
  f12(I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f9(I174, I175, I176, I177, 0, I179, I180, I181, I182, I183) [1 + I177 <= 0 /\ I184 = 0]
  f10(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 
  f8(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204) -> f9(I195, I196, I197, I198, 1 + I199, I200, I201, I202, I203, I204) [1 + I199 <= I195]
  f8(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214) -> f5(I205, I206, I207, I208, I209, I210, I211, -1 + I205, I213, I214) [I205 <= I209]
  f6(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 
  f3(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234) -> f5(I225, I226, I227, I228, I229, I230, I231, -1 + I232, I233, I234) [0 <= I232]
  f3(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) -> f4(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) [1 + I242 <= 0]
  f1(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 

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, x10) -> f18#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 
  1) f18#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1#(I0, I1, I2, I3, I4, 0, I6, 0, rnd9, rnd10) [rnd9 = rnd9 /\ rnd10 = rnd10 /\ y1 = 0]
  2) f2#(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1#(I10, I11, I12, I13, I14, 1 + I15, I16, I17, I18, I19) [1 + I15 <= I10]
  3) f2#(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f6#(I20, I21, I22, I23, I24, I25, -1 + I20, I27, I28, I29) [I20 <= I25 /\ I30 = 0]
  4) f5#(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3#(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 
  5) f7#(I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f6#(I41, I42, I43, I44, I45, I46, -1 + I47, I48, I49, I50) [0 <= I47]
  6) f7#(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60) -> f10#(I51, 0, I53, I54, I55, I56, I57, I58, I59, I60) [1 + I57 <= 0 /\ I61 = 0]
  7) f9#(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8#(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 
  8) f11#(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81) -> f10#(I72, 1 + I73, I74, I75, I76, I77, I78, I79, I80, I81) [1 + I73 <= I72]
  9) f11#(I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f14#(I82, I83, I84, I85, I86, I87, I88, 0, I90, I91) [I82 <= I83]
  10) f13#(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12#(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 
  11) f15#(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14#(I102, I103, I104, I105, I106, I107, I108, 1 + I109, I110, I111) [1 + I109 <= I102]
  12) f15#(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f17#(I112, I113, 0, I115, I116, I117, I118, I119, I120, I121) [I112 <= I119 /\ I122 = 0]
  13) f17#(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16#(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 
  14) f16#(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f17#(I133, I134, 1 + I135, I136, I137, I138, I139, I140, I141, I142) [1 + I135 <= I133]
  15) f16#(I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f13#(I143, I144, I145, -1 + I143, I147, I148, I149, I150, I151, I152) [I143 <= I145 /\ I153 = 0]
  16) f14#(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15#(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 
  17) f12#(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f13#(I164, I165, I166, -1 + I167, I168, I169, I170, I171, I172, I173) [0 <= I167]
  18) f12#(I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f9#(I174, I175, I176, I177, 0, I179, I180, I181, I182, I183) [1 + I177 <= 0 /\ I184 = 0]
  19) f10#(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11#(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 
  20) f8#(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204) -> f9#(I195, I196, I197, I198, 1 + I199, I200, I201, I202, I203, I204) [1 + I199 <= I195]
  21) f8#(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214) -> f5#(I205, I206, I207, I208, I209, I210, I211, -1 + I205, I213, I214) [I205 <= I209]
  22) f6#(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7#(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 
  23) f3#(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234) -> f5#(I225, I226, I227, I228, I229, I230, I231, -1 + I232, I233, I234) [0 <= I232]
  24) f1#(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2#(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 

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#(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3#(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 
  f3#(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234) -> f5#(I225, I226, I227, I228, I229, I230, I231, -1 + I232, I233, I234) [0 <= I232]
R = 
  f19(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 
  f18(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, rnd9, rnd10) [rnd9 = rnd9 /\ rnd10 = rnd10 /\ y1 = 0]
  f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1(I10, I11, I12, I13, I14, 1 + I15, I16, I17, I18, I19) [1 + I15 <= I10]
  f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f6(I20, I21, I22, I23, I24, I25, -1 + I20, I27, I28, I29) [I20 <= I25 /\ I30 = 0]
  f5(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 
  f7(I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f6(I41, I42, I43, I44, I45, I46, -1 + I47, I48, I49, I50) [0 <= I47]
  f7(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60) -> f10(I51, 0, I53, I54, I55, I56, I57, I58, I59, I60) [1 + I57 <= 0 /\ I61 = 0]
  f9(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 
  f11(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81) -> f10(I72, 1 + I73, I74, I75, I76, I77, I78, I79, I80, I81) [1 + I73 <= I72]
  f11(I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f14(I82, I83, I84, I85, I86, I87, I88, 0, I90, I91) [I82 <= I83]
  f13(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 
  f15(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14(I102, I103, I104, I105, I106, I107, I108, 1 + I109, I110, I111) [1 + I109 <= I102]
  f15(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f17(I112, I113, 0, I115, I116, I117, I118, I119, I120, I121) [I112 <= I119 /\ I122 = 0]
  f17(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 
  f16(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f17(I133, I134, 1 + I135, I136, I137, I138, I139, I140, I141, I142) [1 + I135 <= I133]
  f16(I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f13(I143, I144, I145, -1 + I143, I147, I148, I149, I150, I151, I152) [I143 <= I145 /\ I153 = 0]
  f14(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 
  f12(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f13(I164, I165, I166, -1 + I167, I168, I169, I170, I171, I172, I173) [0 <= I167]
  f12(I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f9(I174, I175, I176, I177, 0, I179, I180, I181, I182, I183) [1 + I177 <= 0 /\ I184 = 0]
  f10(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 
  f8(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204) -> f9(I195, I196, I197, I198, 1 + I199, I200, I201, I202, I203, I204) [1 + I199 <= I195]
  f8(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214) -> f5(I205, I206, I207, I208, I209, I210, I211, -1 + I205, I213, I214) [I205 <= I209]
  f6(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 
  f3(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234) -> f5(I225, I226, I227, I228, I229, I230, I231, -1 + I232, I233, I234) [0 <= I232]
  f3(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) -> f4(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) [1 + I242 <= 0]
  f1(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 

