188.95/186.39	YES
188.95/186.39	
188.95/186.39	DP problem for innermost termination.
188.95/186.39	P =
188.95/186.39	  f9#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) -> f8#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) 
188.95/186.39	  f8#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f3#(I0, I1, I2, 0, 0, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) 
188.95/186.39	  f7#(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f2#(I22, I23, -1 + I24, I25, I26, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14, rnd15, rnd16, rnd17, rnd18, rnd19, rnd20, rnd21, rnd22) [0 <= I24 /\ rnd6 = rnd6 /\ y4 = y4 /\ rnd11 = rnd11 /\ y3 = y3 /\ rnd12 = rnd12 /\ y2 = y2 /\ rnd13 = rnd13 /\ y1 = y1 /\ rnd7 = rnd6 + rnd13 /\ rnd10 = rnd6 - rnd13 /\ rnd8 = rnd11 + rnd12 /\ rnd9 = rnd11 - rnd12 /\ y5 = y5 /\ y6 = y1 + y4 /\ y7 = y2 + y3 /\ y8 = y1 + y3 /\ y10 = y2 + y4 /\ rnd22 = rnd22 /\ rnd14 = rnd14 /\ rnd15 = rnd15 /\ rnd16 = rnd16 /\ rnd17 = rnd17 /\ rnd18 = rnd18 /\ rnd19 = rnd19 /\ y9 = y9 /\ y11 = y11 /\ rnd20 = y9 + rnd22 /\ rnd21 = y11 + rnd22]
188.95/186.39	  f7#(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f6#(I44, I45, I45, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) [1 + I46 <= 0]
188.95/186.39	  f6#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f4#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) 
188.95/186.39	  f2#(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f7#(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) 
188.95/186.39	  f3#(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f1#(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) 
188.95/186.39	  f4#(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) -> f6#(I132, I133, -1 + I134, I135, I136, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170) [0 <= I134 /\ I154 = I154 /\ I171 = I171 /\ I159 = I159 /\ I172 = I172 /\ I160 = I160 /\ I173 = I173 /\ I161 = I161 /\ I174 = I174 /\ I155 = I154 + I161 /\ I158 = I154 - I161 /\ I156 = I159 + I160 /\ I157 = I159 - I160 /\ B0 = B0 /\ I175 = I174 + I171 /\ I176 = I173 + I172 /\ I177 = I174 + I172 /\ I178 = I173 + I171 /\ I170 = I170 /\ I162 = I162 /\ I163 = I163 /\ I164 = I164 /\ I165 = I165 /\ I166 = I166 /\ I167 = I167 /\ I179 = I179 /\ I180 = I180 /\ I168 = I179 + I170 /\ I169 = I180 + I170]
188.95/186.39	  f1#(I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f3#(I203, I204, I205, 1 + I206, rnd5, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) [rnd5 = rnd5 /\ 1 + I206 <= I203]
188.95/186.39	  f1#(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246) -> f2#(I225, I226, I226, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246) [I225 <= I228]
188.95/186.39	R = 
188.95/186.39	  f9(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) -> f8(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) 
188.95/186.39	  f8(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f3(I0, I1, I2, 0, 0, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) 
188.95/186.39	  f7(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f2(I22, I23, -1 + I24, I25, I26, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14, rnd15, rnd16, rnd17, rnd18, rnd19, rnd20, rnd21, rnd22) [0 <= I24 /\ rnd6 = rnd6 /\ y4 = y4 /\ rnd11 = rnd11 /\ y3 = y3 /\ rnd12 = rnd12 /\ y2 = y2 /\ rnd13 = rnd13 /\ y1 = y1 /\ rnd7 = rnd6 + rnd13 /\ rnd10 = rnd6 - rnd13 /\ rnd8 = rnd11 + rnd12 /\ rnd9 = rnd11 - rnd12 /\ y5 = y5 /\ y6 = y1 + y4 /\ y7 = y2 + y3 /\ y8 = y1 + y3 /\ y10 = y2 + y4 /\ rnd22 = rnd22 /\ rnd14 = rnd14 /\ rnd15 = rnd15 /\ rnd16 = rnd16 /\ rnd17 = rnd17 /\ rnd18 = rnd18 /\ rnd19 = rnd19 /\ y9 = y9 /\ y11 = y11 /\ rnd20 = y9 + rnd22 /\ rnd21 = y11 + rnd22]
188.95/186.39	  f7(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f6(I44, I45, I45, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) [1 + I46 <= 0]
188.95/186.39	  f6(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f4(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) 
188.95/186.39	  f2(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f7(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) 
188.95/186.39	  f3(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f1(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) 
