40.24/39.97	YES
40.24/39.97	
40.24/39.97	DP problem for innermost termination.
40.24/39.97	P =
40.24/39.97	  f9#(x1, x2, x3, x4, x5, x6, x7, x8) -> f8#(x1, x2, x3, x4, x5, x6, x7, x8) 
40.24/39.97	  f8#(I0, I1, I2, I3, I4, I5, I6, I7) -> f7#(I0, I1, I2, I3, I4, I5, I6, I7) 
40.24/39.97	  f8#(I8, I9, I10, I11, I12, I13, I14, I15) -> f2#(I8, I9, I10, I11, I12, I13, I14, I15) 
40.24/39.97	  f8#(I16, I17, I18, I19, I20, I21, I22, I23) -> f4#(I16, I17, I18, I19, I20, I21, I22, I23) 
40.24/39.97	  f8#(I24, I25, I26, I27, I28, I29, I30, I31) -> f5#(I24, I25, I26, I27, I28, I29, I30, I31) 
40.24/39.97	  f8#(I32, I33, I34, I35, I36, I37, I38, I39) -> f3#(I32, I33, I34, I35, I36, I37, I38, I39) 
40.24/39.97	  f8#(I40, I41, I42, I43, I44, I45, I46, I47) -> f1#(I40, I41, I42, I43, I44, I45, I46, I47) 
40.24/39.97	  f8#(I56, I57, I58, I59, I60, I61, I62, I63) -> f7#(I56, I57, I62, I63, rnd5, rnd6, rnd7, rnd8) [rnd8 = rnd6 /\ rnd7 = rnd5 /\ rnd6 = rnd6 /\ rnd5 = rnd5]
40.24/39.97	  f7#(I64, I65, I66, I67, I68, I69, I70, I71) -> f2#(I64, I65, I70, I71, I72, I69, 0, I73) [I73 = I72 /\ I72 = I72]
40.24/39.97	  f2#(I74, I75, I76, I77, I78, I79, I80, I81) -> f4#(I74, I75, I80, I81, I78, I79, I80, 3) [I80 <= I75]
40.24/39.97	  f2#(I82, I83, I84, I85, I86, I87, I88, I89) -> f5#(I82, I83, I88, I89, I90, I87, I88, I91) [I91 = I90 /\ 1 + I83 <= I88 /\ I90 = I90]
40.24/39.97	  f4#(I92, I93, I94, I95, I96, I97, I98, I99) -> f3#(I92, I93, I98, I99, I96, I97, I98, I99) [I99 <= I92]
40.24/39.97	  f4#(I100, I101, I102, I103, I104, I105, I106, I107) -> f1#(I100, I101, I106, I107, I104, I105, I106, I107) [1 + I100 <= I107]
40.24/39.97	  f3#(I120, I121, I122, I123, I124, I125, I126, I127) -> f4#(I120, I121, I126, I127, I124, I125, I126, 1 + I127) 
40.24/39.97	  f1#(I128, I129, I130, I131, I132, I133, I134, I135) -> f2#(I128, I129, I134, I135, I136, I133, 1 + I134, I137) [I137 = I136 /\ I136 = I136]
40.24/39.97	R = 
40.24/39.97	  f9(x1, x2, x3, x4, x5, x6, x7, x8) -> f8(x1, x2, x3, x4, x5, x6, x7, x8) 
40.24/39.97	  f8(I0, I1, I2, I3, I4, I5, I6, I7) -> f7(I0, I1, I2, I3, I4, I5, I6, I7) 
40.24/39.97	  f8(I8, I9, I10, I11, I12, I13, I14, I15) -> f2(I8, I9, I10, I11, I12, I13, I14, I15) 
40.24/39.97	  f8(I16, I17, I18, I19, I20, I21, I22, I23) -> f4(I16, I17, I18, I19, I20, I21, I22, I23) 
40.24/39.97	  f8(I24, I25, I26, I27, I28, I29, I30, I31) -> f5(I24, I25, I26, I27, I28, I29, I30, I31) 
40.24/39.97	  f8(I32, I33, I34, I35, I36, I37, I38, I39) -> f3(I32, I33, I34, I35, I36, I37, I38, I39) 
