106.01/105.37	YES
106.01/105.37	
106.01/105.37	DP problem for innermost termination.
106.01/105.37	P =
106.01/105.37	  f18#(x1, x2, x3, x4, x5, x6, x7) -> f17#(x1, x2, x3, x4, x5, x6, x7) 
106.01/105.37	  f17#(I0, I1, I2, I3, I4, I5, I6) -> f11#(13, 0, I2, 5, 0, I5, I6) 
106.01/105.37	  f3#(I7, I8, I9, I10, I11, I12, I13) -> f1#(I7, I8, I9, I10, I11, I12, I13) 
106.01/105.37	  f5#(I14, I15, I16, I17, I18, I19, I20) -> f6#(I14, I15, I16, I17, I18, I19, I20) 
106.01/105.37	  f8#(I21, I22, I23, I24, I25, I26, I27) -> f9#(I21, I22, I23, I24, I25, I26, I27) 
106.01/105.37	  f12#(I28, I29, I30, I31, I32, I33, I34) -> f16#(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31]
106.01/105.37	  f12#(I35, I36, I37, I38, I39, I40, I41) -> f10#(I35, 0, I37, I38, I39, I40, I41) [I38 <= I36]
106.01/105.37	  f10#(I42, I43, I44, I45, I46, I47, I48) -> f13#(I42, I43, I44, I45, I46, I47, I48) 
106.01/105.37	  f16#(I49, I50, I51, I52, I53, I54, I55) -> f15#(I49, I50, I51, I52, I53, I54, I55) [I53 <= I50 /\ I50 <= I53]
106.01/105.37	  f16#(I56, I57, I58, I59, I60, I61, I62) -> f14#(I56, I57, I58, I59, I60, I61, I62) [1 + I57 <= I60]
106.01/105.37	  f16#(I63, I64, I65, I66, I67, I68, I69) -> f14#(I63, I64, I65, I66, I67, I68, I69) [1 + I67 <= I64]
106.01/105.37	  f15#(I70, I71, I72, I73, I74, I75, I76) -> f11#(I70, 1 + I71, I72, I73, I74, I75, I76) 
106.01/105.37	  f14#(I77, I78, I79, I80, I81, I82, I83) -> f15#(I77, I78, I79, I80, I81, I82, I83) 
106.01/105.37	  f13#(I84, I85, I86, I87, I88, I89, I90) -> f8#(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87]
106.01/105.37	  f13#(I91, I92, I93, I94, I95, I96, I97) -> f5#(I91, 0, I93, I94, I95, I96, I97) [I94 <= I92]
106.01/105.37	  f11#(I98, I99, I100, I101, I102, I103, I104) -> f12#(I98, I99, I100, I101, I102, I103, I104) 
106.01/105.37	  f9#(I105, I106, I107, I108, I109, I110, I111) -> f7#(I105, I106, I107, I108, I109, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I107 <= I105]
106.01/105.37	  f9#(I112, I113, I114, I115, I116, I117, I118) -> f10#(I112, 1 + I113, I114, I115, I116, I117, I118) [I112 <= I114]
106.01/105.37	  f7#(I119, I120, I121, I122, I123, I124, I125) -> f8#(I119, I120, 1 + I121, I122, I123, I124, I125) 
106.01/105.37	  f6#(I126, I127, I128, I129, I130, I131, I132) -> f4#(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126]
106.01/105.37	  f6#(I135, I136, I137, I138, I139, I140, I141) -> f3#(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136]
106.01/105.37	  f4#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, 1 + I150, I151, I152, I153, I154, I155) 
106.01/105.37	  f1#(I156, I157, I158, I159, I160, I161, I162) -> f3#(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159]
106.01/105.37	R = 
106.01/105.37	  f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 
106.01/105.37	  f17(I0, I1, I2, I3, I4, I5, I6) -> f11(13, 0, I2, 5, 0, I5, I6) 
106.01/105.37	  f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 
106.01/105.37	  f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 
106.01/105.37	  f8(I21, I22, I23, I24, I25, I26, I27) -> f9(I21, I22, I23, I24, I25, I26, I27) 
106.01/105.37	  f12(I28, I29, I30, I31, I32, I33, I34) -> f16(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31]
106.01/105.37	  f12(I35, I36, I37, I38, I39, I40, I41) -> f10(I35, 0, I37, I38, I39, I40, I41) [I38 <= I36]
106.01/105.37	  f10(I42, I43, I44, I45, I46, I47, I48) -> f13(I42, I43, I44, I45, I46, I47, I48) 
106.01/105.37	  f16(I49, I50, I51, I52, I53, I54, I55) -> f15(I49, I50, I51, I52, I53, I54, I55) [I53 <= I50 /\ I50 <= I53]
106.01/105.37	  f16(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I57 <= I60]
106.01/105.37	  f16(I63, I64, I65, I66, I67, I68, I69) -> f14(I63, I64, I65, I66, I67, I68, I69) [1 + I67 <= I64]
106.01/105.37	  f15(I70, I71, I72, I73, I74, I75, I76) -> f11(I70, 1 + I71, I72, I73, I74, I75, I76) 
106.01/105.37	  f14(I77, I78, I79, I80, I81, I82, I83) -> f15(I77, I78, I79, I80, I81, I82, I83) 
106.01/105.37	  f13(I84, I85, I86, I87, I88, I89, I90) -> f8(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87]
106.01/105.37	  f13(I91, I92, I93, I94, I95, I96, I97) -> f5(I91, 0, I93, I94, I95, I96, I97) [I94 <= I92]
106.01/105.37	  f11(I98, I99, I100, I101, I102, I103, I104) -> f12(I98, I99, I100, I101, I102, I103, I104) 
106.01/105.37	  f9(I105, I106, I107, I108, I109, I110, I111) -> f7(I105, I106, I107, I108, I109, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I107 <= I105]
106.01/105.37	  f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, 1 + I113, I114, I115, I116, I117, I118) [I112 <= I114]
106.01/105.37	  f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, 1 + I121, I122, I123, I124, I125) 
106.01/105.37	  f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126]
106.01/105.37	  f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136]
106.01/105.37	  f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 
106.01/105.37	  f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 
106.01/105.37	  f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159]
106.01/105.37	  f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164]
106.01/105.37	
106.01/105.37	The dependency graph for this problem is:
106.01/105.37	  0 -> 1
106.01/105.37	  1 -> 15
106.01/105.37	  2 -> 22
106.01/105.37	  3 -> 19, 20
106.01/105.37	  4 -> 16, 17
106.01/105.37	  5 -> 8, 9, 10
106.01/105.37	  6 -> 7
106.01/105.37	  7 -> 13, 14
106.01/105.37	  8 -> 11
106.01/105.37	  9 -> 12
106.01/105.37	  10 -> 12
106.01/105.37	  11 -> 15
106.01/105.37	  12 -> 11
106.01/105.37	  13 -> 4
106.01/105.37	  14 -> 3
106.01/105.37	  15 -> 5, 6
106.01/105.37	  16 -> 18
106.01/105.37	  17 -> 7
106.01/105.37	  18 -> 4
106.01/105.37	  19 -> 21
106.01/105.37	  20 -> 2
106.01/105.37	  21 -> 3
106.01/105.37	  22 -> 2
106.01/105.37	Where:
106.01/105.37	  0) f18#(x1, x2, x3, x4, x5, x6, x7) -> f17#(x1, x2, x3, x4, x5, x6, x7) 
106.01/105.37	  1) f17#(I0, I1, I2, I3, I4, I5, I6) -> f11#(13, 0, I2, 5, 0, I5, I6) 