188.95/186.39	  f4(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) -> f6(I132, I133, -1 + I134, I135, I136, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170) [0 <= I134 /\ I154 = I154 /\ I171 = I171 /\ I159 = I159 /\ I172 = I172 /\ I160 = I160 /\ I173 = I173 /\ I161 = I161 /\ I174 = I174 /\ I155 = I154 + I161 /\ I158 = I154 - I161 /\ I156 = I159 + I160 /\ I157 = I159 - I160 /\ B0 = B0 /\ I175 = I174 + I171 /\ I176 = I173 + I172 /\ I177 = I174 + I172 /\ I178 = I173 + I171 /\ I170 = I170 /\ I162 = I162 /\ I163 = I163 /\ I164 = I164 /\ I165 = I165 /\ I166 = I166 /\ I167 = I167 /\ I179 = I179 /\ I180 = I180 /\ I168 = I179 + I170 /\ I169 = I180 + I170]
188.95/186.39	  f4(I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f5(I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202) [1 + I183 <= 0]
188.95/186.39	  f1(I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f3(I203, I204, I205, 1 + I206, rnd5, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) [rnd5 = rnd5 /\ 1 + I206 <= I203]
188.95/186.39	  f1(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246) -> f2(I225, I226, I226, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246) [I225 <= I228]
188.95/186.39	
188.95/186.39	The dependency graph for this problem is:
188.95/186.39	  0 -> 1
188.95/186.39	  1 -> 6
188.95/186.39	  2 -> 5
188.95/186.39	  3 -> 4
188.95/186.39	  4 -> 7
188.95/186.39	  5 -> 2, 3
188.95/186.39	  6 -> 8, 9
188.95/186.39	  7 -> 4
188.95/186.39	  8 -> 6
188.95/186.39	  9 -> 5
188.95/186.39	Where:
188.95/186.39	  0) f9#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) -> f8#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) 
188.95/186.39	  1) f8#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f3#(I0, I1, I2, 0, 0, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) 
188.95/186.39	  2) f7#(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f2#(I22, I23, -1 + I24, I25, I26, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14, rnd15, rnd16, rnd17, rnd18, rnd19, rnd20, rnd21, rnd22) [0 <= I24 /\ rnd6 = rnd6 /\ y4 = y4 /\ rnd11 = rnd11 /\ y3 = y3 /\ rnd12 = rnd12 /\ y2 = y2 /\ rnd13 = rnd13 /\ y1 = y1 /\ rnd7 = rnd6 + rnd13 /\ rnd10 = rnd6 - rnd13 /\ rnd8 = rnd11 + rnd12 /\ rnd9 = rnd11 - rnd12 /\ y5 = y5 /\ y6 = y1 + y4 /\ y7 = y2 + y3 /\ y8 = y1 + y3 /\ y10 = y2 + y4 /\ rnd22 = rnd22 /\ rnd14 = rnd14 /\ rnd15 = rnd15 /\ rnd16 = rnd16 /\ rnd17 = rnd17 /\ rnd18 = rnd18 /\ rnd19 = rnd19 /\ y9 = y9 /\ y11 = y11 /\ rnd20 = y9 + rnd22 /\ rnd21 = y11 + rnd22]
188.95/186.39	  3) f7#(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f6#(I44, I45, I45, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) [1 + I46 <= 0]
188.95/186.39	  4) f6#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f4#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) 
188.95/186.39	  5) f2#(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f7#(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) 
188.95/186.39	  6) f3#(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f1#(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) 
188.95/186.39	  7) f4#(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) -> f6#(I132, I133, -1 + I134, I135, I136, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170) [0 <= I134 /\ I154 = I154 /\ I171 = I171 /\ I159 = I159 /\ I172 = I172 /\ I160 = I160 /\ I173 = I173 /\ I161 = I161 /\ I174 = I174 /\ I155 = I154 + I161 /\ I158 = I154 - I161 /\ I156 = I159 + I160 /\ I157 = I159 - I160 /\ B0 = B0 /\ I175 = I174 + I171 /\ I176 = I173 + I172 /\ I177 = I174 + I172 /\ I178 = I173 + I171 /\ I170 = I170 /\ I162 = I162 /\ I163 = I163 /\ I164 = I164 /\ I165 = I165 /\ I166 = I166 /\ I167 = I167 /\ I179 = I179 /\ I180 = I180 /\ I168 = I179 + I170 /\ I169 = I180 + I170]
188.95/186.39	  8) f1#(I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f3#(I203, I204, I205, 1 + I206, rnd5, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) [rnd5 = rnd5 /\ 1 + I206 <= I203]
188.95/186.39	  9) f1#(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246) -> f2#(I225, I226, I226, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246) [I225 <= I228]
188.95/186.39	
188.95/186.39	We have the following SCCs.
