15.62/15.90	YES
15.62/15.90	
15.62/15.90	DP problem for innermost termination.
15.62/15.90	P =
15.62/15.90	  f7#(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f6#(x1, x2, x3, x4, x5, x6, x7, x8, x9) 
15.62/15.90	  f6#(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f5#(I0, I1, I2, I3, I4, I5, I6, I7, I8) 
15.62/15.90	  f6#(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f3#(I9, I10, I11, I12, I13, I14, I15, I16, I17) 
15.62/15.90	  f6#(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f2#(I18, I19, I20, I21, I22, I23, I24, I25, I26) 
15.62/15.90	  f6#(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f1#(I27, I28, I29, I30, I31, I32, I33, I34, I35) 
15.62/15.90	  f6#(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f5#(I51, I52, I53, rnd4, I49, I50, I51, I52, rnd9) [rnd9 = rnd4 /\ rnd4 = rnd4]
15.62/15.90	  f5#(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f3#(I60, I61, I62, I63, I58, I59, I60, I61, I64) [I64 = I63 /\ 0 <= I60 /\ I60 <= 0 /\ I63 = I63]
15.62/15.90	  f5#(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f2#(I71, I72, I73, I68, I69, I70, I71, I72, I71) [1 + I71 <= 0]
15.62/15.90	  f5#(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f2#(I80, I81, I82, I77, I78, I79, I80, I81, I80) [1 <= I80]
15.62/15.90	  f2#(I94, I95, I96, I97, I98, I99, I100, I101, I102) -> f1#(I100, I101, I102, I97, I98, I99, I100, I101, I102) [1 <= I101 /\ 1 <= I102]
15.62/15.90	  f2#(I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f3#(I109, I110, I111, I112, I107, I108, I109, I110, I113) [I113 = I112 /\ I111 <= 0 /\ I112 = I112]
15.62/15.90	  f2#(I114, I115, I116, I117, I118, I119, I120, I121, I122) -> f3#(I120, I121, I122, I123, I118, I119, I120, I121, I124) [I124 = I123 /\ I121 <= 0 /\ I123 = I123]
15.62/15.90	  f1#(I125, I126, I127, I128, I129, I130, I131, I132, I133) -> f2#(I131, I132, I133, I128, I129, I130, I131, I132, -1 * I132 + I133) 
15.62/15.90	R = 
15.62/15.90	  f7(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f6(x1, x2, x3, x4, x5, x6, x7, x8, x9) 
15.62/15.90	  f6(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f5(I0, I1, I2, I3, I4, I5, I6, I7, I8) 
15.62/15.90	  f6(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f3(I9, I10, I11, I12, I13, I14, I15, I16, I17) 
15.62/15.90	  f6(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f2(I18, I19, I20, I21, I22, I23, I24, I25, I26) 
15.62/15.90	  f6(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f1(I27, I28, I29, I30, I31, I32, I33, I34, I35) 
15.62/15.90	  f6(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f4(I36, I37, I38, I39, I40, I41, I42, I43, I44) 
15.62/15.90	  f6(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f5(I51, I52, I53, rnd4, I49, I50, I51, I52, rnd9) [rnd9 = rnd4 /\ rnd4 = rnd4]
15.62/15.90	  f5(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f3(I60, I61, I62, I63, I58, I59, I60, I61, I64) [I64 = I63 /\ 0 <= I60 /\ I60 <= 0 /\ I63 = I63]
15.62/15.90	  f5(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f2(I71, I72, I73, I68, I69, I70, I71, I72, I71) [1 + I71 <= 0]
15.62/15.90	  f5(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f2(I80, I81, I82, I77, I78, I79, I80, I81, I80) [1 <= I80]
15.62/15.90	  f3(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f4(I89, I90, I91, I92, rnd5, rnd6, rnd7, rnd8, I93) [I93 = rnd6 /\ rnd8 = rnd5 /\ rnd7 = I92 /\ rnd6 = rnd6 /\ rnd5 = rnd5 /\ I92 = I92]
15.62/15.90	  f2(I94, I95, I96, I97, I98, I99, I100, I101, I102) -> f1(I100, I101, I102, I97, I98, I99, I100, I101, I102) [1 <= I101 /\ 1 <= I102]
15.62/15.90	  f2(I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f3(I109, I110, I111, I112, I107, I108, I109, I110, I113) [I113 = I112 /\ I111 <= 0 /\ I112 = I112]
15.62/15.90	  f2(I114, I115, I116, I117, I118, I119, I120, I121, I122) -> f3(I120, I121, I122, I123, I118, I119, I120, I121, I124) [I124 = I123 /\ I121 <= 0 /\ I123 = I123]
15.62/15.90	  f1(I125, I126, I127, I128, I129, I130, I131, I132, I133) -> f2(I131, I132, I133, I128, I129, I130, I131, I132, -1 * I132 + I133) 
15.62/15.90	