40.24/39.97	  f8(I40, I41, I42, I43, I44, I45, I46, I47) -> f1(I40, I41, I42, I43, I44, I45, I46, I47) 
40.24/39.97	  f8(I48, I49, I50, I51, I52, I53, I54, I55) -> f6(I48, I49, I50, I51, I52, I53, I54, I55) 
40.24/39.97	  f8(I56, I57, I58, I59, I60, I61, I62, I63) -> f7(I56, I57, I62, I63, rnd5, rnd6, rnd7, rnd8) [rnd8 = rnd6 /\ rnd7 = rnd5 /\ rnd6 = rnd6 /\ rnd5 = rnd5]
40.24/39.97	  f7(I64, I65, I66, I67, I68, I69, I70, I71) -> f2(I64, I65, I70, I71, I72, I69, 0, I73) [I73 = I72 /\ I72 = I72]
40.24/39.97	  f2(I74, I75, I76, I77, I78, I79, I80, I81) -> f4(I74, I75, I80, I81, I78, I79, I80, 3) [I80 <= I75]
40.24/39.97	  f2(I82, I83, I84, I85, I86, I87, I88, I89) -> f5(I82, I83, I88, I89, I90, I87, I88, I91) [I91 = I90 /\ 1 + I83 <= I88 /\ I90 = I90]
40.24/39.97	  f4(I92, I93, I94, I95, I96, I97, I98, I99) -> f3(I92, I93, I98, I99, I96, I97, I98, I99) [I99 <= I92]
40.24/39.97	  f4(I100, I101, I102, I103, I104, I105, I106, I107) -> f1(I100, I101, I106, I107, I104, I105, I106, I107) [1 + I100 <= I107]
40.24/39.97	  f5(I108, I109, I110, I111, I112, I113, I114, I115) -> f6(I108, I109, I114, I115, I116, I117, I118, I119) [I119 = I117 /\ I118 = I116 /\ I117 = I117 /\ I116 = I116]
40.24/39.97	  f3(I120, I121, I122, I123, I124, I125, I126, I127) -> f4(I120, I121, I126, I127, I124, I125, I126, 1 + I127) 
40.24/39.97	  f1(I128, I129, I130, I131, I132, I133, I134, I135) -> f2(I128, I129, I134, I135, I136, I133, 1 + I134, I137) [I137 = I136 /\ I136 = I136]
40.24/39.97	
40.24/39.97	The dependency graph for this problem is:
40.24/39.97	  0 -> 1, 2, 3, 4, 5, 6, 7
40.24/39.97	  1 -> 8
40.24/39.97	  2 -> 9, 10
40.24/39.97	  3 -> 11, 12
40.24/39.97	  4 -> 
40.24/39.97	  5 -> 13
40.24/39.97	  6 -> 14
40.24/39.97	  7 -> 8
40.24/39.97	  8 -> 9, 10
40.24/39.97	  9 -> 11, 12
40.24/39.97	  10 -> 
40.24/39.97	  11 -> 13
40.24/39.97	  12 -> 14
40.24/39.97	  13 -> 11, 12
40.24/39.97	  14 -> 9, 10
40.24/39.97	Where:
40.24/39.97	  0) f9#(x1, x2, x3, x4, x5, x6, x7, x8) -> f8#(x1, x2, x3, x4, x5, x6, x7, x8) 
40.24/39.97	  1) f8#(I0, I1, I2, I3, I4, I5, I6, I7) -> f7#(I0, I1, I2, I3, I4, I5, I6, I7) 
40.24/39.97	  2) f8#(I8, I9, I10, I11, I12, I13, I14, I15) -> f2#(I8, I9, I10, I11, I12, I13, I14, I15) 
40.24/39.97	  3) f8#(I16, I17, I18, I19, I20, I21, I22, I23) -> f4#(I16, I17, I18, I19, I20, I21, I22, I23) 
40.24/39.97	  4) f8#(I24, I25, I26, I27, I28, I29, I30, I31) -> f5#(I24, I25, I26, I27, I28, I29, I30, I31) 
40.24/39.97	  5) f8#(I32, I33, I34, I35, I36, I37, I38, I39) -> f3#(I32, I33, I34, I35, I36, I37, I38, I39) 
