153.88/151.93	YES
153.88/151.93	
153.88/151.93	DP problem for innermost termination.
153.88/151.93	P =
153.88/151.93	  f9#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20) -> f8#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20) 
153.88/151.93	  f8#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f3#(I0, 0, 0, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) 
153.88/151.93	  f7#(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39) -> f2#(-1 + I20, I21, I22, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14, rnd15, rnd16, rnd17, rnd18, rnd19, rnd20) [0 <= I20 /\ rnd4 = rnd4 /\ y4 = y4 /\ rnd9 = rnd9 /\ y3 = y3 /\ rnd10 = rnd10 /\ y2 = y2 /\ rnd11 = rnd11 /\ y1 = y1 /\ rnd5 = rnd4 + rnd11 /\ rnd8 = rnd4 - rnd11 /\ rnd6 = rnd9 + rnd10 /\ rnd7 = rnd9 - rnd10 /\ y5 = y5 /\ y6 = y1 + y4 /\ y7 = y2 + y3 /\ y8 = y1 + y3 /\ y10 = y2 + y4 /\ rnd20 = rnd20 /\ rnd12 = rnd12 /\ rnd13 = rnd13 /\ rnd14 = rnd14 /\ rnd15 = rnd15 /\ rnd16 = rnd16 /\ rnd17 = rnd17 /\ y9 = y9 /\ y11 = y11 /\ rnd18 = y9 + rnd20 /\ rnd19 = y11 + rnd20]
153.88/151.93	  f7#(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f6#(7, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) [1 + I40 <= 0]
153.88/151.93	  f6#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) -> f4#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) 
153.88/151.93	  f2#(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f7#(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) 
153.88/151.93	  f3#(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f1#(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) 
153.88/151.93	  f4#(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139) -> f6#(-1 + I120, I121, I122, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156) [0 <= I120 /\ I140 = I140 /\ I157 = I157 /\ I145 = I145 /\ I158 = I158 /\ I146 = I146 /\ I159 = I159 /\ I147 = I147 /\ I160 = I160 /\ I141 = I140 + I147 /\ I144 = I140 - I147 /\ I142 = I145 + I146 /\ I143 = I145 - I146 /\ B0 = B0 /\ I161 = I160 + I157 /\ I162 = I159 + I158 /\ I163 = I160 + I158 /\ I164 = I159 + I157 /\ I156 = I156 /\ I148 = I148 /\ I149 = I149 /\ I150 = I150 /\ I151 = I151 /\ I152 = I152 /\ I153 = I153 /\ I165 = I165 /\ I166 = I166 /\ I154 = I165 + I156 /\ I155 = I166 + I156]
153.88/151.93	  f1#(I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206) -> f3#(I187, 1 + I188, rnd3, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206) [rnd3 = rnd3 /\ 1 + I188 <= 64]
153.88/151.93	  f1#(I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226) -> f2#(7, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226) [64 <= I208]
153.88/151.93	R = 
153.88/151.93	  f9(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20) -> f8(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20) 
153.88/151.93	  f8(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f3(I0, 0, 0, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) 
153.88/151.93	  f7(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39) -> f2(-1 + I20, I21, I22, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14, rnd15, rnd16, rnd17, rnd18, rnd19, rnd20) [0 <= I20 /\ rnd4 = rnd4 /\ y4 = y4 /\ rnd9 = rnd9 /\ y3 = y3 /\ rnd10 = rnd10 /\ y2 = y2 /\ rnd11 = rnd11 /\ y1 = y1 /\ rnd5 = rnd4 + rnd11 /\ rnd8 = rnd4 - rnd11 /\ rnd6 = rnd9 + rnd10 /\ rnd7 = rnd9 - rnd10 /\ y5 = y5 /\ y6 = y1 + y4 /\ y7 = y2 + y3 /\ y8 = y1 + y3 /\ y10 = y2 + y4 /\ rnd20 = rnd20 /\ rnd12 = rnd12 /\ rnd13 = rnd13 /\ rnd14 = rnd14 /\ rnd15 = rnd15 /\ rnd16 = rnd16 /\ rnd17 = rnd17 /\ y9 = y9 /\ y11 = y11 /\ rnd18 = y9 + rnd20 /\ rnd19 = y11 + rnd20]
153.88/151.93	  f7(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f6(7, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) [1 + I40 <= 0]
153.88/151.93	  f6(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) -> f4(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) 
153.88/151.93	  f2(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f7(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) 
153.88/151.93	  f3(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f1(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) 
