/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 = f13#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17) -> f12#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17) f12#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16) -> f1#(I0, I1, I2, I3, I4, I5, I6, 0, I8, I9, I10, I11, 0, I13, I14, I15, I16) f2#(I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33) -> f5#(I17, 0, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33) [1 + I24 <= 10] f2#(I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f9#(I34, I35, 0, I37, I38, 0, 0, I41, 0, I43, I44, 0, I46, 1000, I48, I49, I50) [10 <= I41] f6#(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67) -> f5#(I51, 1 + I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, rnd13, I64, I65, I66, rnd17) [rnd17 = rnd13 /\ rnd13 = rnd13 /\ 1 + I52 <= 10] f6#(I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84) -> f1#(I68, I69, I70, I71, I72, I73, I74, 1 + I75, I76, I77, I78, I79, I80, I81, I82, I83, I84) [10 <= I69] f4#(I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f8#(I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) f9#(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118) -> f10#(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118) f10#(I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134, I135) -> f4#(0, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134, I135) [1 + I125 <= 10] f8#(I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) -> f7#(I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) [1 + I153 <= 10] f8#(I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186) -> f9#(I170, I171, I172, I173, I174, I175, 1 + I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186) [10 <= I170] f7#(I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) -> f3#(I187, I188, 1 + I189, I190, I191, rnd6, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) [rnd6 = rnd6] f7#(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f3#(I204, I205, I206, I207, I208, I209, I210, I211, 1 + I212, I213, I214, rnd12, I216, I217, I218, I219, I220) [rnd12 = rnd12] f5#(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237) -> f6#(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237) f3#(I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f4#(1 + I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) f1#(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) -> f2#(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) R = f13(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17) -> f12(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17) f12(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16) -> f1(I0, I1, I2, I3, I4, I5, I6, 0, I8, I9, I10, I11, 0, I13, I14, I15, I16) f2(I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33) -> f5(I17, 0, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33) [1 + I24 <= 10] f2(I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f9(I34, I35, 0, I37, I38, 0, 0, I41, 0, I43, I44, 0, I46, 1000, I48, I49, I50) [10 <= I41] f6(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67) -> f5(I51, 1 + I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, rnd13, I64, I65, I66, rnd17) [rnd17 = rnd13 /\ rnd13 = rnd13 /\ 1 + I52 <= 10] f6(I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84) -> f1(I68, I69, I70, I71, I72, I73, I74, 1 + I75, I76, I77, I78, I79, I80, I81, I82, I83, I84) [10 <= I69] f4(I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f8(I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) f9(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118) -> f10(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118) f10(I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134, I135) -> f4(0, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134, I135) [1 + I125 <= 10] f10(I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f11(I136, I137, I138, I138, I141, I141, I142, I143, I144, I144, I147, I147, I148, I149, 1500, rnd16, I152) [rnd16 = rnd16 /\ 10 <= I142] f8(I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) -> f7(I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) [1 + I153 <= 10] f8(I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186) -> f9(I170, I171, I172, I173, I174, I175, 1 + I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186) [10 <= I170] f7(I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) -> f3(I187, I188, 1 + I189, I190, I191, rnd6, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) [rnd6 = rnd6] f7(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f3(I204, I205, I206, I207, I208, I209, I210, I211, 1 + I212, I213, I214, rnd12, I216, I217, I218, I219, I220) [rnd12 = rnd12] f5(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237) -> f6(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237) f3(I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f4(1 + I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) f1(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) -> f2(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) The dependency graph for this problem is: 0 -> 1 1 -> 15 2 -> 13 3 -> 7 4 -> 13 5 -> 15 6 -> 9, 10 7 -> 8 8 -> 6 9 -> 11, 12 10 -> 7 11 -> 14 12 -> 14 13 -> 4, 5 14 -> 6 15 -> 2, 3 Where: 0) f13#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17) -> f12#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17) 1) f12#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16) -> f1#(I0, I1, I2, I3, I4, I5, I6, 0, I8, I9, I10, I11, 0, I13, I14, I15, I16) 2) f2#(I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33) -> f5#(I17, 0, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33) [1 + I24 <= 10] 