47.22/46.48	YES
47.22/46.48	
47.22/46.48	DP problem for innermost termination.
47.22/46.48	P =
47.22/46.48	  f12#(x1, x2, x3, x4, x5, x6, x7, x8) -> f11#(x1, x2, x3, x4, x5, x6, x7, x8) 
47.22/46.48	  f11#(I0, I1, I2, I3, I4, I5, I6, I7) -> f4#(I0, 0, I2, I3, I4, I5, I6, I7) 
47.22/46.48	  f3#(I8, I9, I10, I11, I12, I13, I14, I15) -> f4#(I8, 1 + I9, I10, I11, I12, I13, I14, I15) [1 + I9 <= I8]
47.22/46.48	  f3#(I16, I17, I18, I19, I20, I21, I22, I23) -> f2#(I16, I17, I18, I19, I20, I21, I22, I23) [I16 <= I17]
47.22/46.48	  f2#(I24, I25, I26, I27, I28, I29, I30, I31) -> f8#(I24, 0, I26, I27, I28, I29, I30, I31) 
47.22/46.48	  f10#(I32, I33, I34, I35, I36, I37, I38, I39) -> f9#(I32, I33, I34, rnd4, I36, rnd6, I38, I33) [rnd6 = rnd4 /\ rnd4 = rnd4 /\ 1 + I33 <= I32]
47.22/46.48	  f10#(I40, I41, I42, I43, I44, I45, I46, I47) -> f5#(I40, I41, I42, I43, I44, I45, I46, I47) [I40 <= I41]
47.22/46.48	  f8#(I48, I49, I50, I51, I52, I53, I54, I55) -> f10#(I48, I49, I50, I51, I52, I53, I54, I55) 
47.22/46.48	  f9#(I56, I57, I58, I59, I60, I61, I62, I63) -> f7#(I56, I57, I58, I59, I60, I61, I62, I63) [1 + I61 <= 0]
47.22/46.48	  f9#(I64, I65, I66, I67, I68, I69, I70, I71) -> f7#(I64, I65, I66, I67, I68, I69, I70, I71) [1 <= I69]
47.22/46.48	  f9#(I72, I73, I74, I75, I76, I77, I78, I79) -> f5#(I72, I73, I74, I75, I76, I77, I78, I79) [0 <= I77 /\ I77 <= 0]
47.22/46.48	  f7#(I80, I81, I82, I83, I84, I85, I86, I87) -> f8#(I80, 1 + I81, I82, I83, I84, I85, I86, I87) 
47.22/46.48	  f4#(I96, I97, I98, I99, I100, I101, I102, I103) -> f1#(I96, I97, rnd3, I99, rnd5, I101, I97, I103) [rnd5 = rnd3 /\ rnd3 = rnd3]
47.22/46.48	  f1#(I104, I105, I106, I107, I108, I109, I110, I111) -> f3#(I104, I105, I106, I107, I108, I109, I110, I111) [1 + I108 <= 0]
47.22/46.48	  f1#(I112, I113, I114, I115, I116, I117, I118, I119) -> f3#(I112, I113, I114, I115, I116, I117, I118, I119) [1 <= I116]
47.22/46.48	  f1#(I120, I121, I122, I123, I124, I125, I126, I127) -> f2#(I120, I121, I122, I123, I124, I125, I126, I127) [0 <= I124 /\ I124 <= 0]
47.22/46.48	R = 
47.22/46.48	  f12(x1, x2, x3, x4, x5, x6, x7, x8) -> f11(x1, x2, x3, x4, x5, x6, x7, x8) 
47.22/46.48	  f11(I0, I1, I2, I3, I4, I5, I6, I7) -> f4(I0, 0, I2, I3, I4, I5, I6, I7) 
47.22/46.48	  f3(I8, I9, I10, I11, I12, I13, I14, I15) -> f4(I8, 1 + I9, I10, I11, I12, I13, I14, I15) [1 + I9 <= I8]
47.22/46.48	  f3(I16, I17, I18, I19, I20, I21, I22, I23) -> f2(I16, I17, I18, I19, I20, I21, I22, I23) [I16 <= I17]
47.22/46.48	  f2(I24, I25, I26, I27, I28, I29, I30, I31) -> f8(I24, 0, I26, I27, I28, I29, I30, I31) 