106.01/105.37	  2) f3#(I7, I8, I9, I10, I11, I12, I13) -> f1#(I7, I8, I9, I10, I11, I12, I13) 
106.01/105.37	  3) f5#(I14, I15, I16, I17, I18, I19, I20) -> f6#(I14, I15, I16, I17, I18, I19, I20) 
106.01/105.37	  4) f8#(I21, I22, I23, I24, I25, I26, I27) -> f9#(I21, I22, I23, I24, I25, I26, I27) 
106.01/105.37	  5) f12#(I28, I29, I30, I31, I32, I33, I34) -> f16#(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31]
106.01/105.37	  6) f12#(I35, I36, I37, I38, I39, I40, I41) -> f10#(I35, 0, I37, I38, I39, I40, I41) [I38 <= I36]
106.01/105.37	  7) f10#(I42, I43, I44, I45, I46, I47, I48) -> f13#(I42, I43, I44, I45, I46, I47, I48) 
106.01/105.37	  8) f16#(I49, I50, I51, I52, I53, I54, I55) -> f15#(I49, I50, I51, I52, I53, I54, I55) [I53 <= I50 /\ I50 <= I53]
106.01/105.37	  9) f16#(I56, I57, I58, I59, I60, I61, I62) -> f14#(I56, I57, I58, I59, I60, I61, I62) [1 + I57 <= I60]
106.01/105.37	  10) f16#(I63, I64, I65, I66, I67, I68, I69) -> f14#(I63, I64, I65, I66, I67, I68, I69) [1 + I67 <= I64]
106.01/105.37	  11) f15#(I70, I71, I72, I73, I74, I75, I76) -> f11#(I70, 1 + I71, I72, I73, I74, I75, I76) 
106.01/105.37	  12) f14#(I77, I78, I79, I80, I81, I82, I83) -> f15#(I77, I78, I79, I80, I81, I82, I83) 
106.01/105.37	  13) f13#(I84, I85, I86, I87, I88, I89, I90) -> f8#(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87]
106.01/105.37	  14) f13#(I91, I92, I93, I94, I95, I96, I97) -> f5#(I91, 0, I93, I94, I95, I96, I97) [I94 <= I92]
106.01/105.37	  15) f11#(I98, I99, I100, I101, I102, I103, I104) -> f12#(I98, I99, I100, I101, I102, I103, I104) 
106.01/105.37	  16) f9#(I105, I106, I107, I108, I109, I110, I111) -> f7#(I105, I106, I107, I108, I109, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I107 <= I105]
106.01/105.37	  17) f9#(I112, I113, I114, I115, I116, I117, I118) -> f10#(I112, 1 + I113, I114, I115, I116, I117, I118) [I112 <= I114]
106.01/105.37	  18) f7#(I119, I120, I121, I122, I123, I124, I125) -> f8#(I119, I120, 1 + I121, I122, I123, I124, I125) 
106.01/105.37	  19) f6#(I126, I127, I128, I129, I130, I131, I132) -> f4#(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126]
106.01/105.37	  20) f6#(I135, I136, I137, I138, I139, I140, I141) -> f3#(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136]
106.01/105.37	  21) f4#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, 1 + I150, I151, I152, I153, I154, I155) 
106.01/105.37	  22) f1#(I156, I157, I158, I159, I160, I161, I162) -> f3#(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159]
106.01/105.37	
106.01/105.37	We have the following SCCs.
106.01/105.37	  { 5, 8, 9, 10, 11, 12, 15 }
106.01/105.37	  { 4, 7, 13, 16, 17, 18 }
106.01/105.37	  { 3, 19, 21 }
106.01/105.37	  { 2, 22 }
106.01/105.37	
106.01/105.37	DP problem for innermost termination.
106.01/105.37	P =
106.01/105.37	  f3#(I7, I8, I9, I10, I11, I12, I13) -> f1#(I7, I8, I9, I10, I11, I12, I13) 
106.01/105.37	  f1#(I156, I157, I158, I159, I160, I161, I162) -> f3#(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159]
106.01/105.37	R = 
106.01/105.37	  f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 
106.01/105.37	  f17(I0, I1, I2, I3, I4, I5, I6) -> f11(13, 0, I2, 5, 0, I5, I6) 
106.01/105.37	  f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 
106.01/105.37	  f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 
106.01/105.37	  f8(I21, I22, I23, I24, I25, I26, I27) -> f9(I21, I22, I23, I24, I25, I26, I27) 
106.01/105.37	  f12(I28, I29, I30, I31, I32, I33, I34) -> f16(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31]
106.01/105.37	  f12(I35, I36, I37, I38, I39, I40, I41) -> f10(I35, 0, I37, I38, I39, I40, I41) [I38 <= I36]
106.01/105.37	  f10(I42, I43, I44, I45, I46, I47, I48) -> f13(I42, I43, I44, I45, I46, I47, I48) 
106.01/105.37	  f16(I49, I50, I51, I52, I53, I54, I55) -> f15(I49, I50, I51, I52, I53, I54, I55) [I53 <= I50 /\ I50 <= I53]
106.01/105.37	  f16(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I57 <= I60]
106.01/105.37	  f16(I63, I64, I65, I66, I67, I68, I69) -> f14(I63, I64, I65, I66, I67, I68, I69) [1 + I67 <= I64]
106.01/105.37	  f15(I70, I71, I72, I73, I74, I75, I76) -> f11(I70, 1 + I71, I72, I73, I74, I75, I76) 
106.01/105.37	  f14(I77, I78, I79, I80, I81, I82, I83) -> f15(I77, I78, I79, I80, I81, I82, I83) 
106.01/105.37	  f13(I84, I85, I86, I87, I88, I89, I90) -> f8(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87]
106.01/105.37	  f13(I91, I92, I93, I94, I95, I96, I97) -> f5(I91, 0, I93, I94, I95, I96, I97) [I94 <= I92]
106.01/105.37	  f11(I98, I99, I100, I101, I102, I103, I104) -> f12(I98, I99, I100, I101, I102, I103, I104) 
106.01/105.37	  f9(I105, I106, I107, I108, I109, I110, I111) -> f7(I105, I106, I107, I108, I109, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I107 <= I105]
106.01/105.37	  f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, 1 + I113, I114, I115, I116, I117, I118) [I112 <= I114]
106.01/105.37	  f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, 1 + I121, I122, I123, I124, I125) 
106.01/105.37	  f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126]
106.01/105.37	  f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136]
106.01/105.37	  f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 
106.01/105.37	  f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 
106.01/105.37	  f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159]
106.01/105.37	  f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164]
106.01/105.37	
106.01/105.37	We use the reverse value criterion with the projection function NU:
106.01/105.37	  NU[f1#(z1,z2,z3,z4,z5,z6,z7)] = z4 + -1 * (1 + z2)
106.01/105.37	  NU[f3#(z1,z2,z3,z4,z5,z6,z7)] = z4 + -1 * (1 + z2)
106.01/105.37	
106.01/105.37	This gives the following inequalities:
106.01/105.37	    ==>  I10 + -1 * (1 + I8) >= I10 + -1 * (1 + I8)
106.01/105.37	  1 + I157 <= I159  ==>  I159 + -1 * (1 + I157) > I159 + -1 * (1 + (1 + I157))  with  I159 + -1 * (1 + I157) >= 0
106.01/105.37	
106.01/105.37	We remove all the strictly oriented dependency pairs.
