21.24/21.45	YES
21.24/21.45	
21.24/21.45	DP problem for innermost termination.
21.24/21.45	P =
21.24/21.45	  f9#(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f7#(x1, x2, x3, x4, x5, x6, x7, x8, x9) 
21.24/21.45	  f7#(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f5#(I0, I1, I2, I3, I4, I5, I6, I7, I8) 
21.24/21.45	  f7#(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f6#(I9, I10, I11, I12, I13, I14, I15, I16, I17) 
21.24/21.45	  f7#(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f4#(I18, I19, I20, I21, I22, I23, I24, I25, I26) 
21.24/21.45	  f7#(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f3#(I27, I28, I29, I30, I31, I32, I33, I34, I35) 
21.24/21.45	  f7#(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f1#(I36, I37, I38, I39, I40, I41, I42, I43, I44) 
21.24/21.45	  f5#(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f6#(I78, I79, I80, I81, I82, I77, I78, I83, I84) [I84 = I82 /\ I83 = I81 /\ I82 = I82 /\ I81 = I81]
21.24/21.45	  f6#(I85, I86, I87, I88, I89, I90, I91, I92, I93) -> f4#(I91, I92, I93, I94, I89, I90, I91, I91, I95) [I95 = I94 /\ I94 = I94]
21.24/21.45	  f4#(I96, I97, I98, I99, I100, I101, I102, I103, I104) -> f3#(I102, I103, I104, I99, I100, I101, I102, I103, -1 + I103) [1 <= -1 + I103]
21.24/21.45	  f4#(I105, I106, I107, I108, I109, I110, I111, I112, I113) -> f1#(I111, I112, I113, I108, I109, I110, I111, I112, -1 + I112) [-1 + I112 <= 0]
21.24/21.45	  f3#(I114, I115, I116, I117, I118, I119, I120, I121, I122) -> f5#(I120, I121, I122, I123, I124, I119, I122, I125, I126) [I126 = I124 /\ I125 = I123 /\ I124 = I124 /\ I123 = I123]
21.24/21.45	  f3#(I127, I128, I129, I130, I131, I132, I133, I134, I135) -> f4#(I133, I134, I135, I136, I131, I132, I133, I135, I137) [I137 = I136 /\ I136 = I136]
21.24/21.45	R = 
21.24/21.45	  f9(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f7(x1, x2, x3, x4, x5, x6, x7, x8, x9) 
21.24/21.45	  f7(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f5(I0, I1, I2, I3, I4, I5, I6, I7, I8) 
21.24/21.45	  f7(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f6(I9, I10, I11, I12, I13, I14, I15, I16, I17) 
21.24/21.45	  f7(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f4(I18, I19, I20, I21, I22, I23, I24, I25, I26) 
21.24/21.45	  f7(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f3(I27, I28, I29, I30, I31, I32, I33, I34, I35) 
21.24/21.45	  f7(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f1(I36, I37, I38, I39, I40, I41, I42, I43, I44) 
21.24/21.45	  f7(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f2(I45, I46, I47, I48, I49, I50, I51, I52, I53) 
21.24/21.45	  f7(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f8(I54, I55, I56, I57, I58, I59, I60, I61, I62) 
21.24/21.45	  f7(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8(I69, I70, I71, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9) [rnd9 = rnd6 /\ rnd8 = rnd5 /\ rnd7 = rnd4 /\ rnd6 = rnd6 /\ rnd5 = rnd5 /\ rnd4 = rnd4]
21.24/21.45	  f5(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f6(I78, I79, I80, I81, I82, I77, I78, I83, I84) [I84 = I82 /\ I83 = I81 /\ I82 = I82 /\ I81 = I81]
