49.23/48.83 YES 49.23/48.83 49.23/48.83 DP problem for innermost termination. 49.23/48.83 P = 49.23/48.83 f7#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) -> f6#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 49.23/48.83 f6#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) -> f4#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) 49.23/48.83 f6#(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) -> f5#(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) 49.23/48.83 f6#(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f3#(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) 49.23/48.83 f6#(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) -> f1#(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) 49.23/48.83 f4#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f5#(I68, I69, I70, I71, I64, I65, I66, I67, I68, I69, I70, I71) 49.23/48.83 f5#(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) -> f3#(I80, I81, I82, I83, I76, I77, I78, I79, I80, I81, I82, I83) [1 + I80 <= 1 /\ 1 <= I80] 49.23/48.83 f5#(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) -> f3#(I92, I93, I94, I95, I88, I89, I90, I91, I92, I93, I94, I95) [2 <= I92 /\ 1 <= I92] 49.23/48.83 f5#(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f1#(I104, I105, I106, I107, I100, I101, I102, I103, I104, I105, I106, I107) [I104 <= 0] 49.23/48.83 f5#(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f1#(I116, I117, I118, I119, I112, I113, I114, I115, I116, I117, I118, I119) [1 <= I116 /\ I116 <= 1] 49.23/48.83 f3#(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f4#(I128, I129, I130, I131, I124, I125, I126, I127, -1 + I128, I129, I131, I130) 49.23/48.83 f3#(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f4#(I140, I141, I142, I143, I136, I137, I138, I139, -1 + I140, I143, I142, I141) 49.23/48.83 R = 49.23/48.83 f7(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) -> f6(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 49.23/48.83 f6(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) -> f4(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) 49.23/48.83 f6(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) -> f5(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) 49.23/48.83 f6(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f3(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) 49.23/48.83 f6(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) -> f1(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) 49.23/48.83 f6(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f2(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 49.23/48.83 f4(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f5(I68, I69, I70, I71, I64, I65, I66, I67, I68, I69, I70, I71) 49.23/48.83 f5(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) -> f3(I80, I81, I82, I83, I76, I77, I78, I79, I80, I81, I82, I83) [1 + I80 <= 1 /\ 1 <= I80] 49.23/48.83 f5(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) -> f3(I92, I93, I94, I95, I88, I89, I90, I91, I92, I93, I94, I95) [2 <= I92 /\ 1 <= I92] 49.23/48.83 f5(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f1(I104, I105, I106, I107, I100, I101, I102, I103, I104, I105, I106, I107) [I104 <= 0] 49.23/48.83 f5(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f1(I116, I117, I118, I119, I112, I113, I114, I115, I116, I117, I118, I119) [1 <= I116 /\ I116 <= 1] 49.23/48.83 f3(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f4(I128, I129, I130, I131, I124, I125, I126, I127, -1 + I128, I129, I131, I130) 49.23/48.83 f3(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f4(I140, I141, I142, I143, I136, I137, I138, I139, -1 + I140, I143, I142, I141) 49.23/48.83 f3(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) -> f2(I152, I153, I154, I155, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12) [rnd12 = rnd8 /\ rnd11 = rnd7 /\ rnd10 = rnd6 /\ rnd9 = rnd5 /\ rnd8 = rnd8 /\ rnd7 = rnd7 /\ rnd6 = rnd6 /\ rnd5 = rnd5] 49.23/48.83 f1(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167) -> f2(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175) [I175 = I171 /\ I174 = I170 /\ I173 = I169 /\ I172 = I168 /\ I171 = I171 /\ I170 = I170 /\ I169 = I169 /\ I168 = I168] 49.23/48.83 49.23/48.83 The dependency graph for this problem is: 49.23/48.83 0 -> 1, 2, 3, 4 49.23/48.83 1 -> 5 49.23/48.83 2 -> 7, 8, 9 49.23/48.83 3 -> 10, 11 49.23/48.83 4 -> 49.23/48.83 5 -> 7, 8, 9 49.23/48.83 6 -> 49.23/48.83 7 -> 10, 11 49.23/48.83 8 -> 49.23/48.83 9 -> 49.23/48.83 10 -> 5 49.23/48.83 11 -> 5 49.23/48.83 Where: 49.23/48.83 