14.83/14.73	YES
14.83/14.73	
14.83/14.73	DP problem for innermost termination.
14.83/14.73	P =
14.83/14.73	  f7#(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f6#(x1, x2, x3, x4, x5, x6, x7, x8, x9) 
14.83/14.73	  f6#(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f5#(I0, I1, I2, I3, I4, I5, I6, I7, I8) 
14.83/14.73	  f6#(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f4#(I9, I10, I11, I12, I13, I14, I15, I16, I17) 
14.83/14.73	  f6#(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f3#(I18, I19, I20, I21, I22, I23, I24, I25, I26) 
14.83/14.73	  f6#(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f1#(I27, I28, I29, I30, I31, I32, I33, I34, I35) 
14.83/14.73	  f6#(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f5#(I51, I52, I53, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9) [rnd9 = rnd6 /\ rnd8 = rnd5 /\ rnd7 = rnd4 /\ rnd6 = rnd6 /\ rnd5 = rnd5 /\ rnd4 = rnd4]
14.83/14.73	  f5#(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f4#(I60, I61, I62, I63, I64, I59, I65, I66, 0) [I66 = I64 /\ I65 = I63 /\ I64 = I64 /\ I63 = I63]
14.83/14.73	  f4#(I67, I68, I69, I70, I71, I72, I73, I74, I75) -> f3#(I73, I74, I75, I70, I71, I72, I73, I74, I75) [I74 <= -1 + I73 /\ -1 + I73 <= I74 /\ I73 <= I74]
14.83/14.73	  f4#(I76, I77, I78, I79, I80, I81, I82, I83, I84) -> f1#(I82, I83, I84, I79, I80, I81, I82, I83, I84) [I82 <= I83 /\ I82 <= I83]
14.83/14.73	  f4#(I85, I86, I87, I88, I89, I90, I91, I92, I93) -> f1#(I91, I92, I93, I88, I89, I90, I91, I92, I93) [1 + I92 <= -1 + I91 /\ I91 <= I92]
14.83/14.73	  f4#(I94, I95, I96, I97, I98, I99, I100, I101, I102) -> f3#(I100, I101, I102, I97, I98, I99, I100, I101, I102) [I101 <= I101 /\ I101 <= I101 /\ I101 <= -1 + I100]
14.83/14.73	  f4#(I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f1#(I109, I110, I111, I106, I107, I108, I109, I110, I111) [1 + I110 <= I110 /\ I110 <= -1 + I109]
14.83/14.73	  f4#(I112, I113, I114, I115, I116, I117, I118, I119, I120) -> f1#(I118, I119, I120, I115, I116, I117, I118, I119, I120) [1 + I119 <= I119 /\ I119 <= -1 + I118]
14.83/14.73	  f3#(I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f4#(I127, I128, I129, I124, I125, I126, I127, 1 + I128, 1 + I129) 
14.83/14.73	R = 
14.83/14.73	  f7(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f6(x1, x2, x3, x4, x5, x6, x7, x8, x9) 
14.83/14.73	  f6(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f5(I0, I1, I2, I3, I4, I5, I6, I7, I8) 
14.83/14.73	  f6(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f4(I9, I10, I11, I12, I13, I14, I15, I16, I17) 
14.83/14.73	  f6(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f3(I18, I19, I20, I21, I22, I23, I24, I25, I26) 
14.83/14.73	  f6(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f1(I27, I28, I29, I30, I31, I32, I33, I34, I35) 
14.83/14.73	  f6(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f2(I36, I37, I38, I39, I40, I41, I42, I43, I44) 
14.83/14.73	  f6(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f5(I51, I52, I53, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9) [rnd9 = rnd6 /\ rnd8 = rnd5 /\ rnd7 = rnd4 /\ rnd6 = rnd6 /\ rnd5 = rnd5 /\ rnd4 = rnd4]
14.83/14.73	  f5(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f4(I60, I61, I62, I63, I64, I59, I65, I66, 0) [I66 = I64 /\ I65 = I63 /\ I64 = I64 /\ I63 = I63]
14.83/14.73	  f4(I67, I68, I69, I70, I71, I72, I73, I74, I75) -> f3(I73, I74, I75, I70, I71, I72, I73, I74, I75) [I74 <= -1 + I73 /\ -1 + I73 <= I74 /\ I73 <= I74]
14.83/14.73	  f4(I76, I77, I78, I79, I80, I81, I82, I83, I84) -> f1(I82, I83, I84, I79, I80, I81, I82, I83, I84) [I82 <= I83 /\ I82 <= I83]
