6.19/6.13	YES
6.19/6.13	
6.19/6.13	DP problem for innermost termination.
6.19/6.13	P =
6.19/6.13	  f11#(x1, x2, x3, x4, x5, x6) -> f10#(x1, x2, x3, x4, x5, x6) 
6.19/6.13	  f10#(I0, I1, I2, I3, I4, I5) -> f6#(I0, I1, I2, I3, I4, rnd6) [rnd6 = rnd6]
6.19/6.13	  f2#(I6, I7, I8, I9, I10, I11) -> f9#(I6, I7, I8, I9, I10, I11) [0 <= I7]
6.19/6.13	  f2#(I12, I13, I14, I15, I16, I17) -> f7#(I12, I13, I14, I15, I16, I17) [1 + I13 <= 0]
6.19/6.13	  f9#(I18, I19, I20, I21, I22, I23) -> f7#(I18, I19, I20, I21, I22, I23) [1 + I19 <= I18]
6.19/6.13	  f9#(I24, I25, I26, I27, I28, I29) -> f7#(I24, I25, I26, I27, I28, I29) [I24 <= I25]
6.19/6.13	  f3#(I36, I37, I38, I39, I40, I41) -> f1#(I36, I37, I38, I39, I40, I41) 
6.19/6.13	  f6#(I42, I43, I44, I45, I46, I47) -> f5#(I42, I43, I44, I45, I46, I47) [1 + I47 <= 0]
6.19/6.13	  f6#(I48, I49, I50, I51, I52, I53) -> f5#(I48, I49, I50, I51, I52, I53) [1 <= I53]
6.19/6.13	  f6#(I54, I55, I56, I57, I58, I59) -> f4#(I54, I55, I56, I57, I54, I59) [0 <= I59 /\ I59 <= 0]
6.19/6.13	  f5#(I60, I61, I62, I63, I64, I65) -> f4#(I60, I61, I62, I63, 0, I65) 
6.19/6.13	  f4#(I66, I67, I68, I69, I70, I71) -> f3#(I66, I67, 0, I69, I70, I71) 
6.19/6.13	  f1#(I72, I73, I74, I75, I76, I77) -> f3#(I72, I73, 1 + I74, 2 + I75, I76, I77) [I74 <= I76]
6.19/6.13	  f1#(I78, I79, I80, I81, I82, I83) -> f2#(I78, I79, I80, I81, I82, I83) [1 + I82 <= I80]
6.19/6.13	R = 
6.19/6.13	  f11(x1, x2, x3, x4, x5, x6) -> f10(x1, x2, x3, x4, x5, x6) 
6.19/6.13	  f10(I0, I1, I2, I3, I4, I5) -> f6(I0, I1, I2, I3, I4, rnd6) [rnd6 = rnd6]
6.19/6.13	  f2(I6, I7, I8, I9, I10, I11) -> f9(I6, I7, I8, I9, I10, I11) [0 <= I7]
6.19/6.13	  f2(I12, I13, I14, I15, I16, I17) -> f7(I12, I13, I14, I15, I16, I17) [1 + I13 <= 0]
6.19/6.13	  f9(I18, I19, I20, I21, I22, I23) -> f7(I18, I19, I20, I21, I22, I23) [1 + I19 <= I18]
6.19/6.13	  f9(I24, I25, I26, I27, I28, I29) -> f7(I24, I25, I26, I27, I28, I29) [I24 <= I25]
6.19/6.13	  f7(I30, I31, I32, I33, I34, I35) -> f8(I30, I31, I32, I33, I34, I35) 
6.19/6.13	  f3(I36, I37, I38, I39, I40, I41) -> f1(I36, I37, I38, I39, I40, I41) 
6.19/6.13	  f6(I42, I43, I44, I45, I46, I47) -> f5(I42, I43, I44, I45, I46, I47) [1 + I47 <= 0]
6.19/6.13	  f6(I48, I49, I50, I51, I52, I53) -> f5(I48, I49, I50, I51, I52, I53) [1 <= I53]
6.19/6.13	  f6(I54, I55, I56, I57, I58, I59) -> f4(I54, I55, I56, I57, I54, I59) [0 <= I59 /\ I59 <= 0]
6.19/6.13	  f5(I60, I61, I62, I63, I64, I65) -> f4(I60, I61, I62, I63, 0, I65) 
6.19/6.13	  f4(I66, I67, I68, I69, I70, I71) -> f3(I66, I67, 0, I69, I70, I71) 
6.19/6.13	  f1(I72, I73, I74, I75, I76, I77) -> f3(I72, I73, 1 + I74, 2 + I75, I76, I77) [I74 <= I76]
6.19/6.13	  f1(I78, I79, I80, I81, I82, I83) -> f2(I78, I79, I80, I81, I82, I83) [1 + I82 <= I80]
6.19/6.13	
6.19/6.13	The dependency graph for this problem is:
6.19/6.13	  0 -> 1
6.19/6.13	  1 -> 7, 8, 9
6.19/6.13	  2 -> 4, 5
6.19/6.13	  3 -> 
6.19/6.13	  4 -> 
6.19/6.13	  5 -> 
6.19/6.13	  6 -> 12, 13
6.19/6.13	  7 -> 10
6.19/6.13	  8 -> 10
6.19/6.13	  9 -> 11
6.19/6.13	  10 -> 11
6.19/6.13	  11 -> 6
6.19/6.13	  12 -> 6
6.19/6.13	  13 -> 2, 3
6.19/6.13	Where:
6.19/6.13	  0) f11#(x1, x2, x3, x4, x5, x6) -> f10#(x1, x2, x3, x4, x5, x6) 
6.19/6.13	  1) f10#(I0, I1, I2, I3, I4, I5) -> f6#(I0, I1, I2, I3, I4, rnd6) [rnd6 = rnd6]
6.19/6.13	  2) f2#(I6, I7, I8, I9, I10, I11) -> f9#(I6, I7, I8, I9, I10, I11) [0 <= I7]
6.19/6.13	  3) f2#(I12, I13, I14, I15, I16, I17) -> f7#(I12, I13, I14, I15, I16, I17) [1 + I13 <= 0]
6.19/6.13	  4) f9#(I18, I19, I20, I21, I22, I23) -> f7#(I18, I19, I20, I21, I22, I23) [1 + I19 <= I18]
6.19/6.13	  5) f9#(I24, I25, I26, I27, I28, I29) -> f7#(I24, I25, I26, I27, I28, I29) [I24 <= I25]
6.19/6.13	  6) f3#(I36, I37, I38, I39, I40, I41) -> f1#(I36, I37, I38, I39, I40, I41) 
6.19/6.13	  7) f6#(I42, I43, I44, I45, I46, I47) -> f5#(I42, I43, I44, I45, I46, I47) [1 + I47 <= 0]
6.19/6.13	  8) f6#(I48, I49, I50, I51, I52, I53) -> f5#(I48, I49, I50, I51, I52, I53) [1 <= I53]
6.19/6.13	  9) f6#(I54, I55, I56, I57, I58, I59) -> f4#(I54, I55, I56, I57, I54, I59) [0 <= I59 /\ I59 <= 0]
6.19/6.13	  10) f5#(I60, I61, I62, I63, I64, I65) -> f4#(I60, I61, I62, I63, 0, I65) 
6.19/6.13	  11) f4#(I66, I67, I68, I69, I70, I71) -> f3#(I66, I67, 0, I69, I70, I71) 
6.19/6.13	  12) f1#(I72, I73, I74, I75, I76, I77) -> f3#(I72, I73, 1 + I74, 2 + I75, I76, I77) [I74 <= I76]
6.19/6.13	  13) f1#(I78, I79, I80, I81, I82, I83) -> f2#(I78, I79, I80, I81, I82, I83) [1 + I82 <= I80]
6.19/6.13	
6.19/6.13	We have the following SCCs.
6.19/6.13	  { 6, 12 }
6.19/6.13	
6.19/6.13	DP problem for innermost termination.
6.19/6.13	P =
6.19/6.13	  f3#(I36, I37, I38, I39, I40, I41) -> f1#(I36, I37, I38, I39, I40, I41) 
6.19/6.13	  f1#(I72, I73, I74, I75, I76, I77) -> f3#(I72, I73, 1 + I74, 2 + I75, I76, I77) [I74 <= I76]
6.19/6.13	R = 
6.19/6.13	  f11(x1, x2, x3, x4, x5, x6) -> f10(x1, x2, x3, x4, x5, x6) 
6.19/6.13	  f10(I0, I1, I2, I3, I4, I5) -> f6(I0, I1, I2, I3, I4, rnd6) [rnd6 = rnd6]
6.19/6.13	  f2(I6, I7, I8, I9, I10, I11) -> f9(I6, I7, I8, I9, I10, I11) [0 <= I7]
6.19/6.13	  f2(I12, I13, I14, I15, I16, I17) -> f7(I12, I13, I14, I15, I16, I17) [1 + I13 <= 0]
6.19/6.13	  f9(I18, I19, I20, I21, I22, I23) -> f7(I18, I19, I20, I21, I22, I23) [1 + I19 <= I18]
6.19/6.13	  f9(I24, I25, I26, I27, I28, I29) -> f7(I24, I25, I26, I27, I28, I29) [I24 <= I25]
6.19/6.13	  f7(I30, I31, I32, I33, I34, I35) -> f8(I30, I31, I32, I33, I34, I35) 
6.19/6.13	  f3(I36, I37, I38, I39, I40, I41) -> f1(I36, I37, I38, I39, I40, I41) 
6.19/6.13	  f6(I42, I43, I44, I45, I46, I47) -> f5(I42, I43, I44, I45, I46, I47) [1 + I47 <= 0]