47.22/46.48	  f10(I32, I33, I34, I35, I36, I37, I38, I39) -> f9(I32, I33, I34, rnd4, I36, rnd6, I38, I33) [rnd6 = rnd4 /\ rnd4 = rnd4 /\ 1 + I33 <= I32]
47.22/46.48	  f10(I40, I41, I42, I43, I44, I45, I46, I47) -> f5(I40, I41, I42, I43, I44, I45, I46, I47) [I40 <= I41]
47.22/46.48	  f8(I48, I49, I50, I51, I52, I53, I54, I55) -> f10(I48, I49, I50, I51, I52, I53, I54, I55) 
47.22/46.48	  f9(I56, I57, I58, I59, I60, I61, I62, I63) -> f7(I56, I57, I58, I59, I60, I61, I62, I63) [1 + I61 <= 0]
47.22/46.48	  f9(I64, I65, I66, I67, I68, I69, I70, I71) -> f7(I64, I65, I66, I67, I68, I69, I70, I71) [1 <= I69]
47.22/46.48	  f9(I72, I73, I74, I75, I76, I77, I78, I79) -> f5(I72, I73, I74, I75, I76, I77, I78, I79) [0 <= I77 /\ I77 <= 0]
47.22/46.48	  f7(I80, I81, I82, I83, I84, I85, I86, I87) -> f8(I80, 1 + I81, I82, I83, I84, I85, I86, I87) 
47.22/46.48	  f5(I88, I89, I90, I91, I92, I93, I94, I95) -> f6(I88, I89, I90, I91, I92, I93, I94, I95) 
47.22/46.48	  f4(I96, I97, I98, I99, I100, I101, I102, I103) -> f1(I96, I97, rnd3, I99, rnd5, I101, I97, I103) [rnd5 = rnd3 /\ rnd3 = rnd3]
47.22/46.48	  f1(I104, I105, I106, I107, I108, I109, I110, I111) -> f3(I104, I105, I106, I107, I108, I109, I110, I111) [1 + I108 <= 0]
47.22/46.48	  f1(I112, I113, I114, I115, I116, I117, I118, I119) -> f3(I112, I113, I114, I115, I116, I117, I118, I119) [1 <= I116]
47.22/46.48	  f1(I120, I121, I122, I123, I124, I125, I126, I127) -> f2(I120, I121, I122, I123, I124, I125, I126, I127) [0 <= I124 /\ I124 <= 0]
47.22/46.48	
47.22/46.48	The dependency graph for this problem is:
47.22/46.48	  0 -> 1
47.22/46.48	  1 -> 12
47.22/46.48	  2 -> 12
47.22/46.48	  3 -> 4
47.22/46.48	  4 -> 7
47.22/46.48	  5 -> 8, 9, 10
47.22/46.48	  6 -> 
47.22/46.48	  7 -> 5, 6
47.22/46.48	  8 -> 11
47.22/46.48	  9 -> 11
47.22/46.48	  10 -> 
47.22/46.48	  11 -> 7
47.22/46.48	  12 -> 13, 14, 15
47.22/46.48	  13 -> 2, 3
47.22/46.48	  14 -> 2, 3
47.22/46.48	  15 -> 4
47.22/46.48	Where:
47.22/46.48	  0) f12#(x1, x2, x3, x4, x5, x6, x7, x8) -> f11#(x1, x2, x3, x4, x5, x6, x7, x8) 
47.22/46.48	  1) f11#(I0, I1, I2, I3, I4, I5, I6, I7) -> f4#(I0, 0, I2, I3, I4, I5, I6, I7) 
47.22/46.48	  2) f3#(I8, I9, I10, I11, I12, I13, I14, I15) -> f4#(I8, 1 + I9, I10, I11, I12, I13, I14, I15) [1 + I9 <= I8]
47.22/46.48	  3) f3#(I16, I17, I18, I19, I20, I21, I22, I23) -> f2#(I16, I17, I18, I19, I20, I21, I22, I23) [I16 <= I17]
47.22/46.48	  4) f2#(I24, I25, I26, I27, I28, I29, I30, I31) -> f8#(I24, 0, I26, I27, I28, I29, I30, I31) 