3) f2#(I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f9#(I34, I35, 0, I37, I38, 0, 0, I41, 0, I43, I44, 0, I46, 1000, I48, I49, I50) [10 <= I41] 4) f6#(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67) -> f5#(I51, 1 + I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, rnd13, I64, I65, I66, rnd17) [rnd17 = rnd13 /\ rnd13 = rnd13 /\ 1 + I52 <= 10] 5) f6#(I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84) -> f1#(I68, I69, I70, I71, I72, I73, I74, 1 + I75, I76, I77, I78, I79, I80, I81, I82, I83, I84) [10 <= I69] 6) f4#(I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f8#(I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 7) f9#(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118) -> f10#(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118) 8) f10#(I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134, I135) -> f4#(0, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134, I135) [1 + I125 <= 10] 9) f8#(I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) -> f7#(I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) [1 + I153 <= 10] 10) f8#(I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186) -> f9#(I170, I171, I172, I173, I174, I175, 1 + I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186) [10 <= I170] 11) f7#(I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) -> f3#(I187, I188, 1 + I189, I190, I191, rnd6, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) [rnd6 = rnd6] 12) f7#(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f3#(I204, I205, I206, I207, I208, I209, I210, I211, 1 + I212, I213, I214, rnd12, I216, I217, I218, I219, I220) [rnd12 = rnd12] 13) f5#(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237) -> f6#(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237) 14) f3#(I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f4#(1 + I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 15) f1#(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) -> f2#(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) We have the following SCCs. { 2, 4, 5, 13, 15 } { 6, 7, 8, 9, 10, 11, 12, 14 } DP problem for innermost termination. P = f4#(I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f8#(I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) f9#(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118) -> f10#(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118) f10#(I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134, I135) -> f4#(0, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134, I135) [1 + I125 <= 10] f8#(I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) -> f7#(I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) [1 + I153 <= 10] f8#(I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186) -> f9#(I170, I171, I172, I173, I174, I175, 1 + I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186) [10 <= I170] f7#(I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) -> f3#(I187, I188, 1 + I189, I190, I191, rnd6, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) [rnd6 = rnd6] f7#(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f3#(I204, I205, I206, I207, I208, I209, I210, I211, 1 + I212, I213, I214, rnd12, I216, I217, I218, I219, I220) [rnd12 = rnd12] f3#(I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f4#(1 + I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) R = f13(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17) -> f12(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17) f12(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16) -> f1(I0, I1, I2, I3, I4, I5, I6, 0, I8, I9, I10, I11, 0, I13, I14, I15, I16) f2(I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33) -> f5(I17, 0, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33) [1 + I24 <= 10] f2(I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f9(I34, I35, 0, I37, I38, 0, 0, I41, 0, I43, I44, 0, I46, 1000, I48, I49, I50) [10 <= I41] f6(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67) -> f5(I51, 1 + I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, rnd13, I64, I65, I66, rnd17) [rnd17 = rnd13 /\ rnd13 = rnd13 /\ 1 + I52 <= 10] f6(I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84) -> f1(I68, I69, I70, I71, I72, I73, I74, 1 + I75, I76, I77, I78, I79, I80, I81, I82, I83, I84) [10 <= I69] f4(I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f8(I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) f9(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118) -> f10(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118) f10(I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134, I135) -> f4(0, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134, I135) [1 + I125 <= 10] f10(I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f11(I136, I137, I138, I138, I141, I141, I142, I143, I144, I144, I147, I147, I148, I149, 1500, rnd16, I152) [rnd16 = rnd16 /\ 10 <= I142] f8(I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) -> f7(I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) [1 + I153 <= 10] f8(I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186) -> f9(I170, I171, I172, I173, I174, I175, 1 + I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186) [10 <= I170] f7(I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) -> f3(I187, I188, 1 + I189, I190, I191, rnd6, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) [rnd6 = rnd6] f7(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f3(I204, I205, I206, I207, I208, I209, I210, I211, 1 + I212, I213, I214, rnd12, I216, I217, I218, I219, I220) [rnd12 = rnd12] f5(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237) -> f6(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237) f3(I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f4(1 + I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) f1(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) -> f2(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) We use the extended value criterion with the projection function NU: NU[f3#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16)] = -x6 + 8 NU[f7#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16)] = -x6 + 8 NU[f10#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16)] = -x6 + 9 NU[f9#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16)] = -x6 + 9 NU[f8#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16)] = -x6 + 8 NU[f4#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16)] = -x6 + 8 This gives the following inequalities: ==> -I91 + 8 >= -I91 + 8 ==> -I108 + 9 >= -I108 + 9 1 + I125 <= 10 ==> -I125 + 9 > -I125 + 8 with -I125 + 9 >= 0 1 + I153 <= 10 ==> -I159 + 8 >= -I159 + 8 10 <= I170 ==> -I176 + 8 >= -(1 + I176) + 9 rnd6 = rnd6 ==> -I193 + 8 >= -I193 + 8 rnd12 = rnd12 ==> -I210 + 8 >= -I210 + 8 ==> -I244 + 8 >= -I244 + 8 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f4#(I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f8#(I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) f9#(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118) -> f10#(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118) f8#(I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) -> f7#(I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) [1 + I153 <= 10] f8#(I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186) -> f9#(I170, I171, I172, I173, I174, I175, 1 + I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186) [10 <= I170] f7#(I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) -> f3#(I187, I188, 1 + I189, I190, I191, rnd6, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) [rnd6 = rnd6] f7#(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f3#(I204, I205, I206, I207, I208, I209, I210, I211, 1 + I212, I213, I214, rnd12, I216, I217, I218, I219, I220) [rnd12 = rnd12] f3#(I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f4#(1 + I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) R = f13(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17) -> f12(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17) f12(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16) -> f1(I0, I1, I2, I3, I4, I5, I6, 0, I8, I9, I10, I11, 0, I13, I14, I15, I16) f2(I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33) -> f5(I17, 0, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33) [1 + I24 <= 10] f2(I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f9(I34, I35, 0, I37, I38, 0, 0, I41, 0, I43, I44, 0, I46, 1000, I48, I49, I50) [10 <= I41] f6(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67) -> f5(I51, 1 + I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, rnd13, I64, I65, I66, rnd17) [rnd17 = rnd13 /\ rnd13 = rnd13 /\ 1 + I52 <= 10] f6(I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84) -> f1(I68, I69, I70, I71, I72, I73, I74, 1 + I75, I76, I77, I78, I79, I80, I81, I82, I83, I84) [10 <= I69] f4(I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f8(I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) f9(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118) -> f10(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118) f10(I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134, I135) -> f4(0, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134, I135) [1 + I125 <= 10] f10(I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f11(I136, I137, I138, I138, I141, I141, I142, I143, I144, I144, I147, I147, I148, I149, 1500, rnd16, I152) [rnd16 = rnd16 /\ 10 <= I142] f8(I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) -> f7(I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) [1 + I153 <= 10] f8(I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186) -> f9(I170, I171, I172, I173, I174, I175, 1 + I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186) [10 <= I170] f7(I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) -> f3(I187, I188, 1 + I189, I190, I191, rnd6, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) [rnd6 = rnd6] f7(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f3(I204, I205, I206, I207, I208, I209, I210, I211, 1 + I212, I213, I214, rnd12, I216, I217, I218, I219, I220) [rnd12 = rnd12] f5(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237) -> f6(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237) f3(I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f4(1 + I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) f1(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) -> f2(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) The dependency graph for this problem is: 6 -> 9, 10 7 -> 9 -> 11, 12 10 -> 7 11 -> 14 12 -> 14 14 -> 6 Where: 6) f4#(I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f8#(I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 7) f9#(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118) -> f10#(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118) 9) f8#(I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) -> f7#(I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) [1 + I153 <= 10] 10) f8#(I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186) -> f9#(I170, I171, I172, I173, I174, I175, 1 + I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186) [10 <= I170] 11) f7#(I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) -> f3#(I187, I188, 1 + I189, I190, I191, rnd6, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) [rnd6 = rnd6] 