ITS pair #487097149

details
property	value
status	complete
benchmark	huh.t2.smt2
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n147.star.cs.uiowa.edu
space	From_T2
run statistics
property	value
solver	Ctrl
configuration	Transition
runtime (wallclock)	174.704 seconds
cpu usage	177.006
user time	95.6917
system time	81.3141
max virtual memory	806284.0
max residence set size	23628.0
stage attributes
key	value
starexec-result	YES
output
YES

DP problem for innermost termination.
P =
  f8#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26) -> f4#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26) 
  f5#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25) -> f2#(I0, I1, I2, I3, -1 + I4, rnd6, I18, I7, I8, I9, 1 + I9, I11, I12, I13, I14, I15, rnd17, 0, I18, I19, I20, I5, I22, I23, I24, I25) [0 <= I4 /\ 0 <= I9 /\ y1 = I24 /\ rnd6 = y1 /\ rnd17 = rnd17]
  f2#(I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) -> f5#(I79, I80, I81, I82, I83, I84, I85, I86, I87, I89, I89, I90, I91, I92, I105, I106, I95, I96, I100, I98, I99, I100, I101, I102, I103, I104) [0 <= I83 /\ 0 <= I89 /\ I107 = I107 /\ I108 = I108 /\ 0 <= I107 - I108 /\ I105 = I105 /\ I106 = I106 /\ I96 <= 0 /\ 0 <= I96]
  f4#(I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f1#(I109, I110, I111, I112, I113, I114, I115, rnd8, rnd9, I118, I119, rnd12, I111, I122, I123, I124, I125, I126, I128, I128, I129, I130, I131, I132, I133, I134) [I135 = 0 /\ I136 = 0 /\ I137 = 0 /\ rnd12 = I137 /\ 0 <= -1 - I137 + I111 /\ rnd8 = rnd8 /\ rnd9 = 1 + I137]
  f3#(I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f1#(I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 
  f1#(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187, I188, I189) -> f3#(I164, I165, I166, I167, I168, I169, I170, I190, 1 + I172, I173, I174, 1 + I175, I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187, I188, I189) [I190 = I190 /\ 0 <= -1 - I172 + I176 /\ 0 <= I175]
  f1#(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216) -> f2#(I198, I192, I193, -2 + I202, -1 + I192 + -2 + I202, I217, I218, I198, I199, I200, 1, I202, I203, I204, I219, I220, I221, 0, rnd19, I210, I211, rnd22, I213, I214, I215, I216) [0 <= I202 /\ -1 * I199 + I203 <= 0 /\ 0 <= I202 /\ 0 <= I202 /\ y15 = I198 /\ I222 = y15 /\ y16 = 0 /\ 0 <= I202 /\ y18 = I222 /\ y8 = I216 /\ I223 = y8 /\ y9 = y9 /\ y4 = y16 /\ y13 = 0 /\ 0 <= -1 + I202 /\ y4 <= 0 /\ 0 <= y4 /\ y13 <= 0 /\ 0 <= y13 /\ y17 = y18 /\ 0 <= -1 + I202 /\ y19 = I223 /\ y10 = I211 /\ I224 = y10 /\ y11 = y11 /\ y5 = y17 /\ y14 = 0 /\ 0 <= -2 + I202 /\ y6 = y6 /\ y7 = y7 /\ 0 <= y6 - y7 /\ I219 = I219 /\ I220 = I220 /\ y14 <= 0 /\ 0 <= y14 /\ rnd19 = y19 /\ 0 <= -2 + I202 /\ rnd22 = I224 /\ y12 = I213 /\ I217 = y12 /\ I221 = I221 /\ I218 = rnd19]
R = 