47.22/46.48	  5) f10#(I32, I33, I34, I35, I36, I37, I38, I39) -> f9#(I32, I33, I34, rnd4, I36, rnd6, I38, I33) [rnd6 = rnd4 /\ rnd4 = rnd4 /\ 1 + I33 <= I32]
47.22/46.48	  6) f10#(I40, I41, I42, I43, I44, I45, I46, I47) -> f5#(I40, I41, I42, I43, I44, I45, I46, I47) [I40 <= I41]
47.22/46.48	  7) f8#(I48, I49, I50, I51, I52, I53, I54, I55) -> f10#(I48, I49, I50, I51, I52, I53, I54, I55) 
47.22/46.48	  8) f9#(I56, I57, I58, I59, I60, I61, I62, I63) -> f7#(I56, I57, I58, I59, I60, I61, I62, I63) [1 + I61 <= 0]
47.22/46.48	  9) f9#(I64, I65, I66, I67, I68, I69, I70, I71) -> f7#(I64, I65, I66, I67, I68, I69, I70, I71) [1 <= I69]
47.22/46.48	  10) f9#(I72, I73, I74, I75, I76, I77, I78, I79) -> f5#(I72, I73, I74, I75, I76, I77, I78, I79) [0 <= I77 /\ I77 <= 0]
47.22/46.48	  11) f7#(I80, I81, I82, I83, I84, I85, I86, I87) -> f8#(I80, 1 + I81, I82, I83, I84, I85, I86, I87) 
47.22/46.48	  12) f4#(I96, I97, I98, I99, I100, I101, I102, I103) -> f1#(I96, I97, rnd3, I99, rnd5, I101, I97, I103) [rnd5 = rnd3 /\ rnd3 = rnd3]
47.22/46.48	  13) f1#(I104, I105, I106, I107, I108, I109, I110, I111) -> f3#(I104, I105, I106, I107, I108, I109, I110, I111) [1 + I108 <= 0]
47.22/46.48	  14) f1#(I112, I113, I114, I115, I116, I117, I118, I119) -> f3#(I112, I113, I114, I115, I116, I117, I118, I119) [1 <= I116]
47.22/46.48	  15) f1#(I120, I121, I122, I123, I124, I125, I126, I127) -> f2#(I120, I121, I122, I123, I124, I125, I126, I127) [0 <= I124 /\ I124 <= 0]
47.22/46.48	
47.22/46.48	We have the following SCCs.
47.22/46.48	  { 2, 12, 13, 14 }
47.22/46.48	  { 5, 7, 8, 9, 11 }
47.22/46.48	
47.22/46.48	DP problem for innermost termination.
47.22/46.48	P =
47.22/46.48	  f10#(I32, I33, I34, I35, I36, I37, I38, I39) -> f9#(I32, I33, I34, rnd4, I36, rnd6, I38, I33) [rnd6 = rnd4 /\ rnd4 = rnd4 /\ 1 + I33 <= I32]
47.22/46.48	  f8#(I48, I49, I50, I51, I52, I53, I54, I55) -> f10#(I48, I49, I50, I51, I52, I53, I54, I55) 
47.22/46.48	  f9#(I56, I57, I58, I59, I60, I61, I62, I63) -> f7#(I56, I57, I58, I59, I60, I61, I62, I63) [1 + I61 <= 0]
47.22/46.48	  f9#(I64, I65, I66, I67, I68, I69, I70, I71) -> f7#(I64, I65, I66, I67, I68, I69, I70, I71) [1 <= I69]
47.22/46.48	  f7#(I80, I81, I82, I83, I84, I85, I86, I87) -> f8#(I80, 1 + I81, I82, I83, I84, I85, I86, I87) 
47.22/46.48	R = 
47.22/46.48	  f12(x1, x2, x3, x4, x5, x6, x7, x8) -> f11(x1, x2, x3, x4, x5, x6, x7, x8) 
47.22/46.48	  f11(I0, I1, I2, I3, I4, I5, I6, I7) -> f4(I0, 0, I2, I3, I4, I5, I6, I7) 
47.22/46.48	  f3(I8, I9, I10, I11, I12, I13, I14, I15) -> f4(I8, 1 + I9, I10, I11, I12, I13, I14, I15) [1 + I9 <= I8]