40.24/39.97	  6) f8#(I40, I41, I42, I43, I44, I45, I46, I47) -> f1#(I40, I41, I42, I43, I44, I45, I46, I47) 
40.24/39.97	  7) f8#(I56, I57, I58, I59, I60, I61, I62, I63) -> f7#(I56, I57, I62, I63, rnd5, rnd6, rnd7, rnd8) [rnd8 = rnd6 /\ rnd7 = rnd5 /\ rnd6 = rnd6 /\ rnd5 = rnd5]
40.24/39.97	  8) f7#(I64, I65, I66, I67, I68, I69, I70, I71) -> f2#(I64, I65, I70, I71, I72, I69, 0, I73) [I73 = I72 /\ I72 = I72]
40.24/39.97	  9) f2#(I74, I75, I76, I77, I78, I79, I80, I81) -> f4#(I74, I75, I80, I81, I78, I79, I80, 3) [I80 <= I75]
40.24/39.97	  10) f2#(I82, I83, I84, I85, I86, I87, I88, I89) -> f5#(I82, I83, I88, I89, I90, I87, I88, I91) [I91 = I90 /\ 1 + I83 <= I88 /\ I90 = I90]
40.24/39.97	  11) f4#(I92, I93, I94, I95, I96, I97, I98, I99) -> f3#(I92, I93, I98, I99, I96, I97, I98, I99) [I99 <= I92]
40.24/39.97	  12) f4#(I100, I101, I102, I103, I104, I105, I106, I107) -> f1#(I100, I101, I106, I107, I104, I105, I106, I107) [1 + I100 <= I107]
40.24/39.97	  13) f3#(I120, I121, I122, I123, I124, I125, I126, I127) -> f4#(I120, I121, I126, I127, I124, I125, I126, 1 + I127) 
40.24/39.97	  14) f1#(I128, I129, I130, I131, I132, I133, I134, I135) -> f2#(I128, I129, I134, I135, I136, I133, 1 + I134, I137) [I137 = I136 /\ I136 = I136]
40.24/39.97	
40.24/39.97	We have the following SCCs.
40.24/39.97	  { 9, 11, 12, 13, 14 }
40.24/39.97	
40.24/39.97	DP problem for innermost termination.
40.24/39.97	P =
40.24/39.97	  f2#(I74, I75, I76, I77, I78, I79, I80, I81) -> f4#(I74, I75, I80, I81, I78, I79, I80, 3) [I80 <= I75]
40.24/39.97	  f4#(I92, I93, I94, I95, I96, I97, I98, I99) -> f3#(I92, I93, I98, I99, I96, I97, I98, I99) [I99 <= I92]
40.24/39.97	  f4#(I100, I101, I102, I103, I104, I105, I106, I107) -> f1#(I100, I101, I106, I107, I104, I105, I106, I107) [1 + I100 <= I107]
40.24/39.97	  f3#(I120, I121, I122, I123, I124, I125, I126, I127) -> f4#(I120, I121, I126, I127, I124, I125, I126, 1 + I127) 
40.24/39.97	  f1#(I128, I129, I130, I131, I132, I133, I134, I135) -> f2#(I128, I129, I134, I135, I136, I133, 1 + I134, I137) [I137 = I136 /\ I136 = I136]
40.24/39.97	R = 
40.24/39.97	  f9(x1, x2, x3, x4, x5, x6, x7, x8) -> f8(x1, x2, x3, x4, x5, x6, x7, x8) 
40.24/39.97	  f8(I0, I1, I2, I3, I4, I5, I6, I7) -> f7(I0, I1, I2, I3, I4, I5, I6, I7) 
40.24/39.97	  f8(I8, I9, I10, I11, I12, I13, I14, I15) -> f2(I8, I9, I10, I11, I12, I13, I14, I15) 
40.24/39.97	  f8(I16, I17, I18, I19, I20, I21, I22, I23) -> f4(I16, I17, I18, I19, I20, I21, I22, I23) 
40.24/39.97	  f8(I24, I25, I26, I27, I28, I29, I30, I31) -> f5(I24, I25, I26, I27, I28, I29, I30, I31) 