21.24/21.45	  f6(I85, I86, I87, I88, I89, I90, I91, I92, I93) -> f4(I91, I92, I93, I94, I89, I90, I91, I91, I95) [I95 = I94 /\ I94 = I94]
21.24/21.45	  f4(I96, I97, I98, I99, I100, I101, I102, I103, I104) -> f3(I102, I103, I104, I99, I100, I101, I102, I103, -1 + I103) [1 <= -1 + I103]
21.24/21.45	  f4(I105, I106, I107, I108, I109, I110, I111, I112, I113) -> f1(I111, I112, I113, I108, I109, I110, I111, I112, -1 + I112) [-1 + I112 <= 0]
21.24/21.45	  f3(I114, I115, I116, I117, I118, I119, I120, I121, I122) -> f5(I120, I121, I122, I123, I124, I119, I122, I125, I126) [I126 = I124 /\ I125 = I123 /\ I124 = I124 /\ I123 = I123]
21.24/21.45	  f3(I127, I128, I129, I130, I131, I132, I133, I134, I135) -> f4(I133, I134, I135, I136, I131, I132, I133, I135, I137) [I137 = I136 /\ I136 = I136]
21.24/21.45	  f1(I138, I139, I140, I141, I142, I143, I144, I145, I146) -> f2(I144, I145, I146, I147, I148, I149, I150, I151, I152) [I152 = I149 /\ I151 = I148 /\ I150 = I147 /\ I149 = I149 /\ I148 = I148 /\ I147 = I147]
21.24/21.45	
21.24/21.45	The dependency graph for this problem is:
21.24/21.45	  0 -> 1, 2, 3, 4, 5
21.24/21.45	  1 -> 6
21.24/21.45	  2 -> 7
21.24/21.45	  3 -> 8, 9
21.24/21.45	  4 -> 10, 11
21.24/21.45	  5 -> 
21.24/21.45	  6 -> 7
21.24/21.45	  7 -> 8, 9
21.24/21.45	  8 -> 10, 11
21.24/21.45	  9 -> 
21.24/21.45	  10 -> 6
21.24/21.45	  11 -> 8, 9
21.24/21.45	Where:
21.24/21.45	  0) f9#(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f7#(x1, x2, x3, x4, x5, x6, x7, x8, x9) 
21.24/21.45	  1) f7#(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f5#(I0, I1, I2, I3, I4, I5, I6, I7, I8) 
21.24/21.45	  2) f7#(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f6#(I9, I10, I11, I12, I13, I14, I15, I16, I17) 
21.24/21.45	  3) f7#(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f4#(I18, I19, I20, I21, I22, I23, I24, I25, I26) 
21.24/21.45	  4) f7#(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f3#(I27, I28, I29, I30, I31, I32, I33, I34, I35) 
21.24/21.45	  5) f7#(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f1#(I36, I37, I38, I39, I40, I41, I42, I43, I44) 
21.24/21.45	  6) f5#(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f6#(I78, I79, I80, I81, I82, I77, I78, I83, I84) [I84 = I82 /\ I83 = I81 /\ I82 = I82 /\ I81 = I81]
21.24/21.45	  7) f6#(I85, I86, I87, I88, I89, I90, I91, I92, I93) -> f4#(I91, I92, I93, I94, I89, I90, I91, I91, I95) [I95 = I94 /\ I94 = I94]
21.24/21.45	  8) f4#(I96, I97, I98, I99, I100, I101, I102, I103, I104) -> f3#(I102, I103, I104, I99, I100, I101, I102, I103, -1 + I103) [1 <= -1 + I103]
21.24/21.45	  9) f4#(I105, I106, I107, I108, I109, I110, I111, I112, I113) -> f1#(I111, I112, I113, I108, I109, I110, I111, I112, -1 + I112) [-1 + I112 <= 0]
21.24/21.45	  10) f3#(I114, I115, I116, I117, I118, I119, I120, I121, I122) -> f5#(I120, I121, I122, I123, I124, I119, I122, I125, I126) [I126 = I124 /\ I125 = I123 /\ I124 = I124 /\ I123 = I123]
21.24/21.45	  11) f3#(I127, I128, I129, I130, I131, I132, I133, I134, I135) -> f4#(I133, I134, I135, I136, I131, I132, I133, I135, I137) [I137 = I136 /\ I136 = I136]
21.24/21.45	
21.24/21.45	We have the following SCCs.
21.24/21.45	  { 6, 7, 8, 10, 11 }
21.24/21.45	
21.24/21.45	DP problem for innermost termination.