153.88/151.93	  f4(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139) -> f6(-1 + I120, I121, I122, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156) [0 <= I120 /\ I140 = I140 /\ I157 = I157 /\ I145 = I145 /\ I158 = I158 /\ I146 = I146 /\ I159 = I159 /\ I147 = I147 /\ I160 = I160 /\ I141 = I140 + I147 /\ I144 = I140 - I147 /\ I142 = I145 + I146 /\ I143 = I145 - I146 /\ B0 = B0 /\ I161 = I160 + I157 /\ I162 = I159 + I158 /\ I163 = I160 + I158 /\ I164 = I159 + I157 /\ I156 = I156 /\ I148 = I148 /\ I149 = I149 /\ I150 = I150 /\ I151 = I151 /\ I152 = I152 /\ I153 = I153 /\ I165 = I165 /\ I166 = I166 /\ I154 = I165 + I156 /\ I155 = I166 + I156]
153.88/151.93	  f4(I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186) -> f5(I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186) [1 + I167 <= 0]
153.88/151.93	  f1(I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206) -> f3(I187, 1 + I188, rnd3, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206) [rnd3 = rnd3 /\ 1 + I188 <= 64]
153.88/151.93	  f1(I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226) -> f2(7, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226) [64 <= I208]
153.88/151.93	
153.88/151.93	The dependency graph for this problem is:
153.88/151.93	  0 -> 1
153.88/151.93	  1 -> 6
153.88/151.93	  2 -> 5
153.88/151.93	  3 -> 4
153.88/151.93	  4 -> 7
153.88/151.93	  5 -> 2, 3
153.88/151.93	  6 -> 8, 9
153.88/151.93	  7 -> 4
153.88/151.93	  8 -> 6
153.88/151.93	  9 -> 5
153.88/151.93	Where:
153.88/151.93	  0) f9#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20) -> f8#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20) 
153.88/151.93	  1) f8#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f3#(I0, 0, 0, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) 
153.88/151.93	  2) f7#(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39) -> f2#(-1 + I20, I21, I22, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14, rnd15, rnd16, rnd17, rnd18, rnd19, rnd20) [0 <= I20 /\ rnd4 = rnd4 /\ y4 = y4 /\ rnd9 = rnd9 /\ y3 = y3 /\ rnd10 = rnd10 /\ y2 = y2 /\ rnd11 = rnd11 /\ y1 = y1 /\ rnd5 = rnd4 + rnd11 /\ rnd8 = rnd4 - rnd11 /\ rnd6 = rnd9 + rnd10 /\ rnd7 = rnd9 - rnd10 /\ y5 = y5 /\ y6 = y1 + y4 /\ y7 = y2 + y3 /\ y8 = y1 + y3 /\ y10 = y2 + y4 /\ rnd20 = rnd20 /\ rnd12 = rnd12 /\ rnd13 = rnd13 /\ rnd14 = rnd14 /\ rnd15 = rnd15 /\ rnd16 = rnd16 /\ rnd17 = rnd17 /\ y9 = y9 /\ y11 = y11 /\ rnd18 = y9 + rnd20 /\ rnd19 = y11 + rnd20]
153.88/151.93	  3) f7#(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f6#(7, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) [1 + I40 <= 0]
153.88/151.93	  4) f6#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) -> f4#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) 
153.88/151.93	  5) f2#(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f7#(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) 
153.88/151.93	  6) f3#(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f1#(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) 
153.88/151.93	  7) f4#(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139) -> f6#(-1 + I120, I121, I122, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156) [0 <= I120 /\ I140 = I140 /\ I157 = I157 /\ I145 = I145 /\ I158 = I158 /\ I146 = I146 /\ I159 = I159 /\ I147 = I147 /\ I160 = I160 /\ I141 = I140 + I147 /\ I144 = I140 - I147 /\ I142 = I145 + I146 /\ I143 = I145 - I146 /\ B0 = B0 /\ I161 = I160 + I157 /\ I162 = I159 + I158 /\ I163 = I160 + I158 /\ I164 = I159 + I157 /\ I156 = I156 /\ I148 = I148 /\ I149 = I149 /\ I150 = I150 /\ I151 = I151 /\ I152 = I152 /\ I153 = I153 /\ I165 = I165 /\ I166 = I166 /\ I154 = I165 + I156 /\ I155 = I166 + I156]
153.88/151.93	  8) f1#(I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206) -> f3#(I187, 1 + I188, rnd3, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206) [rnd3 = rnd3 /\ 1 + I188 <= 64]
153.88/151.93	  9) f1#(I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226) -> f2#(7, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226) [64 <= I208]
153.88/151.93	
153.88/151.93	We have the following SCCs.