  f8(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26) -> f4(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26) 
  f5(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25) -> f2(I0, I1, I2, I3, -1 + I4, rnd6, I18, I7, I8, I9, 1 + I9, I11, I12, I13, I14, I15, rnd17, 0, I18, I19, I20, I5, I22, I23, I24, I25) [0 <= I4 /\ 0 <= I9 /\ y1 = I24 /\ rnd6 = y1 /\ rnd17 = rnd17]
  f5(I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51) -> f7(rnd1, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51) [rnd1 = rnd1 /\ 0 <= I31 /\ I31 <= 0 /\ 0 <= I35 /\ 0 <= I30]
  f2(I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77) -> f6(I52, I53, I54, I55, I56, I57, rnd7, I59, I60, I61, I62, I63, I64, rnd14, rnd15, rnd16, I68, I58, I70, I71, I72, I73, I74, I75, I76, I77) [0 <= I56 /\ 0 <= I62 /\ y2 = y2 /\ y3 = y3 /\ 1 + y2 - y3 <= 0 /\ rnd15 = rnd15 /\ rnd16 = rnd16 /\ I78 = I75 /\ rnd7 = I78 /\ rnd14 = rnd14 /\ 0 <= I56 /\ 0 <= -1 + I62]
  f2(I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) -> f5(I79, I80, I81, I82, I83, I84, I85, I86, I87, I89, I89, I90, I91, I92, I105, I106, I95, I96, I100, I98, I99, I100, I101, I102, I103, I104) [0 <= I83 /\ 0 <= I89 /\ I107 = I107 /\ I108 = I108 /\ 0 <= I107 - I108 /\ I105 = I105 /\ I106 = I106 /\ I96 <= 0 /\ 0 <= I96]
  f4(I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f1(I109, I110, I111, I112, I113, I114, I115, rnd8, rnd9, I118, I119, rnd12, I111, I122, I123, I124, I125, I126, I128, I128, I129, I130, I131, I132, I133, I134) [I135 = 0 /\ I136 = 0 /\ I137 = 0 /\ rnd12 = I137 /\ 0 <= -1 - I137 + I111 /\ rnd8 = rnd8 /\ rnd9 = 1 + I137]
  f3(I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f1(I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 
  f1(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187, I188, I189) -> f3(I164, I165, I166, I167, I168, I169, I170, I190, 1 + I172, I173, I174, 1 + I175, I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187, I188, I189) [I190 = I190 /\ 0 <= -1 - I172 + I176 /\ 0 <= I175]
  f1(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216) -> f2(I198, I192, I193, -2 + I202, -1 + I192 + -2 + I202, I217, I218, I198, I199, I200, 1, I202, I203, I204, I219, I220, I221, 0, rnd19, I210, I211, rnd22, I213, I214, I215, I216) [0 <= I202 /\ -1 * I199 + I203 <= 0 /\ 0 <= I202 /\ 0 <= I202 /\ y15 = I198 /\ I222 = y15 /\ y16 = 0 /\ 0 <= I202 /\ y18 = I222 /\ y8 = I216 /\ I223 = y8 /\ y9 = y9 /\ y4 = y16 /\ y13 = 0 /\ 0 <= -1 + I202 /\ y4 <= 0 /\ 0 <= y4 /\ y13 <= 0 /\ 0 <= y13 /\ y17 = y18 /\ 0 <= -1 + I202 /\ y19 = I223 /\ y10 = I211 /\ I224 = y10 /\ y11 = y11 /\ y5 = y17 /\ y14 = 0 /\ 0 <= -2 + I202 /\ y6 = y6 /\ y7 = y7 /\ 0 <= y6 - y7 /\ I219 = I219 /\ I220 = I220 /\ y14 <= 0 /\ 0 <= y14 /\ rnd19 = y19 /\ 0 <= -2 + I202 /\ rnd22 = I224 /\ y12 = I213 /\ I217 = y12 /\ I221 = I221 /\ I218 = rnd19]