15.62/15.90	The dependency graph for this problem is:
15.62/15.90	  0 -> 1, 2, 3, 4, 5
15.62/15.90	  1 -> 6, 7, 8
15.62/15.90	  2 -> 
15.62/15.90	  3 -> 9, 10, 11
15.62/15.90	  4 -> 12
15.62/15.90	  5 -> 6, 7, 8
15.62/15.90	  6 -> 
15.62/15.90	  7 -> 10, 11
15.62/15.90	  8 -> 9, 11
15.62/15.90	  9 -> 12
15.62/15.90	  10 -> 
15.62/15.90	  11 -> 
15.62/15.90	  12 -> 9, 10, 11
15.62/15.90	Where:
15.62/15.90	  0) f7#(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f6#(x1, x2, x3, x4, x5, x6, x7, x8, x9) 
15.62/15.90	  1) f6#(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f5#(I0, I1, I2, I3, I4, I5, I6, I7, I8) 
15.62/15.90	  2) f6#(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f3#(I9, I10, I11, I12, I13, I14, I15, I16, I17) 
15.62/15.90	  3) f6#(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f2#(I18, I19, I20, I21, I22, I23, I24, I25, I26) 
15.62/15.90	  4) f6#(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f1#(I27, I28, I29, I30, I31, I32, I33, I34, I35) 
15.62/15.90	  5) f6#(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f5#(I51, I52, I53, rnd4, I49, I50, I51, I52, rnd9) [rnd9 = rnd4 /\ rnd4 = rnd4]
15.62/15.90	  6) f5#(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f3#(I60, I61, I62, I63, I58, I59, I60, I61, I64) [I64 = I63 /\ 0 <= I60 /\ I60 <= 0 /\ I63 = I63]
15.62/15.90	  7) f5#(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f2#(I71, I72, I73, I68, I69, I70, I71, I72, I71) [1 + I71 <= 0]
15.62/15.90	  8) f5#(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f2#(I80, I81, I82, I77, I78, I79, I80, I81, I80) [1 <= I80]
15.62/15.90	  9) f2#(I94, I95, I96, I97, I98, I99, I100, I101, I102) -> f1#(I100, I101, I102, I97, I98, I99, I100, I101, I102) [1 <= I101 /\ 1 <= I102]
15.62/15.90	  10) f2#(I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f3#(I109, I110, I111, I112, I107, I108, I109, I110, I113) [I113 = I112 /\ I111 <= 0 /\ I112 = I112]
15.62/15.90	  11) f2#(I114, I115, I116, I117, I118, I119, I120, I121, I122) -> f3#(I120, I121, I122, I123, I118, I119, I120, I121, I124) [I124 = I123 /\ I121 <= 0 /\ I123 = I123]
15.62/15.90	  12) f1#(I125, I126, I127, I128, I129, I130, I131, I132, I133) -> f2#(I131, I132, I133, I128, I129, I130, I131, I132, -1 * I132 + I133) 
15.62/15.90	
15.62/15.90	We have the following SCCs.
15.62/15.90	  { 9, 12 }
15.62/15.90	
15.62/15.90	DP problem for innermost termination.
15.62/15.90	P =
15.62/15.90	  f2#(I94, I95, I96, I97, I98, I99, I100, I101, I102) -> f1#(I100, I101, I102, I97, I98, I99, I100, I101, I102) [1 <= I101 /\ 1 <= I102]
15.62/15.90	  f1#(I125, I126, I127, I128, I129, I130, I131, I132, I133) -> f2#(I131, I132, I133, I128, I129, I130, I131, I132, -1 * I132 + I133) 
15.62/15.90	R = 
15.62/15.90	  f7(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f6(x1, x2, x3, x4, x5, x6, x7, x8, x9) 
15.62/15.90	  f6(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f5(I0, I1, I2, I3, I4, I5, I6, I7, I8) 
15.62/15.90	  f6(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f3(I9, I10, I11, I12, I13, I14, I15, I16, I17) 
15.62/15.90	  f6(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f2(I18, I19, I20, I21, I22, I23, I24, I25, I26) 
15.62/15.90	  f6(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f1(I27, I28, I29, I30, I31, I32, I33, I34, I35) 
15.62/15.90	  f6(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f4(I36, I37, I38, I39, I40, I41, I42, I43, I44) 
15.62/15.90	  f6(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f5(I51, I52, I53, rnd4, I49, I50, I51, I52, rnd9) [rnd9 = rnd4 /\ rnd4 = rnd4]
15.62/15.90	  f5(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f3(I60, I61, I62, I63, I58, I59, I60, I61, I64) [I64 = I63 /\ 0 <= I60 /\ I60 <= 0 /\ I63 = I63]
15.62/15.90	  f5(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f2(I71, I72, I73, I68, I69, I70, I71, I72, I71) [1 + I71 <= 0]
15.62/15.90	  f5(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f2(I80, I81, I82, I77, I78, I79, I80, I81, I80) [1 <= I80]