6.19/6.13	  f6(I48, I49, I50, I51, I52, I53) -> f5(I48, I49, I50, I51, I52, I53) [1 <= I53]
6.19/6.13	  f6(I54, I55, I56, I57, I58, I59) -> f4(I54, I55, I56, I57, I54, I59) [0 <= I59 /\ I59 <= 0]
6.19/6.13	  f5(I60, I61, I62, I63, I64, I65) -> f4(I60, I61, I62, I63, 0, I65) 
6.19/6.13	  f4(I66, I67, I68, I69, I70, I71) -> f3(I66, I67, 0, I69, I70, I71) 
6.19/6.13	  f1(I72, I73, I74, I75, I76, I77) -> f3(I72, I73, 1 + I74, 2 + I75, I76, I77) [I74 <= I76]
6.19/6.13	  f1(I78, I79, I80, I81, I82, I83) -> f2(I78, I79, I80, I81, I82, I83) [1 + I82 <= I80]
6.19/6.13	
6.19/6.13	We use the reverse value criterion with the projection function NU:
6.19/6.13	  NU[f1#(z1,z2,z3,z4,z5,z6)] = z5 + -1 * z3
6.19/6.13	  NU[f3#(z1,z2,z3,z4,z5,z6)] = z5 + -1 * z3
6.19/6.13	
6.19/6.13	This gives the following inequalities:
6.19/6.13	    ==>  I40 + -1 * I38 >= I40 + -1 * I38
6.19/6.13	  I74 <= I76  ==>  I76 + -1 * I74 > I76 + -1 * (1 + I74)  with  I76 + -1 * I74 >= 0
6.19/6.13	
6.19/6.13	We remove all the strictly oriented dependency pairs.
6.19/6.13	
6.19/6.13	DP problem for innermost termination.
6.19/6.13	P =
6.19/6.13	  f3#(I36, I37, I38, I39, I40, I41) -> f1#(I36, I37, I38, I39, I40, I41) 
6.19/6.13	R = 
6.19/6.13	  f11(x1, x2, x3, x4, x5, x6) -> f10(x1, x2, x3, x4, x5, x6) 
6.19/6.13	  f10(I0, I1, I2, I3, I4, I5) -> f6(I0, I1, I2, I3, I4, rnd6) [rnd6 = rnd6]
6.19/6.13	  f2(I6, I7, I8, I9, I10, I11) -> f9(I6, I7, I8, I9, I10, I11) [0 <= I7]
6.19/6.13	  f2(I12, I13, I14, I15, I16, I17) -> f7(I12, I13, I14, I15, I16, I17) [1 + I13 <= 0]
6.19/6.13	  f9(I18, I19, I20, I21, I22, I23) -> f7(I18, I19, I20, I21, I22, I23) [1 + I19 <= I18]
6.19/6.13	  f9(I24, I25, I26, I27, I28, I29) -> f7(I24, I25, I26, I27, I28, I29) [I24 <= I25]
6.19/6.13	  f7(I30, I31, I32, I33, I34, I35) -> f8(I30, I31, I32, I33, I34, I35) 
6.19/6.13	  f3(I36, I37, I38, I39, I40, I41) -> f1(I36, I37, I38, I39, I40, I41) 
6.19/6.13	  f6(I42, I43, I44, I45, I46, I47) -> f5(I42, I43, I44, I45, I46, I47) [1 + I47 <= 0]
6.19/6.13	  f6(I48, I49, I50, I51, I52, I53) -> f5(I48, I49, I50, I51, I52, I53) [1 <= I53]
6.19/6.13	  f6(I54, I55, I56, I57, I58, I59) -> f4(I54, I55, I56, I57, I54, I59) [0 <= I59 /\ I59 <= 0]
6.19/6.13	  f5(I60, I61, I62, I63, I64, I65) -> f4(I60, I61, I62, I63, 0, I65) 
6.19/6.13	  f4(I66, I67, I68, I69, I70, I71) -> f3(I66, I67, 0, I69, I70, I71) 
6.19/6.13	  f1(I72, I73, I74, I75, I76, I77) -> f3(I72, I73, 1 + I74, 2 + I75, I76, I77) [I74 <= I76]
6.19/6.13	  f1(I78, I79, I80, I81, I82, I83) -> f2(I78, I79, I80, I81, I82, I83) [1 + I82 <= I80]
6.19/6.13	
6.19/6.13	The dependency graph for this problem is:
6.19/6.13	  6 -> 
6.19/6.13	Where:
6.19/6.13	  6) f3#(I36, I37, I38, I39, I40, I41) -> f1#(I36, I37, I38, I39, I40, I41) 
6.19/6.13	
6.19/6.13	We have the following SCCs.
6.19/6.13	  
6.19/9.11	EOF