The dependency graph for this problem is:
  0 -> 3
  1 -> 2
  2 -> 1
  3 -> 5
  4 -> 5, 6
  5 -> 4
  6 -> 2
Where:
  0) f8#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26) -> f4#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26) 
  1) f5#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25) -> f2#(I0, I1, I2, I3, -1 + I4, rnd6, I18, I7, I8, I9, 1 + I9, I11, I12, I13, I14, I15, rnd17, 0, I18, I19, I20, I5, I22, I23, I24, I25) [0 <= I4 /\ 0 <= I9 /\ y1 = I24 /\ rnd6 = y1 /\ rnd17 = rnd17]
  2) f2#(I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) -> f5#(I79, I80, I81, I82, I83, I84, I85, I86, I87, I89, I89, I90, I91, I92, I105, I106, I95, I96, I100, I98, I99, I100, I101, I102, I103, I104) [0 <= I83 /\ 0 <= I89 /\ I107 = I107 /\ I108 = I108 /\ 0 <= I107 - I108 /\ I105 = I105 /\ I106 = I106 /\ I96 <= 0 /\ 0 <= I96]
  3) f4#(I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f1#(I109, I110, I111, I112, I113, I114, I115, rnd8, rnd9, I118, I119, rnd12, I111, I122, I123, I124, I125, I126, I128, I128, I129, I130, I131, I132, I133, I134) [I135 = 0 /\ I136 = 0 /\ I137 = 0 /\ rnd12 = I137 /\ 0 <= -1 - I137 + I111 /\ rnd8 = rnd8 /\ rnd9 = 1 + I137]
  4) f3#(I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f1#(I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 
  5) f1#(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187, I188, I189) -> f3#(I164, I165, I166, I167, I168, I169, I170, I190, 1 + I172, I173, I174, 1 + I175, I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187, I188, I189) [I190 = I190 /\ 0 <= -1 - I172 + I176 /\ 0 <= I175]
  6) f1#(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216) -> f2#(I198, I192, I193, -2 + I202, -1 + I192 + -2 + I202, I217, I218, I198, I199, I200, 1, I202, I203, I204, I219, I220, I221, 0, rnd19, I210, I211, rnd22, I213, I214, I215, I216) [0 <= I202 /\ -1 * I199 + I203 <= 0 /\ 0 <= I202 /\ 0 <= I202 /\ y15 = I198 /\ I222 = y15 /\ y16 = 0 /\ 0 <= I202 /\ y18 = I222 /\ y8 = I216 /\ I223 = y8 /\ y9 = y9 /\ y4 = y16 /\ y13 = 0 /\ 0 <= -1 + I202 /\ y4 <= 0 /\ 0 <= y4 /\ y13 <= 0 /\ 0 <= y13 /\ y17 = y18 /\ 0 <= -1 + I202 /\ y19 = I223 /\ y10 = I211 /\ I224 = y10 /\ y11 = y11 /\ y5 = y17 /\ y14 = 0 /\ 0 <= -2 + I202 /\ y6 = y6 /\ y7 = y7 /\ 0 <= y6 - y7 /\ I219 = I219 /\ I220 = I220 /\ y14 <= 0 /\ 0 <= y14 /\ rnd19 = y19 /\ 0 <= -2 + I202 /\ rnd22 = I224 /\ y12 = I213 /\ I217 = y12 /\ I221 = I221 /\ I218 = rnd19]

