15.11/15.21	YES
15.11/15.21	
15.11/15.21	DP problem for innermost termination.
15.11/15.21	P =
15.11/15.21	  f9#(x1, x2, x3, x4, x5, x6) -> f7#(x1, x2, x3, x4, x5, x6) 
15.11/15.21	  f7#(I0, I1, I2, I3, I4, I5) -> f5#(I0, I1, I2, I3, I4, I5) 
15.11/15.21	  f7#(I6, I7, I8, I9, I10, I11) -> f6#(I6, I7, I8, I9, I10, I11) 
15.11/15.21	  f7#(I12, I13, I14, I15, I16, I17) -> f4#(I12, I13, I14, I15, I16, I17) 
15.11/15.21	  f7#(I18, I19, I20, I21, I22, I23) -> f3#(I18, I19, I20, I21, I22, I23) 
15.11/15.21	  f7#(I24, I25, I26, I27, I28, I29) -> f1#(I24, I25, I26, I27, I28, I29) 
15.11/15.21	  f5#(I48, I49, I50, I51, I52, I53) -> f6#(I52, I53, I54, I51, I52, I55) [I55 = I54 /\ I54 = I54]
15.11/15.21	  f6#(I56, I57, I58, I59, I60, I61) -> f4#(I60, I61, I58, I59, I60, -1 + I60) 
15.11/15.21	  f4#(I62, I63, I64, I65, I66, I67) -> f3#(I66, I67, I64, I65, I66, I67) [0 <= I67]
15.11/15.21	  f4#(I68, I69, I70, I71, I72, I73) -> f1#(I72, I73, I70, I71, I72, I73) [1 + I73 <= 0]
15.11/15.21	  f3#(I74, I75, I76, I77, I78, I79) -> f5#(I78, I79, I80, I77, I79, I81) [I81 = I80 /\ I80 = I80]
15.11/15.21	  f3#(I82, I83, I84, I85, I86, I87) -> f4#(I86, I87, I84, I85, I86, -1 + I87) 
15.11/15.21	R = 
15.11/15.21	  f9(x1, x2, x3, x4, x5, x6) -> f7(x1, x2, x3, x4, x5, x6) 
15.11/15.21	  f7(I0, I1, I2, I3, I4, I5) -> f5(I0, I1, I2, I3, I4, I5) 
15.11/15.21	  f7(I6, I7, I8, I9, I10, I11) -> f6(I6, I7, I8, I9, I10, I11) 
15.11/15.21	  f7(I12, I13, I14, I15, I16, I17) -> f4(I12, I13, I14, I15, I16, I17) 
15.11/15.21	  f7(I18, I19, I20, I21, I22, I23) -> f3(I18, I19, I20, I21, I22, I23) 
15.11/15.21	  f7(I24, I25, I26, I27, I28, I29) -> f1(I24, I25, I26, I27, I28, I29) 
15.11/15.21	  f7(I30, I31, I32, I33, I34, I35) -> f2(I30, I31, I32, I33, I34, I35) 
15.11/15.21	  f7(I36, I37, I38, I39, I40, I41) -> f8(I36, I37, I38, I39, I40, I41) 
15.11/15.21	  f7(I42, I43, I44, I45, I46, I47) -> f8(I46, I47, rnd3, rnd4, rnd5, rnd6) [rnd6 = rnd4 /\ rnd5 = rnd3 /\ rnd4 = rnd4 /\ rnd3 = rnd3]
15.11/15.21	  f5(I48, I49, I50, I51, I52, I53) -> f6(I52, I53, I54, I51, I52, I55) [I55 = I54 /\ I54 = I54]
15.11/15.21	  f6(I56, I57, I58, I59, I60, I61) -> f4(I60, I61, I58, I59, I60, -1 + I60) 