47.22/46.48	  f3(I16, I17, I18, I19, I20, I21, I22, I23) -> f2(I16, I17, I18, I19, I20, I21, I22, I23) [I16 <= I17]
47.22/46.48	  f2(I24, I25, I26, I27, I28, I29, I30, I31) -> f8(I24, 0, I26, I27, I28, I29, I30, I31) 
47.22/46.48	  f10(I32, I33, I34, I35, I36, I37, I38, I39) -> f9(I32, I33, I34, rnd4, I36, rnd6, I38, I33) [rnd6 = rnd4 /\ rnd4 = rnd4 /\ 1 + I33 <= I32]
47.22/46.48	  f10(I40, I41, I42, I43, I44, I45, I46, I47) -> f5(I40, I41, I42, I43, I44, I45, I46, I47) [I40 <= I41]
47.22/46.48	  f8(I48, I49, I50, I51, I52, I53, I54, I55) -> f10(I48, I49, I50, I51, I52, I53, I54, I55) 
47.22/46.48	  f9(I56, I57, I58, I59, I60, I61, I62, I63) -> f7(I56, I57, I58, I59, I60, I61, I62, I63) [1 + I61 <= 0]
47.22/46.48	  f9(I64, I65, I66, I67, I68, I69, I70, I71) -> f7(I64, I65, I66, I67, I68, I69, I70, I71) [1 <= I69]
47.22/46.48	  f9(I72, I73, I74, I75, I76, I77, I78, I79) -> f5(I72, I73, I74, I75, I76, I77, I78, I79) [0 <= I77 /\ I77 <= 0]
47.22/46.48	  f7(I80, I81, I82, I83, I84, I85, I86, I87) -> f8(I80, 1 + I81, I82, I83, I84, I85, I86, I87) 
47.22/46.48	  f5(I88, I89, I90, I91, I92, I93, I94, I95) -> f6(I88, I89, I90, I91, I92, I93, I94, I95) 
47.22/46.48	  f4(I96, I97, I98, I99, I100, I101, I102, I103) -> f1(I96, I97, rnd3, I99, rnd5, I101, I97, I103) [rnd5 = rnd3 /\ rnd3 = rnd3]
47.22/46.48	  f1(I104, I105, I106, I107, I108, I109, I110, I111) -> f3(I104, I105, I106, I107, I108, I109, I110, I111) [1 + I108 <= 0]
47.22/46.48	  f1(I112, I113, I114, I115, I116, I117, I118, I119) -> f3(I112, I113, I114, I115, I116, I117, I118, I119) [1 <= I116]
47.22/46.48	  f1(I120, I121, I122, I123, I124, I125, I126, I127) -> f2(I120, I121, I122, I123, I124, I125, I126, I127) [0 <= I124 /\ I124 <= 0]
47.22/46.48	
47.22/46.48	We use the extended value criterion with the projection function NU:
47.22/46.48	  NU[f7#(x0,x1,x2,x3,x4,x5,x6,x7)] = x0 - x1 - 2
47.22/46.48	  NU[f8#(x0,x1,x2,x3,x4,x5,x6,x7)] = x0 - x1 - 1
47.22/46.48	  NU[f9#(x0,x1,x2,x3,x4,x5,x6,x7)] = x0 - x1 - 2
47.22/46.48	  NU[f10#(x0,x1,x2,x3,x4,x5,x6,x7)] = x0 - x1 - 1
47.22/46.48	
47.22/46.48	This gives the following inequalities:
47.22/46.48	  rnd6 = rnd4 /\ rnd4 = rnd4 /\ 1 + I33 <= I32  ==>  I32 - I33 - 1 > I32 - I33 - 2  with  I32 - I33 - 1 >= 0
47.22/46.48	    ==>  I48 - I49 - 1 >= I48 - I49 - 1
47.22/46.48	  1 + I61 <= 0  ==>  I56 - I57 - 2 >= I56 - I57 - 2
47.22/46.48	  1 <= I69  ==>  I64 - I65 - 2 >= I64 - I65 - 2
47.22/46.48	    ==>  I80 - I81 - 2 >= I80 - (1 + I81) - 1
47.22/46.48	
47.22/46.48	We remove all the strictly oriented dependency pairs.