188.95/186.39	  { 6, 8 }
188.95/186.39	  { 2, 5 }
188.95/186.39	  { 4, 7 }
188.95/186.39	
188.95/186.39	DP problem for innermost termination.
188.95/186.39	P =
188.95/186.39	  f6#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f4#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) 
188.95/186.39	  f4#(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) -> f6#(I132, I133, -1 + I134, I135, I136, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170) [0 <= I134 /\ I154 = I154 /\ I171 = I171 /\ I159 = I159 /\ I172 = I172 /\ I160 = I160 /\ I173 = I173 /\ I161 = I161 /\ I174 = I174 /\ I155 = I154 + I161 /\ I158 = I154 - I161 /\ I156 = I159 + I160 /\ I157 = I159 - I160 /\ B0 = B0 /\ I175 = I174 + I171 /\ I176 = I173 + I172 /\ I177 = I174 + I172 /\ I178 = I173 + I171 /\ I170 = I170 /\ I162 = I162 /\ I163 = I163 /\ I164 = I164 /\ I165 = I165 /\ I166 = I166 /\ I167 = I167 /\ I179 = I179 /\ I180 = I180 /\ I168 = I179 + I170 /\ I169 = I180 + I170]
188.95/186.39	R = 
188.95/186.39	  f9(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) -> f8(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) 
188.95/186.39	  f8(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f3(I0, I1, I2, 0, 0, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) 
188.95/186.39	  f7(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f2(I22, I23, -1 + I24, I25, I26, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14, rnd15, rnd16, rnd17, rnd18, rnd19, rnd20, rnd21, rnd22) [0 <= I24 /\ rnd6 = rnd6 /\ y4 = y4 /\ rnd11 = rnd11 /\ y3 = y3 /\ rnd12 = rnd12 /\ y2 = y2 /\ rnd13 = rnd13 /\ y1 = y1 /\ rnd7 = rnd6 + rnd13 /\ rnd10 = rnd6 - rnd13 /\ rnd8 = rnd11 + rnd12 /\ rnd9 = rnd11 - rnd12 /\ y5 = y5 /\ y6 = y1 + y4 /\ y7 = y2 + y3 /\ y8 = y1 + y3 /\ y10 = y2 + y4 /\ rnd22 = rnd22 /\ rnd14 = rnd14 /\ rnd15 = rnd15 /\ rnd16 = rnd16 /\ rnd17 = rnd17 /\ rnd18 = rnd18 /\ rnd19 = rnd19 /\ y9 = y9 /\ y11 = y11 /\ rnd20 = y9 + rnd22 /\ rnd21 = y11 + rnd22]
188.95/186.39	  f7(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f6(I44, I45, I45, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) [1 + I46 <= 0]
188.95/186.39	  f6(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f4(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) 
188.95/186.39	  f2(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f7(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) 
188.95/186.39	  f3(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f1(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) 
188.95/186.39	  f4(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) -> f6(I132, I133, -1 + I134, I135, I136, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170) [0 <= I134 /\ I154 = I154 /\ I171 = I171 /\ I159 = I159 /\ I172 = I172 /\ I160 = I160 /\ I173 = I173 /\ I161 = I161 /\ I174 = I174 /\ I155 = I154 + I161 /\ I158 = I154 - I161 /\ I156 = I159 + I160 /\ I157 = I159 - I160 /\ B0 = B0 /\ I175 = I174 + I171 /\ I176 = I173 + I172 /\ I177 = I174 + I172 /\ I178 = I173 + I171 /\ I170 = I170 /\ I162 = I162 /\ I163 = I163 /\ I164 = I164 /\ I165 = I165 /\ I166 = I166 /\ I167 = I167 /\ I179 = I179 /\ I180 = I180 /\ I168 = I179 + I170 /\ I169 = I180 + I170]
188.95/186.39	  f4(I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f5(I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202) [1 + I183 <= 0]
188.95/186.39	  f1(I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f3(I203, I204, I205, 1 + I206, rnd5, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) [rnd5 = rnd5 /\ 1 + I206 <= I203]
188.95/186.39	  f1(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246) -> f2(I225, I226, I226, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246) [I225 <= I228]
188.95/186.39	
188.95/186.39	We use the basic value criterion with the projection function NU:
188.95/186.39	  NU[f4#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14,z15,z16,z17,z18,z19,z20,z21,z22)] = z3
188.95/186.39	  NU[f6#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14,z15,z16,z17,z18,z19,z20,z21,z22)] = z3