15.11/15.21	  f4(I62, I63, I64, I65, I66, I67) -> f3(I66, I67, I64, I65, I66, I67) [0 <= I67]
15.11/15.21	  f4(I68, I69, I70, I71, I72, I73) -> f1(I72, I73, I70, I71, I72, I73) [1 + I73 <= 0]
15.11/15.21	  f3(I74, I75, I76, I77, I78, I79) -> f5(I78, I79, I80, I77, I79, I81) [I81 = I80 /\ I80 = I80]
15.11/15.21	  f3(I82, I83, I84, I85, I86, I87) -> f4(I86, I87, I84, I85, I86, -1 + I87) 
15.11/15.21	  f1(I88, I89, I90, I91, I92, I93) -> f2(I92, I93, I94, I95, I96, I97) [I97 = I95 /\ I96 = I94 /\ I95 = I95 /\ I94 = I94]
15.11/15.21	
15.11/15.21	The dependency graph for this problem is:
15.11/15.21	  0 -> 1, 2, 3, 4, 5
15.11/15.21	  1 -> 6
15.11/15.21	  2 -> 7
15.11/15.21	  3 -> 8, 9
15.11/15.21	  4 -> 10, 11
15.11/15.21	  5 -> 
15.11/15.21	  6 -> 7
15.11/15.21	  7 -> 8, 9
15.11/15.21	  8 -> 10, 11
15.11/15.21	  9 -> 
15.11/15.21	  10 -> 6
15.11/15.21	  11 -> 8, 9
15.11/15.21	Where:
15.11/15.21	  0) f9#(x1, x2, x3, x4, x5, x6) -> f7#(x1, x2, x3, x4, x5, x6) 
15.11/15.21	  1) f7#(I0, I1, I2, I3, I4, I5) -> f5#(I0, I1, I2, I3, I4, I5) 
15.11/15.21	  2) f7#(I6, I7, I8, I9, I10, I11) -> f6#(I6, I7, I8, I9, I10, I11) 
15.11/15.21	  3) f7#(I12, I13, I14, I15, I16, I17) -> f4#(I12, I13, I14, I15, I16, I17) 
15.11/15.21	  4) f7#(I18, I19, I20, I21, I22, I23) -> f3#(I18, I19, I20, I21, I22, I23) 
15.11/15.21	  5) f7#(I24, I25, I26, I27, I28, I29) -> f1#(I24, I25, I26, I27, I28, I29) 
15.11/15.21	  6) f5#(I48, I49, I50, I51, I52, I53) -> f6#(I52, I53, I54, I51, I52, I55) [I55 = I54 /\ I54 = I54]
15.11/15.21	  7) f6#(I56, I57, I58, I59, I60, I61) -> f4#(I60, I61, I58, I59, I60, -1 + I60) 
15.11/15.21	  8) f4#(I62, I63, I64, I65, I66, I67) -> f3#(I66, I67, I64, I65, I66, I67) [0 <= I67]
15.11/15.21	  9) f4#(I68, I69, I70, I71, I72, I73) -> f1#(I72, I73, I70, I71, I72, I73) [1 + I73 <= 0]
15.11/15.21	  10) f3#(I74, I75, I76, I77, I78, I79) -> f5#(I78, I79, I80, I77, I79, I81) [I81 = I80 /\ I80 = I80]
15.11/15.21	  11) f3#(I82, I83, I84, I85, I86, I87) -> f4#(I86, I87, I84, I85, I86, -1 + I87) 
15.11/15.21	
15.11/15.21	We have the following SCCs.
15.11/15.21	  { 6, 7, 8, 10, 11 }
15.11/15.21	
15.11/15.21	DP problem for innermost termination.