47.22/46.48	
47.22/46.48	DP problem for innermost termination.
47.22/46.48	P =
47.22/46.48	  f8#(I48, I49, I50, I51, I52, I53, I54, I55) -> f10#(I48, I49, I50, I51, I52, I53, I54, I55) 
47.22/46.48	  f9#(I56, I57, I58, I59, I60, I61, I62, I63) -> f7#(I56, I57, I58, I59, I60, I61, I62, I63) [1 + I61 <= 0]
47.22/46.48	  f9#(I64, I65, I66, I67, I68, I69, I70, I71) -> f7#(I64, I65, I66, I67, I68, I69, I70, I71) [1 <= I69]
47.22/46.48	  f7#(I80, I81, I82, I83, I84, I85, I86, I87) -> f8#(I80, 1 + I81, I82, I83, I84, I85, I86, I87) 
47.22/46.48	R = 
47.22/46.48	  f12(x1, x2, x3, x4, x5, x6, x7, x8) -> f11(x1, x2, x3, x4, x5, x6, x7, x8) 
47.22/46.48	  f11(I0, I1, I2, I3, I4, I5, I6, I7) -> f4(I0, 0, I2, I3, I4, I5, I6, I7) 
47.22/46.48	  f3(I8, I9, I10, I11, I12, I13, I14, I15) -> f4(I8, 1 + I9, I10, I11, I12, I13, I14, I15) [1 + I9 <= I8]
47.22/46.48	  f3(I16, I17, I18, I19, I20, I21, I22, I23) -> f2(I16, I17, I18, I19, I20, I21, I22, I23) [I16 <= I17]
47.22/46.48	  f2(I24, I25, I26, I27, I28, I29, I30, I31) -> f8(I24, 0, I26, I27, I28, I29, I30, I31) 
47.22/46.48	  f10(I32, I33, I34, I35, I36, I37, I38, I39) -> f9(I32, I33, I34, rnd4, I36, rnd6, I38, I33) [rnd6 = rnd4 /\ rnd4 = rnd4 /\ 1 + I33 <= I32]
47.22/46.48	  f10(I40, I41, I42, I43, I44, I45, I46, I47) -> f5(I40, I41, I42, I43, I44, I45, I46, I47) [I40 <= I41]
47.22/46.48	  f8(I48, I49, I50, I51, I52, I53, I54, I55) -> f10(I48, I49, I50, I51, I52, I53, I54, I55) 
47.22/46.48	  f9(I56, I57, I58, I59, I60, I61, I62, I63) -> f7(I56, I57, I58, I59, I60, I61, I62, I63) [1 + I61 <= 0]
47.22/46.48	  f9(I64, I65, I66, I67, I68, I69, I70, I71) -> f7(I64, I65, I66, I67, I68, I69, I70, I71) [1 <= I69]
47.22/46.48	  f9(I72, I73, I74, I75, I76, I77, I78, I79) -> f5(I72, I73, I74, I75, I76, I77, I78, I79) [0 <= I77 /\ I77 <= 0]
47.22/46.48	  f7(I80, I81, I82, I83, I84, I85, I86, I87) -> f8(I80, 1 + I81, I82, I83, I84, I85, I86, I87) 
47.22/46.48	  f5(I88, I89, I90, I91, I92, I93, I94, I95) -> f6(I88, I89, I90, I91, I92, I93, I94, I95) 
47.22/46.48	  f4(I96, I97, I98, I99, I100, I101, I102, I103) -> f1(I96, I97, rnd3, I99, rnd5, I101, I97, I103) [rnd5 = rnd3 /\ rnd3 = rnd3]
47.22/46.48	  f1(I104, I105, I106, I107, I108, I109, I110, I111) -> f3(I104, I105, I106, I107, I108, I109, I110, I111) [1 + I108 <= 0]