40.24/39.97	  f8(I32, I33, I34, I35, I36, I37, I38, I39) -> f3(I32, I33, I34, I35, I36, I37, I38, I39) 
40.24/39.97	  f8(I40, I41, I42, I43, I44, I45, I46, I47) -> f1(I40, I41, I42, I43, I44, I45, I46, I47) 
40.24/39.97	  f8(I48, I49, I50, I51, I52, I53, I54, I55) -> f6(I48, I49, I50, I51, I52, I53, I54, I55) 
40.24/39.97	  f8(I56, I57, I58, I59, I60, I61, I62, I63) -> f7(I56, I57, I62, I63, rnd5, rnd6, rnd7, rnd8) [rnd8 = rnd6 /\ rnd7 = rnd5 /\ rnd6 = rnd6 /\ rnd5 = rnd5]
40.24/39.97	  f7(I64, I65, I66, I67, I68, I69, I70, I71) -> f2(I64, I65, I70, I71, I72, I69, 0, I73) [I73 = I72 /\ I72 = I72]
40.24/39.97	  f2(I74, I75, I76, I77, I78, I79, I80, I81) -> f4(I74, I75, I80, I81, I78, I79, I80, 3) [I80 <= I75]
40.24/39.97	  f2(I82, I83, I84, I85, I86, I87, I88, I89) -> f5(I82, I83, I88, I89, I90, I87, I88, I91) [I91 = I90 /\ 1 + I83 <= I88 /\ I90 = I90]
40.24/39.97	  f4(I92, I93, I94, I95, I96, I97, I98, I99) -> f3(I92, I93, I98, I99, I96, I97, I98, I99) [I99 <= I92]
40.24/39.97	  f4(I100, I101, I102, I103, I104, I105, I106, I107) -> f1(I100, I101, I106, I107, I104, I105, I106, I107) [1 + I100 <= I107]
40.24/39.97	  f5(I108, I109, I110, I111, I112, I113, I114, I115) -> f6(I108, I109, I114, I115, I116, I117, I118, I119) [I119 = I117 /\ I118 = I116 /\ I117 = I117 /\ I116 = I116]
40.24/39.97	  f3(I120, I121, I122, I123, I124, I125, I126, I127) -> f4(I120, I121, I126, I127, I124, I125, I126, 1 + I127) 
40.24/39.97	  f1(I128, I129, I130, I131, I132, I133, I134, I135) -> f2(I128, I129, I134, I135, I136, I133, 1 + I134, I137) [I137 = I136 /\ I136 = I136]
40.24/39.97	
40.24/39.97	We use the extended value criterion with the projection function NU:
40.24/39.97	  NU[f1#(x0,x1,x2,x3,x4,x5,x6,x7)] = x1 - x6 - 1
40.24/39.97	  NU[f3#(x0,x1,x2,x3,x4,x5,x6,x7)] = x1 - x6 - 1
40.24/39.97	  NU[f4#(x0,x1,x2,x3,x4,x5,x6,x7)] = x1 - x6 - 1
40.24/39.97	  NU[f2#(x0,x1,x2,x3,x4,x5,x6,x7)] = x1 - x6
40.24/39.97	
40.24/39.97	This gives the following inequalities:
40.24/39.97	  I80 <= I75  ==>  I75 - I80 > I75 - I80 - 1  with  I75 - I80 >= 0
40.24/39.97	  I99 <= I92  ==>  I93 - I98 - 1 >= I93 - I98 - 1
40.24/39.97	  1 + I100 <= I107  ==>  I101 - I106 - 1 >= I101 - I106 - 1
40.24/39.97	    ==>  I121 - I126 - 1 >= I121 - I126 - 1
40.24/39.97	  I137 = I136 /\ I136 = I136  ==>  I129 - I134 - 1 >= I129 - (1 + I134)
40.24/39.97	
40.24/39.97	We remove all the strictly oriented dependency pairs.
40.24/39.97	
40.24/39.97	DP problem for innermost termination.