15.11/15.21	P =
15.11/15.21	  f5#(I48, I49, I50, I51, I52, I53) -> f6#(I52, I53, I54, I51, I52, I55) [I55 = I54 /\ I54 = I54]
15.11/15.21	  f6#(I56, I57, I58, I59, I60, I61) -> f4#(I60, I61, I58, I59, I60, -1 + I60) 
15.11/15.21	  f4#(I62, I63, I64, I65, I66, I67) -> f3#(I66, I67, I64, I65, I66, I67) [0 <= I67]
15.11/15.21	  f3#(I74, I75, I76, I77, I78, I79) -> f5#(I78, I79, I80, I77, I79, I81) [I81 = I80 /\ I80 = I80]
15.11/15.21	  f3#(I82, I83, I84, I85, I86, I87) -> f4#(I86, I87, I84, I85, I86, -1 + I87) 
15.11/15.21	R = 
15.11/15.21	  f9(x1, x2, x3, x4, x5, x6) -> f7(x1, x2, x3, x4, x5, x6) 
15.11/15.21	  f7(I0, I1, I2, I3, I4, I5) -> f5(I0, I1, I2, I3, I4, I5) 
15.11/15.21	  f7(I6, I7, I8, I9, I10, I11) -> f6(I6, I7, I8, I9, I10, I11) 
15.11/15.21	  f7(I12, I13, I14, I15, I16, I17) -> f4(I12, I13, I14, I15, I16, I17) 
15.11/15.21	  f7(I18, I19, I20, I21, I22, I23) -> f3(I18, I19, I20, I21, I22, I23) 
15.11/15.21	  f7(I24, I25, I26, I27, I28, I29) -> f1(I24, I25, I26, I27, I28, I29) 
15.11/15.21	  f7(I30, I31, I32, I33, I34, I35) -> f2(I30, I31, I32, I33, I34, I35) 
15.11/15.21	  f7(I36, I37, I38, I39, I40, I41) -> f8(I36, I37, I38, I39, I40, I41) 
15.11/15.21	  f7(I42, I43, I44, I45, I46, I47) -> f8(I46, I47, rnd3, rnd4, rnd5, rnd6) [rnd6 = rnd4 /\ rnd5 = rnd3 /\ rnd4 = rnd4 /\ rnd3 = rnd3]
15.11/15.21	  f5(I48, I49, I50, I51, I52, I53) -> f6(I52, I53, I54, I51, I52, I55) [I55 = I54 /\ I54 = I54]
15.11/15.21	  f6(I56, I57, I58, I59, I60, I61) -> f4(I60, I61, I58, I59, I60, -1 + I60) 
15.11/15.21	  f4(I62, I63, I64, I65, I66, I67) -> f3(I66, I67, I64, I65, I66, I67) [0 <= I67]
15.11/15.21	  f4(I68, I69, I70, I71, I72, I73) -> f1(I72, I73, I70, I71, I72, I73) [1 + I73 <= 0]
15.11/15.21	  f3(I74, I75, I76, I77, I78, I79) -> f5(I78, I79, I80, I77, I79, I81) [I81 = I80 /\ I80 = I80]
15.11/15.21	  f3(I82, I83, I84, I85, I86, I87) -> f4(I86, I87, I84, I85, I86, -1 + I87) 
15.11/15.21	  f1(I88, I89, I90, I91, I92, I93) -> f2(I92, I93, I94, I95, I96, I97) [I97 = I95 /\ I96 = I94 /\ I95 = I95 /\ I94 = I94]
15.11/15.21	
15.11/15.21	We use the extended value criterion with the projection function NU:
15.11/15.21	  NU[f3#(x0,x1,x2,x3,x4,x5)] = x5
15.11/15.21	  NU[f4#(x0,x1,x2,x3,x4,x5)] = x5 + 1
15.11/15.21	  NU[f6#(x0,x1,x2,x3,x4,x5)] = x4
15.11/15.21	  NU[f5#(x0,x1,x2,x3,x4,x5)] = x4
15.11/15.21	
15.11/15.21	This gives the following inequalities:
15.11/15.21	  I55 = I54 /\ I54 = I54  ==>  I52 >= I52
15.11/15.21	    ==>  I60 >= (-1 + I60) + 1
15.11/15.21	  0 <= I67  ==>  I67 + 1 > I67  with  I67 + 1 >= 0
15.11/15.21	  I81 = I80 /\ I80 = I80  ==>  I79 >= I79
15.11/15.21	    ==>  I87 >= (-1 + I87) + 1
15.11/15.21	
15.11/15.21	We remove all the strictly oriented dependency pairs.
15.11/15.21	
15.11/15.21	DP problem for innermost termination.