47.22/46.48	  f1(I112, I113, I114, I115, I116, I117, I118, I119) -> f3(I112, I113, I114, I115, I116, I117, I118, I119) [1 <= I116]
47.22/46.48	  f1(I120, I121, I122, I123, I124, I125, I126, I127) -> f2(I120, I121, I122, I123, I124, I125, I126, I127) [0 <= I124 /\ I124 <= 0]
47.22/46.48	
47.22/46.48	The dependency graph for this problem is:
47.22/46.48	  7 -> 
47.22/46.48	  8 -> 11
47.22/46.48	  9 -> 11
47.22/46.48	  11 -> 7
47.22/46.48	Where:
47.22/46.48	  7) f8#(I48, I49, I50, I51, I52, I53, I54, I55) -> f10#(I48, I49, I50, I51, I52, I53, I54, I55) 
47.22/46.48	  8) f9#(I56, I57, I58, I59, I60, I61, I62, I63) -> f7#(I56, I57, I58, I59, I60, I61, I62, I63) [1 + I61 <= 0]
47.22/46.48	  9) f9#(I64, I65, I66, I67, I68, I69, I70, I71) -> f7#(I64, I65, I66, I67, I68, I69, I70, I71) [1 <= I69]
47.22/46.48	  11) f7#(I80, I81, I82, I83, I84, I85, I86, I87) -> f8#(I80, 1 + I81, I82, I83, I84, I85, I86, I87) 
47.22/46.48	
47.22/46.48	We have the following SCCs.
47.22/46.48	  
47.22/46.48	
47.22/46.48	DP problem for innermost termination.
47.22/46.48	P =
47.22/46.48	  f3#(I8, I9, I10, I11, I12, I13, I14, I15) -> f4#(I8, 1 + I9, I10, I11, I12, I13, I14, I15) [1 + I9 <= I8]
47.22/46.48	  f4#(I96, I97, I98, I99, I100, I101, I102, I103) -> f1#(I96, I97, rnd3, I99, rnd5, I101, I97, I103) [rnd5 = rnd3 /\ rnd3 = rnd3]
47.22/46.48	  f1#(I104, I105, I106, I107, I108, I109, I110, I111) -> f3#(I104, I105, I106, I107, I108, I109, I110, I111) [1 + I108 <= 0]
47.22/46.48	  f1#(I112, I113, I114, I115, I116, I117, I118, I119) -> f3#(I112, I113, I114, I115, I116, I117, I118, I119) [1 <= I116]
47.22/46.48	R = 
47.22/46.48	  f12(x1, x2, x3, x4, x5, x6, x7, x8) -> f11(x1, x2, x3, x4, x5, x6, x7, x8) 
47.22/46.48	  f11(I0, I1, I2, I3, I4, I5, I6, I7) -> f4(I0, 0, I2, I3, I4, I5, I6, I7) 
47.22/46.48	  f3(I8, I9, I10, I11, I12, I13, I14, I15) -> f4(I8, 1 + I9, I10, I11, I12, I13, I14, I15) [1 + I9 <= I8]
47.22/46.48	  f3(I16, I17, I18, I19, I20, I21, I22, I23) -> f2(I16, I17, I18, I19, I20, I21, I22, I23) [I16 <= I17]
47.22/46.48	  f2(I24, I25, I26, I27, I28, I29, I30, I31) -> f8(I24, 0, I26, I27, I28, I29, I30, I31) 