We have the following SCCs.
  { 4, 5 }
  { 1, 2 }

DP problem for innermost termination.
P =
  f5#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25) -> f2#(I0, I1, I2, I3, -1 + I4, rnd6, I18, I7, I8, I9, 1 + I9, I11, I12, I13, I14, I15, rnd17, 0, I18, I19, I20, I5, I22, I23, I24, I25) [0 <= I4 /\ 0 <= I9 /\ y1 = I24 /\ rnd6 = y1 /\ rnd17 = rnd17]
  f2#(I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) -> f5#(I79, I80, I81, I82, I83, I84, I85, I86, I87, I89, I89, I90, I91, I92, I105, I106, I95, I96, I100, I98, I99, I100, I101, I102, I103, I104) [0 <= I83 /\ 0 <= I89 /\ I107 = I107 /\ I108 = I108 /\ 0 <= I107 - I108 /\ I105 = I105 /\ I106 = I106 /\ I96 <= 0 /\ 0 <= I96]
R = 
  f8(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26) -> f4(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26) 
  f5(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25) -> f2(I0, I1, I2, I3, -1 + I4, rnd6, I18, I7, I8, I9, 1 + I9, I11, I12, I13, I14, I15, rnd17, 0, I18, I19, I20, I5, I22, I23, I24, I25) [0 <= I4 /\ 0 <= I9 /\ y1 = I24 /\ rnd6 = y1 /\ rnd17 = rnd17]
  f5(I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51) -> f7(rnd1, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51) [rnd1 = rnd1 /\ 0 <= I31 /\ I31 <= 0 /\ 0 <= I35 /\ 0 <= I30]
  f2(I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77) -> f6(I52, I53, I54, I55, I56, I57, rnd7, I59, I60, I61, I62, I63, I64, rnd14, rnd15, rnd16, I68, I58, I70, I71, I72, I73, I74, I75, I76, I77) [0 <= I56 /\ 0 <= I62 /\ y2 = y2 /\ y3 = y3 /\ 1 + y2 - y3 <= 0 /\ rnd15 = rnd15 /\ rnd16 = rnd16 /\ I78 = I75 /\ rnd7 = I78 /\ rnd14 = rnd14 /\ 0 <= I56 /\ 0 <= -1 + I62]
  f2(I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) -> f5(I79, I80, I81, I82, I83, I84, I85, I86, I87, I89, I89, I90, I91, I92, I105, I106, I95, I96, I100, I98, I99, I100, I101, I102, I103, I104) [0 <= I83 /\ 0 <= I89 /\ I107 = I107 /\ I108 = I108 /\ 0 <= I107 - I108 /\ I105 = I105 /\ I106 = I106 /\ I96 <= 0 /\ 0 <= I96]
  f4(I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f1(I109, I110, I111, I112, I113, I114, I115, rnd8, rnd9, I118, I119, rnd12, I111, I122, I123, I124, I125, I126, I128, I128, I129, I130, I131, I132, I133, I134) [I135 = 0 /\ I136 = 0 /\ I137 = 0 /\ rnd12 = I137 /\ 0 <= -1 - I137 + I111 /\ rnd8 = rnd8 /\ rnd9 = 1 + I137]
  f3(I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f1(I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 
  f1(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187, I188, I189) -> f3(I164, I165, I166, I167, I168, I169, I170, I190, 1 + I172, I173, I174, 1 + I175, I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187, I188, I189) [I190 = I190 /\ 0 <= -1 - I172 + I176 /\ 0 <= I175]
  f1(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216) -> f2(I198, I192, I193, -2 + I202, -1 + I192 + -2 + I202, I217, I218, I198, I199, I200, 1, I202, I203, I204, I219, I220, I221, 0, rnd19, I210, I211, rnd22, I213, I214, I215, I216) [0 <= I202 /\ -1 * I199 + I203 <= 0 /\ 0 <= I202 /\ 0 <= I202 /\ y15 = I198 /\ I222 = y15 /\ y16 = 0 /\ 0 <= I202 /\ y18 = I222 /\ y8 = I216 /\ I223 = y8 /\ y9 = y9 /\ y4 = y16 /\ y13 = 0 /\ 0 <= -1 + I202 /\ y4 <= 0 /\ 0 <= y4 /\ y13 <= 0 /\ 0 <= y13 /\ y17 = y18 /\ 0 <= -1 + I202 /\ y19 = I223 /\ y10 = I211 /\ I224 = y10 /\ y11 = y11 /\ y5 = y17 /\ y14 = 0 /\ 0 <= -2 + I202 /\ y6 = y6 /\ y7 = y7 /\ 0 <= y6 - y7 /\ I219 = I219 /\ I220 = I220 /\ y14 <= 0 /\ 0 <= y14 /\ rnd19 = y19 /\ 0 <= -2 + I202 /\ rnd22 = I224 /\ y12 = I213 /\ I217 = y12 /\ I221 = I221 /\ I218 = rnd19]