153.88/151.93	  { 6, 8 }
153.88/151.93	  { 2, 5 }
153.88/151.93	  { 4, 7 }
153.88/151.93	
153.88/151.93	DP problem for innermost termination.
153.88/151.93	P =
153.88/151.93	  f6#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) -> f4#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) 
153.88/151.93	  f4#(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139) -> f6#(-1 + I120, I121, I122, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156) [0 <= I120 /\ I140 = I140 /\ I157 = I157 /\ I145 = I145 /\ I158 = I158 /\ I146 = I146 /\ I159 = I159 /\ I147 = I147 /\ I160 = I160 /\ I141 = I140 + I147 /\ I144 = I140 - I147 /\ I142 = I145 + I146 /\ I143 = I145 - I146 /\ B0 = B0 /\ I161 = I160 + I157 /\ I162 = I159 + I158 /\ I163 = I160 + I158 /\ I164 = I159 + I157 /\ I156 = I156 /\ I148 = I148 /\ I149 = I149 /\ I150 = I150 /\ I151 = I151 /\ I152 = I152 /\ I153 = I153 /\ I165 = I165 /\ I166 = I166 /\ I154 = I165 + I156 /\ I155 = I166 + I156]
153.88/151.93	R = 
153.88/151.93	  f9(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20) -> f8(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20) 
153.88/151.93	  f8(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f3(I0, 0, 0, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) 
153.88/151.93	  f7(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39) -> f2(-1 + I20, I21, I22, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14, rnd15, rnd16, rnd17, rnd18, rnd19, rnd20) [0 <= I20 /\ rnd4 = rnd4 /\ y4 = y4 /\ rnd9 = rnd9 /\ y3 = y3 /\ rnd10 = rnd10 /\ y2 = y2 /\ rnd11 = rnd11 /\ y1 = y1 /\ rnd5 = rnd4 + rnd11 /\ rnd8 = rnd4 - rnd11 /\ rnd6 = rnd9 + rnd10 /\ rnd7 = rnd9 - rnd10 /\ y5 = y5 /\ y6 = y1 + y4 /\ y7 = y2 + y3 /\ y8 = y1 + y3 /\ y10 = y2 + y4 /\ rnd20 = rnd20 /\ rnd12 = rnd12 /\ rnd13 = rnd13 /\ rnd14 = rnd14 /\ rnd15 = rnd15 /\ rnd16 = rnd16 /\ rnd17 = rnd17 /\ y9 = y9 /\ y11 = y11 /\ rnd18 = y9 + rnd20 /\ rnd19 = y11 + rnd20]
153.88/151.93	  f7(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f6(7, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) [1 + I40 <= 0]
153.88/151.93	  f6(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) -> f4(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) 
153.88/151.93	  f2(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f7(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) 
153.88/151.93	  f3(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f1(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) 
153.88/151.93	  f4(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139) -> f6(-1 + I120, I121, I122, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156) [0 <= I120 /\ I140 = I140 /\ I157 = I157 /\ I145 = I145 /\ I158 = I158 /\ I146 = I146 /\ I159 = I159 /\ I147 = I147 /\ I160 = I160 /\ I141 = I140 + I147 /\ I144 = I140 - I147 /\ I142 = I145 + I146 /\ I143 = I145 - I146 /\ B0 = B0 /\ I161 = I160 + I157 /\ I162 = I159 + I158 /\ I163 = I160 + I158 /\ I164 = I159 + I157 /\ I156 = I156 /\ I148 = I148 /\ I149 = I149 /\ I150 = I150 /\ I151 = I151 /\ I152 = I152 /\ I153 = I153 /\ I165 = I165 /\ I166 = I166 /\ I154 = I165 + I156 /\ I155 = I166 + I156]
153.88/151.93	  f4(I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186) -> f5(I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186) [1 + I167 <= 0]
153.88/151.93	  f1(I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206) -> f3(I187, 1 + I188, rnd3, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206) [rnd3 = rnd3 /\ 1 + I188 <= 64]
153.88/151.93	  f1(I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226) -> f2(7, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226) [64 <= I208]
153.88/151.93	
153.88/151.93	We use the basic value criterion with the projection function NU:
153.88/151.93	  NU[f4#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14,z15,z16,z17,z18,z19,z20)] = z1
153.88/151.93	  NU[f6#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14,z15,z16,z17,z18,z19,z20)] = z1