188.95/186.39	
188.95/186.39	This gives the following inequalities:
188.95/186.39	    ==>  I68 (>! \union =) I68
188.95/186.39	  0 <= I134 /\ I154 = I154 /\ I171 = I171 /\ I159 = I159 /\ I172 = I172 /\ I160 = I160 /\ I173 = I173 /\ I161 = I161 /\ I174 = I174 /\ I155 = I154 + I161 /\ I158 = I154 - I161 /\ I156 = I159 + I160 /\ I157 = I159 - I160 /\ B0 = B0 /\ I175 = I174 + I171 /\ I176 = I173 + I172 /\ I177 = I174 + I172 /\ I178 = I173 + I171 /\ I170 = I170 /\ I162 = I162 /\ I163 = I163 /\ I164 = I164 /\ I165 = I165 /\ I166 = I166 /\ I167 = I167 /\ I179 = I179 /\ I180 = I180 /\ I168 = I179 + I170 /\ I169 = I180 + I170  ==>  I134 >! -1 + I134
188.95/186.39	
188.95/186.39	We remove all the strictly oriented dependency pairs.
188.95/186.39	
188.95/186.39	DP problem for innermost termination.
188.95/186.39	P =
188.95/186.39	  f6#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f4#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) 
188.95/186.39	R = 
188.95/186.39	  f9(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) -> f8(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) 
188.95/186.39	  f8(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f3(I0, I1, I2, 0, 0, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) 
188.95/186.39	  f7(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f2(I22, I23, -1 + I24, I25, I26, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14, rnd15, rnd16, rnd17, rnd18, rnd19, rnd20, rnd21, rnd22) [0 <= I24 /\ rnd6 = rnd6 /\ y4 = y4 /\ rnd11 = rnd11 /\ y3 = y3 /\ rnd12 = rnd12 /\ y2 = y2 /\ rnd13 = rnd13 /\ y1 = y1 /\ rnd7 = rnd6 + rnd13 /\ rnd10 = rnd6 - rnd13 /\ rnd8 = rnd11 + rnd12 /\ rnd9 = rnd11 - rnd12 /\ y5 = y5 /\ y6 = y1 + y4 /\ y7 = y2 + y3 /\ y8 = y1 + y3 /\ y10 = y2 + y4 /\ rnd22 = rnd22 /\ rnd14 = rnd14 /\ rnd15 = rnd15 /\ rnd16 = rnd16 /\ rnd17 = rnd17 /\ rnd18 = rnd18 /\ rnd19 = rnd19 /\ y9 = y9 /\ y11 = y11 /\ rnd20 = y9 + rnd22 /\ rnd21 = y11 + rnd22]
188.95/186.39	  f7(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f6(I44, I45, I45, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) [1 + I46 <= 0]
188.95/186.39	  f6(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f4(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) 
188.95/186.39	  f2(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f7(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) 
188.95/186.39	  f3(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f1(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) 
188.95/186.39	  f4(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) -> f6(I132, I133, -1 + I134, I135, I136, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170) [0 <= I134 /\ I154 = I154 /\ I171 = I171 /\ I159 = I159 /\ I172 = I172 /\ I160 = I160 /\ I173 = I173 /\ I161 = I161 /\ I174 = I174 /\ I155 = I154 + I161 /\ I158 = I154 - I161 /\ I156 = I159 + I160 /\ I157 = I159 - I160 /\ B0 = B0 /\ I175 = I174 + I171 /\ I176 = I173 + I172 /\ I177 = I174 + I172 /\ I178 = I173 + I171 /\ I170 = I170 /\ I162 = I162 /\ I163 = I163 /\ I164 = I164 /\ I165 = I165 /\ I166 = I166 /\ I167 = I167 /\ I179 = I179 /\ I180 = I180 /\ I168 = I179 + I170 /\ I169 = I180 + I170]
188.95/186.39	  f4(I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f5(I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202) [1 + I183 <= 0]
188.95/186.39	  f1(I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f3(I203, I204, I205, 1 + I206, rnd5, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) [rnd5 = rnd5 /\ 1 + I206 <= I203]
188.95/186.39	  f1(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246) -> f2(I225, I226, I226, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246) [I225 <= I228]
188.95/186.39	
188.95/186.39	The dependency graph for this problem is:
188.95/186.39	  4 -> 
188.95/186.39	Where:
188.95/186.39	  4) f6#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f4#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) 
188.95/186.39	
188.95/186.39	We have the following SCCs.