106.01/105.37	
106.01/105.37	DP problem for innermost termination.
106.01/105.37	P =
106.01/105.37	  f3#(I7, I8, I9, I10, I11, I12, I13) -> f1#(I7, I8, I9, I10, I11, I12, I13) 
106.01/105.37	R = 
106.01/105.37	  f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 
106.01/105.37	  f17(I0, I1, I2, I3, I4, I5, I6) -> f11(13, 0, I2, 5, 0, I5, I6) 
106.01/105.37	  f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 
106.01/105.37	  f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 
106.01/105.37	  f8(I21, I22, I23, I24, I25, I26, I27) -> f9(I21, I22, I23, I24, I25, I26, I27) 
106.01/105.37	  f12(I28, I29, I30, I31, I32, I33, I34) -> f16(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31]
106.01/105.37	  f12(I35, I36, I37, I38, I39, I40, I41) -> f10(I35, 0, I37, I38, I39, I40, I41) [I38 <= I36]
106.01/105.37	  f10(I42, I43, I44, I45, I46, I47, I48) -> f13(I42, I43, I44, I45, I46, I47, I48) 
106.01/105.37	  f16(I49, I50, I51, I52, I53, I54, I55) -> f15(I49, I50, I51, I52, I53, I54, I55) [I53 <= I50 /\ I50 <= I53]
106.01/105.37	  f16(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I57 <= I60]
106.01/105.37	  f16(I63, I64, I65, I66, I67, I68, I69) -> f14(I63, I64, I65, I66, I67, I68, I69) [1 + I67 <= I64]
106.01/105.37	  f15(I70, I71, I72, I73, I74, I75, I76) -> f11(I70, 1 + I71, I72, I73, I74, I75, I76) 
106.01/105.37	  f14(I77, I78, I79, I80, I81, I82, I83) -> f15(I77, I78, I79, I80, I81, I82, I83) 
106.01/105.37	  f13(I84, I85, I86, I87, I88, I89, I90) -> f8(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87]
106.01/105.37	  f13(I91, I92, I93, I94, I95, I96, I97) -> f5(I91, 0, I93, I94, I95, I96, I97) [I94 <= I92]
106.01/105.37	  f11(I98, I99, I100, I101, I102, I103, I104) -> f12(I98, I99, I100, I101, I102, I103, I104) 
106.01/105.37	  f9(I105, I106, I107, I108, I109, I110, I111) -> f7(I105, I106, I107, I108, I109, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I107 <= I105]
106.01/105.37	  f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, 1 + I113, I114, I115, I116, I117, I118) [I112 <= I114]
106.01/105.37	  f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, 1 + I121, I122, I123, I124, I125) 
106.01/105.37	  f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126]
106.01/105.37	  f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136]
106.01/105.37	  f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 
106.01/105.37	  f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 
106.01/105.37	  f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159]
106.01/105.37	  f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164]
106.01/105.37	
106.01/105.37	The dependency graph for this problem is:
106.01/105.37	  2 -> 
106.01/105.37	Where:
106.01/105.37	  2) f3#(I7, I8, I9, I10, I11, I12, I13) -> f1#(I7, I8, I9, I10, I11, I12, I13) 
106.01/105.37	
106.01/105.37	We have the following SCCs.
106.01/105.37	  
106.01/105.37	
106.01/105.37	DP problem for innermost termination.
106.01/105.37	P =
106.01/105.37	  f5#(I14, I15, I16, I17, I18, I19, I20) -> f6#(I14, I15, I16, I17, I18, I19, I20) 
106.01/105.37	  f6#(I126, I127, I128, I129, I130, I131, I132) -> f4#(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126]
106.01/105.37	  f4#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, 1 + I150, I151, I152, I153, I154, I155) 
106.01/105.37	R = 
106.01/105.37	  f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 
106.01/105.37	  f17(I0, I1, I2, I3, I4, I5, I6) -> f11(13, 0, I2, 5, 0, I5, I6) 
106.01/105.37	  f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 
106.01/105.37	  f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 
106.01/105.37	  f8(I21, I22, I23, I24, I25, I26, I27) -> f9(I21, I22, I23, I24, I25, I26, I27) 
106.01/105.37	  f12(I28, I29, I30, I31, I32, I33, I34) -> f16(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31]
106.01/105.37	  f12(I35, I36, I37, I38, I39, I40, I41) -> f10(I35, 0, I37, I38, I39, I40, I41) [I38 <= I36]
106.01/105.37	  f10(I42, I43, I44, I45, I46, I47, I48) -> f13(I42, I43, I44, I45, I46, I47, I48) 
106.01/105.37	  f16(I49, I50, I51, I52, I53, I54, I55) -> f15(I49, I50, I51, I52, I53, I54, I55) [I53 <= I50 /\ I50 <= I53]
106.01/105.37	  f16(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I57 <= I60]
106.01/105.37	  f16(I63, I64, I65, I66, I67, I68, I69) -> f14(I63, I64, I65, I66, I67, I68, I69) [1 + I67 <= I64]
106.01/105.37	  f15(I70, I71, I72, I73, I74, I75, I76) -> f11(I70, 1 + I71, I72, I73, I74, I75, I76) 
106.01/105.37	  f14(I77, I78, I79, I80, I81, I82, I83) -> f15(I77, I78, I79, I80, I81, I82, I83) 
106.01/105.37	  f13(I84, I85, I86, I87, I88, I89, I90) -> f8(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87]
106.01/105.37	  f13(I91, I92, I93, I94, I95, I96, I97) -> f5(I91, 0, I93, I94, I95, I96, I97) [I94 <= I92]
106.01/105.37	  f11(I98, I99, I100, I101, I102, I103, I104) -> f12(I98, I99, I100, I101, I102, I103, I104) 
106.01/105.37	  f9(I105, I106, I107, I108, I109, I110, I111) -> f7(I105, I106, I107, I108, I109, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I107 <= I105]
106.01/105.37	  f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, 1 + I113, I114, I115, I116, I117, I118) [I112 <= I114]
106.01/105.37	  f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, 1 + I121, I122, I123, I124, I125) 
106.01/105.37	  f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126]
106.01/105.37	  f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136]
106.01/105.37	  f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 
106.01/105.37	  f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 
106.01/105.37	  f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159]
106.01/105.37	  f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164]
106.01/105.37	
106.01/105.37	We use the extended value criterion with the projection function NU:
106.01/105.37	  NU[f4#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x1 - 2
106.01/105.37	  NU[f6#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x1 - 1
106.01/105.37	  NU[f5#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x1 - 1
106.01/105.37	
106.01/105.37	This gives the following inequalities:
106.01/105.37	    ==>  I14 - I15 - 1 >= I14 - I15 - 1
106.01/105.37	  I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126  ==>  I126 - I127 - 1 > I126 - I127 - 2  with  I126 - I127 - 1 >= 0
106.01/105.37	    ==>  I149 - I150 - 2 >= I149 - (1 + I150) - 1
106.01/105.37	
106.01/105.37	We remove all the strictly oriented dependency pairs.