153.88/151.93	
153.88/151.93	This gives the following inequalities:
153.88/151.93	    ==>  I60 (>! \union =) I60
153.88/151.93	  0 <= I120 /\ I140 = I140 /\ I157 = I157 /\ I145 = I145 /\ I158 = I158 /\ I146 = I146 /\ I159 = I159 /\ I147 = I147 /\ I160 = I160 /\ I141 = I140 + I147 /\ I144 = I140 - I147 /\ I142 = I145 + I146 /\ I143 = I145 - I146 /\ B0 = B0 /\ I161 = I160 + I157 /\ I162 = I159 + I158 /\ I163 = I160 + I158 /\ I164 = I159 + I157 /\ I156 = I156 /\ I148 = I148 /\ I149 = I149 /\ I150 = I150 /\ I151 = I151 /\ I152 = I152 /\ I153 = I153 /\ I165 = I165 /\ I166 = I166 /\ I154 = I165 + I156 /\ I155 = I166 + I156  ==>  I120 >! -1 + I120
153.88/151.93	
153.88/151.93	We remove all the strictly oriented dependency pairs.
153.88/151.93	
153.88/151.93	DP problem for innermost termination.
153.88/151.93	P =
153.88/151.93	  f6#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) -> f4#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) 
153.88/151.93	R = 
153.88/151.93	  f9(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20) -> f8(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20) 
153.88/151.93	  f8(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f3(I0, 0, 0, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) 
153.88/151.93	  f7(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39) -> f2(-1 + I20, I21, I22, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14, rnd15, rnd16, rnd17, rnd18, rnd19, rnd20) [0 <= I20 /\ rnd4 = rnd4 /\ y4 = y4 /\ rnd9 = rnd9 /\ y3 = y3 /\ rnd10 = rnd10 /\ y2 = y2 /\ rnd11 = rnd11 /\ y1 = y1 /\ rnd5 = rnd4 + rnd11 /\ rnd8 = rnd4 - rnd11 /\ rnd6 = rnd9 + rnd10 /\ rnd7 = rnd9 - rnd10 /\ y5 = y5 /\ y6 = y1 + y4 /\ y7 = y2 + y3 /\ y8 = y1 + y3 /\ y10 = y2 + y4 /\ rnd20 = rnd20 /\ rnd12 = rnd12 /\ rnd13 = rnd13 /\ rnd14 = rnd14 /\ rnd15 = rnd15 /\ rnd16 = rnd16 /\ rnd17 = rnd17 /\ y9 = y9 /\ y11 = y11 /\ rnd18 = y9 + rnd20 /\ rnd19 = y11 + rnd20]
153.88/151.93	  f7(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f6(7, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) [1 + I40 <= 0]
153.88/151.93	  f6(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) -> f4(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) 
153.88/151.93	  f2(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f7(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) 
153.88/151.93	  f3(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f1(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) 
153.88/151.93	  f4(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139) -> f6(-1 + I120, I121, I122, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156) [0 <= I120 /\ I140 = I140 /\ I157 = I157 /\ I145 = I145 /\ I158 = I158 /\ I146 = I146 /\ I159 = I159 /\ I147 = I147 /\ I160 = I160 /\ I141 = I140 + I147 /\ I144 = I140 - I147 /\ I142 = I145 + I146 /\ I143 = I145 - I146 /\ B0 = B0 /\ I161 = I160 + I157 /\ I162 = I159 + I158 /\ I163 = I160 + I158 /\ I164 = I159 + I157 /\ I156 = I156 /\ I148 = I148 /\ I149 = I149 /\ I150 = I150 /\ I151 = I151 /\ I152 = I152 /\ I153 = I153 /\ I165 = I165 /\ I166 = I166 /\ I154 = I165 + I156 /\ I155 = I166 + I156]
153.88/151.93	  f4(I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186) -> f5(I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186) [1 + I167 <= 0]
153.88/151.93	  f1(I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206) -> f3(I187, 1 + I188, rnd3, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206) [rnd3 = rnd3 /\ 1 + I188 <= 64]
153.88/151.93	  f1(I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226) -> f2(7, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226) [64 <= I208]
153.88/151.93	
153.88/151.93	The dependency graph for this problem is:
153.88/151.93	  4 -> 
153.88/151.93	Where:
153.88/151.93	  4) f6#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) -> f4#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) 
153.88/151.93	
153.88/151.93	We have the following SCCs.