We use the basic value criterion with the projection function NU:
  NU[f3#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10)] = z8
  NU[f5#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10)] = z8

This gives the following inequalities:
    ==>  I38 (>! \union =) I38
  0 <= I232  ==>  I232 >! -1 + I232

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f5#(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3#(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 
R = 
  f19(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 
  f18(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, rnd9, rnd10) [rnd9 = rnd9 /\ rnd10 = rnd10 /\ y1 = 0]
  f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1(I10, I11, I12, I13, I14, 1 + I15, I16, I17, I18, I19) [1 + I15 <= I10]
  f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f6(I20, I21, I22, I23, I24, I25, -1 + I20, I27, I28, I29) [I20 <= I25 /\ I30 = 0]
  f5(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 
  f7(I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f6(I41, I42, I43, I44, I45, I46, -1 + I47, I48, I49, I50) [0 <= I47]
  f7(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60) -> f10(I51, 0, I53, I54, I55, I56, I57, I58, I59, I60) [1 + I57 <= 0 /\ I61 = 0]
  f9(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 
  f11(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81) -> f10(I72, 1 + I73, I74, I75, I76, I77, I78, I79, I80, I81) [1 + I73 <= I72]
  f11(I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f14(I82, I83, I84, I85, I86, I87, I88, 0, I90, I91) [I82 <= I83]
  f13(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 
  f15(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14(I102, I103, I104, I105, I106, I107, I108, 1 + I109, I110, I111) [1 + I109 <= I102]
  f15(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f17(I112, I113, 0, I115, I116, I117, I118, I119, I120, I121) [I112 <= I119 /\ I122 = 0]
  f17(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 
  f16(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f17(I133, I134, 1 + I135, I136, I137, I138, I139, I140, I141, I142) [1 + I135 <= I133]
  f16(I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f13(I143, I144, I145, -1 + I143, I147, I148, I149, I150, I151, I152) [I143 <= I145 /\ I153 = 0]
  f14(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 
  f12(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f13(I164, I165, I166, -1 + I167, I168, I169, I170, I171, I172, I173) [0 <= I167]
  f12(I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f9(I174, I175, I176, I177, 0, I179, I180, I181, I182, I183) [1 + I177 <= 0 /\ I184 = 0]
  f10(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 
  f8(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204) -> f9(I195, I196, I197, I198, 1 + I199, I200, I201, I202, I203, I204) [1 + I199 <= I195]
  f8(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214) -> f5(I205, I206, I207, I208, I209, I210, I211, -1 + I205, I213, I214) [I205 <= I209]
  f6(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 
  f3(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234) -> f5(I225, I226, I227, I228, I229, I230, I231, -1 + I232, I233, I234) [0 <= I232]
  f3(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) -> f4(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) [1 + I242 <= 0]
  f1(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 

The dependency graph for this problem is:
  4 -> 
Where:
  4) f5#(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3#(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 

We have the following SCCs.
  

DP problem for innermost termination.
P =
  f9#(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8#(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 
  f8#(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204) -> f9#(I195, I196, I197, I198, 1 + I199, I200, I201, I202, I203, I204) [1 + I199 <= I195]
R = 
  f19(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 
  f18(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, rnd9, rnd10) [rnd9 = rnd9 /\ rnd10 = rnd10 /\ y1 = 0]
  f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1(I10, I11, I12, I13, I14, 1 + I15, I16, I17, I18, I19) [1 + I15 <= I10]
  f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f6(I20, I21, I22, I23, I24, I25, -1 + I20, I27, I28, I29) [I20 <= I25 /\ I30 = 0]
  f5(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 
  f7(I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f6(I41, I42, I43, I44, I45, I46, -1 + I47, I48, I49, I50) [0 <= I47]
  f7(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60) -> f10(I51, 0, I53, I54, I55, I56, I57, I58, I59, I60) [1 + I57 <= 0 /\ I61 = 0]
  f9(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 
  f11(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81) -> f10(I72, 1 + I73, I74, I75, I76, I77, I78, I79, I80, I81) [1 + I73 <= I72]
  f11(I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f14(I82, I83, I84, I85, I86, I87, I88, 0, I90, I91) [I82 <= I83]
  f13(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 
  f15(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14(I102, I103, I104, I105, I106, I107, I108, 1 + I109, I110, I111) [1 + I109 <= I102]
  f15(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f17(I112, I113, 0, I115, I116, I117, I118, I119, I120, I121) [I112 <= I119 /\ I122 = 0]
  f17(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 
  f16(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f17(I133, I134, 1 + I135, I136, I137, I138, I139, I140, I141, I142) [1 + I135 <= I133]
  f16(I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f13(I143, I144, I145, -1 + I143, I147, I148, I149, I150, I151, I152) [I143 <= I145 /\ I153 = 0]
  f14(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 
  f12(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f13(I164, I165, I166, -1 + I167, I168, I169, I170, I171, I172, I173) [0 <= I167]
  f12(I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f9(I174, I175, I176, I177, 0, I179, I180, I181, I182, I183) [1 + I177 <= 0 /\ I184 = 0]
  f10(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 
  f8(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204) -> f9(I195, I196, I197, I198, 1 + I199, I200, I201, I202, I203, I204) [1 + I199 <= I195]
  f8(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214) -> f5(I205, I206, I207, I208, I209, I210, I211, -1 + I205, I213, I214) [I205 <= I209]
  f6(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 
  f3(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234) -> f5(I225, I226, I227, I228, I229, I230, I231, -1 + I232, I233, I234) [0 <= I232]
  f3(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) -> f4(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) [1 + I242 <= 0]
  f1(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 

We use the reverse value criterion with the projection function NU:
  NU[f8#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10)] = z1 + -1 * (1 + z5)
  NU[f9#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10)] = z1 + -1 * (1 + z5)

This gives the following inequalities:
    ==>  I62 + -1 * (1 + I66) >= I62 + -1 * (1 + I66)
  1 + I199 <= I195  ==>  I195 + -1 * (1 + I199) > I195 + -1 * (1 + (1 + I199))  with  I195 + -1 * (1 + I199) >= 0