106.01/105.37	
106.01/105.37	DP problem for innermost termination.
106.01/105.37	P =
106.01/105.37	  f5#(I14, I15, I16, I17, I18, I19, I20) -> f6#(I14, I15, I16, I17, I18, I19, I20) 
106.01/105.37	  f4#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, 1 + I150, I151, I152, I153, I154, I155) 
106.01/105.37	R = 
106.01/105.37	  f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 
106.01/105.37	  f17(I0, I1, I2, I3, I4, I5, I6) -> f11(13, 0, I2, 5, 0, I5, I6) 
106.01/105.37	  f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 
106.01/105.37	  f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 
106.01/105.37	  f8(I21, I22, I23, I24, I25, I26, I27) -> f9(I21, I22, I23, I24, I25, I26, I27) 
106.01/105.37	  f12(I28, I29, I30, I31, I32, I33, I34) -> f16(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31]
106.01/105.37	  f12(I35, I36, I37, I38, I39, I40, I41) -> f10(I35, 0, I37, I38, I39, I40, I41) [I38 <= I36]
106.01/105.37	  f10(I42, I43, I44, I45, I46, I47, I48) -> f13(I42, I43, I44, I45, I46, I47, I48) 
106.01/105.37	  f16(I49, I50, I51, I52, I53, I54, I55) -> f15(I49, I50, I51, I52, I53, I54, I55) [I53 <= I50 /\ I50 <= I53]
106.01/105.37	  f16(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I57 <= I60]
106.01/105.37	  f16(I63, I64, I65, I66, I67, I68, I69) -> f14(I63, I64, I65, I66, I67, I68, I69) [1 + I67 <= I64]
106.01/105.37	  f15(I70, I71, I72, I73, I74, I75, I76) -> f11(I70, 1 + I71, I72, I73, I74, I75, I76) 
106.01/105.37	  f14(I77, I78, I79, I80, I81, I82, I83) -> f15(I77, I78, I79, I80, I81, I82, I83) 
106.01/105.37	  f13(I84, I85, I86, I87, I88, I89, I90) -> f8(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87]
106.01/105.37	  f13(I91, I92, I93, I94, I95, I96, I97) -> f5(I91, 0, I93, I94, I95, I96, I97) [I94 <= I92]
106.01/105.37	  f11(I98, I99, I100, I101, I102, I103, I104) -> f12(I98, I99, I100, I101, I102, I103, I104) 
106.01/105.37	  f9(I105, I106, I107, I108, I109, I110, I111) -> f7(I105, I106, I107, I108, I109, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I107 <= I105]
106.01/105.37	  f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, 1 + I113, I114, I115, I116, I117, I118) [I112 <= I114]
106.01/105.37	  f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, 1 + I121, I122, I123, I124, I125) 
106.01/105.37	  f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126]
106.01/105.37	  f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136]
106.01/105.37	  f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 
106.01/105.37	  f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 
106.01/105.37	  f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159]
106.01/105.37	  f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164]
106.01/105.37	
106.01/105.37	The dependency graph for this problem is:
106.01/105.37	  3 -> 
106.01/105.37	  21 -> 3
106.01/105.37	Where:
106.01/105.37	  3) f5#(I14, I15, I16, I17, I18, I19, I20) -> f6#(I14, I15, I16, I17, I18, I19, I20) 
106.01/105.37	  21) f4#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, 1 + I150, I151, I152, I153, I154, I155) 
106.01/105.37	
106.01/105.37	We have the following SCCs.
106.01/105.37	  
106.01/105.37	
106.01/105.37	DP problem for innermost termination.
106.01/105.37	P =
106.01/105.37	  f8#(I21, I22, I23, I24, I25, I26, I27) -> f9#(I21, I22, I23, I24, I25, I26, I27) 
106.01/105.37	  f10#(I42, I43, I44, I45, I46, I47, I48) -> f13#(I42, I43, I44, I45, I46, I47, I48) 
106.01/105.37	  f13#(I84, I85, I86, I87, I88, I89, I90) -> f8#(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87]
106.01/105.37	  f9#(I105, I106, I107, I108, I109, I110, I111) -> f7#(I105, I106, I107, I108, I109, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I107 <= I105]
106.01/105.37	  f9#(I112, I113, I114, I115, I116, I117, I118) -> f10#(I112, 1 + I113, I114, I115, I116, I117, I118) [I112 <= I114]
106.01/105.37	  f7#(I119, I120, I121, I122, I123, I124, I125) -> f8#(I119, I120, 1 + I121, I122, I123, I124, I125) 
106.01/105.37	R = 
106.01/105.37	  f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 
106.01/105.37	  f17(I0, I1, I2, I3, I4, I5, I6) -> f11(13, 0, I2, 5, 0, I5, I6) 
106.01/105.37	  f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 
106.01/105.37	  f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 
106.01/105.37	  f8(I21, I22, I23, I24, I25, I26, I27) -> f9(I21, I22, I23, I24, I25, I26, I27) 
106.01/105.37	  f12(I28, I29, I30, I31, I32, I33, I34) -> f16(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31]
106.01/105.37	  f12(I35, I36, I37, I38, I39, I40, I41) -> f10(I35, 0, I37, I38, I39, I40, I41) [I38 <= I36]
106.01/105.37	  f10(I42, I43, I44, I45, I46, I47, I48) -> f13(I42, I43, I44, I45, I46, I47, I48) 
106.01/105.37	  f16(I49, I50, I51, I52, I53, I54, I55) -> f15(I49, I50, I51, I52, I53, I54, I55) [I53 <= I50 /\ I50 <= I53]
106.01/105.37	  f16(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I57 <= I60]
106.01/105.37	  f16(I63, I64, I65, I66, I67, I68, I69) -> f14(I63, I64, I65, I66, I67, I68, I69) [1 + I67 <= I64]
106.01/105.37	  f15(I70, I71, I72, I73, I74, I75, I76) -> f11(I70, 1 + I71, I72, I73, I74, I75, I76) 
106.01/105.37	  f14(I77, I78, I79, I80, I81, I82, I83) -> f15(I77, I78, I79, I80, I81, I82, I83) 
106.01/105.37	  f13(I84, I85, I86, I87, I88, I89, I90) -> f8(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87]
106.01/105.37	  f13(I91, I92, I93, I94, I95, I96, I97) -> f5(I91, 0, I93, I94, I95, I96, I97) [I94 <= I92]
106.01/105.37	  f11(I98, I99, I100, I101, I102, I103, I104) -> f12(I98, I99, I100, I101, I102, I103, I104) 
106.01/105.37	  f9(I105, I106, I107, I108, I109, I110, I111) -> f7(I105, I106, I107, I108, I109, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I107 <= I105]
106.01/105.37	  f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, 1 + I113, I114, I115, I116, I117, I118) [I112 <= I114]
106.01/105.37	  f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, 1 + I121, I122, I123, I124, I125) 
106.01/105.37	  f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126]
106.01/105.37	  f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136]
106.01/105.37	  f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 
106.01/105.37	  f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 
106.01/105.37	  f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159]
106.01/105.37	  f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164]
106.01/105.37	
106.01/105.37	We use the extended value criterion with the projection function NU:
106.01/105.37	  NU[f7#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2
106.01/105.37	  NU[f13#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 1
106.01/105.37	  NU[f10#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 1
106.01/105.37	  NU[f9#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2
106.01/105.37	  NU[f8#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2
106.01/105.37	
106.01/105.37	This gives the following inequalities:
106.01/105.37	    ==>  -I22 + I24 - 2 >= -I22 + I24 - 2
106.01/105.37	    ==>  -I43 + I45 - 1 >= -I43 + I45 - 1
106.01/105.37	  1 + I85 <= I87  ==>  -I85 + I87 - 1 > -I85 + I87 - 2  with  -I85 + I87 - 1 >= 0
106.01/105.37	  rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I107 <= I105  ==>  -I106 + I108 - 2 >= -I106 + I108 - 2
106.01/105.37	  I112 <= I114  ==>  -I113 + I115 - 2 >= -(1 + I113) + I115 - 1
106.01/105.37	    ==>  -I120 + I122 - 2 >= -I120 + I122 - 2
106.01/105.37	
106.01/105.37	We remove all the strictly oriented dependency pairs.