153.88/151.93	  
153.88/151.93	
153.88/151.93	DP problem for innermost termination.
153.88/151.93	P =
153.88/151.93	  f7#(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39) -> f2#(-1 + I20, I21, I22, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14, rnd15, rnd16, rnd17, rnd18, rnd19, rnd20) [0 <= I20 /\ rnd4 = rnd4 /\ y4 = y4 /\ rnd9 = rnd9 /\ y3 = y3 /\ rnd10 = rnd10 /\ y2 = y2 /\ rnd11 = rnd11 /\ y1 = y1 /\ rnd5 = rnd4 + rnd11 /\ rnd8 = rnd4 - rnd11 /\ rnd6 = rnd9 + rnd10 /\ rnd7 = rnd9 - rnd10 /\ y5 = y5 /\ y6 = y1 + y4 /\ y7 = y2 + y3 /\ y8 = y1 + y3 /\ y10 = y2 + y4 /\ rnd20 = rnd20 /\ rnd12 = rnd12 /\ rnd13 = rnd13 /\ rnd14 = rnd14 /\ rnd15 = rnd15 /\ rnd16 = rnd16 /\ rnd17 = rnd17 /\ y9 = y9 /\ y11 = y11 /\ rnd18 = y9 + rnd20 /\ rnd19 = y11 + rnd20]
153.88/151.93	  f2#(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f7#(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) 
153.88/151.93	R = 
153.88/151.93	  f9(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20) -> f8(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20) 
153.88/151.93	  f8(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f3(I0, 0, 0, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) 
153.88/151.93	  f7(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39) -> f2(-1 + I20, I21, I22, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14, rnd15, rnd16, rnd17, rnd18, rnd19, rnd20) [0 <= I20 /\ rnd4 = rnd4 /\ y4 = y4 /\ rnd9 = rnd9 /\ y3 = y3 /\ rnd10 = rnd10 /\ y2 = y2 /\ rnd11 = rnd11 /\ y1 = y1 /\ rnd5 = rnd4 + rnd11 /\ rnd8 = rnd4 - rnd11 /\ rnd6 = rnd9 + rnd10 /\ rnd7 = rnd9 - rnd10 /\ y5 = y5 /\ y6 = y1 + y4 /\ y7 = y2 + y3 /\ y8 = y1 + y3 /\ y10 = y2 + y4 /\ rnd20 = rnd20 /\ rnd12 = rnd12 /\ rnd13 = rnd13 /\ rnd14 = rnd14 /\ rnd15 = rnd15 /\ rnd16 = rnd16 /\ rnd17 = rnd17 /\ y9 = y9 /\ y11 = y11 /\ rnd18 = y9 + rnd20 /\ rnd19 = y11 + rnd20]
153.88/151.93	  f7(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f6(7, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) [1 + I40 <= 0]
153.88/151.93	  f6(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) -> f4(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) 
153.88/151.93	  f2(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f7(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) 
153.88/151.93	  f3(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f1(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) 
153.88/151.93	  f4(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139) -> f6(-1 + I120, I121, I122, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156) [0 <= I120 /\ I140 = I140 /\ I157 = I157 /\ I145 = I145 /\ I158 = I158 /\ I146 = I146 /\ I159 = I159 /\ I147 = I147 /\ I160 = I160 /\ I141 = I140 + I147 /\ I144 = I140 - I147 /\ I142 = I145 + I146 /\ I143 = I145 - I146 /\ B0 = B0 /\ I161 = I160 + I157 /\ I162 = I159 + I158 /\ I163 = I160 + I158 /\ I164 = I159 + I157 /\ I156 = I156 /\ I148 = I148 /\ I149 = I149 /\ I150 = I150 /\ I151 = I151 /\ I152 = I152 /\ I153 = I153 /\ I165 = I165 /\ I166 = I166 /\ I154 = I165 + I156 /\ I155 = I166 + I156]
153.88/151.93	  f4(I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186) -> f5(I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186) [1 + I167 <= 0]
153.88/151.93	  f1(I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206) -> f3(I187, 1 + I188, rnd3, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206) [rnd3 = rnd3 /\ 1 + I188 <= 64]
153.88/151.93	  f1(I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226) -> f2(7, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226) [64 <= I208]
153.88/151.93	
153.88/151.93	We use the basic value criterion with the projection function NU:
153.88/151.93	  NU[f2#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14,z15,z16,z17,z18,z19,z20)] = z1
153.88/151.93	  NU[f7#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14,z15,z16,z17,z18,z19,z20)] = z1