14.83/14.73	  f4(I85, I86, I87, I88, I89, I90, I91, I92, I93) -> f1(I91, I92, I93, I88, I89, I90, I91, I92, I93) [1 + I92 <= -1 + I91 /\ I91 <= I92]
14.83/14.73	  f4(I94, I95, I96, I97, I98, I99, I100, I101, I102) -> f3(I100, I101, I102, I97, I98, I99, I100, I101, I102) [I101 <= I101 /\ I101 <= I101 /\ I101 <= -1 + I100]
14.83/14.73	  f4(I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f1(I109, I110, I111, I106, I107, I108, I109, I110, I111) [1 + I110 <= I110 /\ I110 <= -1 + I109]
14.83/14.73	  f4(I112, I113, I114, I115, I116, I117, I118, I119, I120) -> f1(I118, I119, I120, I115, I116, I117, I118, I119, I120) [1 + I119 <= I119 /\ I119 <= -1 + I118]
14.83/14.73	  f3(I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f4(I127, I128, I129, I124, I125, I126, I127, 1 + I128, 1 + I129) 
14.83/14.73	  f1(I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f2(I136, I137, I138, I139, I140, I141, I142, I143, I144) [I144 = I141 /\ I143 = I140 /\ I142 = I139 /\ I141 = I141 /\ I140 = I140 /\ I139 = I139]
14.83/14.73	
14.83/14.73	The dependency graph for this problem is:
14.83/14.73	  0 -> 1, 2, 3, 4, 5
14.83/14.73	  1 -> 6
14.83/14.73	  2 -> 8, 10
14.83/14.73	  3 -> 13
14.83/14.73	  4 -> 
14.83/14.73	  5 -> 6
14.83/14.73	  6 -> 8, 10
14.83/14.73	  7 -> 
14.83/14.73	  8 -> 
14.83/14.73	  9 -> 
14.83/14.73	  10 -> 13
14.83/14.73	  11 -> 
14.83/14.73	  12 -> 
14.83/14.73	  13 -> 8, 10
14.83/14.73	Where:
14.83/14.73	  0) f7#(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f6#(x1, x2, x3, x4, x5, x6, x7, x8, x9) 
14.83/14.73	  1) f6#(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f5#(I0, I1, I2, I3, I4, I5, I6, I7, I8) 
14.83/14.73	  2) f6#(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f4#(I9, I10, I11, I12, I13, I14, I15, I16, I17) 
14.83/14.73	  3) f6#(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f3#(I18, I19, I20, I21, I22, I23, I24, I25, I26) 
14.83/14.73	  4) f6#(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f1#(I27, I28, I29, I30, I31, I32, I33, I34, I35) 
14.83/14.73	  5) f6#(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f5#(I51, I52, I53, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9) [rnd9 = rnd6 /\ rnd8 = rnd5 /\ rnd7 = rnd4 /\ rnd6 = rnd6 /\ rnd5 = rnd5 /\ rnd4 = rnd4]
14.83/14.73	  6) f5#(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f4#(I60, I61, I62, I63, I64, I59, I65, I66, 0) [I66 = I64 /\ I65 = I63 /\ I64 = I64 /\ I63 = I63]
14.83/14.73	  7) f4#(I67, I68, I69, I70, I71, I72, I73, I74, I75) -> f3#(I73, I74, I75, I70, I71, I72, I73, I74, I75) [I74 <= -1 + I73 /\ -1 + I73 <= I74 /\ I73 <= I74]
14.83/14.73	  8) f4#(I76, I77, I78, I79, I80, I81, I82, I83, I84) -> f1#(I82, I83, I84, I79, I80, I81, I82, I83, I84) [I82 <= I83 /\ I82 <= I83]
14.83/14.73	  9) f4#(I85, I86, I87, I88, I89, I90, I91, I92, I93) -> f1#(I91, I92, I93, I88, I89, I90, I91, I92, I93) [1 + I92 <= -1 + I91 /\ I91 <= I92]
14.83/14.73	  10) f4#(I94, I95, I96, I97, I98, I99, I100, I101, I102) -> f3#(I100, I101, I102, I97, I98, I99, I100, I101, I102) [I101 <= I101 /\ I101 <= I101 /\ I101 <= -1 + I100]
14.83/14.73	  11) f4#(I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f1#(I109, I110, I111, I106, I107, I108, I109, I110, I111) [1 + I110 <= I110 /\ I110 <= -1 + I109]
14.83/14.73	  12) f4#(I112, I113, I114, I115, I116, I117, I118, I119, I120) -> f1#(I118, I119, I120, I115, I116, I117, I118, I119, I120) [1 + I119 <= I119 /\ I119 <= -1 + I118]
14.83/14.73	  13) f3#(I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f4#(I127, I128, I129, I124, I125, I126, I127, 1 + I128, 1 + I129) 
14.83/14.73	
14.83/14.73	We have the following SCCs.