106.01/105.37	
106.01/105.37	DP problem for innermost termination.
106.01/105.37	P =
106.01/105.37	  f8#(I21, I22, I23, I24, I25, I26, I27) -> f9#(I21, I22, I23, I24, I25, I26, I27) 
106.01/105.37	  f10#(I42, I43, I44, I45, I46, I47, I48) -> f13#(I42, I43, I44, I45, I46, I47, I48) 
106.01/105.37	  f9#(I105, I106, I107, I108, I109, I110, I111) -> f7#(I105, I106, I107, I108, I109, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I107 <= I105]
106.01/105.37	  f9#(I112, I113, I114, I115, I116, I117, I118) -> f10#(I112, 1 + I113, I114, I115, I116, I117, I118) [I112 <= I114]
106.01/105.37	  f7#(I119, I120, I121, I122, I123, I124, I125) -> f8#(I119, I120, 1 + I121, I122, I123, I124, I125) 
106.01/105.37	R = 
106.01/105.37	  f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 
106.01/105.37	  f17(I0, I1, I2, I3, I4, I5, I6) -> f11(13, 0, I2, 5, 0, I5, I6) 
106.01/105.37	  f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 
106.01/105.37	  f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 
106.01/105.37	  f8(I21, I22, I23, I24, I25, I26, I27) -> f9(I21, I22, I23, I24, I25, I26, I27) 
106.01/105.37	  f12(I28, I29, I30, I31, I32, I33, I34) -> f16(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31]
106.01/105.37	  f12(I35, I36, I37, I38, I39, I40, I41) -> f10(I35, 0, I37, I38, I39, I40, I41) [I38 <= I36]
106.01/105.37	  f10(I42, I43, I44, I45, I46, I47, I48) -> f13(I42, I43, I44, I45, I46, I47, I48) 
106.01/105.37	  f16(I49, I50, I51, I52, I53, I54, I55) -> f15(I49, I50, I51, I52, I53, I54, I55) [I53 <= I50 /\ I50 <= I53]
106.01/105.37	  f16(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I57 <= I60]
106.01/105.37	  f16(I63, I64, I65, I66, I67, I68, I69) -> f14(I63, I64, I65, I66, I67, I68, I69) [1 + I67 <= I64]
106.01/105.37	  f15(I70, I71, I72, I73, I74, I75, I76) -> f11(I70, 1 + I71, I72, I73, I74, I75, I76) 
106.01/105.37	  f14(I77, I78, I79, I80, I81, I82, I83) -> f15(I77, I78, I79, I80, I81, I82, I83) 
106.01/105.37	  f13(I84, I85, I86, I87, I88, I89, I90) -> f8(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87]
106.01/105.37	  f13(I91, I92, I93, I94, I95, I96, I97) -> f5(I91, 0, I93, I94, I95, I96, I97) [I94 <= I92]
106.01/105.37	  f11(I98, I99, I100, I101, I102, I103, I104) -> f12(I98, I99, I100, I101, I102, I103, I104) 
106.01/105.37	  f9(I105, I106, I107, I108, I109, I110, I111) -> f7(I105, I106, I107, I108, I109, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I107 <= I105]
106.01/105.37	  f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, 1 + I113, I114, I115, I116, I117, I118) [I112 <= I114]
106.01/105.37	  f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, 1 + I121, I122, I123, I124, I125) 
106.01/105.37	  f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126]
106.01/105.37	  f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136]
106.01/105.37	  f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 
106.01/105.37	  f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 
106.01/105.37	  f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159]
106.01/105.37	  f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164]
106.01/105.37	
106.01/105.37	The dependency graph for this problem is:
106.01/105.37	  4 -> 16, 17
106.01/105.37	  7 -> 
106.01/105.37	  16 -> 18
106.01/105.37	  17 -> 7
106.01/105.37	  18 -> 4
106.01/105.37	Where:
106.01/105.37	  4) f8#(I21, I22, I23, I24, I25, I26, I27) -> f9#(I21, I22, I23, I24, I25, I26, I27) 
106.01/105.37	  7) f10#(I42, I43, I44, I45, I46, I47, I48) -> f13#(I42, I43, I44, I45, I46, I47, I48) 
106.01/105.37	  16) f9#(I105, I106, I107, I108, I109, I110, I111) -> f7#(I105, I106, I107, I108, I109, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I107 <= I105]
106.01/105.37	  17) f9#(I112, I113, I114, I115, I116, I117, I118) -> f10#(I112, 1 + I113, I114, I115, I116, I117, I118) [I112 <= I114]
106.01/105.37	  18) f7#(I119, I120, I121, I122, I123, I124, I125) -> f8#(I119, I120, 1 + I121, I122, I123, I124, I125) 
106.01/105.37	
106.01/105.37	We have the following SCCs.
106.01/105.37	  { 4, 16, 18 }
106.01/105.37	
106.01/105.37	DP problem for innermost termination.