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f9#(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8#(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 
R = 
  f19(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 
  f18(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, rnd9, rnd10) [rnd9 = rnd9 /\ rnd10 = rnd10 /\ y1 = 0]
  f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1(I10, I11, I12, I13, I14, 1 + I15, I16, I17, I18, I19) [1 + I15 <= I10]
  f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f6(I20, I21, I22, I23, I24, I25, -1 + I20, I27, I28, I29) [I20 <= I25 /\ I30 = 0]
  f5(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 
  f7(I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f6(I41, I42, I43, I44, I45, I46, -1 + I47, I48, I49, I50) [0 <= I47]
  f7(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60) -> f10(I51, 0, I53, I54, I55, I56, I57, I58, I59, I60) [1 + I57 <= 0 /\ I61 = 0]
  f9(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 
  f11(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81) -> f10(I72, 1 + I73, I74, I75, I76, I77, I78, I79, I80, I81) [1 + I73 <= I72]
  f11(I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f14(I82, I83, I84, I85, I86, I87, I88, 0, I90, I91) [I82 <= I83]
  f13(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 
  f15(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14(I102, I103, I104, I105, I106, I107, I108, 1 + I109, I110, I111) [1 + I109 <= I102]
  f15(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f17(I112, I113, 0, I115, I116, I117, I118, I119, I120, I121) [I112 <= I119 /\ I122 = 0]
  f17(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 
  f16(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f17(I133, I134, 1 + I135, I136, I137, I138, I139, I140, I141, I142) [1 + I135 <= I133]
  f16(I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f13(I143, I144, I145, -1 + I143, I147, I148, I149, I150, I151, I152) [I143 <= I145 /\ I153 = 0]
  f14(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 
  f12(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f13(I164, I165, I166, -1 + I167, I168, I169, I170, I171, I172, I173) [0 <= I167]
  f12(I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f9(I174, I175, I176, I177, 0, I179, I180, I181, I182, I183) [1 + I177 <= 0 /\ I184 = 0]
  f10(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 
  f8(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204) -> f9(I195, I196, I197, I198, 1 + I199, I200, I201, I202, I203, I204) [1 + I199 <= I195]
  f8(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214) -> f5(I205, I206, I207, I208, I209, I210, I211, -1 + I205, I213, I214) [I205 <= I209]
  f6(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 
  f3(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234) -> f5(I225, I226, I227, I228, I229, I230, I231, -1 + I232, I233, I234) [0 <= I232]
  f3(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) -> f4(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) [1 + I242 <= 0]
  f1(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 

The dependency graph for this problem is:
  7 -> 
Where:
  7) f9#(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8#(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 

We have the following SCCs.
  

DP problem for innermost termination.
P =
  f13#(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12#(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 
  f12#(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f13#(I164, I165, I166, -1 + I167, I168, I169, I170, I171, I172, I173) [0 <= I167]
R = 
  f19(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 
  f18(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, rnd9, rnd10) [rnd9 = rnd9 /\ rnd10 = rnd10 /\ y1 = 0]
  f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1(I10, I11, I12, I13, I14, 1 + I15, I16, I17, I18, I19) [1 + I15 <= I10]
  f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f6(I20, I21, I22, I23, I24, I25, -1 + I20, I27, I28, I29) [I20 <= I25 /\ I30 = 0]
  f5(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 
  f7(I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f6(I41, I42, I43, I44, I45, I46, -1 + I47, I48, I49, I50) [0 <= I47]
  f7(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60) -> f10(I51, 0, I53, I54, I55, I56, I57, I58, I59, I60) [1 + I57 <= 0 /\ I61 = 0]
  f9(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 
  f11(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81) -> f10(I72, 1 + I73, I74, I75, I76, I77, I78, I79, I80, I81) [1 + I73 <= I72]
  f11(I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f14(I82, I83, I84, I85, I86, I87, I88, 0, I90, I91) [I82 <= I83]
  f13(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 
  f15(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14(I102, I103, I104, I105, I106, I107, I108, 1 + I109, I110, I111) [1 + I109 <= I102]
  f15(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f17(I112, I113, 0, I115, I116, I117, I118, I119, I120, I121) [I112 <= I119 /\ I122 = 0]
  f17(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 
  f16(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f17(I133, I134, 1 + I135, I136, I137, I138, I139, I140, I141, I142) [1 + I135 <= I133]
  f16(I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f13(I143, I144, I145, -1 + I143, I147, I148, I149, I150, I151, I152) [I143 <= I145 /\ I153 = 0]
  f14(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 
  f12(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f13(I164, I165, I166, -1 + I167, I168, I169, I170, I171, I172, I173) [0 <= I167]
  f12(I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f9(I174, I175, I176, I177, 0, I179, I180, I181, I182, I183) [1 + I177 <= 0 /\ I184 = 0]
  f10(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 
  f8(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204) -> f9(I195, I196, I197, I198, 1 + I199, I200, I201, I202, I203, I204) [1 + I199 <= I195]
  f8(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214) -> f5(I205, I206, I207, I208, I209, I210, I211, -1 + I205, I213, I214) [I205 <= I209]
  f6(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 
  f3(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234) -> f5(I225, I226, I227, I228, I229, I230, I231, -1 + I232, I233, I234) [0 <= I232]
  f3(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) -> f4(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) [1 + I242 <= 0]
  f1(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 

We use the basic value criterion with the projection function NU:
  NU[f12#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10)] = z4
  NU[f13#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10)] = z4

This gives the following inequalities:
    ==>  I95 (>! \union =) I95
  0 <= I167  ==>  I167 >! -1 + I167