188.95/186.39	  
188.95/186.39	
188.95/186.39	DP problem for innermost termination.
188.95/186.39	P =
188.95/186.39	  f7#(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f2#(I22, I23, -1 + I24, I25, I26, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14, rnd15, rnd16, rnd17, rnd18, rnd19, rnd20, rnd21, rnd22) [0 <= I24 /\ rnd6 = rnd6 /\ y4 = y4 /\ rnd11 = rnd11 /\ y3 = y3 /\ rnd12 = rnd12 /\ y2 = y2 /\ rnd13 = rnd13 /\ y1 = y1 /\ rnd7 = rnd6 + rnd13 /\ rnd10 = rnd6 - rnd13 /\ rnd8 = rnd11 + rnd12 /\ rnd9 = rnd11 - rnd12 /\ y5 = y5 /\ y6 = y1 + y4 /\ y7 = y2 + y3 /\ y8 = y1 + y3 /\ y10 = y2 + y4 /\ rnd22 = rnd22 /\ rnd14 = rnd14 /\ rnd15 = rnd15 /\ rnd16 = rnd16 /\ rnd17 = rnd17 /\ rnd18 = rnd18 /\ rnd19 = rnd19 /\ y9 = y9 /\ y11 = y11 /\ rnd20 = y9 + rnd22 /\ rnd21 = y11 + rnd22]
188.95/186.39	  f2#(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f7#(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) 
188.95/186.39	R = 
188.95/186.39	  f9(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) -> f8(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) 
188.95/186.39	  f8(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f3(I0, I1, I2, 0, 0, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) 
188.95/186.39	  f7(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f2(I22, I23, -1 + I24, I25, I26, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14, rnd15, rnd16, rnd17, rnd18, rnd19, rnd20, rnd21, rnd22) [0 <= I24 /\ rnd6 = rnd6 /\ y4 = y4 /\ rnd11 = rnd11 /\ y3 = y3 /\ rnd12 = rnd12 /\ y2 = y2 /\ rnd13 = rnd13 /\ y1 = y1 /\ rnd7 = rnd6 + rnd13 /\ rnd10 = rnd6 - rnd13 /\ rnd8 = rnd11 + rnd12 /\ rnd9 = rnd11 - rnd12 /\ y5 = y5 /\ y6 = y1 + y4 /\ y7 = y2 + y3 /\ y8 = y1 + y3 /\ y10 = y2 + y4 /\ rnd22 = rnd22 /\ rnd14 = rnd14 /\ rnd15 = rnd15 /\ rnd16 = rnd16 /\ rnd17 = rnd17 /\ rnd18 = rnd18 /\ rnd19 = rnd19 /\ y9 = y9 /\ y11 = y11 /\ rnd20 = y9 + rnd22 /\ rnd21 = y11 + rnd22]
188.95/186.39	  f7(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f6(I44, I45, I45, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) [1 + I46 <= 0]
188.95/186.39	  f6(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f4(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) 
188.95/186.39	  f2(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f7(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) 
188.95/186.39	  f3(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f1(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) 
188.95/186.39	  f4(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) -> f6(I132, I133, -1 + I134, I135, I136, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170) [0 <= I134 /\ I154 = I154 /\ I171 = I171 /\ I159 = I159 /\ I172 = I172 /\ I160 = I160 /\ I173 = I173 /\ I161 = I161 /\ I174 = I174 /\ I155 = I154 + I161 /\ I158 = I154 - I161 /\ I156 = I159 + I160 /\ I157 = I159 - I160 /\ B0 = B0 /\ I175 = I174 + I171 /\ I176 = I173 + I172 /\ I177 = I174 + I172 /\ I178 = I173 + I171 /\ I170 = I170 /\ I162 = I162 /\ I163 = I163 /\ I164 = I164 /\ I165 = I165 /\ I166 = I166 /\ I167 = I167 /\ I179 = I179 /\ I180 = I180 /\ I168 = I179 + I170 /\ I169 = I180 + I170]
188.95/186.39	  f4(I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f5(I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202) [1 + I183 <= 0]
188.95/186.39	  f1(I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f3(I203, I204, I205, 1 + I206, rnd5, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) [rnd5 = rnd5 /\ 1 + I206 <= I203]
188.95/186.39	  f1(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246) -> f2(I225, I226, I226, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246) [I225 <= I228]
188.95/186.39	
188.95/186.39	We use the basic value criterion with the projection function NU:
188.95/186.39	  NU[f2#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14,z15,z16,z17,z18,z19,z20,z21,z22)] = z3
188.95/186.39	  NU[f7#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14,z15,z16,z17,z18,z19,z20,z21,z22)] = z3