153.88/151.93	
153.88/151.93	This gives the following inequalities:
153.88/151.93	  0 <= I20 /\ rnd4 = rnd4 /\ y4 = y4 /\ rnd9 = rnd9 /\ y3 = y3 /\ rnd10 = rnd10 /\ y2 = y2 /\ rnd11 = rnd11 /\ y1 = y1 /\ rnd5 = rnd4 + rnd11 /\ rnd8 = rnd4 - rnd11 /\ rnd6 = rnd9 + rnd10 /\ rnd7 = rnd9 - rnd10 /\ y5 = y5 /\ y6 = y1 + y4 /\ y7 = y2 + y3 /\ y8 = y1 + y3 /\ y10 = y2 + y4 /\ rnd20 = rnd20 /\ rnd12 = rnd12 /\ rnd13 = rnd13 /\ rnd14 = rnd14 /\ rnd15 = rnd15 /\ rnd16 = rnd16 /\ rnd17 = rnd17 /\ y9 = y9 /\ y11 = y11 /\ rnd18 = y9 + rnd20 /\ rnd19 = y11 + rnd20  ==>  I20 >! -1 + I20
153.88/151.93	    ==>  I80 (>! \union =) I80
153.88/151.93	
153.88/151.93	We remove all the strictly oriented dependency pairs.
153.88/151.93	
153.88/151.93	DP problem for innermost termination.
153.88/151.93	P =
153.88/151.93	  f2#(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f7#(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) 
153.88/151.93	R = 
153.88/151.93	  f9(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20) -> f8(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20) 
153.88/151.93	  f8(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f3(I0, 0, 0, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) 
153.88/151.93	  f7(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39) -> f2(-1 + I20, I21, I22, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14, rnd15, rnd16, rnd17, rnd18, rnd19, rnd20) [0 <= I20 /\ rnd4 = rnd4 /\ y4 = y4 /\ rnd9 = rnd9 /\ y3 = y3 /\ rnd10 = rnd10 /\ y2 = y2 /\ rnd11 = rnd11 /\ y1 = y1 /\ rnd5 = rnd4 + rnd11 /\ rnd8 = rnd4 - rnd11 /\ rnd6 = rnd9 + rnd10 /\ rnd7 = rnd9 - rnd10 /\ y5 = y5 /\ y6 = y1 + y4 /\ y7 = y2 + y3 /\ y8 = y1 + y3 /\ y10 = y2 + y4 /\ rnd20 = rnd20 /\ rnd12 = rnd12 /\ rnd13 = rnd13 /\ rnd14 = rnd14 /\ rnd15 = rnd15 /\ rnd16 = rnd16 /\ rnd17 = rnd17 /\ y9 = y9 /\ y11 = y11 /\ rnd18 = y9 + rnd20 /\ rnd19 = y11 + rnd20]
153.88/151.93	  f7(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f6(7, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) [1 + I40 <= 0]
153.88/151.93	  f6(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) -> f4(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) 
153.88/151.93	  f2(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f7(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) 
153.88/151.93	  f3(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f1(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) 
153.88/151.93	  f4(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139) -> f6(-1 + I120, I121, I122, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156) [0 <= I120 /\ I140 = I140 /\ I157 = I157 /\ I145 = I145 /\ I158 = I158 /\ I146 = I146 /\ I159 = I159 /\ I147 = I147 /\ I160 = I160 /\ I141 = I140 + I147 /\ I144 = I140 - I147 /\ I142 = I145 + I146 /\ I143 = I145 - I146 /\ B0 = B0 /\ I161 = I160 + I157 /\ I162 = I159 + I158 /\ I163 = I160 + I158 /\ I164 = I159 + I157 /\ I156 = I156 /\ I148 = I148 /\ I149 = I149 /\ I150 = I150 /\ I151 = I151 /\ I152 = I152 /\ I153 = I153 /\ I165 = I165 /\ I166 = I166 /\ I154 = I165 + I156 /\ I155 = I166 + I156]
153.88/151.93	  f4(I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186) -> f5(I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186) [1 + I167 <= 0]
153.88/151.93	  f1(I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206) -> f3(I187, 1 + I188, rnd3, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206) [rnd3 = rnd3 /\ 1 + I188 <= 64]
153.88/151.93	  f1(I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226) -> f2(7, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226) [64 <= I208]
153.88/151.93	
153.88/151.93	The dependency graph for this problem is:
153.88/151.93	  5 -> 
153.88/151.93	Where:
153.88/151.93	  5) f2#(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f7#(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) 
153.88/151.93	
153.88/151.93	We have the following SCCs.