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f13#(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12#(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 
R = 
  f19(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 
  f18(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, rnd9, rnd10) [rnd9 = rnd9 /\ rnd10 = rnd10 /\ y1 = 0]
  f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1(I10, I11, I12, I13, I14, 1 + I15, I16, I17, I18, I19) [1 + I15 <= I10]
  f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f6(I20, I21, I22, I23, I24, I25, -1 + I20, I27, I28, I29) [I20 <= I25 /\ I30 = 0]
  f5(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 
  f7(I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f6(I41, I42, I43, I44, I45, I46, -1 + I47, I48, I49, I50) [0 <= I47]
  f7(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60) -> f10(I51, 0, I53, I54, I55, I56, I57, I58, I59, I60) [1 + I57 <= 0 /\ I61 = 0]
  f9(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 
  f11(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81) -> f10(I72, 1 + I73, I74, I75, I76, I77, I78, I79, I80, I81) [1 + I73 <= I72]
  f11(I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f14(I82, I83, I84, I85, I86, I87, I88, 0, I90, I91) [I82 <= I83]
  f13(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 
  f15(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14(I102, I103, I104, I105, I106, I107, I108, 1 + I109, I110, I111) [1 + I109 <= I102]
  f15(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f17(I112, I113, 0, I115, I116, I117, I118, I119, I120, I121) [I112 <= I119 /\ I122 = 0]
  f17(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 
  f16(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f17(I133, I134, 1 + I135, I136, I137, I138, I139, I140, I141, I142) [1 + I135 <= I133]
  f16(I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f13(I143, I144, I145, -1 + I143, I147, I148, I149, I150, I151, I152) [I143 <= I145 /\ I153 = 0]
  f14(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 
  f12(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f13(I164, I165, I166, -1 + I167, I168, I169, I170, I171, I172, I173) [0 <= I167]
  f12(I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f9(I174, I175, I176, I177, 0, I179, I180, I181, I182, I183) [1 + I177 <= 0 /\ I184 = 0]
  f10(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 
  f8(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204) -> f9(I195, I196, I197, I198, 1 + I199, I200, I201, I202, I203, I204) [1 + I199 <= I195]
  f8(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214) -> f5(I205, I206, I207, I208, I209, I210, I211, -1 + I205, I213, I214) [I205 <= I209]
  f6(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 
  f3(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234) -> f5(I225, I226, I227, I228, I229, I230, I231, -1 + I232, I233, I234) [0 <= I232]
  f3(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) -> f4(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) [1 + I242 <= 0]
  f1(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 

The dependency graph for this problem is:
  10 -> 
Where:
  10) f13#(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12#(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 

We have the following SCCs.
  

DP problem for innermost termination.
P =
  f17#(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16#(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 
  f16#(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f17#(I133, I134, 1 + I135, I136, I137, I138, I139, I140, I141, I142) [1 + I135 <= I133]
R = 
  f19(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 
  f18(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, rnd9, rnd10) [rnd9 = rnd9 /\ rnd10 = rnd10 /\ y1 = 0]
  f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1(I10, I11, I12, I13, I14, 1 + I15, I16, I17, I18, I19) [1 + I15 <= I10]
  f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f6(I20, I21, I22, I23, I24, I25, -1 + I20, I27, I28, I29) [I20 <= I25 /\ I30 = 0]
  f5(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 
  f7(I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f6(I41, I42, I43, I44, I45, I46, -1 + I47, I48, I49, I50) [0 <= I47]
  f7(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60) -> f10(I51, 0, I53, I54, I55, I56, I57, I58, I59, I60) [1 + I57 <= 0 /\ I61 = 0]
  f9(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 
  f11(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81) -> f10(I72, 1 + I73, I74, I75, I76, I77, I78, I79, I80, I81) [1 + I73 <= I72]
  f11(I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f14(I82, I83, I84, I85, I86, I87, I88, 0, I90, I91) [I82 <= I83]
  f13(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 
  f15(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14(I102, I103, I104, I105, I106, I107, I108, 1 + I109, I110, I111) [1 + I109 <= I102]
  f15(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f17(I112, I113, 0, I115, I116, I117, I118, I119, I120, I121) [I112 <= I119 /\ I122 = 0]
  f17(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 
  f16(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f17(I133, I134, 1 + I135, I136, I137, I138, I139, I140, I141, I142) [1 + I135 <= I133]
  f16(I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f13(I143, I144, I145, -1 + I143, I147, I148, I149, I150, I151, I152) [I143 <= I145 /\ I153 = 0]
  f14(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 
  f12(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f13(I164, I165, I166, -1 + I167, I168, I169, I170, I171, I172, I173) [0 <= I167]
  f12(I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f9(I174, I175, I176, I177, 0, I179, I180, I181, I182, I183) [1 + I177 <= 0 /\ I184 = 0]
  f10(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 
  f8(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204) -> f9(I195, I196, I197, I198, 1 + I199, I200, I201, I202, I203, I204) [1 + I199 <= I195]
  f8(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214) -> f5(I205, I206, I207, I208, I209, I210, I211, -1 + I205, I213, I214) [I205 <= I209]
  f6(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 
  f3(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234) -> f5(I225, I226, I227, I228, I229, I230, I231, -1 + I232, I233, I234) [0 <= I232]
  f3(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) -> f4(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) [1 + I242 <= 0]
  f1(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 

We use the reverse value criterion with the projection function NU:
  NU[f16#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10)] = z1 + -1 * (1 + z3)
  NU[f17#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10)] = z1 + -1 * (1 + z3)

This gives the following inequalities:
    ==>  I123 + -1 * (1 + I125) >= I123 + -1 * (1 + I125)
  1 + I135 <= I133  ==>  I133 + -1 * (1 + I135) > I133 + -1 * (1 + (1 + I135))  with  I133 + -1 * (1 + I135) >= 0