106.01/105.37	P =
106.01/105.37	  f8#(I21, I22, I23, I24, I25, I26, I27) -> f9#(I21, I22, I23, I24, I25, I26, I27) 
106.01/105.37	  f9#(I105, I106, I107, I108, I109, I110, I111) -> f7#(I105, I106, I107, I108, I109, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I107 <= I105]
106.01/105.37	  f7#(I119, I120, I121, I122, I123, I124, I125) -> f8#(I119, I120, 1 + I121, I122, I123, I124, I125) 
106.01/105.37	R = 
106.01/105.37	  f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 
106.01/105.37	  f17(I0, I1, I2, I3, I4, I5, I6) -> f11(13, 0, I2, 5, 0, I5, I6) 
106.01/105.37	  f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 
106.01/105.37	  f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 
106.01/105.37	  f8(I21, I22, I23, I24, I25, I26, I27) -> f9(I21, I22, I23, I24, I25, I26, I27) 
106.01/105.37	  f12(I28, I29, I30, I31, I32, I33, I34) -> f16(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31]
106.01/105.37	  f12(I35, I36, I37, I38, I39, I40, I41) -> f10(I35, 0, I37, I38, I39, I40, I41) [I38 <= I36]
106.01/105.37	  f10(I42, I43, I44, I45, I46, I47, I48) -> f13(I42, I43, I44, I45, I46, I47, I48) 
106.01/105.37	  f16(I49, I50, I51, I52, I53, I54, I55) -> f15(I49, I50, I51, I52, I53, I54, I55) [I53 <= I50 /\ I50 <= I53]
106.01/105.37	  f16(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I57 <= I60]
106.01/105.37	  f16(I63, I64, I65, I66, I67, I68, I69) -> f14(I63, I64, I65, I66, I67, I68, I69) [1 + I67 <= I64]
106.01/105.37	  f15(I70, I71, I72, I73, I74, I75, I76) -> f11(I70, 1 + I71, I72, I73, I74, I75, I76) 
106.01/105.37	  f14(I77, I78, I79, I80, I81, I82, I83) -> f15(I77, I78, I79, I80, I81, I82, I83) 
106.01/105.37	  f13(I84, I85, I86, I87, I88, I89, I90) -> f8(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87]
106.01/105.37	  f13(I91, I92, I93, I94, I95, I96, I97) -> f5(I91, 0, I93, I94, I95, I96, I97) [I94 <= I92]
106.01/105.37	  f11(I98, I99, I100, I101, I102, I103, I104) -> f12(I98, I99, I100, I101, I102, I103, I104) 
106.01/105.37	  f9(I105, I106, I107, I108, I109, I110, I111) -> f7(I105, I106, I107, I108, I109, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I107 <= I105]
106.01/105.37	  f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, 1 + I113, I114, I115, I116, I117, I118) [I112 <= I114]
106.01/105.37	  f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, 1 + I121, I122, I123, I124, I125) 
106.01/105.37	  f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126]
106.01/105.37	  f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136]
106.01/105.37	  f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 
106.01/105.37	  f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 
106.01/105.37	  f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159]
106.01/105.37	  f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164]
106.01/105.37	
106.01/105.37	We use the extended value criterion with the projection function NU:
106.01/105.37	  NU[f7#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x2 - 2
106.01/105.37	  NU[f9#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x2 - 1
106.01/105.37	  NU[f8#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x2 - 1
106.01/105.37	
106.01/105.37	This gives the following inequalities:
106.01/105.37	    ==>  I21 - I23 - 1 >= I21 - I23 - 1
106.01/105.37	  rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I107 <= I105  ==>  I105 - I107 - 1 > I105 - I107 - 2  with  I105 - I107 - 1 >= 0
106.01/105.37	    ==>  I119 - I121 - 2 >= I119 - (1 + I121) - 1
106.01/105.37	
106.01/105.37	We remove all the strictly oriented dependency pairs.
106.01/105.37	
106.01/105.37	DP problem for innermost termination.
106.01/105.37	P =
106.01/105.37	  f8#(I21, I22, I23, I24, I25, I26, I27) -> f9#(I21, I22, I23, I24, I25, I26, I27) 
106.01/105.37	  f7#(I119, I120, I121, I122, I123, I124, I125) -> f8#(I119, I120, 1 + I121, I122, I123, I124, I125) 
106.01/105.37	R = 
106.01/105.37	  f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 
106.01/105.37	  f17(I0, I1, I2, I3, I4, I5, I6) -> f11(13, 0, I2, 5, 0, I5, I6) 
106.01/105.37	  f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 
106.01/105.37	  f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 
106.01/105.37	  f8(I21, I22, I23, I24, I25, I26, I27) -> f9(I21, I22, I23, I24, I25, I26, I27) 
106.01/105.37	  f12(I28, I29, I30, I31, I32, I33, I34) -> f16(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31]
106.01/105.37	  f12(I35, I36, I37, I38, I39, I40, I41) -> f10(I35, 0, I37, I38, I39, I40, I41) [I38 <= I36]
106.01/105.37	  f10(I42, I43, I44, I45, I46, I47, I48) -> f13(I42, I43, I44, I45, I46, I47, I48) 
106.01/105.37	  f16(I49, I50, I51, I52, I53, I54, I55) -> f15(I49, I50, I51, I52, I53, I54, I55) [I53 <= I50 /\ I50 <= I53]
106.01/105.37	  f16(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I57 <= I60]
106.01/105.37	  f16(I63, I64, I65, I66, I67, I68, I69) -> f14(I63, I64, I65, I66, I67, I68, I69) [1 + I67 <= I64]
106.01/105.37	  f15(I70, I71, I72, I73, I74, I75, I76) -> f11(I70, 1 + I71, I72, I73, I74, I75, I76) 
106.01/105.37	  f14(I77, I78, I79, I80, I81, I82, I83) -> f15(I77, I78, I79, I80, I81, I82, I83) 
106.01/105.37	  f13(I84, I85, I86, I87, I88, I89, I90) -> f8(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87]
106.01/105.37	  f13(I91, I92, I93, I94, I95, I96, I97) -> f5(I91, 0, I93, I94, I95, I96, I97) [I94 <= I92]
106.01/105.37	  f11(I98, I99, I100, I101, I102, I103, I104) -> f12(I98, I99, I100, I101, I102, I103, I104) 
106.01/105.37	  f9(I105, I106, I107, I108, I109, I110, I111) -> f7(I105, I106, I107, I108, I109, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I107 <= I105]
106.01/105.37	  f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, 1 + I113, I114, I115, I116, I117, I118) [I112 <= I114]
106.01/105.37	  f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, 1 + I121, I122, I123, I124, I125) 
106.01/105.37	  f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126]
106.01/105.37	  f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136]
106.01/105.37	  f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 
106.01/105.37	  f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 
106.01/105.37	  f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159]
106.01/105.37	  f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164]
106.01/105.37	
106.01/105.37	The dependency graph for this problem is:
106.01/105.37	  4 -> 
106.01/105.37	  18 -> 4
106.01/105.37	Where:
106.01/105.37	  4) f8#(I21, I22, I23, I24, I25, I26, I27) -> f9#(I21, I22, I23, I24, I25, I26, I27) 
106.01/105.37	  18) f7#(I119, I120, I121, I122, I123, I124, I125) -> f8#(I119, I120, 1 + I121, I122, I123, I124, I125) 
106.01/105.37	
106.01/105.37	We have the following SCCs.