40.24/39.97	P =
40.24/39.97	  f4#(I92, I93, I94, I95, I96, I97, I98, I99) -> f3#(I92, I93, I98, I99, I96, I97, I98, I99) [I99 <= I92]
40.24/39.97	  f4#(I100, I101, I102, I103, I104, I105, I106, I107) -> f1#(I100, I101, I106, I107, I104, I105, I106, I107) [1 + I100 <= I107]
40.24/39.97	  f3#(I120, I121, I122, I123, I124, I125, I126, I127) -> f4#(I120, I121, I126, I127, I124, I125, I126, 1 + I127) 
40.24/39.97	  f1#(I128, I129, I130, I131, I132, I133, I134, I135) -> f2#(I128, I129, I134, I135, I136, I133, 1 + I134, I137) [I137 = I136 /\ I136 = I136]
40.24/39.97	R = 
40.24/39.97	  f9(x1, x2, x3, x4, x5, x6, x7, x8) -> f8(x1, x2, x3, x4, x5, x6, x7, x8) 
40.24/39.97	  f8(I0, I1, I2, I3, I4, I5, I6, I7) -> f7(I0, I1, I2, I3, I4, I5, I6, I7) 
40.24/39.97	  f8(I8, I9, I10, I11, I12, I13, I14, I15) -> f2(I8, I9, I10, I11, I12, I13, I14, I15) 
40.24/39.97	  f8(I16, I17, I18, I19, I20, I21, I22, I23) -> f4(I16, I17, I18, I19, I20, I21, I22, I23) 
40.24/39.97	  f8(I24, I25, I26, I27, I28, I29, I30, I31) -> f5(I24, I25, I26, I27, I28, I29, I30, I31) 
40.24/39.97	  f8(I32, I33, I34, I35, I36, I37, I38, I39) -> f3(I32, I33, I34, I35, I36, I37, I38, I39) 
40.24/39.97	  f8(I40, I41, I42, I43, I44, I45, I46, I47) -> f1(I40, I41, I42, I43, I44, I45, I46, I47) 
40.24/39.97	  f8(I48, I49, I50, I51, I52, I53, I54, I55) -> f6(I48, I49, I50, I51, I52, I53, I54, I55) 
40.24/39.97	  f8(I56, I57, I58, I59, I60, I61, I62, I63) -> f7(I56, I57, I62, I63, rnd5, rnd6, rnd7, rnd8) [rnd8 = rnd6 /\ rnd7 = rnd5 /\ rnd6 = rnd6 /\ rnd5 = rnd5]
40.24/39.97	  f7(I64, I65, I66, I67, I68, I69, I70, I71) -> f2(I64, I65, I70, I71, I72, I69, 0, I73) [I73 = I72 /\ I72 = I72]
40.24/39.97	  f2(I74, I75, I76, I77, I78, I79, I80, I81) -> f4(I74, I75, I80, I81, I78, I79, I80, 3) [I80 <= I75]
40.24/39.97	  f2(I82, I83, I84, I85, I86, I87, I88, I89) -> f5(I82, I83, I88, I89, I90, I87, I88, I91) [I91 = I90 /\ 1 + I83 <= I88 /\ I90 = I90]
40.24/39.97	  f4(I92, I93, I94, I95, I96, I97, I98, I99) -> f3(I92, I93, I98, I99, I96, I97, I98, I99) [I99 <= I92]
40.24/39.97	  f4(I100, I101, I102, I103, I104, I105, I106, I107) -> f1(I100, I101, I106, I107, I104, I105, I106, I107) [1 + I100 <= I107]
40.24/39.97	  f5(I108, I109, I110, I111, I112, I113, I114, I115) -> f6(I108, I109, I114, I115, I116, I117, I118, I119) [I119 = I117 /\ I118 = I116 /\ I117 = I117 /\ I116 = I116]
40.24/39.97	  f3(I120, I121, I122, I123, I124, I125, I126, I127) -> f4(I120, I121, I126, I127, I124, I125, I126, 1 + I127) 
40.24/39.97	  f1(I128, I129, I130, I131, I132, I133, I134, I135) -> f2(I128, I129, I134, I135, I136, I133, 1 + I134, I137) [I137 = I136 /\ I136 = I136]
40.24/39.97	
40.24/39.97	The dependency graph for this problem is:
40.24/39.97	  11 -> 13
40.24/39.97	  12 -> 14
40.24/39.97	  13 -> 11, 12
40.24/39.97	  14 -> 
40.24/39.97	Where:
40.24/39.97	  11) f4#(I92, I93, I94, I95, I96, I97, I98, I99) -> f3#(I92, I93, I98, I99, I96, I97, I98, I99) [I99 <= I92]
40.24/39.97	  12) f4#(I100, I101, I102, I103, I104, I105, I106, I107) -> f1#(I100, I101, I106, I107, I104, I105, I106, I107) [1 + I100 <= I107]
40.24/39.97	  13) f3#(I120, I121, I122, I123, I124, I125, I126, I127) -> f4#(I120, I121, I126, I127, I124, I125, I126, 1 + I127) 
40.24/39.97	  14) f1#(I128, I129, I130, I131, I132, I133, I134, I135) -> f2#(I128, I129, I134, I135, I136, I133, 1 + I134, I137) [I137 = I136 /\ I136 = I136]
40.24/39.97	
40.24/39.97	We have the following SCCs.
40.24/39.97	  { 11, 13 }
40.24/39.97	
40.24/39.97	DP problem for innermost termination.
