/export/starexec/sandbox/solver/bin/starexec_run_Transition /export/starexec/sandbox/benchmark/theBenchmark.smt2 /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES DP problem for innermost termination. P = f12#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) -> f11#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) f11#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) -> f2#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) f11#(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) -> f10#(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) f11#(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f8#(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) f11#(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) -> f7#(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) f11#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f6#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) f11#(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) -> f5#(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) f11#(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) -> f4#(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) f11#(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f1#(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) f11#(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f10#(I116, I117, I118, I119, rnd5, rnd6, I114, I115, I116, I117, rnd11, rnd12) [rnd12 = rnd6 /\ rnd11 = rnd5 /\ rnd6 = rnd6 /\ rnd5 = rnd5] f10#(I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f8#(I144, I145, I146, I147, I148, I149, I142, I143, I144, I145, I150, I151) [I151 = I149 /\ I150 = I148 /\ I149 = I149 /\ I148 = I148] f10#(I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f7#(I160, I161, I162, I163, I164, I165, I158, I159, I160, I161, I166, I167) [I167 = I165 /\ I166 = I164 /\ I165 = I165 /\ I164 = I164] f7#(I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f6#(I196, I197, I198, I199, I200, I193, I194, I195, I196, I197, I197, I201) [I201 = I200 /\ I200 = I200] f6#(I202, I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213) -> f5#(I210, I211, I212, I213, I214, I207, I208, I209, I210, I211, I212, I215) [I215 = I214 /\ 8 <= I212 /\ I214 = I214] f6#(I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226, I227) -> f4#(I224, I225, I226, I227, I228, I221, I222, I223, I224, I225, I226, I229) [I229 = I228 /\ I226 <= 7 /\ I228 = I228] f5#(I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241) -> f6#(I238, I239, I240, I241, I242, I235, I236, I237, I238, I239, -8 + I240, I243) [I243 = I242 /\ I242 = I242] f4#(I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254, I255) -> f1#(I252, I253, I254, I255, I248, I249, I250, I251, I252, I253, I254, I254) [1 <= I254] f4#(I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267) -> f2#(I264, I265, I266, I267, I268, I261, I262, I263, I264, I265, I266, I269) [I269 = I268 /\ I266 <= 0 /\ I268 = I268] f3#(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281) -> f1#(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281) f1#(I282, I283, I284, I285, I286, I287, I288, I289, I290, I291, I292, I293) -> f3#(I290, I291, I292, I293, I286, I287, I288, I289, I290, I291, I292, -1 + I293) [1 <= -1 + I293] f1#(I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304, I305) -> f2#(I302, I303, I304, I305, I298, I299, I300, I301, I302, I303, I304, I305) [-1 + I305 <= 0] R = f12(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) -> f11(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) f11(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) -> f2(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) f11(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) -> f10(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) f11(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f8(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) f11(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) -> f7(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) f11(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f9(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) f11(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f6(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) f11(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) -> f5(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) f11(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) -> f4(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) f11(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f1(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) f11(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f10(I116, I117, I118, I119, rnd5, rnd6, I114, I115, I116, I117, rnd11, rnd12) [rnd12 = rnd6 /\ rnd11 = rnd5 /\ rnd6 = rnd6 /\ rnd5 = rnd5] f2(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f9(I128, I129, I130, I131, I132, I133, rnd7, rnd8, rnd9, rnd10, I134, I135) [I135 = rnd8 /\ I134 = rnd7 /\ rnd10 = I133 /\ rnd9 = I132 /\ rnd8 = rnd8 /\ rnd7 = rnd7 /\ I133 = I133 /\ I132 = I132] f10(I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f8(I144, I145, I146, I147, I148, I149, I142, I143, I144, I145, I150, I151) [I151 = I149 /\ I150 = I148 /\ I149 = I149 /\ I148 = I148] f10(I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f7(I160, I161, I162, I163, I164, I165, I158, I159, I160, I161, I166, I167) [I167 = I165 /\ I166 = I164 /\ I165 = I165 /\ I164 = I164] f8(I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f9(I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187) [I187 = I183 /\ I186 = I182 /\ I185 = I181 /\ I184 = I180 /\ I183 = I183 /\ I182 = I182 /\ I181 = I181 /\ I180 = I180] f7(I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f6(I196, I197, I198, I199, I200, I193, I194, I195, I196, I197, I197, I201) [I201 = I200 /\ I200 = I200] f6(I202, I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213) -> f5(I210, I211, I212, I213, I214, I207, I208, I209, I210, I211, I212, I215) [I215 = I214 /\ 8 <= I212 /\ I214 = I214] f6(I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226, I227) -> f4(I224, I225, I226, I227, I228, I221, I222, I223, I224, I225, I226, I229) [I229 = I228 /\ I226 <= 7 /\ I228 = I228] f5(I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241) -> f6(I238, I239, I240, I241, I242, I235, I236, I237, I238, I239, -8 + I240, I243) [I243 = I242 /\ I242 = I242] f4(I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254, I255) -> f1(I252, I253, I254, I255, I248, I249, I250, I251, I252, I253, I254, I254) [1 <= I254] f4(I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267) -> f2(I264, I265, I266, I267, I268, I261, I262, I263, I264, I265, I266, I269) [I269 = I268 /\ I266 <= 0 /\ I268 = I268] f3(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281) -> f1(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281) f1(I282, I283, I284, I285, I286, I287, I288, I289, I290, I291, I292, I293) -> f3(I290, I291, I292, I293, I286, I287, I288, I289, I290, I291, I292, -1 + I293) [1 <= -1 + I293] f1(I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304, I305) -> f2(I302, I303, I304, I305, I298, I299, I300, I301, I302, I303, I304, I305) [-1 + I305 <= 0] The dependency graph for this problem is: 0 -> 1, 2, 3, 4, 5, 6, 7, 8, 9 1 -> 2 -> 10, 11 3 -> 4 -> 12 5 -> 13, 14 6 -> 15 7 -> 16, 17 8 -> 19, 20 9 -> 10, 11 10 -> 11 -> 12 12 -> 13, 14 13 -> 15 14 -> 16, 17 15 -> 13, 14 16 -> 19, 20 17 -> 18 -> 19, 20 19 -> 18 20 -> Where: 0) f12#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) -> f11#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 1) f11#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) -> f2#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) 2) f11#(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) -> f10#(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) 3) f11#(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f8#(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) 4) f11#(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) -> f7#(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) 5) f11#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f6#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 6) f11#(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) -> f5#(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) 7) f11#(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) -> f4#(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) 8) f11#(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f1#(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) 9) f11#(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f10#(I116, I117, I118, I119, rnd5, rnd6, I114, I115, I116, I117, rnd11, rnd12) [rnd12 = rnd6 /\ rnd11 = rnd5 /\ rnd6 = rnd6 /\ rnd5 = rnd5] 10) f10#(I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f8#(I144, I145, I146, I147, I148, I149, I142, I143, I144, I145, I150, I151) [I151 = I149 /\ I150 = I148 /\ I149 = I149 /\ I148 = I148] 11) f10#(I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f7#(I160, I161, I162, I163, I164, I165, I158, I159, I160, I161, I166, I167) [I167 = I165 /\ I166 = I164 /\ I165 = I165 /\ I164 = I164] 12) f7#(I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f6#(I196, I197, I198, I199, I200, I193, I194, I195, I196, I197, I197, I201) [I201 = I200 /\ I200 = I200] 13) f6#(I202, I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213) -> f5#(I210, I211, I212, I213, I214, I207, I208, I209, I210, I211, I212, I215) [I215 = I214 /\ 8 <= I212 /\ I214 = I214] 14) f6#(I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226, I227) -> f4#(I224, I225, I226, I227, I228, I221, I222, I223, I224, I225, I226, I229) [I229 = I228 /\ I226 <= 7 /\ I228 = I228] 15) f5#(I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241) -> f6#(I238, I239, I240, I241, I242, I235, I236, I237, I238, I239, -8 + I240, I243) [I243 = I242 /\ I242 = I242] 16) f4#(I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254, I255) -> f1#(I252, I253, I254, I255, I248, I249, I250, I251, I252, I253, I254, I254) [1 <= I254] 17) f4#(I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267) -> f2#(I264, I265, I266, I267, I268, I261, I262, I263, I264, I265, I266, I269) [I269 = I268 /\ I266 <= 0 /\ I268 = I268] 18) f3#(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281) -> f1#(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281) 19) f1#(I282, I283, I284, I285, I286, I287, I288, I289, I290, I291, I292, I293) -> f3#(I290, I291, I292, I293, I286, I287, I288, I289, I290, I291, I292, -1 + I293) [1 <= -1 + I293] 20) f1#(I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304, I305) -> f2#(I302, I303, I304, I305, I298, I299, I300, I301, I302, I303, I304, I305) [-1 + I305 <= 0] We have the following SCCs. { 13, 15 } { 18, 19 } DP problem for innermost termination. P = f3#(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281) -> f1#(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281) f1#(I282, I283, I284, I285, I286, I287, I288, I289, I290, I291, I292, I293) -> f3#(I290, I291, I292, I293, I286, I287, I288, I289, I290, I291, I292, -1 + I293) [1 <= -1 + I293] R = f12(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) -> f11(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) f11(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) -> f2(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) f11(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) -> f10(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) f11(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f8(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) f11(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) -> f7(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) f11(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f9(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) f11(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f6(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) f11(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) -> f5(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) f11(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) -> f4(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) f11(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f1(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) f11(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f10(I116, I117, I118, I119, rnd5, rnd6, I114, I115, I116, I117, rnd11, rnd12) [rnd12 = rnd6 /\ rnd11 = rnd5 /\ rnd6 = rnd6 /\ rnd5 = rnd5] f2(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f9(I128, I129, I130, I131, I132, I133, rnd7, rnd8, rnd9, rnd10, I134, I135) [I135 = rnd8 /\ I134 = rnd7 /\ rnd10 = I133 /\ rnd9 = I132 /\ rnd8 = rnd8 /\ rnd7 = rnd7 /\ I133 = I133 /\ I132 = I132] f10(I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f8(I144, I145, I146, I147, I148, I149, I142, I143, I144, I145, I150, I151) [I151 = I149 /\ I150 = I148 /\ I149 = I149 /\ I148 = I148] f10(I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f7(I160, I161, I162, I163, I164, I165, I158, I159, I160, I161, I166, I167) [I167 = I165 /\ I166 = I164 /\ I165 = I165 /\ I164 = I164] f8(I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f9(I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187) [I187 = I183 /\ I186 = I182 /\ I185 = I181 /\ I184 = I180 /\ I183 = I183 /\ I182 = I182 /\ I181 = I181 /\ I180 = I180] f7(I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f6(I196, I197, I198, I199, I200, I193, I194, I195, I196, I197, I197, I201) [I201 = I200 /\ I200 = I200] f6(I202, I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213) -> f5(I210, I211, I212, I213, I214, I207, I208, I209, I210, I211, I212, I215) [I215 = I214 /\ 8 <= I212 /\ I214 = I214] f6(I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226, I227) -> f4(I224, I225, I226, I227, I228, I221, I222, I223, I224, I225, I226, I229) [I229 = I228 /\ I226 <= 7 /\ I228 = I228] f5(I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241) -> f6(I238, I239, I240, I241, I242, I235, I236, I237, I238, I239, -8 + I240, I243) [I243 = I242 /\ I242 = I242] f4(I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254, I255) -> f1(I252, I253, I254, I255, I248, I249, I250, I251, I252, I253, I254, I254) [1 <= I254] f4(I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267) -> f2(I264, I265, I266, I267, I268, I261, I262, I263, I264, I265, I266, I269) [I269 = I268 /\ I266 <= 0 /\ I268 = I268] f3(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281) -> f1(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281) f1(I282, I283, I284, I285, I286, I287, I288, I289, I290, I291, I292, I293) -> f3(I290, I291, I292, I293, I286, I287, I288, I289, I290, I291, I292, -1 + I293) [1 <= -1 + I293] f1(I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304, I305) -> f2(I302, I303, I304, I305, I298, I299, I300, I301, I302, I303, I304, I305) [-1 + I305 <= 0] We use the basic value criterion with the projection function NU: NU[f1#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12)] = z12 NU[f3#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12)] = z12 This gives the following inequalities: ==> I281 (>! \union =) I281 1 <= -1 + I293 ==> I293 >! -1 + I293 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f3#(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281) -> f1#(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281) R = f12(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) -> f11(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) f11(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) -> f2(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) f11(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) -> f10(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) f11(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f8(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) f11(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) -> f7(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) f11(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f9(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) f11(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f6(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) f11(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) -> f5(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) f11(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) -> f4(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) f11(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f1(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) f11(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f10(I116, I117, I118, I119, rnd5, rnd6, I114, I115, I116, I117, rnd11, rnd12) [rnd12 = rnd6 /\ rnd11 = rnd5 /\ rnd6 = rnd6 /\ rnd5 = rnd5] f2(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f9(I128, I129, I130, I131, I132, I133, rnd7, rnd8, rnd9, rnd10, I134, I135) [I135 = rnd8 /\ I134 = rnd7 /\ rnd10 = I133 /\ rnd9 = I132 /\ rnd8 = rnd8 /\ rnd7 = rnd7 /\ I133 = I133 /\ I132 = I132] f10(I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f8(I144, I145, I146, I147, I148, I149, I142, I143, I144, I145, I150, I151) [I151 = I149 /\ I150 = I148 /\ I149 = I149 /\ I148 = I148] f10(I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f7(I160, I161, I162, I163, I164, I165, I158, I159, I160, I161, I166, I167) [I167 = I165 /\ I166 = I164 /\ I165 = I165 /\ I164 = I164] f8(I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f9(I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187) [I187 = I183 /\ I186 = I182 /\ I185 = I181 /\ I184 = I180 /\ I183 = I183 /\ I182 = I182 /\ I181 = I181 /\ I180 = I180] f7(I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f6(I196, I197, I198, I199, I200, I193, I194, I195, I196, I197, I197, I201) [I201 = I200 /\ I200 = I200] f6(I202, I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213) -> f5(I210, I211, I212, I213, I214, I207, I208, I209, I210, I211, I212, I215) [I215 = I214 /\ 8 <= I212 /\ I214 = I214] f6(I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226, I227) -> f4(I224, I225, I226, I227, I228, I221, I222, I223, I224, I225, I226, I229) [I229 = I228 /\ I226 <= 7 /\ I228 = I228] f5(I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241) -> f6(I238, I239, I240, I241, I242, I235, I236, I237, I238, I239, -8 + I240, I243) [I243 = I242 /\ I242 = I242] f4(I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254, I255) -> f1(I252, I253, I254, I255, I248, I249, I250, I251, I252, I253, I254, I254) [1 <= I254] f4(I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267) -> f2(I264, I265, I266, I267, I268, I261, I262, I263, I264, I265, I266, I269) [I269 = I268 /\ I266 <= 0 /\ I268 = I268] f3(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281) -> f1(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281) f1(I282, I283, I284, I285, I286, I287, I288, I289, I290, I291, I292, I293) -> f3(I290, I291, I292, I293, I286, I287, I288, I289, I290, I291, I292, -1 + I293) [1 <= -1 + I293] f1(I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304, I305) -> f2(I302, I303, I304, I305, I298, I299, I300, I301, I302, I303, I304, I305) [-1 + I305 <= 0] The dependency graph for this problem is: 18 -> Where: 18) f3#(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281) -> f1#(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281) We have the following SCCs. DP problem for innermost termination. P = f6#(I202, I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213) -> f5#(I210, I211, I212, I213, I214, I207, I208, I209, I210, I211, I212, I215) [I215 = I214 /\ 8 <= I212 /\ I214 = I214] f5#(I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241) -> f6#(I238, I239, I240, I241, I242, I235, I236, I237, I238, I239, -8 + I240, I243) [I243 = I242 /\ I242 = I242] R = f12(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) -> f11(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) f11(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) -> f2(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) f11(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) -> f10(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) f11(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f8(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) f11(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) -> f7(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) f11(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f9(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) f11(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f6(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) f11(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) -> f5(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) f11(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) -> f4(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) f11(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f1(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) f11(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f10(I116, I117, I118, I119, rnd5, rnd6, I114, I115, I116, I117, rnd11, rnd12) [rnd12 = rnd6 /\ rnd11 = rnd5 /\ rnd6 = rnd6 /\ rnd5 = rnd5] f2(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f9(I128, I129, I130, I131, I132, I133, rnd7, rnd8, rnd9, rnd10, I134, I135) [I135 = rnd8 /\ I134 = rnd7 /\ rnd10 = I133 /\ rnd9 = I132 /\ rnd8 = rnd8 /\ rnd7 = rnd7 /\ I133 = I133 /\ I132 = I132] f10(I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f8(I144, I145, I146, I147, I148, I149, I142, I143, I144, I145, I150, I151) [I151 = I149 /\ I150 = I148 /\ I149 = I149 /\ I148 = I148] f10(I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f7(I160, I161, I162, I163, I164, I165, I158, I159, I160, I161, I166, I167) [I167 = I165 /\ I166 = I164 /\ I165 = I165 /\ I164 = I164] f8(I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f9(I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187) [I187 = I183 /\ I186 = I182 /\ I185 = I181 /\ I184 = I180 /\ I183 = I183 /\ I182 = I182 /\ I181 = I181 /\ I180 = I180] f7(I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f6(I196, I197, I198, I199, I200, I193, I194, I195, I196, I197, I197, I201) [I201 = I200 /\ I200 = I200] f6(I202, I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213) -> f5(I210, I211, I212, I213, I214, I207, I208, I209, I210, I211, I212, I215) [I215 = I214 /\ 8 <= I212 /\ I214 = I214] f6(I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226, I227) -> f4(I224, I225, I226, I227, I228, I221, I222, I223, I224, I225, I226, I229) [I229 = I228 /\ I226 <= 7 /\ I228 = I228] f5(I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241) -> f6(I238, I239, I240, I241, I242, I235, I236, I237, I238, I239, -8 + I240, I243) [I243 = I242 /\ I242 = I242] f4(I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254, I255) -> f1(I252, I253, I254, I255, I248, I249, I250, I251, I252, I253, I254, I254) [1 <= I254] f4(I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267) -> f2(I264, I265, I266, I267, I268, I261, I262, I263, I264, I265, I266, I269) [I269 = I268 /\ I266 <= 0 /\ I268 = I268] f3(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281) -> f1(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281) f1(I282, I283, I284, I285, I286, I287, I288, I289, I290, I291, I292, I293) -> f3(I290, I291, I292, I293, I286, I287, I288, I289, I290, I291, I292, -1 + I293) [1 <= -1 + I293] f1(I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304, I305) -> f2(I302, I303, I304, I305, I298, I299, I300, I301, I302, I303, I304, I305) [-1 + I305 <= 