47.22/46.48	  f10(I32, I33, I34, I35, I36, I37, I38, I39) -> f9(I32, I33, I34, rnd4, I36, rnd6, I38, I33) [rnd6 = rnd4 /\ rnd4 = rnd4 /\ 1 + I33 <= I32]
47.22/46.48	  f10(I40, I41, I42, I43, I44, I45, I46, I47) -> f5(I40, I41, I42, I43, I44, I45, I46, I47) [I40 <= I41]
47.22/46.48	  f8(I48, I49, I50, I51, I52, I53, I54, I55) -> f10(I48, I49, I50, I51, I52, I53, I54, I55) 
47.22/46.48	  f9(I56, I57, I58, I59, I60, I61, I62, I63) -> f7(I56, I57, I58, I59, I60, I61, I62, I63) [1 + I61 <= 0]
47.22/46.48	  f9(I64, I65, I66, I67, I68, I69, I70, I71) -> f7(I64, I65, I66, I67, I68, I69, I70, I71) [1 <= I69]
47.22/46.48	  f9(I72, I73, I74, I75, I76, I77, I78, I79) -> f5(I72, I73, I74, I75, I76, I77, I78, I79) [0 <= I77 /\ I77 <= 0]
47.22/46.48	  f7(I80, I81, I82, I83, I84, I85, I86, I87) -> f8(I80, 1 + I81, I82, I83, I84, I85, I86, I87) 
47.22/46.48	  f5(I88, I89, I90, I91, I92, I93, I94, I95) -> f6(I88, I89, I90, I91, I92, I93, I94, I95) 
47.22/46.48	  f4(I96, I97, I98, I99, I100, I101, I102, I103) -> f1(I96, I97, rnd3, I99, rnd5, I101, I97, I103) [rnd5 = rnd3 /\ rnd3 = rnd3]
47.22/46.48	  f1(I104, I105, I106, I107, I108, I109, I110, I111) -> f3(I104, I105, I106, I107, I108, I109, I110, I111) [1 + I108 <= 0]
47.22/46.48	  f1(I112, I113, I114, I115, I116, I117, I118, I119) -> f3(I112, I113, I114, I115, I116, I117, I118, I119) [1 <= I116]
47.22/46.48	  f1(I120, I121, I122, I123, I124, I125, I126, I127) -> f2(I120, I121, I122, I123, I124, I125, I126, I127) [0 <= I124 /\ I124 <= 0]
47.22/46.48	
47.22/46.48	We use the extended value criterion with the projection function NU:
47.22/46.48	  NU[f1#(x0,x1,x2,x3,x4,x5,x6,x7)] = x0 - x1 - 1
47.22/46.48	  NU[f4#(x0,x1,x2,x3,x4,x5,x6,x7)] = x0 - x1 - 1
47.22/46.48	  NU[f3#(x0,x1,x2,x3,x4,x5,x6,x7)] = x0 - x1 - 1
47.22/46.48	
47.22/46.48	This gives the following inequalities:
47.22/46.48	  1 + I9 <= I8  ==>  I8 - I9 - 1 > I8 - (1 + I9) - 1  with  I8 - I9 - 1 >= 0
47.22/46.48	  rnd5 = rnd3 /\ rnd3 = rnd3  ==>  I96 - I97 - 1 >= I96 - I97 - 1
47.22/46.48	  1 + I108 <= 0  ==>  I104 - I105 - 1 >= I104 - I105 - 1
47.22/46.48	  1 <= I116  ==>  I112 - I113 - 1 >= I112 - I113 - 1
47.22/46.48	
47.22/46.48	We remove all the strictly oriented dependency pairs.
47.22/46.48	
47.22/46.48	DP problem for innermost termination.