We use the basic value criterion with the projection function NU:
  NU[f2#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14,z15,z16,z17,z18,z19,z20,z21,z22,z23,z24,z25,z26)] = z5
  NU[f5#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14,z15,z16,z17,z18,z19,z20,z21,z22,z23,z24,z25,z26)] = z5

This gives the following inequalities:
  0 <= I4 /\ 0 <= I9 /\ y1 = I24 /\ rnd6 = y1 /\ rnd17 = rnd17  ==>  I4 >! -1 + I4
  0 <= I83 /\ 0 <= I89 /\ I107 = I107 /\ I108 = I108 /\ 0 <= I107 - I108 /\ I105 = I105 /\ I106 = I106 /\ I96 <= 0 /\ 0 <= I96  ==>  I83 (>! \union =) I83

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f2#(I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) -> f5#(I79, I80, I81, I82, I83, I84, I85, I86, I87, I89, I89, I90, I91, I92, I105, I106, I95, I96, I100, I98, I99, I100, I101, I102, I103, I104) [0 <= I83 /\ 0 <= I89 /\ I107 = I107 /\ I108 = I108 /\ 0 <= I107 - I108 /\ I105 = I105 /\ I106 = I106 /\ I96 <= 0 /\ 0 <= I96]
R = 
  f8(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26) -> f4(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26) 
  f5(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25) -> f2(I0, I1, I2, I3, -1 + I4, rnd6, I18, I7, I8, I9, 1 + I9, I11, I12, I13, I14, I15, rnd17, 0, I18, I19, I20, I5, I22, I23, I24, I25) [0 <= I4 /\ 0 <= I9 /\ y1 = I24 /\ rnd6 = y1 /\ rnd17 = rnd17]
  f5(I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51) -> f7(rnd1, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51) [rnd1 = rnd1 /\ 0 <= I31 /\ I31 <= 0 /\ 0 <= I35 /\ 0 <= I30]
  f2(I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77) -> f6(I52, I53, I54, I55, I56, I57, rnd7, I59, I60, I61, I62, I63, I64, rnd14, rnd15, rnd16, I68, I58, I70, I71, I72, I73, I74, I75, I76, I77) [0 <= I56 /\ 0 <= I62 /\ y2 = y2 /\ y3 = y3 /\ 1 + y2 - y3 <= 0 /\ rnd15 = rnd15 /\ rnd16 = rnd16 /\ I78 = I75 /\ rnd7 = I78 /\ rnd14 = rnd14 /\ 0 <= I56 /\ 0 <= -1 + I62]
  f2(I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) -> f5(I79, I80, I81, I82, I83, I84, I85, I86, I87, I89, I89, I90, I91, I92, I105, I106, I95, I96, I100, I98, I99, I100, I101, I102, I103, I104) [0 <= I83 /\ 0 <= I89 /\ I107 = I107 /\ I108 = I108 /\ 0 <= I107 - I108 /\ I105 = I105 /\ I106 = I106 /\ I96 <= 0 /\ 0 <= I96]
  f4(I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f1(I109, I110, I111, I112, I113, I114, I115, rnd8, rnd9, I118, I119, rnd12, I111, I122, I123, I124, I125, I126, I128, I128, I129, I130, I131, I132, I133, I134) [I135 = 0 /\ I136 = 0 /\ I137 = 0 /\ rnd12 = I137 /\ 0 <= -1 - I137 + I111 /\ rnd8 = rnd8 /\ rnd9 = 1 + I137]
  f3(I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f1(I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 
  f1(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187, I188, I189) -> f3(I164, I165, I166, I167, I168, I169, I170, I190, 1 + I172, I173, I174, 1 + I175, I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187, I188, I189) [I190 = I190 /\ 0 <= -1 - I172 + I176 /\ 0 <= I175]
  f1(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216) -> f2(I198, I192, I193, -2 + I202, -1 + I192 + -2 + I202, I217, I218, I198, I199, I200, 1, I202, I203, I204, I219, I220, I221, 0, rnd19, I210, I211, rnd22, I213, I214, I215, I216) [0 <= I202 /\ -1 * I199 + I203 <= 0 /\ 0 <= I202 /\ 0 <= I202 /\ y15 = I198 /\ I222 = y15 /\ y16 = 0 /\ 0 <= I202 /\ y18 = I222 /\ y8 = I216 /\ I223 = y8 /\ y9 = y9 /\ y4 = y16 /\ y13 = 0 /\ 0 <= -1 + I202 /\ y4 <= 0 /\ 0 <= y4 /\ y13 <= 0 /\ 0 <= y13 /\ y17 = y18 /\ 0 <= -1 + I202 /\ y19 = I223 /\ y10 = I211 /\ I224 = y10 /\ y11 = y11 /\ y5 = y17 /\ y14 = 0 /\ 0 <= -2 + I202 /\ y6 = y6 /\ y7 = y7 /\ 0 <= y6 - y7 /\ I219 = I219 /\ I220 = I220 /\ y14 <= 0 /\ 0 <= y14 /\ rnd19 = y19 /\ 0 <= -2 + I202 /\ rnd22 = I224 /\ y12 = I213 /\ I217 = y12 /\ I221 = I221 /\ I218 = rnd19]