0] We use the reverse value criterion with the projection function NU: NU[f5#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12)] = -8 + z11 + -1 * 8 NU[f6#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12)] = z11 + -1 * 8 This gives the following inequalities: I215 = I214 /\ 8 <= I212 /\ I214 = I214 ==> I212 + -1 * 8 > -8 + I212 + -1 * 8 with I212 + -1 * 8 >= 0 I243 = I242 /\ I242 = I242 ==> -8 + I240 + -1 * 8 >= -8 + I240 + -1 * 8 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f5#(I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241) -> f6#(I238, I239, I240, I241, I242, I235, I236, I237, I238, I239, -8 + I240, I243) [I243 = I242 /\ I242 = I242] R = f12(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) -> f11(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) f11(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) -> f2(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) f11(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) -> f10(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) f11(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f8(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) f11(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) -> f7(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) f11(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f9(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) f11(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f6(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) f11(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) -> f5(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) f11(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) -> f4(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) f11(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f1(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) f11(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f10(I116, I117, I118, I119, rnd5, rnd6, I114, I115, I116, I117, rnd11, rnd12) [rnd12 = rnd6 /\ rnd11 = rnd5 /\ rnd6 = rnd6 /\ rnd5 = rnd5] f2(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f9(I128, I129, I130, I131, I132, I133, rnd7, rnd8, rnd9, rnd10, I134, I135) [I135 = rnd8 /\ I134 = rnd7 /\ rnd10 = I133 /\ rnd9 = I132 /\ rnd8 = rnd8 /\ rnd7 = rnd7 /\ I133 = I133 /\ I132 = I132] f10(I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f8(I144, I145, I146, I147, I148, I149, I142, I143, I144, I145, I150, I151) [I151 = I149 /\ I150 = I148 /\ I149 = I149 /\ I148 = I148] f10(I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f7(I160, I161, I162, I163, I164, I165, I158, I159, I160, I161, I166, I167) [I167 = I165 /\ I166 = I164 /\ I165 = I165 /\ I164 = I164] f8(I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f9(I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187) [I187 = I183 /\ I186 = I182 /\ I185 = I181 /\ I184 = I180 /\ I183 = I183 /\ I182 = I182 /\ I181 = I181 /\ I180 = I180] f7(I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f6(I196, I197, I198, I199, I200, I193, I194, I195, I196, I197, I197, I201) [I201 = I200 /\ I200 = I200] f6(I202, I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213) -> f5(I210, I211, I212, I213, I214, I207, I208, I209, I210, I211, I212, I215) [I215 = I214 /\ 8 <= I212 /\ I214 = I214] f6(I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226, I227) -> f4(I224, I225, I226, I227, I228, I221, I222, I223, I224, I225, I226, I229) [I229 = I228 /\ I226 <= 7 /\ I228 = I228] f5(I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241) -> f6(I238, I239, I240, I241, I242, I235, I236, I237, I238, I239, -8 + I240, I243) [I243 = I242 /\ I242 = I242] f4(I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254, I255) -> f1(I252, I253, I254, I255, I248, I249, I250, I251, I252, I253, I254, I254) [1 <= I254] f4(I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267) -> f2(I264, I265, I266, I267, I268, I261, I262, I263, I264, I265, I266, I269) [I269 = I268 /\ I266 <= 0 /\ I268 = I268] f3(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281) -> f1(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281) f1(I282, I283, I284, I285, I286, I287, I288, I289, I290, I291, I292, I293) -> f3(I290, I291, I292, I293, I286, I287, I288, I289, I290, I291, I292, -1 + I293) [1 <= -1 + I293] f1(I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304, I305) -> f2(I302, I303, I304, I305, I298, I299, I300, I301, I302, I303, I304, I305) [-1 + I305 <= 0] The dependency graph for this problem is: 15 -> Where: 15) f5#(I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241) -> f6#(I238, I239, I240, I241, I242, I235, I236, I237, I238, I239, -8 + I240, I243) [I243 = I242 /\ I242 = I242] We have the following SCCs.