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f17#(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16#(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 
R = 
  f19(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 
  f18(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, rnd9, rnd10) [rnd9 = rnd9 /\ rnd10 = rnd10 /\ y1 = 0]
  f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1(I10, I11, I12, I13, I14, 1 + I15, I16, I17, I18, I19) [1 + I15 <= I10]
  f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f6(I20, I21, I22, I23, I24, I25, -1 + I20, I27, I28, I29) [I20 <= I25 /\ I30 = 0]
  f5(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 
  f7(I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f6(I41, I42, I43, I44, I45, I46, -1 + I47, I48, I49, I50) [0 <= I47]
  f7(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60) -> f10(I51, 0, I53, I54, I55, I56, I57, I58, I59, I60) [1 + I57 <= 0 /\ I61 = 0]
  f9(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 
  f11(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81) -> f10(I72, 1 + I73, I74, I75, I76, I77, I78, I79, I80, I81) [1 + I73 <= I72]
  f11(I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f14(I82, I83, I84, I85, I86, I87, I88, 0, I90, I91) [I82 <= I83]
  f13(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 
  f15(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14(I102, I103, I104, I105, I106, I107, I108, 1 + I109, I110, I111) [1 + I109 <= I102]
  f15(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f17(I112, I113, 0, I115, I116, I117, I118, I119, I120, I121) [I112 <= I119 /\ I122 = 0]
  f17(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 
  f16(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f17(I133, I134, 1 + I135, I136, I137, I138, I139, I140, I141, I142) [1 + I135 <= I133]
  f16(I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f13(I143, I144, I145, -1 + I143, I147, I148, I149, I150, I151, I152) [I143 <= I145 /\ I153 = 0]
  f14(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 
  f12(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f13(I164, I165, I166, -1 + I167, I168, I169, I170, I171, I172, I173) [0 <= I167]
  f12(I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f9(I174, I175, I176, I177, 0, I179, I180, I181, I182, I183) [1 + I177 <= 0 /\ I184 = 0]
  f10(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 
  f8(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204) -> f9(I195, I196, I197, I198, 1 + I199, I200, I201, I202, I203, I204) [1 + I199 <= I195]
  f8(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214) -> f5(I205, I206, I207, I208, I209, I210, I211, -1 + I205, I213, I214) [I205 <= I209]
  f6(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 
  f3(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234) -> f5(I225, I226, I227, I228, I229, I230, I231, -1 + I232, I233, I234) [0 <= I232]
  f3(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) -> f4(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) [1 + I242 <= 0]
  f1(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 

The dependency graph for this problem is:
  13 -> 
Where:
  13) f17#(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16#(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 

We have the following SCCs.
  

DP problem for innermost termination.
P =
  f15#(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14#(I102, I103, I104, I105, I106, I107, I108, 1 + I109, I110, I111) [1 + I109 <= I102]
  f14#(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15#(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 
R = 
  f19(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 
  f18(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, rnd9, rnd10) [rnd9 = rnd9 /\ rnd10 = rnd10 /\ y1 = 0]
  f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1(I10, I11, I12, I13, I14, 1 + I15, I16, I17, I18, I19) [1 + I15 <= I10]
  f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f6(I20, I21, I22, I23, I24, I25, -1 + I20, I27, I28, I29) [I20 <= I25 /\ I30 = 0]
  f5(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 
  f7(I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f6(I41, I42, I43, I44, I45, I46, -1 + I47, I48, I49, I50) [0 <= I47]
  f7(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60) -> f10(I51, 0, I53, I54, I55, I56, I57, I58, I59, I60) [1 + I57 <= 0 /\ I61 = 0]
  f9(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 
  f11(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81) -> f10(I72, 1 + I73, I74, I75, I76, I77, I78, I79, I80, I81) [1 + I73 <= I72]
  f11(I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f14(I82, I83, I84, I85, I86, I87, I88, 0, I90, I91) [I82 <= I83]
  f13(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 
  f15(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14(I102, I103, I104, I105, I106, I107, I108, 1 + I109, I110, I111) [1 + I109 <= I102]
  f15(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f17(I112, I113, 0, I115, I116, I117, I118, I119, I120, I121) [I112 <= I119 /\ I122 = 0]
  f17(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 
  f16(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f17(I133, I134, 1 + I135, I136, I137, I138, I139, I140, I141, I142) [1 + I135 <= I133]
  f16(I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f13(I143, I144, I145, -1 + I143, I147, I148, I149, I150, I151, I152) [I143 <= I145 /\ I153 = 0]
  f14(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 
  f12(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f13(I164, I165, I166, -1 + I167, I168, I169, I170, I171, I172, I173) [0 <= I167]
  f12(I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f9(I174, I175, I176, I177, 0, I179, I180, I181, I182, I183) [1 + I177 <= 0 /\ I184 = 0]
  f10(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 
  f8(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204) -> f9(I195, I196, I197, I198, 1 + I199, I200, I201, I202, I203, I204) [1 + I199 <= I195]
  f8(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214) -> f5(I205, I206, I207, I208, I209, I210, I211, -1 + I205, I213, I214) [I205 <= I209]
  f6(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 
  f3(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234) -> f5(I225, I226, I227, I228, I229, I230, I231, -1 + I232, I233, I234) [0 <= I232]
  f3(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) -> f4(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) [1 + I242 <= 0]
  f1(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 

We use the reverse value criterion with the projection function NU:
  NU[f14#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10)] = z1 + -1 * (1 + z8)
  NU[f15#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10)] = z1 + -1 * (1 + z8)

This gives the following inequalities:
  1 + I109 <= I102  ==>  I102 + -1 * (1 + I109) > I102 + -1 * (1 + (1 + I109))  with  I102 + -1 * (1 + I109) >= 0
    ==>  I154 + -1 * (1 + I161) >= I154 + -1 * (1 + I161)

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f14#(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15#(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 
R = 
  f19(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 
  f18(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, rnd9, rnd10) [rnd9 = rnd9 /\ rnd10 = rnd10 /\ y1 = 0]
  f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1(I10, I11, I12, I13, I14, 1 + I15, I16, I17, I18, I19) [1 + I15 <= I10]
  f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f6(I20, I21, I22, I23, I24, I25, -1 + I20, I27, I28, I29) [I20 <= I25 /\ I30 = 0]
  f5(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 
  f7(I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f6(I41, I42, I43, I44, I45, I46, -1 + I47, I48, I49, I50) [0 <= I47]
  f7(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60) -> f10(I51, 0, I53, I54, I55, I56, I57, I58, I59, I60) [1 + I57 <= 0 /\ I61 = 0]
  f9(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 
  f11(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81) -> f10(I72, 1 + I73, I74, I75, I76, I77, I78, I79, I80, I81) [1 + I73 <= I72]
  f11(I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f14(I82, I83, I84, I85, I86, I87, I88, 0, I90, I91) [I82 <= I83]
  f13(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 
  f15(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14(I102, I103, I104, I105, I106, I107, I108, 1 + I109, I110, I111) [1 + I109 <= I102]
  f15(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f17(I112, I113, 0, I115, I116, I117, I118, I119, I120, I121) [I112 <= I119 /\ I122 = 0]
  f17(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 
  f16(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f17(I133, I134, 1 + I135, I136, I137, I138, I139, I140, I141, I142) [1 + I135 <= I133]
  f16(I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f13(I143, I144, I145, -1 + I143, I147, I148, I149, I150, I151, I152) [I143 <= I145 /\ I153 = 0]
  f14(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 
  f12(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f13(I164, I165, I166, -1 + I167, I168, I169, I170, I171, I172, I173) [0 <= I167]
  f12(I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f9(I174, I175, I176, I177, 0, I179, I180, I181, I182, I183) [1 + I177 <= 0 /\ I184 = 0]
  f10(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 
  f8(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204) -> f9(I195, I196, I197, I198, 1 + I199, I200, I201, I202, I203, I204) [1 + I199 <= I195]
  f8(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214) -> f5(I205, I206, I207, I208, I209, I210, I211, -1 + I205, I213, I214) [I205 <= I209]
  f6(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 
  f3(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234) -> f5(I225, I226, I227, I228, I229, I230, I231, -1 + I232, I233, I234) [0 <= I232]
  f3(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) -> f4(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) [1 + I242 <= 0]
  f1(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 