The dependency graph for this problem is:
  2 -> 
Where:
  2) f2#(I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) -> f5#(I79, I80, I81, I82, I83, I84, I85, I86, I87, I89, I89, I90, I91, I92, I105, I106, I95, I96, I100, I98, I99, I100, I101, I102, I103, I104) [0 <= I83 /\ 0 <= I89 /\ I107 = I107 /\ I108 = I108 /\ 0 <= I107 - I108 /\ I105 = I105 /\ I106 = I106 /\ I96 <= 0 /\ 0 <= I96]

We have the following SCCs.
  

DP problem for innermost termination.
P =
  f3#(I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f1#(I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 
  f1#(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187, I188, I189) -> f3#(I164, I165, I166, I167, I168, I169, I170, I190, 1 + I172, I173, I174, 1 + I175, I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187, I188, I189) [I190 = I190 /\ 0 <= -1 - I172 + I176 /\ 0 <= I175]
R = 
  f8(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26) -> f4(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26) 
  f5(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25) -> f2(I0, I1, I2, I3, -1 + I4, rnd6, I18, I7, I8, I9, 1 + I9, I11, I12, I13, I14, I15, rnd17, 0, I18, I19, I20, I5, I22, I23, I24, I25) [0 <= I4 /\ 0 <= I9 /\ y1 = I24 /\ rnd6 = y1 /\ rnd17 = rnd17]
  f5(I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51) -> f7(rnd1, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51) [rnd1 = rnd1 /\ 0 <= I31 /\ I31 <= 0 /\ 0 <= I35 /\ 0 <= I30]
  f2(I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77) -> f6(I52, I53, I54, I55, I56, I57, rnd7, I59, I60, I61, I62, I63, I64, rnd14, rnd15, rnd16, I68, I58, I70, I71, I72, I73, I74, I75, I76, I77) [0 <= I56 /\ 0 <= I62 /\ y2 = y2 /\ y3 = y3 /\ 1 + y2 - y3 <= 0 /\ rnd15 = rnd15 /\ rnd16 = rnd16 /\ I78 = I75 /\ rnd7 = I78 /\ rnd14 = rnd14 /\ 0 <= I56 /\ 0 <= -1 + I62]
  f2(I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) -> f5(I79, I80, I81, I82, I83, I84, I85, I86, I87, I89, I89, I90, I91, I92, I105, I106, I95, I96, I100, I98, I99, I100, I101, I102, I103, I104) [0 <= I83 /\ 0 <= I89 /\ I107 = I107 /\ I108 = I108 /\ 0 <= I107 - I108 /\ I105 = I105 /\ I106 = I106 /\ I96 <= 0 /\ 0 <= I96]
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