10.08/10.26	YES
10.08/10.26	
10.08/10.26	DP problem for innermost termination.
10.08/10.26	P =
10.08/10.26	  f7#(x1, x2, x3, x4, x5, x6) -> f6#(x1, x2, x3, x4, x5, x6) 
10.08/10.26	  f6#(I0, I1, I2, I3, I4, I5) -> f3#(I0, I1, I2, I3, I4, I5) 
10.08/10.26	  f6#(I6, I7, I8, I9, I10, I11) -> f5#(I6, I7, I8, I9, I10, I11) 
10.08/10.26	  f6#(I12, I13, I14, I15, I16, I17) -> f4#(I12, I13, I14, I15, I16, I17) 
10.08/10.26	  f6#(I18, I19, I20, I21, I22, I23) -> f1#(I18, I19, I20, I21, I22, I23) 
10.08/10.26	  f3#(I30, I31, I32, I33, I34, I35) -> f5#(I34, I35, I32, I33, I34, I35) 
10.08/10.26	  f5#(I36, I37, I38, I39, I40, I41) -> f4#(I40, I41, I38, I39, I40, I41) [I40 <= 0]
10.08/10.26	  f5#(I42, I43, I44, I45, I46, I47) -> f4#(I46, I47, I44, I45, I46, I47) [I47 <= 0]
10.08/10.26	  f5#(I48, I49, I50, I51, I52, I53) -> f1#(I52, I53, I50, I51, I52, I53) [1 <= I53 /\ 1 <= I52]
10.08/10.26	  f1#(I80, I81, I82, I83, I84, I85) -> f3#(I84, I85, I82, I83, -1 + I84, -1 + I85) 
10.08/10.26	R = 
10.08/10.26	  f7(x1, x2, x3, x4, x5, x6) -> f6(x1, x2, x3, x4, x5, x6) 
10.08/10.26	  f6(I0, I1, I2, I3, I4, I5) -> f3(I0, I1, I2, I3, I4, I5) 
10.08/10.26	  f6(I6, I7, I8, I9, I10, I11) -> f5(I6, I7, I8, I9, I10, I11) 
10.08/10.26	  f6(I12, I13, I14, I15, I16, I17) -> f4(I12, I13, I14, I15, I16, I17) 
10.08/10.26	  f6(I18, I19, I20, I21, I22, I23) -> f1(I18, I19, I20, I21, I22, I23) 
10.08/10.26	  f6(I24, I25, I26, I27, I28, I29) -> f2(I24, I25, I26, I27, I28, I29) 
10.08/10.26	  f3(I30, I31, I32, I33, I34, I35) -> f5(I34, I35, I32, I33, I34, I35) 
10.08/10.26	  f5(I36, I37, I38, I39, I40, I41) -> f4(I40, I41, I38, I39, I40, I41) [I40 <= 0]
10.08/10.26	  f5(I42, I43, I44, I45, I46, I47) -> f4(I46, I47, I44, I45, I46, I47) [I47 <= 0]
10.08/10.26	  f5(I48, I49, I50, I51, I52, I53) -> f1(I52, I53, I50, I51, I52, I53) [1 <= I53 /\ 1 <= I52]
10.08/10.26	  f4(I54, I55, I56, I57, I58, I59) -> f2(I58, I59, rnd3, rnd4, rnd5, rnd6) [rnd6 = rnd4 /\ rnd5 = rnd3 /\ 1 + I58 <= 0 /\ rnd4 = rnd4 /\ rnd3 = rnd3]
10.08/10.26	  f4(I60, I61, I62, I63, I64, I65) -> f2(I64, I65, I66, I67, I68, I69) [I69 = I67 /\ I68 = I66 /\ 1 <= I64 /\ I67 = I67 /\ I66 = I66]
10.08/10.26	  f4(I70, I71, I72, I73, I74, I75) -> f2(I74, I75, I76, I77, I78, I79) [I79 = I77 /\ I78 = I76 /\ 0 <= I74 /\ I74 <= 0 /\ I77 = I77 /\ I76 = I76]
10.08/10.26	  f1(I80, I81, I82, I83, I84, I85) -> f3(I84, I85, I82, I83, -1 + I84, -1 + I85) 
10.08/10.26	  f1(I86, I87, I88, I89, I90, I91) -> f2(I90, I91, I92, I93, I94, I95) [I95 = I93 /\ I94 = I92 /\ I93 = I93 /\ I92 = I92]
10.08/10.26	
10.08/10.26	The dependency graph for this problem is:
10.08/10.26	  0 -> 1, 2, 3, 4
10.08/10.26	  1 -> 5
10.08/10.26	  2 -> 6, 7, 8
10.08/10.26	  3 -> 
10.08/10.26	  4 -> 9
10.08/10.26	  5 -> 6, 7, 8
10.08/10.26	  6 -> 
10.08/10.26	  7 -> 
10.08/10.26	  8 -> 9
10.08/10.26	  9 -> 5
10.08/10.26	Where:
10.08/10.26	  0) f7#(x1, x2, x3, x4, x5, x6) -> f6#(x1, x2, x3, x4, x5, x6) 
10.08/10.26	  1) f6#(I0, I1, I2, I3, I4, I5) -> f3#(I0, I1, I2, I3, I4, I5) 
10.08/10.26	  2) f6#(I6, I7, I8, I9, I10, I11) -> f5#(I6, I7, I8, I9, I10, I11) 
10.08/10.26	  3) f6#(I12, I13, I14, I15, I16, I17) -> f4#(I12, I13, I14, I15, I16, I17) 