0) f7#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) -> f6#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 49.23/48.83 1) f6#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) -> f4#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) 49.23/48.83 2) f6#(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) -> f5#(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) 49.23/48.83 3) f6#(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f3#(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) 49.23/48.83 4) f6#(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) -> f1#(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) 49.23/48.83 5) f4#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f5#(I68, I69, I70, I71, I64, I65, I66, I67, I68, I69, I70, I71) 49.23/48.83 6) f5#(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) -> f3#(I80, I81, I82, I83, I76, I77, I78, I79, I80, I81, I82, I83) [1 + I80 <= 1 /\ 1 <= I80] 49.23/48.83 7) f5#(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) -> f3#(I92, I93, I94, I95, I88, I89, I90, I91, I92, I93, I94, I95) [2 <= I92 /\ 1 <= I92] 49.23/48.83 8) f5#(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f1#(I104, I105, I106, I107, I100, I101, I102, I103, I104, I105, I106, I107) [I104 <= 0] 49.23/48.83 9) f5#(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f1#(I116, I117, I118, I119, I112, I113, I114, I115, I116, I117, I118, I119) [1 <= I116 /\ I116 <= 1] 49.23/48.83 10) f3#(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f4#(I128, I129, I130, I131, I124, I125, I126, I127, -1 + I128, I129, I131, I130) 49.23/48.83 11) f3#(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f4#(I140, I141, I142, I143, I136, I137, I138, I139, -1 + I140, I143, I142, I141) 49.23/48.83 49.23/48.83 We have the following SCCs. 49.23/48.83 { 5, 7, 10, 11 } 49.23/48.83 49.23/48.83 DP problem for innermost termination. 49.23/48.83 P = 49.23/48.83 f4#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f5#(I68, I69, I70, I71, I64, I65, I66, I67, I68, I69, I70, I71) 49.23/48.83 f5#(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) -> f3#(I92, I93, I94, I95, I88, I89, I90, I91, I92, I93, I94, I95) [2 <= I92 /\ 1 <= I92] 49.23/48.83 f3#(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f4#(I128, I129, I130, I131, I124, I125, I126, I127, -1 + I128, I129, I131, I130) 49.23/48.83 f3#(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f4#(I140, I141, I142, I143, I136, I137, I138, I139, -1 + I140, I143, I142, I141) 49.23/48.83 R = 49.23/48.83 f7(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) -> f6(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 49.23/48.83 f6(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) -> f4(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) 49.23/48.83 f6(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) -> f5(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) 49.23/48.83 f6(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f3(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) 49.23/48.83 f6(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) -> f1(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) 49.23/48.83 f6(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f2(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 49.23/48.83 f4(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f5(I68, I69, I70, I71, I64, I65, I66, I67, I68, I69, I70, I71) 49.23/48.83 f5(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) -> f3(I80, I81, I82, I83, I76, I77, I78, I79, I80, I81, I82, I83) [1 + I80 <= 1 /\ 1 <= I80] 49.23/48.83 f5(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) -> f3(I92, I93, I94, I95, I88, I89, I90, I91, I92, I93, I94, I95) [2 <= I92 /\ 1 <= I92] 49.23/48.83 f5(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f1(I104, I105, I106, I107, I100, I101, I102, I103, I104, I105, I106, I107) [I104 <= 0] 49.23/48.83 f5(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f1(I116, I117, I118, I119, I112, I113, I114, I115, I116, I117, I118, I119) [1 <= I116 /\ I116 <= 1] 49.23/48.83 f3(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f4(I128, I129, I130, I131, I124, I125, I126, I127, -1 + I128, I129, I131, I130) 49.23/48.83 f3(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f4(I140, I141, I142, I143, I136, I137, I138, I139, -1 + I140, I143, I142, I141) 49.23/48.83 f3(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) -> f2(I152, I153, I154, I155, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12) [rnd12 = rnd8 /\ rnd11 = rnd7 /\ rnd10 = rnd6 /\ rnd9 = rnd5 /\ rnd8 = rnd8 /\ rnd7 = rnd7 /\ rnd6 = rnd6 /\ rnd5 = rnd5] 49.23/48.83 f1(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167) -> f2(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175) [I175 = I171 /\ I174 = I170 /\ I173 = I169 /\ I172 = I168 /\ I171 = I171 /\ I170 = I170 /\ I169 = I169 /\ I168 = I168] 49.23/48.83 49.23/48.83 We use the extended value criterion with the projection function NU: 49.23/48.83 NU[f3#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11)] = x8 - 3 49.23/48.83 NU[f5#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11)] = x8 - 2 49.23/48.83 NU[f4#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11)] = x8 - 2 49.23/48.83 49.23/48.83 This gives the following inequalities: 49.23/48.83 ==> I68 - 2 >= I68 - 2 49.23/48.83 2 <= I92 /\ 1 <= I92 ==> I92 - 2 > I92 - 3 with I92 - 2 >= 0 49.23/48.83 ==> I128 - 3 >= (-1 + I128) - 2 49.23/48.83 ==> I140 - 3 >= (-1 + I140) - 2 49.23/48.83 49.23/48.83 We remove all the strictly oriented dependency pairs. 49.23/48.83 49.23/48.83 DP problem for innermost termination. 49.23/48.83 P = 49.23/48.83 f4#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f5#(I68, I69, I70, I71, I64, I65, I66, I67, I68, I69, I70, I71) 49.23/48.83 f3#(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f4#(I128, I129, I130, I131, I124, I125, I126, I127, -1 + I128, I129, I131, I130) 49.23/48.83 f3#(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f4#(I140, I141, I142, I143, I136, I137, I138, I139, -1 + I140, I143, I142, I141) 49.23/48.83 R = 49.23/48.83 f7(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) -> f6(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 49.23/48.83 f6(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) -> f4(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) 49.23/48.83 f6(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) -> f5(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) 49.23/48.83 f6(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f3(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) 49.23/48.83 f6(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) -> f1(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) 49.23/48.83 f6(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f2(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 49.23/48.83 f4(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f5(I68, I69, I70, I71, I64, I65, I66, I67, I68, I69, I70, I71) 49.23/48.83 f5(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) -> f3(I80, I81, I82, I83, I76, I77, I78, I79, I80, I81, I82, I83) [1 + I80 <= 1 /\ 1 <= I80] 49.23/48.83 f5(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) -> f3(I92, I93, I94, I95, I88, I89, I90, I91, I92, I93, I94, I95) [2 <= I92 /\ 1 <= I92] 49.23/48.83 f5(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f1(I104, I105, I106, I107, I100, I101, I102, I103, I104, I105, I106, I107) [I104 <= 0] 49.23/48.83 f5(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f1(I116, I117, I118, I119, I112, I113, I114, I115, I116, I117, I118, I119) [1 <= I116 /\ I116 <= 1] 49.23/48.83 f3(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f4(I128, I129, I130, I131, I124, I125, I126, I127, -1 + I128, I129, I131, I130) 49.23/48.83 f3(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f4(I140, I141, I142, I143, I136, I137, I138, I139, -1 + I140, I143, I142, I141) 49.23/48.83 f3(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) -> f2(I152, I153, I154, I155, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12) [rnd12 = rnd8 /\ rnd11 = rnd7 /\ rnd10 = rnd6 /\ rnd9 = rnd5 /\ rnd8 = rnd8 /\ rnd7 = rnd7 /\ rnd6 = rnd6 /\ rnd5 = rnd5] 49.23/48.83 f1(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167) -> f2(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175) [I175 = I171 /\ I174 = I170 /\ I173 = I169 /\ I172 = I168 /\ I171 = I171 /\ I170 = I170 /\ I169 = I169 /\ I168 = I168] 49.23/48.83 49.23/48.83 The dependency graph for this problem is: 49.23/48.83 5 -> 49.23/48.83 10 -> 5 49.23/48.83 11 -> 5 49.23/48.83 Where: 49.23/48.83 5) f4#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f5#(I68, I69, I70, I71, I64, I65, I66, I67, I68, I69, I70, I71) 49.23/48.83 10) f3#(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f4#(I128, I129, I130, I131, I124, I125, I126, I127, -1 + I128, I129, I131, I130) 49.23/48.83 11) f3#(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f4#(I140, I141, I142, I143, I136, I137, I138, I139, -1 + I140, I143, I142, I141) 49.23/48.83 49.23/48.83 We have the following SCCs. 49.23/48.83 49.23/51.80 EOF