153.88/151.93	  
153.88/151.93	
153.88/151.93	DP problem for innermost termination.
153.88/151.93	P =
153.88/151.93	  f3#(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f1#(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) 
153.88/151.93	  f1#(I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206) -> f3#(I187, 1 + I188, rnd3, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206) [rnd3 = rnd3 /\ 1 + I188 <= 64]
153.88/151.93	R = 
153.88/151.93	  f9(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20) -> f8(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20) 
153.88/151.93	  f8(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f3(I0, 0, 0, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) 
153.88/151.93	  f7(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39) -> f2(-1 + I20, I21, I22, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14, rnd15, rnd16, rnd17, rnd18, rnd19, rnd20) [0 <= I20 /\ rnd4 = rnd4 /\ y4 = y4 /\ rnd9 = rnd9 /\ y3 = y3 /\ rnd10 = rnd10 /\ y2 = y2 /\ rnd11 = rnd11 /\ y1 = y1 /\ rnd5 = rnd4 + rnd11 /\ rnd8 = rnd4 - rnd11 /\ rnd6 = rnd9 + rnd10 /\ rnd7 = rnd9 - rnd10 /\ y5 = y5 /\ y6 = y1 + y4 /\ y7 = y2 + y3 /\ y8 = y1 + y3 /\ y10 = y2 + y4 /\ rnd20 = rnd20 /\ rnd12 = rnd12 /\ rnd13 = rnd13 /\ rnd14 = rnd14 /\ rnd15 = rnd15 /\ rnd16 = rnd16 /\ rnd17 = rnd17 /\ y9 = y9 /\ y11 = y11 /\ rnd18 = y9 + rnd20 /\ rnd19 = y11 + rnd20]
153.88/151.93	  f7(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f6(7, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) [1 + I40 <= 0]
153.88/151.93	  f6(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) -> f4(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) 
153.88/151.93	  f2(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f7(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) 
153.88/151.93	  f3(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f1(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) 
153.88/151.93	  f4(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139) -> f6(-1 + I120, I121, I122, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156) [0 <= I120 /\ I140 = I140 /\ I157 = I157 /\ I145 = I145 /\ I158 = I158 /\ I146 = I146 /\ I159 = I159 /\ I147 = I147 /\ I160 = I160 /\ I141 = I140 + I147 /\ I144 = I140 - I147 /\ I142 = I145 + I146 /\ I143 = I145 - I146 /\ B0 = B0 /\ I161 = I160 + I157 /\ I162 = I159 + I158 /\ I163 = I160 + I158 /\ I164 = I159 + I157 /\ I156 = I156 /\ I148 = I148 /\ I149 = I149 /\ I150 = I150 /\ I151 = I151 /\ I152 = I152 /\ I153 = I153 /\ I165 = I165 /\ I166 = I166 /\ I154 = I165 + I156 /\ I155 = I166 + I156]
153.88/151.93	  f4(I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186) -> f5(I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186) [1 + I167 <= 0]
153.88/151.93	  f1(I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206) -> f3(I187, 1 + I188, rnd3, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206) [rnd3 = rnd3 /\ 1 + I188 <= 64]
153.88/151.93	  f1(I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226) -> f2(7, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226) [64 <= I208]
153.88/151.93	
153.88/151.93	We use the reverse value criterion with the projection function NU:
153.88/151.93	  NU[f1#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14,z15,z16,z17,z18,z19,z20)] = 64 + -1 * (1 + z2)
153.88/151.93	  NU[f3#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14,z15,z16,z17,z18,z19,z20)] = 64 + -1 * (1 + z2)
153.88/151.93	
153.88/151.93	This gives the following inequalities:
153.88/151.93	    ==>  64 + -1 * (1 + I101) >= 64 + -1 * (1 + I101)
153.88/151.93	  rnd3 = rnd3 /\ 1 + I188 <= 64  ==>  64 + -1 * (1 + I188) > 64 + -1 * (1 + (1 + I188))  with  64 + -1 * (1 + I188) >= 0
153.88/151.93	
153.88/151.93	We remove all the strictly oriented dependency pairs.