14.83/14.73	  { 10, 13 }
14.83/14.73	
14.83/14.73	DP problem for innermost termination.
14.83/14.73	P =
14.83/14.73	  f4#(I94, I95, I96, I97, I98, I99, I100, I101, I102) -> f3#(I100, I101, I102, I97, I98, I99, I100, I101, I102) [I101 <= I101 /\ I101 <= I101 /\ I101 <= -1 + I100]
14.83/14.73	  f3#(I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f4#(I127, I128, I129, I124, I125, I126, I127, 1 + I128, 1 + I129) 
14.83/14.73	R = 
14.83/14.73	  f7(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f6(x1, x2, x3, x4, x5, x6, x7, x8, x9) 
14.83/14.73	  f6(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f5(I0, I1, I2, I3, I4, I5, I6, I7, I8) 
14.83/14.73	  f6(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f4(I9, I10, I11, I12, I13, I14, I15, I16, I17) 
14.83/14.73	  f6(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f3(I18, I19, I20, I21, I22, I23, I24, I25, I26) 
14.83/14.73	  f6(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f1(I27, I28, I29, I30, I31, I32, I33, I34, I35) 
14.83/14.73	  f6(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f2(I36, I37, I38, I39, I40, I41, I42, I43, I44) 
14.83/14.73	  f6(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f5(I51, I52, I53, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9) [rnd9 = rnd6 /\ rnd8 = rnd5 /\ rnd7 = rnd4 /\ rnd6 = rnd6 /\ rnd5 = rnd5 /\ rnd4 = rnd4]
14.83/14.73	  f5(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f4(I60, I61, I62, I63, I64, I59, I65, I66, 0) [I66 = I64 /\ I65 = I63 /\ I64 = I64 /\ I63 = I63]
14.83/14.73	  f4(I67, I68, I69, I70, I71, I72, I73, I74, I75) -> f3(I73, I74, I75, I70, I71, I72, I73, I74, I75) [I74 <= -1 + I73 /\ -1 + I73 <= I74 /\ I73 <= I74]
14.83/14.73	  f4(I76, I77, I78, I79, I80, I81, I82, I83, I84) -> f1(I82, I83, I84, I79, I80, I81, I82, I83, I84) [I82 <= I83 /\ I82 <= I83]
14.83/14.73	  f4(I85, I86, I87, I88, I89, I90, I91, I92, I93) -> f1(I91, I92, I93, I88, I89, I90, I91, I92, I93) [1 + I92 <= -1 + I91 /\ I91 <= I92]
14.83/14.73	  f4(I94, I95, I96, I97, I98, I99, I100, I101, I102) -> f3(I100, I101, I102, I97, I98, I99, I100, I101, I102) [I101 <= I101 /\ I101 <= I101 /\ I101 <= -1 + I100]
14.83/14.73	  f4(I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f1(I109, I110, I111, I106, I107, I108, I109, I110, I111) [1 + I110 <= I110 /\ I110 <= -1 + I109]
14.83/14.73	  f4(I112, I113, I114, I115, I116, I117, I118, I119, I120) -> f1(I118, I119, I120, I115, I116, I117, I118, I119, I120) [1 + I119 <= I119 /\ I119 <= -1 + I118]
14.83/14.73	  f3(I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f4(I127, I128, I129, I124, I125, I126, I127, 1 + I128, 1 + I129) 
14.83/14.73	  f1(I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f2(I136, I137, I138, I139, I140, I141, I142, I143, I144) [I144 = I141 /\ I143 = I140 /\ I142 = I139 /\ I141 = I141 /\ I140 = I140 /\ I139 = I139]
14.83/14.73	
14.83/14.73	We use the reverse value criterion with the projection function NU:
14.83/14.73	  NU[f3#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = -1 + z7 + -1 * (1 + z8)
14.83/14.73	  NU[f4#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = -1 + z7 + -1 * z8
14.83/14.73	
14.83/14.73	This gives the following inequalities:
14.83/14.73	  I101 <= I101 /\ I101 <= I101 /\ I101 <= -1 + I100  ==>  -1 + I100 + -1 * I101 > -1 + I100 + -1 * (1 + I101)  with  -1 + I100 + -1 * I101 >= 0
14.83/14.73	    ==>  -1 + I127 + -1 * (1 + I128) >= -1 + I127 + -1 * (1 + I128)
14.83/14.73	
14.83/14.73	We remove all the strictly oriented dependency pairs.