106.01/105.37	  
106.01/105.37	
106.01/105.37	DP problem for innermost termination.
106.01/105.37	P =
106.01/105.37	  f12#(I28, I29, I30, I31, I32, I33, I34) -> f16#(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31]
106.01/105.37	  f16#(I49, I50, I51, I52, I53, I54, I55) -> f15#(I49, I50, I51, I52, I53, I54, I55) [I53 <= I50 /\ I50 <= I53]
106.01/105.37	  f16#(I56, I57, I58, I59, I60, I61, I62) -> f14#(I56, I57, I58, I59, I60, I61, I62) [1 + I57 <= I60]
106.01/105.37	  f16#(I63, I64, I65, I66, I67, I68, I69) -> f14#(I63, I64, I65, I66, I67, I68, I69) [1 + I67 <= I64]
106.01/105.37	  f15#(I70, I71, I72, I73, I74, I75, I76) -> f11#(I70, 1 + I71, I72, I73, I74, I75, I76) 
106.01/105.37	  f14#(I77, I78, I79, I80, I81, I82, I83) -> f15#(I77, I78, I79, I80, I81, I82, I83) 
106.01/105.37	  f11#(I98, I99, I100, I101, I102, I103, I104) -> f12#(I98, I99, I100, I101, I102, I103, I104) 
106.01/105.37	R = 
106.01/105.37	  f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 
106.01/105.37	  f17(I0, I1, I2, I3, I4, I5, I6) -> f11(13, 0, I2, 5, 0, I5, I6) 
106.01/105.37	  f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 
106.01/105.37	  f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 
106.01/105.37	  f8(I21, I22, I23, I24, I25, I26, I27) -> f9(I21, I22, I23, I24, I25, I26, I27) 
106.01/105.37	  f12(I28, I29, I30, I31, I32, I33, I34) -> f16(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31]
106.01/105.37	  f12(I35, I36, I37, I38, I39, I40, I41) -> f10(I35, 0, I37, I38, I39, I40, I41) [I38 <= I36]
106.01/105.37	  f10(I42, I43, I44, I45, I46, I47, I48) -> f13(I42, I43, I44, I45, I46, I47, I48) 
106.01/105.37	  f16(I49, I50, I51, I52, I53, I54, I55) -> f15(I49, I50, I51, I52, I53, I54, I55) [I53 <= I50 /\ I50 <= I53]
106.01/105.37	  f16(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I57 <= I60]
106.01/105.37	  f16(I63, I64, I65, I66, I67, I68, I69) -> f14(I63, I64, I65, I66, I67, I68, I69) [1 + I67 <= I64]
106.01/105.37	  f15(I70, I71, I72, I73, I74, I75, I76) -> f11(I70, 1 + I71, I72, I73, I74, I75, I76) 
106.01/105.37	  f14(I77, I78, I79, I80, I81, I82, I83) -> f15(I77, I78, I79, I80, I81, I82, I83) 
106.01/105.37	  f13(I84, I85, I86, I87, I88, I89, I90) -> f8(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87]
106.01/105.37	  f13(I91, I92, I93, I94, I95, I96, I97) -> f5(I91, 0, I93, I94, I95, I96, I97) [I94 <= I92]
106.01/105.37	  f11(I98, I99, I100, I101, I102, I103, I104) -> f12(I98, I99, I100, I101, I102, I103, I104) 
106.01/105.37	  f9(I105, I106, I107, I108, I109, I110, I111) -> f7(I105, I106, I107, I108, I109, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I107 <= I105]
106.01/105.37	  f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, 1 + I113, I114, I115, I116, I117, I118) [I112 <= I114]
106.01/105.37	  f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, 1 + I121, I122, I123, I124, I125) 
106.01/105.37	  f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126]
106.01/105.37	  f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136]
106.01/105.37	  f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 
106.01/105.37	  f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 
106.01/105.37	  f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159]
106.01/105.37	  f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164]
106.01/105.37	
106.01/105.37	We use the extended value criterion with the projection function NU:
106.01/105.37	  NU[f11#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x4
106.01/105.37	  NU[f14#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x4 - 1
106.01/105.37	  NU[f15#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x4 - 1
106.01/105.37	  NU[f16#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x4
106.01/105.37	  NU[f12#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x4
106.01/105.37	
106.01/105.37	This gives the following inequalities:
106.01/105.37	  1 + I29 <= I31  ==>  -I29 + I32 >= -I29 + I32
106.01/105.37	  I53 <= I50 /\ I50 <= I53  ==>  -I50 + I53 > -I50 + I53 - 1  with  -I50 + I53 >= 0
106.01/105.37	  1 + I57 <= I60  ==>  -I57 + I60 > -I57 + I60 - 1  with  -I57 + I60 >= 0
106.01/105.37	  1 + I67 <= I64  ==>  -I64 + I67 >= -I64 + I67 - 1
106.01/105.37	    ==>  -I71 + I74 - 1 >= -(1 + I71) + I74
106.01/105.37	    ==>  -I78 + I81 - 1 >= -I78 + I81 - 1
106.01/105.37	    ==>  -I99 + I102 >= -I99 + I102
106.01/105.37	
106.01/105.37	We remove all the strictly oriented dependency pairs.
106.01/105.37	
106.01/105.37	DP problem for innermost termination.