15.11/15.21	P =
15.11/15.21	  f5#(I48, I49, I50, I51, I52, I53) -> f6#(I52, I53, I54, I51, I52, I55) [I55 = I54 /\ I54 = I54]
15.11/15.21	  f6#(I56, I57, I58, I59, I60, I61) -> f4#(I60, I61, I58, I59, I60, -1 + I60) 
15.11/15.21	  f3#(I74, I75, I76, I77, I78, I79) -> f5#(I78, I79, I80, I77, I79, I81) [I81 = I80 /\ I80 = I80]
15.11/15.21	  f3#(I82, I83, I84, I85, I86, I87) -> f4#(I86, I87, I84, I85, I86, -1 + I87) 
15.11/15.21	R = 
15.11/15.21	  f9(x1, x2, x3, x4, x5, x6) -> f7(x1, x2, x3, x4, x5, x6) 
15.11/15.21	  f7(I0, I1, I2, I3, I4, I5) -> f5(I0, I1, I2, I3, I4, I5) 
15.11/15.21	  f7(I6, I7, I8, I9, I10, I11) -> f6(I6, I7, I8, I9, I10, I11) 
15.11/15.21	  f7(I12, I13, I14, I15, I16, I17) -> f4(I12, I13, I14, I15, I16, I17) 
15.11/15.21	  f7(I18, I19, I20, I21, I22, I23) -> f3(I18, I19, I20, I21, I22, I23) 
15.11/15.21	  f7(I24, I25, I26, I27, I28, I29) -> f1(I24, I25, I26, I27, I28, I29) 
15.11/15.21	  f7(I30, I31, I32, I33, I34, I35) -> f2(I30, I31, I32, I33, I34, I35) 
15.11/15.21	  f7(I36, I37, I38, I39, I40, I41) -> f8(I36, I37, I38, I39, I40, I41) 
15.11/15.21	  f7(I42, I43, I44, I45, I46, I47) -> f8(I46, I47, rnd3, rnd4, rnd5, rnd6) [rnd6 = rnd4 /\ rnd5 = rnd3 /\ rnd4 = rnd4 /\ rnd3 = rnd3]
15.11/15.21	  f5(I48, I49, I50, I51, I52, I53) -> f6(I52, I53, I54, I51, I52, I55) [I55 = I54 /\ I54 = I54]
15.11/15.21	  f6(I56, I57, I58, I59, I60, I61) -> f4(I60, I61, I58, I59, I60, -1 + I60) 
15.11/15.21	  f4(I62, I63, I64, I65, I66, I67) -> f3(I66, I67, I64, I65, I66, I67) [0 <= I67]
15.11/15.21	  f4(I68, I69, I70, I71, I72, I73) -> f1(I72, I73, I70, I71, I72, I73) [1 + I73 <= 0]
15.11/15.21	  f3(I74, I75, I76, I77, I78, I79) -> f5(I78, I79, I80, I77, I79, I81) [I81 = I80 /\ I80 = I80]
15.11/15.21	  f3(I82, I83, I84, I85, I86, I87) -> f4(I86, I87, I84, I85, I86, -1 + I87) 
15.11/15.21	  f1(I88, I89, I90, I91, I92, I93) -> f2(I92, I93, I94, I95, I96, I97) [I97 = I95 /\ I96 = I94 /\ I95 = I95 /\ I94 = I94]
15.11/15.21	
15.11/15.21	The dependency graph for this problem is:
15.11/15.21	  6 -> 7
15.11/15.21	  7 -> 
15.11/15.21	  10 -> 6
15.11/15.21	  11 -> 
15.11/15.21	Where:
15.11/15.21	  6) f5#(I48, I49, I50, I51, I52, I53) -> f6#(I52, I53, I54, I51, I52, I55) [I55 = I54 /\ I54 = I54]
15.11/15.21	  7) f6#(I56, I57, I58, I59, I60, I61) -> f4#(I60, I61, I58, I59, I60, -1 + I60) 
15.11/15.21	  10) f3#(I74, I75, I76, I77, I78, I79) -> f5#(I78, I79, I80, I77, I79, I81) [I81 = I80 /\ I80 = I80]
15.11/15.21	  11) f3#(I82, I83, I84, I85, I86, I87) -> f4#(I86, I87, I84, I85, I86, -1 + I87) 
15.11/15.21	
15.11/15.21	We have the following SCCs.
15.11/15.21	  
15.11/18.18	EOF