The dependency graph for this problem is:
  16 -> 
Where:
  16) f14#(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15#(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 

We have the following SCCs.
  

DP problem for innermost termination.
P =
  f11#(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81) -> f10#(I72, 1 + I73, I74, I75, I76, I77, I78, I79, I80, I81) [1 + I73 <= I72]
  f10#(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11#(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 
R = 
  f19(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 
  f18(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, rnd9, rnd10) [rnd9 = rnd9 /\ rnd10 = rnd10 /\ y1 = 0]
  f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1(I10, I11, I12, I13, I14, 1 + I15, I16, I17, I18, I19) [1 + I15 <= I10]
  f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f6(I20, I21, I22, I23, I24, I25, -1 + I20, I27, I28, I29) [I20 <= I25 /\ I30 = 0]
  f5(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 
  f7(I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f6(I41, I42, I43, I44, I45, I46, -1 + I47, I48, I49, I50) [0 <= I47]
  f7(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60) -> f10(I51, 0, I53, I54, I55, I56, I57, I58, I59, I60) [1 + I57 <= 0 /\ I61 = 0]
  f9(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 
  f11(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81) -> f10(I72, 1 + I73, I74, I75, I76, I77, I78, I79, I80, I81) [1 + I73 <= I72]
  f11(I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f14(I82, I83, I84, I85, I86, I87, I88, 0, I90, I91) [I82 <= I83]
  f13(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 
  f15(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14(I102, I103, I104, I105, I106, I107, I108, 1 + I109, I110, I111) [1 + I109 <= I102]
  f15(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f17(I112, I113, 0, I115, I116, I117, I118, I119, I120, I121) [I112 <= I119 /\ I122 = 0]
  f17(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 
  f16(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f17(I133, I134, 1 + I135, I136, I137, I138, I139, I140, I141, I142) [1 + I135 <= I133]
  f16(I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f13(I143, I144, I145, -1 + I143, I147, I148, I149, I150, I151, I152) [I143 <= I145 /\ I153 = 0]
  f14(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 
  f12(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f13(I164, I165, I166, -1 + I167, I168, I169, I170, I171, I172, I173) [0 <= I167]
  f12(I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f9(I174, I175, I176, I177, 0, I179, I180, I181, I182, I183) [1 + I177 <= 0 /\ I184 = 0]
  f10(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 
  f8(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204) -> f9(I195, I196, I197, I198, 1 + I199, I200, I201, I202, I203, I204) [1 + I199 <= I195]
  f8(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214) -> f5(I205, I206, I207, I208, I209, I210, I211, -1 + I205, I213, I214) [I205 <= I209]
  f6(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 
  f3(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234) -> f5(I225, I226, I227, I228, I229, I230, I231, -1 + I232, I233, I234) [0 <= I232]
  f3(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) -> f4(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) [1 + I242 <= 0]
  f1(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 

We use the reverse value criterion with the projection function NU:
  NU[f10#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10)] = z1 + -1 * (1 + z2)
  NU[f11#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10)] = z1 + -1 * (1 + z2)

This gives the following inequalities:
  1 + I73 <= I72  ==>  I72 + -1 * (1 + I73) > I72 + -1 * (1 + (1 + I73))  with  I72 + -1 * (1 + I73) >= 0
    ==>  I185 + -1 * (1 + I186) >= I185 + -1 * (1 + I186)

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f10#(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11#(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 
R = 
  f19(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 
  f18(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, rnd9, rnd10) [rnd9 = rnd9 /\ rnd10 = rnd10 /\ y1 = 0]
  f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1(I10, I11, I12, I13, I14, 1 + I15, I16, I17, I18, I19) [1 + I15 <= I10]
  f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f6(I20, I21, I22, I23, I24, I25, -1 + I20, I27, I28, I29) [I20 <= I25 /\ I30 = 0]
  f5(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 
  f7(I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f6(I41, I42, I43, I44, I45, I46, -1 + I47, I48, I49, I50) [0 <= I47]
  f7(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60) -> f10(I51, 0, I53, I54, I55, I56, I57, I58, I59, I60) [1 + I57 <= 0 /\ I61 = 0]
  f9(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 
  f11(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81) -> f10(I72, 1 + I73, I74, I75, I76, I77, I78, I79, I80, I81) [1 + I73 <= I72]
  f11(I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f14(I82, I83, I84, I85, I86, I87, I88, 0, I90, I91) [I82 <= I83]
  f13(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 
  f15(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14(I102, I103, I104, I105, I106, I107, I108, 1 + I109, I110, I111) [1 + I109 <= I102]
  f15(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f17(I112, I113, 0, I115, I116, I117, I118, I119, I120, I121) [I112 <= I119 /\ I122 = 0]
  f17(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 
  f16(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f17(I133, I134, 1 + I135, I136, I137, I138, I139, I140, I141, I142) [1 + I135 <= I133]
  f16(I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f13(I143, I144, I145, -1 + I143, I147, I148, I149, I150, I151, I152) [I143 <= I145 /\ I153 = 0]
  f14(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 
  f12(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f13(I164, I165, I166, -1 + I167, I168, I169, I170, I171, I172, I173) [0 <= I167]
  f12(I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f9(I174, I175, I176, I177, 0, I179, I180, I181, I182, I183) [1 + I177 <= 0 /\ I184 = 0]
  f10(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 
  f8(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204) -> f9(I195, I196, I197, I198, 1 + I199, I200, I201, I202, I203, I204) [1 + I199 <= I195]
  f8(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214) -> f5(I205, I206, I207, I208, I209, I210, I211, -1 + I205, I213, I214) [I205 <= I209]
  f6(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 
  f3(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234) -> f5(I225, I226, I227, I228, I229, I230, I231, -1 + I232, I233, I234) [0 <= I232]
  f3(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) -> f4(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) [1 + I242 <= 0]
  f1(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 