21.24/21.45	P =
21.24/21.45	  f5#(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f6#(I78, I79, I80, I81, I82, I77, I78, I83, I84) [I84 = I82 /\ I83 = I81 /\ I82 = I82 /\ I81 = I81]
21.24/21.45	  f6#(I85, I86, I87, I88, I89, I90, I91, I92, I93) -> f4#(I91, I92, I93, I94, I89, I90, I91, I91, I95) [I95 = I94 /\ I94 = I94]
21.24/21.45	  f4#(I96, I97, I98, I99, I100, I101, I102, I103, I104) -> f3#(I102, I103, I104, I99, I100, I101, I102, I103, -1 + I103) [1 <= -1 + I103]
21.24/21.45	  f3#(I114, I115, I116, I117, I118, I119, I120, I121, I122) -> f5#(I120, I121, I122, I123, I124, I119, I122, I125, I126) [I126 = I124 /\ I125 = I123 /\ I124 = I124 /\ I123 = I123]
21.24/21.45	  f3#(I127, I128, I129, I130, I131, I132, I133, I134, I135) -> f4#(I133, I134, I135, I136, I131, I132, I133, I135, I137) [I137 = I136 /\ I136 = I136]
21.24/21.45	R = 
21.24/21.45	  f9(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f7(x1, x2, x3, x4, x5, x6, x7, x8, x9) 
21.24/21.45	  f7(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f5(I0, I1, I2, I3, I4, I5, I6, I7, I8) 
21.24/21.45	  f7(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f6(I9, I10, I11, I12, I13, I14, I15, I16, I17) 
21.24/21.45	  f7(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f4(I18, I19, I20, I21, I22, I23, I24, I25, I26) 
21.24/21.45	  f7(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f3(I27, I28, I29, I30, I31, I32, I33, I34, I35) 
21.24/21.45	  f7(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f1(I36, I37, I38, I39, I40, I41, I42, I43, I44) 
21.24/21.45	  f7(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f2(I45, I46, I47, I48, I49, I50, I51, I52, I53) 
21.24/21.45	  f7(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f8(I54, I55, I56, I57, I58, I59, I60, I61, I62) 
21.24/21.45	  f7(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8(I69, I70, I71, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9) [rnd9 = rnd6 /\ rnd8 = rnd5 /\ rnd7 = rnd4 /\ rnd6 = rnd6 /\ rnd5 = rnd5 /\ rnd4 = rnd4]
21.24/21.45	  f5(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f6(I78, I79, I80, I81, I82, I77, I78, I83, I84) [I84 = I82 /\ I83 = I81 /\ I82 = I82 /\ I81 = I81]
21.24/21.45	  f6(I85, I86, I87, I88, I89, I90, I91, I92, I93) -> f4(I91, I92, I93, I94, I89, I90, I91, I91, I95) [I95 = I94 /\ I94 = I94]
21.24/21.45	  f4(I96, I97, I98, I99, I100, I101, I102, I103, I104) -> f3(I102, I103, I104, I99, I100, I101, I102, I103, -1 + I103) [1 <= -1 + I103]
21.24/21.45	  f4(I105, I106, I107, I108, I109, I110, I111, I112, I113) -> f1(I111, I112, I113, I108, I109, I110, I111, I112, -1 + I112) [-1 + I112 <= 0]
21.24/21.45	  f3(I114, I115, I116, I117, I118, I119, I120, I121, I122) -> f5(I120, I121, I122, I123, I124, I119, I122, I125, I126) [I126 = I124 /\ I125 = I123 /\ I124 = I124 /\ I123 = I123]
21.24/21.45	  f3(I127, I128, I129, I130, I131, I132, I133, I134, I135) -> f4(I133, I134, I135, I136, I131, I132, I133, I135, I137) [I137 = I136 /\ I136 = I136]
21.24/21.45	  f1(I138, I139, I140, I141, I142, I143, I144, I145, I146) -> f2(I144, I145, I146, I147, I148, I149, I150, I151, I152) [I152 = I149 /\ I151 = I148 /\ I150 = I147 /\ I149 = I149 /\ I148 = I148 /\ I147 = I147]
21.24/21.45	
21.24/21.45	We use the basic value criterion with the projection function NU:
21.24/21.45	  NU[f3#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = z9
21.24/21.45	  NU[f4#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = z8
21.24/21.45	  NU[f6#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = z7
21.24/21.45	  NU[f5#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = z7
21.24/21.45	
21.24/21.45	This gives the following inequalities:
21.24/21.45	  I84 = I82 /\ I83 = I81 /\ I82 = I82 /\ I81 = I81  ==>  I78 (>! \union =) I78
21.24/21.45	  I95 = I94 /\ I94 = I94  ==>  I91 (>! \union =) I91
21.24/21.45	  1 <= -1 + I103  ==>  I103 >! -1 + I103
21.24/21.45	  I126 = I124 /\ I125 = I123 /\ I124 = I124 /\ I123 = I123  ==>  I122 (>! \union =) I122
21.24/21.45	  I137 = I136 /\ I136 = I136  ==>  I135 (>! \union =) I135
21.24/21.45	
21.24/21.45	We remove all the strictly oriented dependency pairs.
21.24/21.45	
21.24/21.45	DP problem for innermost termination.