14.83/14.73	
14.83/14.73	DP problem for innermost termination.
14.83/14.73	P =
14.83/14.73	  f3#(I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f4#(I127, I128, I129, I124, I125, I126, I127, 1 + I128, 1 + I129) 
14.83/14.73	R = 
14.83/14.73	  f7(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f6(x1, x2, x3, x4, x5, x6, x7, x8, x9) 
14.83/14.73	  f6(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f5(I0, I1, I2, I3, I4, I5, I6, I7, I8) 
14.83/14.73	  f6(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f4(I9, I10, I11, I12, I13, I14, I15, I16, I17) 
14.83/14.73	  f6(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f3(I18, I19, I20, I21, I22, I23, I24, I25, I26) 
14.83/14.73	  f6(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f1(I27, I28, I29, I30, I31, I32, I33, I34, I35) 
14.83/14.73	  f6(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f2(I36, I37, I38, I39, I40, I41, I42, I43, I44) 
14.83/14.73	  f6(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f5(I51, I52, I53, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9) [rnd9 = rnd6 /\ rnd8 = rnd5 /\ rnd7 = rnd4 /\ rnd6 = rnd6 /\ rnd5 = rnd5 /\ rnd4 = rnd4]
14.83/14.73	  f5(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f4(I60, I61, I62, I63, I64, I59, I65, I66, 0) [I66 = I64 /\ I65 = I63 /\ I64 = I64 /\ I63 = I63]
14.83/14.73	  f4(I67, I68, I69, I70, I71, I72, I73, I74, I75) -> f3(I73, I74, I75, I70, I71, I72, I73, I74, I75) [I74 <= -1 + I73 /\ -1 + I73 <= I74 /\ I73 <= I74]
14.83/14.73	  f4(I76, I77, I78, I79, I80, I81, I82, I83, I84) -> f1(I82, I83, I84, I79, I80, I81, I82, I83, I84) [I82 <= I83 /\ I82 <= I83]
14.83/14.73	  f4(I85, I86, I87, I88, I89, I90, I91, I92, I93) -> f1(I91, I92, I93, I88, I89, I90, I91, I92, I93) [1 + I92 <= -1 + I91 /\ I91 <= I92]
14.83/14.73	  f4(I94, I95, I96, I97, I98, I99, I100, I101, I102) -> f3(I100, I101, I102, I97, I98, I99, I100, I101, I102) [I101 <= I101 /\ I101 <= I101 /\ I101 <= -1 + I100]
14.83/14.73	  f4(I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f1(I109, I110, I111, I106, I107, I108, I109, I110, I111) [1 + I110 <= I110 /\ I110 <= -1 + I109]
14.83/14.73	  f4(I112, I113, I114, I115, I116, I117, I118, I119, I120) -> f1(I118, I119, I120, I115, I116, I117, I118, I119, I120) [1 + I119 <= I119 /\ I119 <= -1 + I118]
14.83/14.73	  f3(I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f4(I127, I128, I129, I124, I125, I126, I127, 1 + I128, 1 + I129) 
14.83/14.73	  f1(I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f2(I136, I137, I138, I139, I140, I141, I142, I143, I144) [I144 = I141 /\ I143 = I140 /\ I142 = I139 /\ I141 = I141 /\ I140 = I140 /\ I139 = I139]
14.83/14.73	
14.83/14.73	The dependency graph for this problem is:
14.83/14.73	  13 -> 
14.83/14.73	Where:
14.83/14.73	  13) f3#(I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f4#(I127, I128, I129, I124, I125, I126, I127, 1 + I128, 1 + I129) 
14.83/14.73	
14.83/14.73	We have the following SCCs.
14.83/14.73	  
14.83/17.70	EOF