The dependency graph for this problem is:
  19 -> 
Where:
  19) f10#(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11#(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 

We have the following SCCs.
  

DP problem for innermost termination.
P =
  f7#(I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f6#(I41, I42, I43, I44, I45, I46, -1 + I47, I48, I49, I50) [0 <= I47]
  f6#(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7#(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 
R = 
  f19(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 
  f18(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, rnd9, rnd10) [rnd9 = rnd9 /\ rnd10 = rnd10 /\ y1 = 0]
  f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1(I10, I11, I12, I13, I14, 1 + I15, I16, I17, I18, I19) [1 + I15 <= I10]
  f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f6(I20, I21, I22, I23, I24, I25, -1 + I20, I27, I28, I29) [I20 <= I25 /\ I30 = 0]
  f5(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 
  f7(I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f6(I41, I42, I43, I44, I45, I46, -1 + I47, I48, I49, I50) [0 <= I47]
  f7(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60) -> f10(I51, 0, I53, I54, I55, I56, I57, I58, I59, I60) [1 + I57 <= 0 /\ I61 = 0]
  f9(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 
  f11(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81) -> f10(I72, 1 + I73, I74, I75, I76, I77, I78, I79, I80, I81) [1 + I73 <= I72]
  f11(I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f14(I82, I83, I84, I85, I86, I87, I88, 0, I90, I91) [I82 <= I83]
  f13(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 
  f15(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14(I102, I103, I104, I105, I106, I107, I108, 1 + I109, I110, I111) [1 + I109 <= I102]
  f15(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f17(I112, I113, 0, I115, I116, I117, I118, I119, I120, I121) [I112 <= I119 /\ I122 = 0]
  f17(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 
  f16(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f17(I133, I134, 1 + I135, I136, I137, I138, I139, I140, I141, I142) [1 + I135 <= I133]
  f16(I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f13(I143, I144, I145, -1 + I143, I147, I148, I149, I150, I151, I152) [I143 <= I145 /\ I153 = 0]
  f14(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 
  f12(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f13(I164, I165, I166, -1 + I167, I168, I169, I170, I171, I172, I173) [0 <= I167]
  f12(I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f9(I174, I175, I176, I177, 0, I179, I180, I181, I182, I183) [1 + I177 <= 0 /\ I184 = 0]
  f10(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 
  f8(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204) -> f9(I195, I196, I197, I198, 1 + I199, I200, I201, I202, I203, I204) [1 + I199 <= I195]
  f8(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214) -> f5(I205, I206, I207, I208, I209, I210, I211, -1 + I205, I213, I214) [I205 <= I209]
  f6(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 
  f3(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234) -> f5(I225, I226, I227, I228, I229, I230, I231, -1 + I232, I233, I234) [0 <= I232]
  f3(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) -> f4(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) [1 + I242 <= 0]
  f1(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 

We use the basic value criterion with the projection function NU:
  NU[f6#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10)] = z7
  NU[f7#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10)] = z7

This gives the following inequalities:
  0 <= I47  ==>  I47 >! -1 + I47
    ==>  I221 (>! \union =) I221

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f6#(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7#(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 
R = 
  f19(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 
  f18(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, rnd9, rnd10) [rnd9 = rnd9 /\ rnd10 = rnd10 /\ y1 = 0]
  f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1(I10, I11, I12, I13, I14, 1 + I15, I16, I17, I18, I19) [1 + I15 <= I10]
  f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f6(I20, I21, I22, I23, I24, I25, -1 + I20, I27, I28, I29) [I20 <= I25 /\ I30 = 0]
  f5(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 
  f7(I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f6(I41, I42, I43, I44, I45, I46, -1 + I47, I48, I49, I50) [0 <= I47]
  f7(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60) -> f10(I51, 0, I53, I54, I55, I56, I57, I58, I59, I60) [1 + I57 <= 0 /\ I61 = 0]
  f9(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 
  f11(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81) -> f10(I72, 1 + I73, I74, I75, I76, I77, I78, I79, I80, I81) [1 + I73 <= I72]
  f11(I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f14(I82, I83, I84, I85, I86, I87, I88, 0, I90, I91) [I82 <= I83]
  f13(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 
  f15(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14(I102, I103, I104, I105, I106, I107, I108, 1 + I109, I110, I111) [1 + I109 <= I102]
  f15(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f17(I112, I113, 0, I115, I116, I117, I118, I119, I120, I121) [I112 <= I119 /\ I122 = 0]
  f17(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 
  f16(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f17(I133, I134, 1 + I135, I136, I137, I138, I139, I140, I141, I142) [1 + I135 <= I133]
  f16(I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f13(I143, I144, I145, -1 + I143, I147, I148, I149, I150, I151, I152) [I143 <= I145 /\ I153 = 0]
  f14(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 
  f12(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f13(I164, I165, I166, -1 + I167, I168, I169, I170, I171, I172, I173) [0 <= I167]
  f12(I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f9(I174, I175, I176, I177, 0, I179, I180, I181, I182, I183) [1 + I177 <= 0 /\ I184 = 0]
  f10(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 
  f8(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204) -> f9(I195, I196, I197, I198, 1 + I199, I200, I201, I202, I203, I204) [1 + I199 <= I195]
  f8(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214) -> f5(I205, I206, I207, I208, I209, I210, I211, -1 + I205, I213, I214) [I205 <= I209]
  f6(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 
  f3(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234) -> f5(I225, I226, I227, I228, I229, I230, I231, -1 + I232, I233, I234) [0 <= I232]
  f3(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) -> f4(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) [1 + I242 <= 0]
  f1(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 

The dependency graph for this problem is:
  22 -> 
Where:
  22) f6#(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7#(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 

We have the following SCCs.
  