47.22/46.48	P =
47.22/46.48	  f4#(I96, I97, I98, I99, I100, I101, I102, I103) -> f1#(I96, I97, rnd3, I99, rnd5, I101, I97, I103) [rnd5 = rnd3 /\ rnd3 = rnd3]
47.22/46.48	  f1#(I104, I105, I106, I107, I108, I109, I110, I111) -> f3#(I104, I105, I106, I107, I108, I109, I110, I111) [1 + I108 <= 0]
47.22/46.48	  f1#(I112, I113, I114, I115, I116, I117, I118, I119) -> f3#(I112, I113, I114, I115, I116, I117, I118, I119) [1 <= I116]
47.22/46.48	R = 
47.22/46.48	  f12(x1, x2, x3, x4, x5, x6, x7, x8) -> f11(x1, x2, x3, x4, x5, x6, x7, x8) 
47.22/46.48	  f11(I0, I1, I2, I3, I4, I5, I6, I7) -> f4(I0, 0, I2, I3, I4, I5, I6, I7) 
47.22/46.48	  f3(I8, I9, I10, I11, I12, I13, I14, I15) -> f4(I8, 1 + I9, I10, I11, I12, I13, I14, I15) [1 + I9 <= I8]
47.22/46.48	  f3(I16, I17, I18, I19, I20, I21, I22, I23) -> f2(I16, I17, I18, I19, I20, I21, I22, I23) [I16 <= I17]
47.22/46.48	  f2(I24, I25, I26, I27, I28, I29, I30, I31) -> f8(I24, 0, I26, I27, I28, I29, I30, I31) 
47.22/46.48	  f10(I32, I33, I34, I35, I36, I37, I38, I39) -> f9(I32, I33, I34, rnd4, I36, rnd6, I38, I33) [rnd6 = rnd4 /\ rnd4 = rnd4 /\ 1 + I33 <= I32]
47.22/46.48	  f10(I40, I41, I42, I43, I44, I45, I46, I47) -> f5(I40, I41, I42, I43, I44, I45, I46, I47) [I40 <= I41]
47.22/46.48	  f8(I48, I49, I50, I51, I52, I53, I54, I55) -> f10(I48, I49, I50, I51, I52, I53, I54, I55) 
47.22/46.48	  f9(I56, I57, I58, I59, I60, I61, I62, I63) -> f7(I56, I57, I58, I59, I60, I61, I62, I63) [1 + I61 <= 0]
47.22/46.48	  f9(I64, I65, I66, I67, I68, I69, I70, I71) -> f7(I64, I65, I66, I67, I68, I69, I70, I71) [1 <= I69]
47.22/46.48	  f9(I72, I73, I74, I75, I76, I77, I78, I79) -> f5(I72, I73, I74, I75, I76, I77, I78, I79) [0 <= I77 /\ I77 <= 0]
47.22/46.48	  f7(I80, I81, I82, I83, I84, I85, I86, I87) -> f8(I80, 1 + I81, I82, I83, I84, I85, I86, I87) 
47.22/46.48	  f5(I88, I89, I90, I91, I92, I93, I94, I95) -> f6(I88, I89, I90, I91, I92, I93, I94, I95) 
47.22/46.48	  f4(I96, I97, I98, I99, I100, I101, I102, I103) -> f1(I96, I97, rnd3, I99, rnd5, I101, I97, I103) [rnd5 = rnd3 /\ rnd3 = rnd3]
47.22/46.48	  f1(I104, I105, I106, I107, I108, I109, I110, I111) -> f3(I104, I105, I106, I107, I108, I109, I110, I111) [1 + I108 <= 0]
47.22/46.48	  f1(I112, I113, I114, I115, I116, I117, I118, I119) -> f3(I112, I113, I114, I115, I116, I117, I118, I119) [1 <= I116]
47.22/46.48	  f1(I120, I121, I122, I123, I124, I125, I126, I127) -> f2(I120, I121, I122, I123, I124, I125, I126, I127) [0 <= I124 /\ I124 <= 0]
47.22/46.48	
47.22/46.48	The dependency graph for this problem is:
47.22/46.48	  12 -> 13, 14
47.22/46.48	  13 -> 
47.22/46.48	  14 -> 
47.22/46.48	Where:
47.22/46.48	  12) f4#(I96, I97, I98, I99, I100, I101, I102, I103) -> f1#(I96, I97, rnd3, I99, rnd5, I101, I97, I103) [rnd5 = rnd3 /\ rnd3 = rnd3]
47.22/46.48	  13) f1#(I104, I105, I106, I107, I108, I109, I110, I111) -> f3#(I104, I105, I106, I107, I108, I109, I110, I111) [1 + I108 <= 0]
47.22/46.48	  14) f1#(I112, I113, I114, I115, I116, I117, I118, I119) -> f3#(I112, I113, I114, I115, I116, I117, I118, I119) [1 <= I116]
47.22/46.48	
47.22/46.48	We have the following SCCs.
47.22/46.48	  
47.22/49.45	EOF