153.88/151.93	
153.88/151.93	DP problem for innermost termination.
153.88/151.93	P =
153.88/151.93	  f3#(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f1#(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) 
153.88/151.93	R = 
153.88/151.93	  f9(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20) -> f8(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20) 
153.88/151.93	  f8(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f3(I0, 0, 0, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) 
153.88/151.93	  f7(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39) -> f2(-1 + I20, I21, I22, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14, rnd15, rnd16, rnd17, rnd18, rnd19, rnd20) [0 <= I20 /\ rnd4 = rnd4 /\ y4 = y4 /\ rnd9 = rnd9 /\ y3 = y3 /\ rnd10 = rnd10 /\ y2 = y2 /\ rnd11 = rnd11 /\ y1 = y1 /\ rnd5 = rnd4 + rnd11 /\ rnd8 = rnd4 - rnd11 /\ rnd6 = rnd9 + rnd10 /\ rnd7 = rnd9 - rnd10 /\ y5 = y5 /\ y6 = y1 + y4 /\ y7 = y2 + y3 /\ y8 = y1 + y3 /\ y10 = y2 + y4 /\ rnd20 = rnd20 /\ rnd12 = rnd12 /\ rnd13 = rnd13 /\ rnd14 = rnd14 /\ rnd15 = rnd15 /\ rnd16 = rnd16 /\ rnd17 = rnd17 /\ y9 = y9 /\ y11 = y11 /\ rnd18 = y9 + rnd20 /\ rnd19 = y11 + rnd20]
153.88/151.93	  f7(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f6(7, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) [1 + I40 <= 0]
153.88/151.93	  f6(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) -> f4(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) 
153.88/151.93	  f2(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f7(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) 
153.88/151.93	  f3(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f1(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) 
153.88/151.93	  f4(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139) -> f6(-1 + I120, I121, I122, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156) [0 <= I120 /\ I140 = I140 /\ I157 = I157 /\ I145 = I145 /\ I158 = I158 /\ I146 = I146 /\ I159 = I159 /\ I147 = I147 /\ I160 = I160 /\ I141 = I140 + I147 /\ I144 = I140 - I147 /\ I142 = I145 + I146 /\ I143 = I145 - I146 /\ B0 = B0 /\ I161 = I160 + I157 /\ I162 = I159 + I158 /\ I163 = I160 + I158 /\ I164 = I159 + I157 /\ I156 = I156 /\ I148 = I148 /\ I149 = I149 /\ I150 = I150 /\ I151 = I151 /\ I152 = I152 /\ I153 = I153 /\ I165 = I165 /\ I166 = I166 /\ I154 = I165 + I156 /\ I155 = I166 + I156]
153.88/151.93	  f4(I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186) -> f5(I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186) [1 + I167 <= 0]
153.88/151.93	  f1(I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206) -> f3(I187, 1 + I188, rnd3, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206) [rnd3 = rnd3 /\ 1 + I188 <= 64]
153.88/151.93	  f1(I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226) -> f2(7, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226) [64 <= I208]
153.88/151.93	
153.88/151.93	The dependency graph for this problem is:
153.88/151.93	  6 -> 
153.88/151.93	Where:
153.88/151.93	  6) f3#(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f1#(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) 
153.88/151.93	
153.88/151.93	We have the following SCCs.
153.88/151.93	  
153.88/154.88	EOF