10.08/10.26	  4) f6#(I18, I19, I20, I21, I22, I23) -> f1#(I18, I19, I20, I21, I22, I23) 
10.08/10.26	  5) f3#(I30, I31, I32, I33, I34, I35) -> f5#(I34, I35, I32, I33, I34, I35) 
10.08/10.26	  6) f5#(I36, I37, I38, I39, I40, I41) -> f4#(I40, I41, I38, I39, I40, I41) [I40 <= 0]
10.08/10.26	  7) f5#(I42, I43, I44, I45, I46, I47) -> f4#(I46, I47, I44, I45, I46, I47) [I47 <= 0]
10.08/10.26	  8) f5#(I48, I49, I50, I51, I52, I53) -> f1#(I52, I53, I50, I51, I52, I53) [1 <= I53 /\ 1 <= I52]
10.08/10.26	  9) f1#(I80, I81, I82, I83, I84, I85) -> f3#(I84, I85, I82, I83, -1 + I84, -1 + I85) 
10.08/10.26	
10.08/10.26	We have the following SCCs.
10.08/10.26	  { 5, 8, 9 }
10.08/10.26	
10.08/10.26	DP problem for innermost termination.
10.08/10.26	P =
10.08/10.26	  f3#(I30, I31, I32, I33, I34, I35) -> f5#(I34, I35, I32, I33, I34, I35) 
10.08/10.26	  f5#(I48, I49, I50, I51, I52, I53) -> f1#(I52, I53, I50, I51, I52, I53) [1 <= I53 /\ 1 <= I52]
10.08/10.26	  f1#(I80, I81, I82, I83, I84, I85) -> f3#(I84, I85, I82, I83, -1 + I84, -1 + I85) 
10.08/10.26	R = 
10.08/10.26	  f7(x1, x2, x3, x4, x5, x6) -> f6(x1, x2, x3, x4, x5, x6) 
10.08/10.26	  f6(I0, I1, I2, I3, I4, I5) -> f3(I0, I1, I2, I3, I4, I5) 
10.08/10.26	  f6(I6, I7, I8, I9, I10, I11) -> f5(I6, I7, I8, I9, I10, I11) 
10.08/10.26	  f6(I12, I13, I14, I15, I16, I17) -> f4(I12, I13, I14, I15, I16, I17) 
10.08/10.26	  f6(I18, I19, I20, I21, I22, I23) -> f1(I18, I19, I20, I21, I22, I23) 
10.08/10.26	  f6(I24, I25, I26, I27, I28, I29) -> f2(I24, I25, I26, I27, I28, I29) 
10.08/10.26	  f3(I30, I31, I32, I33, I34, I35) -> f5(I34, I35, I32, I33, I34, I35) 
10.08/10.26	  f5(I36, I37, I38, I39, I40, I41) -> f4(I40, I41, I38, I39, I40, I41) [I40 <= 0]
10.08/10.26	  f5(I42, I43, I44, I45, I46, I47) -> f4(I46, I47, I44, I45, I46, I47) [I47 <= 0]
10.08/10.26	  f5(I48, I49, I50, I51, I52, I53) -> f1(I52, I53, I50, I51, I52, I53) [1 <= I53 /\ 1 <= I52]
10.08/10.26	  f4(I54, I55, I56, I57, I58, I59) -> f2(I58, I59, rnd3, rnd4, rnd5, rnd6) [rnd6 = rnd4 /\ rnd5 = rnd3 /\ 1 + I58 <= 0 /\ rnd4 = rnd4 /\ rnd3 = rnd3]
10.08/10.26	  f4(I60, I61, I62, I63, I64, I65) -> f2(I64, I65, I66, I67, I68, I69) [I69 = I67 /\ I68 = I66 /\ 1 <= I64 /\ I67 = I67 /\ I66 = I66]
10.08/10.26	  f4(I70, I71, I72, I73, I74, I75) -> f2(I74, I75, I76, I77, I78, I79) [I79 = I77 /\ I78 = I76 /\ 0 <= I74 /\ I74 <= 0 /\ I77 = I77 /\ I76 = I76]
10.08/10.26	  f1(I80, I81, I82, I83, I84, I85) -> f3(I84, I85, I82, I83, -1 + I84, -1 + I85) 
10.08/10.26	  f1(I86, I87, I88, I89, I90, I91) -> f2(I90, I91, I92, I93, I94, I95) [I95 = I93 /\ I94 = I92 /\ I93 = I93 /\ I92 = I92]
10.08/10.26	
10.08/10.26	We use the extended value criterion with the projection function NU:
10.08/10.26	  NU[f1#(x0,x1,x2,x3,x4,x5)] = x5
10.08/10.26	  NU[f5#(x0,x1,x2,x3,x4,x5)] = x5 + 1
10.08/10.26	  NU[f3#(x0,x1,x2,x3,x4,x5)] = x5 + 1
10.08/10.26	
10.08/10.26	This gives the following inequalities:
10.08/10.26	    ==>  I35 + 1 >= I35 + 1
10.08/10.26	  1 <= I53 /\ 1 <= I52  ==>  I53 + 1 > I53  with  I53 + 1 >= 0
10.08/10.26	    ==>  I85 >= (-1 + I85) + 1
10.08/10.26	
10.08/10.26	We remove all the strictly oriented dependency pairs.