106.01/105.37	P =
106.01/105.37	  f12#(I28, I29, I30, I31, I32, I33, I34) -> f16#(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31]
106.01/105.37	  f16#(I63, I64, I65, I66, I67, I68, I69) -> f14#(I63, I64, I65, I66, I67, I68, I69) [1 + I67 <= I64]
106.01/105.37	  f15#(I70, I71, I72, I73, I74, I75, I76) -> f11#(I70, 1 + I71, I72, I73, I74, I75, I76) 
106.01/105.37	  f14#(I77, I78, I79, I80, I81, I82, I83) -> f15#(I77, I78, I79, I80, I81, I82, I83) 
106.01/105.37	  f11#(I98, I99, I100, I101, I102, I103, I104) -> f12#(I98, I99, I100, I101, I102, I103, I104) 
106.01/105.37	R = 
106.01/105.37	  f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 
106.01/105.37	  f17(I0, I1, I2, I3, I4, I5, I6) -> f11(13, 0, I2, 5, 0, I5, I6) 
106.01/105.37	  f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 
106.01/105.37	  f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 
106.01/105.37	  f8(I21, I22, I23, I24, I25, I26, I27) -> f9(I21, I22, I23, I24, I25, I26, I27) 
106.01/105.37	  f12(I28, I29, I30, I31, I32, I33, I34) -> f16(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31]
106.01/105.37	  f12(I35, I36, I37, I38, I39, I40, I41) -> f10(I35, 0, I37, I38, I39, I40, I41) [I38 <= I36]
106.01/105.37	  f10(I42, I43, I44, I45, I46, I47, I48) -> f13(I42, I43, I44, I45, I46, I47, I48) 
106.01/105.37	  f16(I49, I50, I51, I52, I53, I54, I55) -> f15(I49, I50, I51, I52, I53, I54, I55) [I53 <= I50 /\ I50 <= I53]
106.01/105.37	  f16(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I57 <= I60]
106.01/105.37	  f16(I63, I64, I65, I66, I67, I68, I69) -> f14(I63, I64, I65, I66, I67, I68, I69) [1 + I67 <= I64]
106.01/105.37	  f15(I70, I71, I72, I73, I74, I75, I76) -> f11(I70, 1 + I71, I72, I73, I74, I75, I76) 
106.01/105.37	  f14(I77, I78, I79, I80, I81, I82, I83) -> f15(I77, I78, I79, I80, I81, I82, I83) 
106.01/105.37	  f13(I84, I85, I86, I87, I88, I89, I90) -> f8(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87]
106.01/105.37	  f13(I91, I92, I93, I94, I95, I96, I97) -> f5(I91, 0, I93, I94, I95, I96, I97) [I94 <= I92]
106.01/105.37	  f11(I98, I99, I100, I101, I102, I103, I104) -> f12(I98, I99, I100, I101, I102, I103, I104) 
106.01/105.37	  f9(I105, I106, I107, I108, I109, I110, I111) -> f7(I105, I106, I107, I108, I109, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I107 <= I105]
106.01/105.37	  f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, 1 + I113, I114, I115, I116, I117, I118) [I112 <= I114]
106.01/105.37	  f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, 1 + I121, I122, I123, I124, I125) 
106.01/105.37	  f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126]
106.01/105.37	  f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136]
106.01/105.37	  f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 
106.01/105.37	  f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 
106.01/105.37	  f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159]
106.01/105.37	  f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164]
106.01/105.37	
106.01/105.37	We use the extended value criterion with the projection function NU:
106.01/105.37	  NU[f11#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 1
106.01/105.37	  NU[f15#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2
106.01/105.37	  NU[f14#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2
106.01/105.37	  NU[f16#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2
106.01/105.37	  NU[f12#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 1
106.01/105.37	
106.01/105.37	This gives the following inequalities:
106.01/105.37	  1 + I29 <= I31  ==>  -I29 + I31 - 1 > -I29 + I31 - 2  with  -I29 + I31 - 1 >= 0
106.01/105.37	  1 + I67 <= I64  ==>  -I64 + I66 - 2 >= -I64 + I66 - 2
106.01/105.37	    ==>  -I71 + I73 - 2 >= -(1 + I71) + I73 - 1
106.01/105.37	    ==>  -I78 + I80 - 2 >= -I78 + I80 - 2
106.01/105.37	    ==>  -I99 + I101 - 1 >= -I99 + I101 - 1
106.01/105.37	
106.01/105.37	We remove all the strictly oriented dependency pairs.
106.01/105.37	
106.01/105.37	DP problem for innermost termination.
106.01/105.37	P =
106.01/105.37	  f16#(I63, I64, I65, I66, I67, I68, I69) -> f14#(I63, I64, I65, I66, I67, I68, I69) [1 + I67 <= I64]
106.01/105.37	  f15#(I70, I71, I72, I73, I74, I75, I76) -> f11#(I70, 1 + I71, I72, I73, I74, I75, I76) 
106.01/105.37	  f14#(I77, I78, I79, I80, I81, I82, I83) -> f15#(I77, I78, I79, I80, I81, I82, I83) 
106.01/105.37	  f11#(I98, I99, I100, I101, I102, I103, I104) -> f12#(I98, I99, I100, I101, I102, I103, I104) 
106.01/105.37	R = 
106.01/105.37	  f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 
106.01/105.37	  f17(I0, I1, I2, I3, I4, I5, I6) -> f11(13, 0, I2, 5, 0, I5, I6) 
106.01/105.37	  f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 
106.01/105.37	  f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 
106.01/105.37	  f8(I21, I22, I23, I24, I25, I26, I27) -> f9(I21, I22, I23, I24, I25, I26, I27) 
106.01/105.37	  f12(I28, I29, I30, I31, I32, I33, I34) -> f16(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31]
106.01/105.37	  f12(I35, I36, I37, I38, I39, I40, I41) -> f10(I35, 0, I37, I38, I39, I40, I41) [I38 <= I36]
106.01/105.37	  f10(I42, I43, I44, I45, I46, I47, I48) -> f13(I42, I43, I44, I45, I46, I47, I48) 
106.01/105.37	  f16(I49, I50, I51, I52, I53, I54, I55) -> f15(I49, I50, I51, I52, I53, I54, I55) [I53 <= I50 /\ I50 <= I53]
106.01/105.37	  f16(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I57 <= I60]
106.01/105.37	  f16(I63, I64, I65, I66, I67, I68, I69) -> f14(I63, I64, I65, I66, I67, I68, I69) [1 + I67 <= I64]
106.01/105.37	  f15(I70, I71, I72, I73, I74, I75, I76) -> f11(I70, 1 + I71, I72, I73, I74, I75, I76) 
106.01/105.37	  f14(I77, I78, I79, I80, I81, I82, I83) -> f15(I77, I78, I79, I80, I81, I82, I83) 
106.01/105.37	  f13(I84, I85, I86, I87, I88, I89, I90) -> f8(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87]
106.01/105.37	  f13(I91, I92, I93, I94, I95, I96, I97) -> f5(I91, 0, I93, I94, I95, I96, I97) [I94 <= I92]
106.01/105.37	  f11(I98, I99, I100, I101, I102, I103, I104) -> f12(I98, I99, I100, I101, I102, I103, I104) 
106.01/105.37	  f9(I105, I106, I107, I108, I109, I110, I111) -> f7(I105, I106, I107, I108, I109, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I107 <= I105]
106.01/105.37	  f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, 1 + I113, I114, I115, I116, I117, I118) [I112 <= I114]
106.01/105.37	  f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, 1 + I121, I122, I123, I124, I125) 
106.01/105.37	  f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126]
106.01/105.37	  f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136]
106.01/105.37	  f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 
106.01/105.37	  f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 
106.01/105.37	  f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159]
106.01/105.37	  f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164]
106.01/105.37	
106.01/105.37	The dependency graph for this problem is:
106.01/105.37	  10 -> 12
106.01/105.37	  11 -> 15
106.01/105.37	  12 -> 11
106.01/105.37	  15 -> 
106.01/105.37	Where:
106.01/105.37	  10) f16#(I63, I64, I65, I66, I67, I68, I69) -> f14#(I63, I64, I65, I66, I67, I68, I69) [1 + I67 <= I64]
106.01/105.37	  11) f15#(I70, I71, I72, I73, I74, I75, I76) -> f11#(I70, 1 + I71, I72, I73, I74, I75, I76) 
106.01/105.37	  12) f14#(I77, I78, I79, I80, I81, I82, I83) -> f15#(I77, I78, I79, I80, I81, I82, I83) 
106.01/105.37	  15) f11#(I98, I99, I100, I101, I102, I103, I104) -> f12#(I98, I99, I100, I101, I102, I103, I104) 
106.01/105.37	
106.01/105.37	We have the following SCCs.
106.01/105.37	  
106.01/108.34	EOF