188.95/186.39	
188.95/186.39	This gives the following inequalities:
188.95/186.39	  0 <= I24 /\ rnd6 = rnd6 /\ y4 = y4 /\ rnd11 = rnd11 /\ y3 = y3 /\ rnd12 = rnd12 /\ y2 = y2 /\ rnd13 = rnd13 /\ y1 = y1 /\ rnd7 = rnd6 + rnd13 /\ rnd10 = rnd6 - rnd13 /\ rnd8 = rnd11 + rnd12 /\ rnd9 = rnd11 - rnd12 /\ y5 = y5 /\ y6 = y1 + y4 /\ y7 = y2 + y3 /\ y8 = y1 + y3 /\ y10 = y2 + y4 /\ rnd22 = rnd22 /\ rnd14 = rnd14 /\ rnd15 = rnd15 /\ rnd16 = rnd16 /\ rnd17 = rnd17 /\ rnd18 = rnd18 /\ rnd19 = rnd19 /\ y9 = y9 /\ y11 = y11 /\ rnd20 = y9 + rnd22 /\ rnd21 = y11 + rnd22  ==>  I24 >! -1 + I24
188.95/186.39	    ==>  I90 (>! \union =) I90
188.95/186.39	
188.95/186.39	We remove all the strictly oriented dependency pairs.
188.95/186.39	
188.95/186.39	DP problem for innermost termination.
188.95/186.39	P =
188.95/186.39	  f2#(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f7#(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) 
188.95/186.39	R = 
188.95/186.39	  f9(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) -> f8(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) 
188.95/186.39	  f8(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f3(I0, I1, I2, 0, 0, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) 
188.95/186.39	  f7(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f2(I22, I23, -1 + I24, I25, I26, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14, rnd15, rnd16, rnd17, rnd18, rnd19, rnd20, rnd21, rnd22) [0 <= I24 /\ rnd6 = rnd6 /\ y4 = y4 /\ rnd11 = rnd11 /\ y3 = y3 /\ rnd12 = rnd12 /\ y2 = y2 /\ rnd13 = rnd13 /\ y1 = y1 /\ rnd7 = rnd6 + rnd13 /\ rnd10 = rnd6 - rnd13 /\ rnd8 = rnd11 + rnd12 /\ rnd9 = rnd11 - rnd12 /\ y5 = y5 /\ y6 = y1 + y4 /\ y7 = y2 + y3 /\ y8 = y1 + y3 /\ y10 = y2 + y4 /\ rnd22 = rnd22 /\ rnd14 = rnd14 /\ rnd15 = rnd15 /\ rnd16 = rnd16 /\ rnd17 = rnd17 /\ rnd18 = rnd18 /\ rnd19 = rnd19 /\ y9 = y9 /\ y11 = y11 /\ rnd20 = y9 + rnd22 /\ rnd21 = y11 + rnd22]
188.95/186.39	  f7(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f6(I44, I45, I45, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) [1 + I46 <= 0]
188.95/186.39	  f6(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f4(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) 
188.95/186.39	  f2(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f7(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) 
188.95/186.39	  f3(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f1(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) 
188.95/186.39	  f4(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) -> f6(I132, I133, -1 + I134, I135, I136, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170) [0 <= I134 /\ I154 = I154 /\ I171 = I171 /\ I159 = I159 /\ I172 = I172 /\ I160 = I160 /\ I173 = I173 /\ I161 = I161 /\ I174 = I174 /\ I155 = I154 + I161 /\ I158 = I154 - I161 /\ I156 = I159 + I160 /\ I157 = I159 - I160 /\ B0 = B0 /\ I175 = I174 + I171 /\ I176 = I173 + I172 /\ I177 = I174 + I172 /\ I178 = I173 + I171 /\ I170 = I170 /\ I162 = I162 /\ I163 = I163 /\ I164 = I164 /\ I165 = I165 /\ I166 = I166 /\ I167 = I167 /\ I179 = I179 /\ I180 = I180 /\ I168 = I179 + I170 /\ I169 = I180 + I170]
188.95/186.39	  f4(I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f5(I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202) [1 + I183 <= 0]
188.95/186.39	  f1(I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f3(I203, I204, I205, 1 + I206, rnd5, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) [rnd5 = rnd5 /\ 1 + I206 <= I203]
188.95/186.39	  f1(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246) -> f2(I225, I226, I226, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246) [I225 <= I228]
188.95/186.39	
188.95/186.39	The dependency graph for this problem is:
188.95/186.39	  5 -> 
188.95/186.39	Where:
188.95/186.39	  5) f2#(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f7#(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) 
188.95/186.39	
188.95/186.39	We have the following SCCs.