10.08/10.26	
10.08/10.26	DP problem for innermost termination.
10.08/10.26	P =
10.08/10.26	  f3#(I30, I31, I32, I33, I34, I35) -> f5#(I34, I35, I32, I33, I34, I35) 
10.08/10.26	  f1#(I80, I81, I82, I83, I84, I85) -> f3#(I84, I85, I82, I83, -1 + I84, -1 + I85) 
10.08/10.26	R = 
10.08/10.26	  f7(x1, x2, x3, x4, x5, x6) -> f6(x1, x2, x3, x4, x5, x6) 
10.08/10.26	  f6(I0, I1, I2, I3, I4, I5) -> f3(I0, I1, I2, I3, I4, I5) 
10.08/10.26	  f6(I6, I7, I8, I9, I10, I11) -> f5(I6, I7, I8, I9, I10, I11) 
10.08/10.26	  f6(I12, I13, I14, I15, I16, I17) -> f4(I12, I13, I14, I15, I16, I17) 
10.08/10.26	  f6(I18, I19, I20, I21, I22, I23) -> f1(I18, I19, I20, I21, I22, I23) 
10.08/10.26	  f6(I24, I25, I26, I27, I28, I29) -> f2(I24, I25, I26, I27, I28, I29) 
10.08/10.26	  f3(I30, I31, I32, I33, I34, I35) -> f5(I34, I35, I32, I33, I34, I35) 
10.08/10.26	  f5(I36, I37, I38, I39, I40, I41) -> f4(I40, I41, I38, I39, I40, I41) [I40 <= 0]
10.08/10.26	  f5(I42, I43, I44, I45, I46, I47) -> f4(I46, I47, I44, I45, I46, I47) [I47 <= 0]
10.08/10.26	  f5(I48, I49, I50, I51, I52, I53) -> f1(I52, I53, I50, I51, I52, I53) [1 <= I53 /\ 1 <= I52]
10.08/10.26	  f4(I54, I55, I56, I57, I58, I59) -> f2(I58, I59, rnd3, rnd4, rnd5, rnd6) [rnd6 = rnd4 /\ rnd5 = rnd3 /\ 1 + I58 <= 0 /\ rnd4 = rnd4 /\ rnd3 = rnd3]
10.08/10.26	  f4(I60, I61, I62, I63, I64, I65) -> f2(I64, I65, I66, I67, I68, I69) [I69 = I67 /\ I68 = I66 /\ 1 <= I64 /\ I67 = I67 /\ I66 = I66]
10.08/10.26	  f4(I70, I71, I72, I73, I74, I75) -> f2(I74, I75, I76, I77, I78, I79) [I79 = I77 /\ I78 = I76 /\ 0 <= I74 /\ I74 <= 0 /\ I77 = I77 /\ I76 = I76]
10.08/10.26	  f1(I80, I81, I82, I83, I84, I85) -> f3(I84, I85, I82, I83, -1 + I84, -1 + I85) 
10.08/10.26	  f1(I86, I87, I88, I89, I90, I91) -> f2(I90, I91, I92, I93, I94, I95) [I95 = I93 /\ I94 = I92 /\ I93 = I93 /\ I92 = I92]
10.08/10.26	
10.08/10.26	The dependency graph for this problem is:
10.08/10.26	  5 -> 
10.08/10.26	  9 -> 5
10.08/10.26	Where:
10.08/10.26	  5) f3#(I30, I31, I32, I33, I34, I35) -> f5#(I34, I35, I32, I33, I34, I35) 
10.08/10.26	  9) f1#(I80, I81, I82, I83, I84, I85) -> f3#(I84, I85, I82, I83, -1 + I84, -1 + I85) 
10.08/10.26	
10.08/10.26	We have the following SCCs.
10.08/10.26	  
10.08/13.24	EOF