12) f7#(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f3#(I204, I205, I206, I207, I208, I209, I210, I211, 1 + I212, I213, I214, rnd12, I216, I217, I218, I219, I220) [rnd12 = rnd12] 14) f3#(I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f4#(1 + I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) We have the following SCCs. { 6, 9, 11, 12, 14 } DP problem for innermost termination. P = f4#(I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f8#(I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) f8#(I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) -> f7#(I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) [1 + I153 <= 10] f7#(I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) -> f3#(I187, I188, 1 + I189, I190, I191, rnd6, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) [rnd6 = rnd6] f7#(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f3#(I204, I205, I206, I207, I208, I209, I210, I211, 1 + I212, I213, I214, rnd12, I216, I217, I218, I219, I220) [rnd12 = rnd12] f3#(I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f4#(1 + I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) R = f13(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17) -> f12(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17) f12(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16) -> f1(I0, I1, I2, I3, I4, I5, I6, 0, I8, I9, I10, I11, 0, I13, I14, I15, I16) f2(I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33) -> f5(I17, 0, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33) [1 + I24 <= 10] f2(I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f9(I34, I35, 0, I37, I38, 0, 0, I41, 0, I43, I44, 0, I46, 1000, I48, I49, I50) [10 <= I41] f6(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67) -> f5(I51, 1 + I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, rnd13, I64, I65, I66, rnd17) [rnd17 = rnd13 /\ rnd13 = rnd13 /\ 1 + I52 <= 10] f6(I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84) -> f1(I68, I69, I70, I71, I72, I73, I74, 1 + I75, I76, I77, I78, I79, I80, I81, I82, I83, I84) [10 <= I69] f4(I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f8(I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) f9(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118) -> f10(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118) f10(I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134, I135) -> f4(0, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134, I135) [1 + I125 <= 10] f10(I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f11(I136, I137, I138, I138, I141, I141, I142, I143, I144, I144, I147, I147, I148, I149, 1500, rnd16, I152) [rnd16 = rnd16 /\ 10 <= I142] f8(I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) -> f7(I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) [1 + I153 <= 10] f8(I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186) -> f9(I170, I171, I172, I173, I174, I175, 1 + I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186) [10 <= I170] f7(I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) -> f3(I187, I188, 1 + I189, I190, I191, rnd6, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) [rnd6 = rnd6] f7(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f3(I204, I205, I206, I207, I208, I209, I210, I211, 1 + I212, I213, I214, rnd12, I216, I217, I218, I219, I220) [rnd12 = rnd12] f5(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237) -> f6(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237) f3(I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f4(1 + I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) f1(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) -> f2(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) We use the extended value criterion with the projection function NU: NU[f3#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16)] = -x0 + 8 NU[f7#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16)] = -x0 + 8 NU[f8#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16)] = -x0 + 9 NU[f4#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16)] = -x0 + 9 This gives the following inequalities: ==> -I85 + 9 >= -I85 + 9 1 + I153 <= 10 ==> -I153 + 9 > -I153 + 8 with -I153 + 9 >= 0 rnd6 = rnd6 ==> -I187 + 8 >= -I187 + 8 rnd12 = rnd12 ==> -I204 + 8 >= -I204 + 8 ==> -I238 + 8 >= -(1 + I238) + 9 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f4#(I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f8#(I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) f7#(I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) -> f3#(I187, I188, 1 + I189, I190, I191, rnd6, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) [rnd6 = rnd6] f7#(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f3#(I204, I205, I206, I207, I208, I209, I210, I211, 1 + I212, I213, I214, rnd12, I216, I217, I218, I219, I220) [rnd12 = rnd12] f3#(I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f4#(1 + I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) R = f13(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17) -> f12(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17) f12(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16) -> f1(I0, I1, I2, I3, I4, I5, I6, 0, I8, I9, I10, I11, 0, I13, I14, I15, I16) f2(I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33) -> f5(I17, 0, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33) [1 + I24 <= 10] f2(I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f9(I34, I35, 0, I37, I38, 0, 0, I41, 0, I43, I44, 0, I46, 1000, I48, I49, I50) [10 <= I41] f6(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67) -> f5(I51, 1 + I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, rnd13, I64, I65, I66, rnd17) [rnd17 = rnd13 /\ rnd13 = rnd13 /\ 1 + I52 <= 10] f6(I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84) -> f1(I68, I69, I70, I71, I72, I73, I74, 1 + I75, I76, I77, I78, I79, I80, I81, I82, I83, I84) [10 <= I69] f4(I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f8(I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) f9(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118) -> f10(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118) f10(I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134, I135) -> f4(0, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134, I135) [1 + I125 <= 10] f10(I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f11(I136, I137, I138, I138, I141, I141, I142, I143, I144, I144, I147, I147, I148, I149, 1500, rnd16, I152) [rnd16 = rnd16 /\ 10 <= I142] f8(I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) -> f7(I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) [1 + I153 <= 10] f8(I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186) -> f9(I170, I171, I172, I173, I174, I175, 1 + I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186) [10 <= I170] f7(I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) -> f3(I187, I188, 1 + I189, I190, I191, rnd6, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) [rnd6 = rnd6] f7(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f3(I204, I205, I206, I207, I208, I209, I210, I211, 1 + I212, I213, I214, rnd12, I216, I217, I218, I219, I220) [rnd12 = rnd12] f5(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237) -> f6(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237) f3(I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f4(1 + I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) f1(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) -> f2(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) The dependency graph for this problem is: 6 -> 11 -> 14 12 -> 14 14 -> 6 Where: 6) f4#(I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f8#(I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 11) f7#(I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) -> f3#(I187, I188, 1 + I189, I190, I191, rnd6, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) [rnd6 = rnd6] 12) f7#(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f3#(I204, I205, I206, I207, I208, I209, I210, I211, 1 + I212, I213, I214, rnd12, I216, I217, I218, I219, I220) [rnd12 = rnd12] 14) f3#(I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f4#(1 + I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) We have the following SCCs. DP problem for innermost termination. P = f2#(I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33) -> f5#(I17, 0, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33) [1 + I24 <= 10] f6#(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67) -> f5#(I51, 1 + I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, rnd13, I64, I65, I66, rnd17) [rnd17 = rnd13 /\ rnd13 = rnd13 /\ 1 + I52 <= 10] f6#(I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84) -> f1#(I68, I69, I70, I71, I72, I73, I74, 1 + I75, I76, I77, I78, I79, I80, I81, I82, I83, I84) [10 <= I69] f5#(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237) -> f6#(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237) f1#(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) -> f2#(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) R = f13(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17) -> f12(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17) f12(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16) -> f1(I0, I1, I2, I3, I4, I5, I6, 0, I8, I9, I10, I11, 0, I13, I14, I15, I16) f2(I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33) -> f5(I17, 0, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33) [1 + I24 <= 10] f2(I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f9(I34, I35, 0, I37, I38, 0, 0, I41, 0, I43, I44, 0, I46, 1000, I48, I49, I50) [10 <= I41] f6(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67) -> f5(I51, 1 + I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, rnd13, I64, I65, I66, rnd17) [rnd17 = rnd13 /\ rnd13 = rnd13 /\ 1 + I52 <= 10] f6(I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84) -> f1(I68, I69, I70, I71, I72, I73, I74, 1 + I75, I76, I77, I78, I79, I80, I81, I82, I83, I84) [10 <= I69] f4(I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f8(I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) f9(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118) -> f10(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118) f10(I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134, I135) -> f4(0, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134, I135) [1 + I125 <= 10] f10(I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f11(I136, I137, I138, I138, I141, I141, I142, I143, I144, I144, I147, I147, I148, I149, 1500, rnd16, I152) [rnd16 = rnd16 /\ 10 <= I142] f8(I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) -> f7(I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) [1 + I153 <= 10] f8(I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186) -> f9(I170, I171, I172, I173, I174, I175, 1 + I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186) [10 <= I170] f7(I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) -> f3(I187, I188, 1 + I189, I190, I191, rnd6, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) [rnd6 = rnd6] f7(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f3(I204, I205, I206, I207, I208, I209, I210, I211, 1 + I212, I213, I214, rnd12, I216, I217, I218, I219, I220) [rnd12 = rnd12] f5(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237) -> f6(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237) f3(I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f4(1 + I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) f1(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) -> f2(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) We use the extended value criterion with the projection function NU: NU[f1#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16)] = -x7 + 9 NU[f6#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16)] = -x7 + 8 NU[f5#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16)] = -x7 + 8 NU[f2#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16)] = -x7 + 9 This gives the following inequalities: 1 + I24 <= 10 ==> -I24 + 9 > -I24 + 8 with -I24 + 9 >= 0 rnd17 = rnd13 /\ rnd13 = rnd13 /\ 1 + I52 <= 10 ==> -I58 + 8 >= -I58 + 8 10 <= I69 ==> -I75 + 8 >= -(1 + I75) + 9 ==> -I228 + 8 >= -I228 + 8 ==> -I262 + 9 >= -I262 + 9 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f6#(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67) -> f5#(I51, 1 + I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, rnd13, I64, I65, I66, rnd17) [rnd17 = rnd13 /\ rnd13 = rnd13 /\ 1 + I52 <= 10] f6#(I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84) -> f1#(I68, I69, I70, I71, I72, I73, I74, 1 + I75, I76, I77, I78, I79, I80, I81, I82, I83, I84) [10 <= I69] f5#(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237) -> f6#(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237) f1#(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) -> f2#(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) R = f13(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17) -> f12(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17) f12(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16) -> f1(I0, I1, I2, I3, I4, I5, I6, 0, I8, I9, I10, I11, 0, I13, I14, I15, I16) f2(I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33) -> f5(I17, 0, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33) [1 + I24 <= 10] f2(I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f9(I34, I35, 0, I37, I38, 0, 0, I41, 0, I43, I44, 0, I46, 1000, I48, I49, I50) [10 <= I41] f6(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67) -> f5(I51, 1 + I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, rnd13, I64, I65, I66, rnd17) [rnd17 = rnd13 /\ rnd13 = rnd13 /\ 1 + I52 <= 10] f6(I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84) -> f1(I68, I69, I70, I71, I72, I73, I74, 1 + I75, I76, I77, I78, I79, I80, I81, I82, I83, I84) [10 <= I69] f4(I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f8(I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) f9(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118) -> f10(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118) f10(I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134, I135) -> f4(0, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134, I135) [1 + I125 <= 10] f10(I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f11(I136, I137, I138, I138, I141, I141, I142, I143, I144, I144, I147, I147, I148, I149, 1500, rnd16, I152) [rnd16 = rnd16 /\ 10 <= I142] f8(I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) -> f7(I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) [1 + I153 <= 10] f8(I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186) -> f9(I170, I171, I172, I173, I174, I175, 1 + I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186) [10 <= I170] f7(I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) -> f3(I187, I188, 1 + I189, I190, I191, rnd6, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) [rnd6 = rnd6] f7(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f3(I204, I205, I206, I207, I208, I209, I210, I211, 1 + I212, I213, I214, rnd12, I216, I217, I218, I219, I220) [rnd12 = rnd12] f5(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237) -> f6(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237) f3(I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f4(1 + I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) f1(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) -> f2(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) The dependency graph for this problem is: 4 -> 13 5 -> 15 13 -> 4, 5 15 -> Where: 4) f6#(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67) -> f5#(I51, 1 + I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, rnd13, I64, I65, I66, rnd17) [rnd17 = rnd13 /\ rnd13 = rnd13 /\ 1 + I52 <= 10] 5) f6#(I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84) -> f1#(I68, I69, I70, I71, I72, I73, I74, 1 + I75, I76, I77, I78, I79, I80, I81, I82, I83, I84) [10 <= I69] 13) f5#(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237) -> f6#(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237) 15) f1#(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) -> f2#(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) We have the following SCCs. { 4, 13 } DP problem for innermost termination. P = f6#(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67) -> f5#(I51, 1 + I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, rnd13, I64, I65, I66, rnd17) [rnd17 = rnd13 /\ rnd13 = rnd13 /\ 1 + I52 <= 10] f5#(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237) -> f6#(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237) R = f13(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17) -> f12(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17) f12(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16) -> f1(I0, I1, I2, I3, I4, I5, I6, 0, I8, I9, I10, I11, 0, I13, I14, I15, I16) f2(I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33) -> f5(I17, 0, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33) [1 + I24 <= 10] f2(I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f9(I34, I35, 0, I37, I38, 0, 0, I41, 0, I43, I44, 0, I46, 1000, I48, I49, I50) [10 <= I41] f6(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67) -> f5(I51, 1 + I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, rnd13, I64, I65, I66, rnd17) [rnd17 = rnd13 /\ rnd13 = rnd13 /\ 1 + I52 <= 10] f6(I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84) -> f1(I68, I69, I70, I71, I72, I73, I74, 1 + I75, I76, I77, I78, I79, I80, I81, I82, I83, I84) [10 <= I69] f4(I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f8(I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) f9(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118) -> f10(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118) f10(I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134, I135) -> f4(0, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134, I135) [1 + I125 <= 10] f10(I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f11(I136, I137, I138, I138, I141, I141, I142, I143, I144, I144, I147, I147, I148, I149, 1500, rnd16, I152) [rnd16 = rnd16 /\ 10 <= I142] f8(I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) -> f7(I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) [1 + I153 <= 10] f8(I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186) -> f9(I170, I171, I172, I173, I174, I175, 1 + I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186) [10 <= I170] f7(I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) -> f3(I187, I188, 1 + I189, I190, I191, rnd6, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) [rnd6 = rnd6] f7(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f3(I204, I205, I206, I207, I208, I209, I210, I211, 1 + I212, I213, I214, rnd12, I216, I217, I218, I219, I220) [rnd12 = rnd12] f5(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237) -> f6(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237) f3(I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f4(1 + I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) f1(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) -> f2(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) 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,z13,z14,z15,z16,z17)] = 10 + -1 * (1 + z2) NU[f6#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14,z15,z16,z17)] = 10 + -1 * (1 + z2) This gives the following inequalities: rnd17 = rnd13 /\ rnd13 = rnd13 /\ 1 + I52 <= 10 ==> 10 + -1 * (1 + I52) > 10 + -1 * (1 + (1 + I52)) with 10 + -1 * (1 + I52) >= 0 ==> 10 + -1 * (1 + I222) >= 10 + -1 * (1 + I222) We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f5#(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237) -> f6#(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237) R = f13(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17) -> f12(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17) f12(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16) -> f1(I0, I1, I2, I3, I4, I5, I6, 0, I8, I9, I10, I11, 0, I13, I14, I15, I16) f2(I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33) -> f5(I17, 0, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33) [1 + I24 <= 10] f2(I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f9(I34, I35, 0, I37, I38, 0, 0, I41, 0, I43, I44, 0, I46, 1000, I48, I49, I50) [10 <= I41] f6(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67) -> f5(I51, 1 + I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, rnd13, I64, I65, I66, rnd17) [rnd17 = rnd13 /\ rnd13 = rnd13 /\ 1 + I52 <= 10] f6(I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84) -> f1(I68, I69, I70, I71, I72, I73, I74, 1 + I75, I76, I77, I78, I79, I80, I81, I82, I83, I84) [10 <= I69] f4(I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f8(I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) f9(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118) -> f10(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118) f10(I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134, I135) -> f4(0, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134, I135) [1 + I125 <= 10] f10(I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f11(I136, I137, I138, I138, I141, I141, I142, I143, I144, I144, I147, I147, I148, I149, 1500, rnd16, I152) [rnd16 = rnd16 /\ 10 <= I142] f8(I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) -> f7(I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) [1 + I153 <= 10] f8(I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186) -> f9(I170, I171, I172, I173, I174, I175, 1 + I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186) [10 <= I170] f7(I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) -> f3(I187, I188, 1 + I189, I190, I191, rnd6, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) [rnd6 = rnd6] f7(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f3(I204, I205, I206, I207, I208, I209, I210, I211, 1 + I212, I213, I214, rnd12, I216, I217, I218, I219, I220) [rnd12 = rnd12] f5(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237) -> f6(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237) f3(I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f4(1 + I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) f1(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) -> f2(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270, I271) The dependency graph for this problem is: 13 -> Where: 13) f5#(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237) -> f6#(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237) We have the following SCCs.