40.24/39.97	P =
40.24/39.97	  f4#(I92, I93, I94, I95, I96, I97, I98, I99) -> f3#(I92, I93, I98, I99, I96, I97, I98, I99) [I99 <= I92]
40.24/39.97	  f3#(I120, I121, I122, I123, I124, I125, I126, I127) -> f4#(I120, I121, I126, I127, I124, I125, I126, 1 + I127) 
40.24/39.97	R = 
40.24/39.97	  f9(x1, x2, x3, x4, x5, x6, x7, x8) -> f8(x1, x2, x3, x4, x5, x6, x7, x8) 
40.24/39.97	  f8(I0, I1, I2, I3, I4, I5, I6, I7) -> f7(I0, I1, I2, I3, I4, I5, I6, I7) 
40.24/39.97	  f8(I8, I9, I10, I11, I12, I13, I14, I15) -> f2(I8, I9, I10, I11, I12, I13, I14, I15) 
40.24/39.97	  f8(I16, I17, I18, I19, I20, I21, I22, I23) -> f4(I16, I17, I18, I19, I20, I21, I22, I23) 
40.24/39.97	  f8(I24, I25, I26, I27, I28, I29, I30, I31) -> f5(I24, I25, I26, I27, I28, I29, I30, I31) 
40.24/39.97	  f8(I32, I33, I34, I35, I36, I37, I38, I39) -> f3(I32, I33, I34, I35, I36, I37, I38, I39) 
40.24/39.97	  f8(I40, I41, I42, I43, I44, I45, I46, I47) -> f1(I40, I41, I42, I43, I44, I45, I46, I47) 
40.24/39.97	  f8(I48, I49, I50, I51, I52, I53, I54, I55) -> f6(I48, I49, I50, I51, I52, I53, I54, I55) 
40.24/39.97	  f8(I56, I57, I58, I59, I60, I61, I62, I63) -> f7(I56, I57, I62, I63, rnd5, rnd6, rnd7, rnd8) [rnd8 = rnd6 /\ rnd7 = rnd5 /\ rnd6 = rnd6 /\ rnd5 = rnd5]
40.24/39.97	  f7(I64, I65, I66, I67, I68, I69, I70, I71) -> f2(I64, I65, I70, I71, I72, I69, 0, I73) [I73 = I72 /\ I72 = I72]
40.24/39.97	  f2(I74, I75, I76, I77, I78, I79, I80, I81) -> f4(I74, I75, I80, I81, I78, I79, I80, 3) [I80 <= I75]
40.24/39.97	  f2(I82, I83, I84, I85, I86, I87, I88, I89) -> f5(I82, I83, I88, I89, I90, I87, I88, I91) [I91 = I90 /\ 1 + I83 <= I88 /\ I90 = I90]
40.24/39.97	  f4(I92, I93, I94, I95, I96, I97, I98, I99) -> f3(I92, I93, I98, I99, I96, I97, I98, I99) [I99 <= I92]
40.24/39.97	  f4(I100, I101, I102, I103, I104, I105, I106, I107) -> f1(I100, I101, I106, I107, I104, I105, I106, I107) [1 + I100 <= I107]
40.24/39.97	  f5(I108, I109, I110, I111, I112, I113, I114, I115) -> f6(I108, I109, I114, I115, I116, I117, I118, I119) [I119 = I117 /\ I118 = I116 /\ I117 = I117 /\ I116 = I116]
40.24/39.97	  f3(I120, I121, I122, I123, I124, I125, I126, I127) -> f4(I120, I121, I126, I127, I124, I125, I126, 1 + I127) 
40.24/39.97	  f1(I128, I129, I130, I131, I132, I133, I134, I135) -> f2(I128, I129, I134, I135, I136, I133, 1 + I134, I137) [I137 = I136 /\ I136 = I136]
40.24/39.97	
40.24/39.97	We use the reverse value criterion with the projection function NU:
40.24/39.97	  NU[f3#(z1,z2,z3,z4,z5,z6,z7,z8)] = z1 + -1 * (1 + z8)
40.24/39.97	  NU[f4#(z1,z2,z3,z4,z5,z6,z7,z8)] = z1 + -1 * z8
40.24/39.97	
40.24/39.97	This gives the following inequalities:
40.24/39.97	  I99 <= I92  ==>  I92 + -1 * I99 > I92 + -1 * (1 + I99)  with  I92 + -1 * I99 >= 0
40.24/39.97	    ==>  I120 + -1 * (1 + I127) >= I120 + -1 * (1 + I127)
40.24/39.97	
40.24/39.97	We remove all the strictly oriented dependency pairs.