188.95/186.39	  
188.95/186.39	
188.95/186.39	DP problem for innermost termination.
188.95/186.39	P =
188.95/186.39	  f3#(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f1#(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) 
188.95/186.39	  f1#(I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f3#(I203, I204, I205, 1 + I206, rnd5, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) [rnd5 = rnd5 /\ 1 + I206 <= I203]
188.95/186.39	R = 
188.95/186.39	  f9(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) -> f8(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) 
188.95/186.39	  f8(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f3(I0, I1, I2, 0, 0, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) 
188.95/186.39	  f7(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f2(I22, I23, -1 + I24, I25, I26, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14, rnd15, rnd16, rnd17, rnd18, rnd19, rnd20, rnd21, rnd22) [0 <= I24 /\ rnd6 = rnd6 /\ y4 = y4 /\ rnd11 = rnd11 /\ y3 = y3 /\ rnd12 = rnd12 /\ y2 = y2 /\ rnd13 = rnd13 /\ y1 = y1 /\ rnd7 = rnd6 + rnd13 /\ rnd10 = rnd6 - rnd13 /\ rnd8 = rnd11 + rnd12 /\ rnd9 = rnd11 - rnd12 /\ y5 = y5 /\ y6 = y1 + y4 /\ y7 = y2 + y3 /\ y8 = y1 + y3 /\ y10 = y2 + y4 /\ rnd22 = rnd22 /\ rnd14 = rnd14 /\ rnd15 = rnd15 /\ rnd16 = rnd16 /\ rnd17 = rnd17 /\ rnd18 = rnd18 /\ rnd19 = rnd19 /\ y9 = y9 /\ y11 = y11 /\ rnd20 = y9 + rnd22 /\ rnd21 = y11 + rnd22]
188.95/186.39	  f7(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f6(I44, I45, I45, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) [1 + I46 <= 0]
188.95/186.39	  f6(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f4(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) 
188.95/186.39	  f2(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f7(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) 
188.95/186.39	  f3(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f1(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) 
188.95/186.39	  f4(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) -> f6(I132, I133, -1 + I134, I135, I136, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170) [0 <= I134 /\ I154 = I154 /\ I171 = I171 /\ I159 = I159 /\ I172 = I172 /\ I160 = I160 /\ I173 = I173 /\ I161 = I161 /\ I174 = I174 /\ I155 = I154 + I161 /\ I158 = I154 - I161 /\ I156 = I159 + I160 /\ I157 = I159 - I160 /\ B0 = B0 /\ I175 = I174 + I171 /\ I176 = I173 + I172 /\ I177 = I174 + I172 /\ I178 = I173 + I171 /\ I170 = I170 /\ I162 = I162 /\ I163 = I163 /\ I164 = I164 /\ I165 = I165 /\ I166 = I166 /\ I167 = I167 /\ I179 = I179 /\ I180 = I180 /\ I168 = I179 + I170 /\ I169 = I180 + I170]
188.95/186.39	  f4(I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f5(I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202) [1 + I183 <= 0]
188.95/186.39	  f1(I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f3(I203, I204, I205, 1 + I206, rnd5, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) [rnd5 = rnd5 /\ 1 + I206 <= I203]
188.95/186.39	  f1(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246) -> f2(I225, I226, I226, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246) [I225 <= I228]
188.95/186.39	
188.95/186.39	We use the reverse value criterion with the projection function NU:
188.95/186.39	  NU[f1#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14,z15,z16,z17,z18,z19,z20,z21,z22)] = z1 + -1 * (1 + z4)
188.95/186.39	  NU[f3#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14,z15,z16,z17,z18,z19,z20,z21,z22)] = z1 + -1 * (1 + z4)
188.95/186.39	
188.95/186.39	This gives the following inequalities:
188.95/186.39	    ==>  I110 + -1 * (1 + I113) >= I110 + -1 * (1 + I113)
188.95/186.39	  rnd5 = rnd5 /\ 1 + I206 <= I203  ==>  I203 + -1 * (1 + I206) > I203 + -1 * (1 + (1 + I206))  with  I203 + -1 * (1 + I206) >= 0
188.95/186.39	
188.95/186.39	We remove all the strictly oriented dependency pairs.