DP problem for innermost termination.
P =
  f2#(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1#(I10, I11, I12, I13, I14, 1 + I15, I16, I17, I18, I19) [1 + I15 <= I10]
  f1#(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2#(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 
R = 
  f19(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 
  f18(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, rnd9, rnd10) [rnd9 = rnd9 /\ rnd10 = rnd10 /\ y1 = 0]
  f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1(I10, I11, I12, I13, I14, 1 + I15, I16, I17, I18, I19) [1 + I15 <= I10]
  f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f6(I20, I21, I22, I23, I24, I25, -1 + I20, I27, I28, I29) [I20 <= I25 /\ I30 = 0]
  f5(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 
  f7(I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f6(I41, I42, I43, I44, I45, I46, -1 + I47, I48, I49, I50) [0 <= I47]
  f7(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60) -> f10(I51, 0, I53, I54, I55, I56, I57, I58, I59, I60) [1 + I57 <= 0 /\ I61 = 0]
  f9(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 
  f11(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81) -> f10(I72, 1 + I73, I74, I75, I76, I77, I78, I79, I80, I81) [1 + I73 <= I72]
  f11(I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f14(I82, I83, I84, I85, I86, I87, I88, 0, I90, I91) [I82 <= I83]
  f13(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 
  f15(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14(I102, I103, I104, I105, I106, I107, I108, 1 + I109, I110, I111) [1 + I109 <= I102]
  f15(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f17(I112, I113, 0, I115, I116, I117, I118, I119, I120, I121) [I112 <= I119 /\ I122 = 0]
  f17(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 
  f16(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f17(I133, I134, 1 + I135, I136, I137, I138, I139, I140, I141, I142) [1 + I135 <= I133]
  f16(I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f13(I143, I144, I145, -1 + I143, I147, I148, I149, I150, I151, I152) [I143 <= I145 /\ I153 = 0]
  f14(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 
  f12(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f13(I164, I165, I166, -1 + I167, I168, I169, I170, I171, I172, I173) [0 <= I167]
  f12(I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f9(I174, I175, I176, I177, 0, I179, I180, I181, I182, I183) [1 + I177 <= 0 /\ I184 = 0]
  f10(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 
  f8(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204) -> f9(I195, I196, I197, I198, 1 + I199, I200, I201, I202, I203, I204) [1 + I199 <= I195]
  f8(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214) -> f5(I205, I206, I207, I208, I209, I210, I211, -1 + I205, I213, I214) [I205 <= I209]
  f6(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 
  f3(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234) -> f5(I225, I226, I227, I228, I229, I230, I231, -1 + I232, I233, I234) [0 <= I232]
  f3(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) -> f4(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) [1 + I242 <= 0]
  f1(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 

We use the reverse value criterion with the projection function NU:
  NU[f1#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10)] = z1 + -1 * (1 + z6)
  NU[f2#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10)] = z1 + -1 * (1 + z6)

This gives the following inequalities:
  1 + I15 <= I10  ==>  I10 + -1 * (1 + I15) > I10 + -1 * (1 + (1 + I15))  with  I10 + -1 * (1 + I15) >= 0
    ==>  I245 + -1 * (1 + I250) >= I245 + -1 * (1 + I250)

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f1#(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2#(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 
R = 
  f19(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 
  f18(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, rnd9, rnd10) [rnd9 = rnd9 /\ rnd10 = rnd10 /\ y1 = 0]
  f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1(I10, I11, I12, I13, I14, 1 + I15, I16, I17, I18, I19) [1 + I15 <= I10]
  f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f6(I20, I21, I22, I23, I24, I25, -1 + I20, I27, I28, I29) [I20 <= I25 /\ I30 = 0]
  f5(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 
  f7(I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f6(I41, I42, I43, I44, I45, I46, -1 + I47, I48, I49, I50) [0 <= I47]
  f7(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60) -> f10(I51, 0, I53, I54, I55, I56, I57, I58, I59, I60) [1 + I57 <= 0 /\ I61 = 0]
  f9(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 
  f11(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81) -> f10(I72, 1 + I73, I74, I75, I76, I77, I78, I79, I80, I81) [1 + I73 <= I72]
  f11(I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f14(I82, I83, I84, I85, I86, I87, I88, 0, I90, I91) [I82 <= I83]
  f13(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 
  f15(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14(I102, I103, I104, I105, I106, I107, I108, 1 + I109, I110, I111) [1 + I109 <= I102]
  f15(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f17(I112, I113, 0, I115, I116, I117, I118, I119, I120, I121) [I112 <= I119 /\ I122 = 0]
  f17(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 
  f16(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f17(I133, I134, 1 + I135, I136, I137, I138, I139, I140, I141, I142) [1 + I135 <= I133]
  f16(I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f13(I143, I144, I145, -1 + I143, I147, I148, I149, I150, I151, I152) [I143 <= I145 /\ I153 = 0]
  f14(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 
  f12(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f13(I164, I165, I166, -1 + I167, I168, I169, I170, I171, I172, I173) [0 <= I167]
  f12(I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f9(I174, I175, I176, I177, 0, I179, I180, I181, I182, I183) [1 + I177 <= 0 /\ I184 = 0]
  f10(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 
  f8(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204) -> f9(I195, I196, I197, I198, 1 + I199, I200, I201, I202, I203, I204) [1 + I199 <= I195]
  f8(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214) -> f5(I205, I206, I207, I208, I209, I210, I211, -1 + I205, I213, I214) [I205 <= I209]
  f6(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 
  f3(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234) -> f5(I225, I226, I227, I228, I229, I230, I231, -1 + I232, I233, I234) [0 <= I232]
  f3(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) -> f4(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) [1 + I242 <= 0]
  f1(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 

The dependency graph for this problem is:
  24 -> 
Where:
  24) f1#(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2#(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 

We have the following SCCs.