40.24/39.97	
40.24/39.97	DP problem for innermost termination.
40.24/39.97	P =
40.24/39.97	  f3#(I120, I121, I122, I123, I124, I125, I126, I127) -> f4#(I120, I121, I126, I127, I124, I125, I126, 1 + I127) 
40.24/39.97	R = 
40.24/39.97	  f9(x1, x2, x3, x4, x5, x6, x7, x8) -> f8(x1, x2, x3, x4, x5, x6, x7, x8) 
40.24/39.97	  f8(I0, I1, I2, I3, I4, I5, I6, I7) -> f7(I0, I1, I2, I3, I4, I5, I6, I7) 
40.24/39.97	  f8(I8, I9, I10, I11, I12, I13, I14, I15) -> f2(I8, I9, I10, I11, I12, I13, I14, I15) 
40.24/39.97	  f8(I16, I17, I18, I19, I20, I21, I22, I23) -> f4(I16, I17, I18, I19, I20, I21, I22, I23) 
40.24/39.97	  f8(I24, I25, I26, I27, I28, I29, I30, I31) -> f5(I24, I25, I26, I27, I28, I29, I30, I31) 
40.24/39.97	  f8(I32, I33, I34, I35, I36, I37, I38, I39) -> f3(I32, I33, I34, I35, I36, I37, I38, I39) 
40.24/39.97	  f8(I40, I41, I42, I43, I44, I45, I46, I47) -> f1(I40, I41, I42, I43, I44, I45, I46, I47) 
40.24/39.97	  f8(I48, I49, I50, I51, I52, I53, I54, I55) -> f6(I48, I49, I50, I51, I52, I53, I54, I55) 
40.24/39.97	  f8(I56, I57, I58, I59, I60, I61, I62, I63) -> f7(I56, I57, I62, I63, rnd5, rnd6, rnd7, rnd8) [rnd8 = rnd6 /\ rnd7 = rnd5 /\ rnd6 = rnd6 /\ rnd5 = rnd5]
40.24/39.97	  f7(I64, I65, I66, I67, I68, I69, I70, I71) -> f2(I64, I65, I70, I71, I72, I69, 0, I73) [I73 = I72 /\ I72 = I72]
40.24/39.97	  f2(I74, I75, I76, I77, I78, I79, I80, I81) -> f4(I74, I75, I80, I81, I78, I79, I80, 3) [I80 <= I75]
40.24/39.97	  f2(I82, I83, I84, I85, I86, I87, I88, I89) -> f5(I82, I83, I88, I89, I90, I87, I88, I91) [I91 = I90 /\ 1 + I83 <= I88 /\ I90 = I90]
40.24/39.97	  f4(I92, I93, I94, I95, I96, I97, I98, I99) -> f3(I92, I93, I98, I99, I96, I97, I98, I99) [I99 <= I92]
40.24/39.97	  f4(I100, I101, I102, I103, I104, I105, I106, I107) -> f1(I100, I101, I106, I107, I104, I105, I106, I107) [1 + I100 <= I107]
40.24/39.97	  f5(I108, I109, I110, I111, I112, I113, I114, I115) -> f6(I108, I109, I114, I115, I116, I117, I118, I119) [I119 = I117 /\ I118 = I116 /\ I117 = I117 /\ I116 = I116]
40.24/39.97	  f3(I120, I121, I122, I123, I124, I125, I126, I127) -> f4(I120, I121, I126, I127, I124, I125, I126, 1 + I127) 
40.24/39.97	  f1(I128, I129, I130, I131, I132, I133, I134, I135) -> f2(I128, I129, I134, I135, I136, I133, 1 + I134, I137) [I137 = I136 /\ I136 = I136]
40.24/39.97	
40.24/39.97	The dependency graph for this problem is:
40.24/39.97	  13 -> 
40.24/39.97	Where:
40.24/39.97	  13) f3#(I120, I121, I122, I123, I124, I125, I126, I127) -> f4#(I120, I121, I126, I127, I124, I125, I126, 1 + I127) 
40.24/39.98	
40.24/39.98	We have the following SCCs.
40.24/39.98	  
40.24/42.95	EOF