15.62/15.90	  f3(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f4(I89, I90, I91, I92, rnd5, rnd6, rnd7, rnd8, I93) [I93 = rnd6 /\ rnd8 = rnd5 /\ rnd7 = I92 /\ rnd6 = rnd6 /\ rnd5 = rnd5 /\ I92 = I92]
15.62/15.90	  f2(I94, I95, I96, I97, I98, I99, I100, I101, I102) -> f1(I100, I101, I102, I97, I98, I99, I100, I101, I102) [1 <= I101 /\ 1 <= I102]
15.62/15.90	  f2(I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f3(I109, I110, I111, I112, I107, I108, I109, I110, I113) [I113 = I112 /\ I111 <= 0 /\ I112 = I112]
15.62/15.90	  f2(I114, I115, I116, I117, I118, I119, I120, I121, I122) -> f3(I120, I121, I122, I123, I118, I119, I120, I121, I124) [I124 = I123 /\ I121 <= 0 /\ I123 = I123]
15.62/15.90	  f1(I125, I126, I127, I128, I129, I130, I131, I132, I133) -> f2(I131, I132, I133, I128, I129, I130, I131, I132, -1 * I132 + I133) 
15.62/15.90	
15.62/15.90	We use the reverse value criterion with the projection function NU:
15.62/15.90	  NU[f1#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = -1 * z8 + z9 + -1 * 1
15.62/15.90	  NU[f2#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = z9 + -1 * 1
15.62/15.90	
15.62/15.90	This gives the following inequalities:
15.62/15.90	  1 <= I101 /\ 1 <= I102  ==>  I102 + -1 * 1 > -1 * I101 + I102 + -1 * 1  with  I102 + -1 * 1 >= 0
15.62/15.90	    ==>  -1 * I132 + I133 + -1 * 1 >= -1 * I132 + I133 + -1 * 1
15.62/15.90	
15.62/15.90	We remove all the strictly oriented dependency pairs.
15.62/15.90	
15.62/15.90	DP problem for innermost termination.
15.62/15.90	P =
15.62/15.90	  f1#(I125, I126, I127, I128, I129, I130, I131, I132, I133) -> f2#(I131, I132, I133, I128, I129, I130, I131, I132, -1 * I132 + I133) 
15.62/15.90	R = 
15.62/15.90	  f7(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f6(x1, x2, x3, x4, x5, x6, x7, x8, x9) 
15.62/15.90	  f6(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f5(I0, I1, I2, I3, I4, I5, I6, I7, I8) 
15.62/15.90	  f6(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f3(I9, I10, I11, I12, I13, I14, I15, I16, I17) 
15.62/15.90	  f6(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f2(I18, I19, I20, I21, I22, I23, I24, I25, I26) 
15.62/15.90	  f6(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f1(I27, I28, I29, I30, I31, I32, I33, I34, I35) 
15.62/15.90	  f6(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f4(I36, I37, I38, I39, I40, I41, I42, I43, I44) 
15.62/15.90	  f6(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f5(I51, I52, I53, rnd4, I49, I50, I51, I52, rnd9) [rnd9 = rnd4 /\ rnd4 = rnd4]
15.62/15.90	  f5(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f3(I60, I61, I62, I63, I58, I59, I60, I61, I64) [I64 = I63 /\ 0 <= I60 /\ I60 <= 0 /\ I63 = I63]
15.62/15.90	  f5(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f2(I71, I72, I73, I68, I69, I70, I71, I72, I71) [1 + I71 <= 0]
15.62/15.90	  f5(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f2(I80, I81, I82, I77, I78, I79, I80, I81, I80) [1 <= I80]
15.62/15.90	  f3(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f4(I89, I90, I91, I92, rnd5, rnd6, rnd7, rnd8, I93) [I93 = rnd6 /\ rnd8 = rnd5 /\ rnd7 = I92 /\ rnd6 = rnd6 /\ rnd5 = rnd5 /\ I92 = I92]
15.62/15.90	  f2(I94, I95, I96, I97, I98, I99, I100, I101, I102) -> f1(I100, I101, I102, I97, I98, I99, I100, I101, I102) [1 <= I101 /\ 1 <= I102]
15.62/15.90	  f2(I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f3(I109, I110, I111, I112, I107, I108, I109, I110, I113) [I113 = I112 /\ I111 <= 0 /\ I112 = I112]
15.62/15.90	  f2(I114, I115, I116, I117, I118, I119, I120, I121, I122) -> f3(I120, I121, I122, I123, I118, I119, I120, I121, I124) [I124 = I123 /\ I121 <= 0 /\ I123 = I123]
15.62/15.90	  f1(I125, I126, I127, I128, I129, I130, I131, I132, I133) -> f2(I131, I132, I133, I128, I129, I130, I131, I132, -1 * I132 + I133) 
15.62/15.90	
15.62/15.90	The dependency graph for this problem is:
15.62/15.90	  12 -> 
15.62/15.90	Where:
15.62/15.90	  12) f1#(I125, I126, I127, I128, I129, I130, I131, I132, I133) -> f2#(I131, I132, I133, I128, I129, I130, I131, I132, -1 * I132 + I133) 
15.62/15.90	
15.62/15.90	We have the following SCCs.
15.62/15.90	  
15.62/18.87	EOF