188.95/186.39	
188.95/186.39	DP problem for innermost termination.
188.95/186.39	P =
188.95/186.39	  f3#(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f1#(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) 
188.95/186.39	R = 
188.95/186.39	  f9(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) -> f8(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) 
188.95/186.39	  f8(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f3(I0, I1, I2, 0, 0, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) 
188.95/186.39	  f7(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f2(I22, I23, -1 + I24, I25, I26, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14, rnd15, rnd16, rnd17, rnd18, rnd19, rnd20, rnd21, rnd22) [0 <= I24 /\ rnd6 = rnd6 /\ y4 = y4 /\ rnd11 = rnd11 /\ y3 = y3 /\ rnd12 = rnd12 /\ y2 = y2 /\ rnd13 = rnd13 /\ y1 = y1 /\ rnd7 = rnd6 + rnd13 /\ rnd10 = rnd6 - rnd13 /\ rnd8 = rnd11 + rnd12 /\ rnd9 = rnd11 - rnd12 /\ y5 = y5 /\ y6 = y1 + y4 /\ y7 = y2 + y3 /\ y8 = y1 + y3 /\ y10 = y2 + y4 /\ rnd22 = rnd22 /\ rnd14 = rnd14 /\ rnd15 = rnd15 /\ rnd16 = rnd16 /\ rnd17 = rnd17 /\ rnd18 = rnd18 /\ rnd19 = rnd19 /\ y9 = y9 /\ y11 = y11 /\ rnd20 = y9 + rnd22 /\ rnd21 = y11 + rnd22]
188.95/186.39	  f7(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f6(I44, I45, I45, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) [1 + I46 <= 0]
188.95/186.39	  f6(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f4(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) 
188.95/186.39	  f2(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f7(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) 
188.95/186.39	  f3(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f1(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) 
188.95/186.39	  f4(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) -> f6(I132, I133, -1 + I134, I135, I136, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170) [0 <= I134 /\ I154 = I154 /\ I171 = I171 /\ I159 = I159 /\ I172 = I172 /\ I160 = I160 /\ I173 = I173 /\ I161 = I161 /\ I174 = I174 /\ I155 = I154 + I161 /\ I158 = I154 - I161 /\ I156 = I159 + I160 /\ I157 = I159 - I160 /\ B0 = B0 /\ I175 = I174 + I171 /\ I176 = I173 + I172 /\ I177 = I174 + I172 /\ I178 = I173 + I171 /\ I170 = I170 /\ I162 = I162 /\ I163 = I163 /\ I164 = I164 /\ I165 = I165 /\ I166 = I166 /\ I167 = I167 /\ I179 = I179 /\ I180 = I180 /\ I168 = I179 + I170 /\ I169 = I180 + I170]
188.95/186.39	  f4(I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f5(I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202) [1 + I183 <= 0]
188.95/186.39	  f1(I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f3(I203, I204, I205, 1 + I206, rnd5, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) [rnd5 = rnd5 /\ 1 + I206 <= I203]
188.95/186.39	  f1(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246) -> f2(I225, I226, I226, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246) [I225 <= I228]
188.95/186.39	
188.95/186.39	The dependency graph for this problem is:
188.95/186.39	  6 -> 
188.95/186.39	Where:
188.95/186.39	  6) f3#(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f1#(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) 
188.95/186.39	
188.95/186.39	We have the following SCCs.
188.95/186.39	  
188.95/189.33	EOF