21.24/21.45	P =
21.24/21.45	  f5#(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f6#(I78, I79, I80, I81, I82, I77, I78, I83, I84) [I84 = I82 /\ I83 = I81 /\ I82 = I82 /\ I81 = I81]
21.24/21.45	  f6#(I85, I86, I87, I88, I89, I90, I91, I92, I93) -> f4#(I91, I92, I93, I94, I89, I90, I91, I91, I95) [I95 = I94 /\ I94 = I94]
21.24/21.45	  f3#(I114, I115, I116, I117, I118, I119, I120, I121, I122) -> f5#(I120, I121, I122, I123, I124, I119, I122, I125, I126) [I126 = I124 /\ I125 = I123 /\ I124 = I124 /\ I123 = I123]
21.24/21.45	  f3#(I127, I128, I129, I130, I131, I132, I133, I134, I135) -> f4#(I133, I134, I135, I136, I131, I132, I133, I135, I137) [I137 = I136 /\ I136 = I136]
21.24/21.45	R = 
21.24/21.45	  f9(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f7(x1, x2, x3, x4, x5, x6, x7, x8, x9) 
21.24/21.45	  f7(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f5(I0, I1, I2, I3, I4, I5, I6, I7, I8) 
21.24/21.45	  f7(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f6(I9, I10, I11, I12, I13, I14, I15, I16, I17) 
21.24/21.45	  f7(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f4(I18, I19, I20, I21, I22, I23, I24, I25, I26) 
21.24/21.45	  f7(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f3(I27, I28, I29, I30, I31, I32, I33, I34, I35) 
21.24/21.45	  f7(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f1(I36, I37, I38, I39, I40, I41, I42, I43, I44) 
21.24/21.45	  f7(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f2(I45, I46, I47, I48, I49, I50, I51, I52, I53) 
21.24/21.45	  f7(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f8(I54, I55, I56, I57, I58, I59, I60, I61, I62) 
21.24/21.45	  f7(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8(I69, I70, I71, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9) [rnd9 = rnd6 /\ rnd8 = rnd5 /\ rnd7 = rnd4 /\ rnd6 = rnd6 /\ rnd5 = rnd5 /\ rnd4 = rnd4]
21.24/21.45	  f5(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f6(I78, I79, I80, I81, I82, I77, I78, I83, I84) [I84 = I82 /\ I83 = I81 /\ I82 = I82 /\ I81 = I81]
21.24/21.45	  f6(I85, I86, I87, I88, I89, I90, I91, I92, I93) -> f4(I91, I92, I93, I94, I89, I90, I91, I91, I95) [I95 = I94 /\ I94 = I94]
21.24/21.45	  f4(I96, I97, I98, I99, I100, I101, I102, I103, I104) -> f3(I102, I103, I104, I99, I100, I101, I102, I103, -1 + I103) [1 <= -1 + I103]
21.24/21.45	  f4(I105, I106, I107, I108, I109, I110, I111, I112, I113) -> f1(I111, I112, I113, I108, I109, I110, I111, I112, -1 + I112) [-1 + I112 <= 0]
21.24/21.45	  f3(I114, I115, I116, I117, I118, I119, I120, I121, I122) -> f5(I120, I121, I122, I123, I124, I119, I122, I125, I126) [I126 = I124 /\ I125 = I123 /\ I124 = I124 /\ I123 = I123]
21.24/21.45	  f3(I127, I128, I129, I130, I131, I132, I133, I134, I135) -> f4(I133, I134, I135, I136, I131, I132, I133, I135, I137) [I137 = I136 /\ I136 = I136]
21.24/21.45	  f1(I138, I139, I140, I141, I142, I143, I144, I145, I146) -> f2(I144, I145, I146, I147, I148, I149, I150, I151, I152) [I152 = I149 /\ I151 = I148 /\ I150 = I147 /\ I149 = I149 /\ I148 = I148 /\ I147 = I147]
21.24/21.45	
21.24/21.45	The dependency graph for this problem is:
21.24/21.45	  6 -> 7
21.24/21.45	  7 -> 
21.24/21.45	  10 -> 6
21.24/21.45	  11 -> 
21.24/21.45	Where:
21.24/21.45	  6) f5#(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f6#(I78, I79, I80, I81, I82, I77, I78, I83, I84) [I84 = I82 /\ I83 = I81 /\ I82 = I82 /\ I81 = I81]
21.24/21.45	  7) f6#(I85, I86, I87, I88, I89, I90, I91, I92, I93) -> f4#(I91, I92, I93, I94, I89, I90, I91, I91, I95) [I95 = I94 /\ I94 = I94]
21.24/21.45	  10) f3#(I114, I115, I116, I117, I118, I119, I120, I121, I122) -> f5#(I120, I121, I122, I123, I124, I119, I122, I125, I126) [I126 = I124 /\ I125 = I123 /\ I124 = I124 /\ I123 = I123]
21.24/21.45	  11) f3#(I127, I128, I129, I130, I131, I132, I133, I134, I135) -> f4#(I133, I134, I135, I136, I131, I132, I133, I135, I137) [I137 = I136 /\ I136 = I136]
21.24/21.45	
21.24/21.45	We have the following SCCs.
21.24/21.45	  
21.24/24.43	EOF