/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 = f17#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> f16#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) f16#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10) -> f1#(I0, I1, I2, I3, I4, 0, I6, 0, I8, I9, I10) f2#(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f3#(I11, I12, 0, I14, I15, I16, I17, I18, I19, I20, I21) [1 + I16 <= I19] f2#(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f5#(I22, I23, I24, I25, I26, I27, 0, I29, I30, I31, I32) [I30 <= I27] f4#(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f3#(I33, I34, 1 + I35, I36, I37, I38, I39, rnd8, I41, rnd10, I43) [rnd10 = rnd8 /\ rnd8 = rnd8 /\ 1 + I35 <= I41] f4#(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f1#(I44, I45, I46, I47, I48, 1 + I49, I50, I51, I52, I53, I54) [I52 <= I46] f9#(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f7#(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) f8#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f10#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) f6#(I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f14#(I77, I78, I79, 0, I81, I82, I83, I84, I85, I86, I87) [1 + I83 <= I85] f6#(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f11#(I88, I89, I90, I91, 0, I93, I94, I95, I96, I97, I98) [I96 <= I94] f15#(I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f14#(I99, I100, I101, 1 + I102, I103, I104, I105, I110, I107, I108, rnd11) [rnd11 = I110 /\ I110 = I110 /\ 1 + I102 <= I107] f15#(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f5#(I111, I112, I113, I114, I115, I116, 1 + I117, I118, I119, I120, I121) [I119 <= I114] f11#(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f12#(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) f14#(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f15#(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) f12#(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154) -> f8#(I144, 0, I146, I147, I148, I149, I150, I151, I152, I153, I154) [1 + I148 <= I152] f10#(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176) -> f9#(0, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176) [1 + I167 <= I174] f10#(I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187) -> f11#(I177, I178, I179, I180, 1 + I181, I182, I183, I184, I185, I186, I187) [I185 <= I178] f7#(I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f9#(1 + I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) [1 + I188 <= I196] f7#(I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f8#(I199, 1 + I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) [I207 <= I199] f5#(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f6#(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) f3#(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) -> f4#(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) f1#(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242) -> f2#(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242) R = f17(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> f16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) f16(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, I8, I9, I10) f2(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f3(I11, I12, 0, I14, I15, I16, I17, I18, I19, I20, I21) [1 + I16 <= I19] f2(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f5(I22, I23, I24, I25, I26, I27, 0, I29, I30, I31, I32) [I30 <= I27] f4(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f3(I33, I34, 1 + I35, I36, I37, I38, I39, rnd8, I41, rnd10, I43) [rnd10 = rnd8 /\ rnd8 = rnd8 /\ 1 + I35 <= I41] f4(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f1(I44, I45, I46, I47, I48, 1 + I49, I50, I51, I52, I53, I54) [I52 <= I46] f9(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f7(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) f8(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f10(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) f6(I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f14(I77, I78, I79, 0, I81, I82, I83, I84, I85, I86, I87) [1 + I83 <= I85] f6(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f11(I88, I89, I90, I91, 0, I93, I94, I95, I96, I97, I98) [I96 <= I94] f15(I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f14(I99, I100, I101, 1 + I102, I103, I104, I105, I110, I107, I108, rnd11) [rnd11 = I110 /\ I110 = I110 /\ 1 + I102 <= I107] f15(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f5(I111, I112, I113, I114, I115, I116, 1 + I117, I118, I119, I120, I121) [I119 <= I114] f11(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f12(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) f14(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f15(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) f12(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154) -> f8(I144, 0, I146, I147, I148, I149, I150, I151, I152, I153, I154) [1 + I148 <= I152] f12(I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f13(I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165) [I163 <= I159] f10(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176) -> f9(0, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176) [1 + I167 <= I174] f10(I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187) -> f11(I177, I178, I179, I180, 1 + I181, I182, I183, I184, I185, I186, I187) [I185 <= I178] f7(I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f9(1 + I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) [1 + I188 <= I196] f7(I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f8(I199, 1 + I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) [I207 <= I199] f5(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f6(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) f3(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) -> f4(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) f1(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242) -> f2(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242) The dependency graph for this problem is: 0 -> 1 1 -> 21 2 -> 20 3 -> 19 4 -> 20 5 -> 21 6 -> 17, 18 7 -> 15, 16 8 -> 13 9 -> 12 10 -> 13 11 -> 19 12 -> 14 13 -> 10, 11 14 -> 7 15 -> 6 16 -> 12 17 -> 6 18 -> 7 19 -> 8, 9 20 -> 4, 5 21 -> 2, 3 Where: 0) f17#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> f16#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 1) f16#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10) -> f1#(I0, I1, I2, I3, I4, 0, I6, 0, I8, I9, I10) 2) f2#(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f3#(I11, I12, 0, I14, I15, I16, I17, I18, I19, I20, I21) [1 + I16 <= I19] 3) f2#(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f5#(I22, I23, I24, I25, I26, I27, 0, I29, I30, I31, I32) [I30 <= I27] 4) f4#(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f3#(I33, I34, 1 + I35, I36, I37, I38, I39, rnd8, I41, rnd10, I43) [rnd10 = rnd8 /\ rnd8 = rnd8 /\ 1 + I35 <= I41] 5) f4#(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f1#(I44, I45, I46, I47, I48, 1 + I49, I50, I51, I52, I53, I54) [I52 <= I46] 6) f9#(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f7#(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) 7) f8#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f10#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) 8) f6#(I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f14#(I77, I78, I79, 0, I81, I82, I83, I84, I85, I86, I87) [1 + I83 <= I85] 9) f6#(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f11#(I88, I89, I90, I91, 0, I93, I94, I95, I96, I97, I98) [I96 <= I94] 10) f15#(I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f14#(I99, I100, I101, 1 + I102, I103, I104, I105, I110, I107, I108, rnd11) [rnd11 = I110 /\ I110 = I110 /\ 1 + I102 <= I107] 11) f15#(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f5#(I111, I112, I113, I114, I115, I116, 1 + I117, I118, I119, I120, I121) [I119 <= I114] 12) f11#(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f12#(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 13) f14#(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f15#(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) 14) f12#(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154) -> f8#(I144, 0, I146, I147, I148, I149, I150, I151, I152, I153, I154) [1 + I148 <= I152] 15) f10#(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176) -> f9#(0, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176) [1 + I167 <= I174] 16) f10#(I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187) -> f11#(I177, I178, I179, I180, 1 + I181, I182, I183, I184, I185, I186, I187) [I185 <= I178] 17) f7#(I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f9#(1 + I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) [1 + I188 <= I196] 18) f7#(I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f8#(I199, 1 + I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) [I207 <= I199] 19) f5#(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f6#(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) 20) f3#(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) -> f4#(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) 21) f1#(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242) -> f2#(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242) We have the following SCCs. { 2, 4, 5, 20, 21 } { 8, 10, 11, 13, 19 } { 6, 7, 12, 14, 15, 16, 17, 18 } DP problem for innermost termination. P = f9#(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f7#(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) f8#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f10#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) f11#(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f12#(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) f12#(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154) -> f8#(I144, 0, I146, I147, I148, I149, I150, I151, I152, I153, I154) [1 + I148 <= I152] f10#(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176) -> f9#(0, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176) [1 + I167 <= I174] f10#(I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187) -> f11#(I177, I178, I179, I180, 1 + I181, I182, I183, I184, I185, I186, I187) [I185 <= I178] f7#(I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f9#(1 + I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) [1 + I188 <= I196] f7#(I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f8#(I199, 1 + I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) [I207 <= I199] R = f17(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> f16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) f16(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, I8, I9, I10) f2(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f3(I11, I12, 0, I14, I15, I16, I17, I18, I19, I20, I21) [1 + I16 <= I19] f2(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f5(I22, I23, I24, I25, I26, I27, 0, I29, I30, I31, I32) [I30 <= I27] f4(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f3(I33, I34, 1 + I35, I36, I37, I38, I39, rnd8, I41, rnd10, I43) [rnd10 = rnd8 /\ rnd8 = rnd8 /\ 1 + I35 <= I41] f4(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f1(I44, I45, I46, I47, I48, 1 + I49, I50, I51, I52, I53, I54) [I52 <= I46] f9(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f7(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) f8(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f10(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) f6(I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f14(I77, I78, I79, 0, I81, I82, I83, I84, I85, I86, I87) [1 + I83 <= I85] f6(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f11(I88, I89, I90, I91, 0, I93, I94, I95, I96, I97, I98) [I96 <= I94] f15(I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f14(I99, I100, I101, 1 + I102, I103, I104, I105, I110, I107, I108, rnd11) [rnd11 = I110 /\ I110 = I110 /\ 1 + I102 <= I107] f15(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f5(I111, I112, I113, I114, I115, I116, 1 + I117, I118, I119, I120, I121) [I119 <= I114] f11(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f12(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) f14(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f15(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) f12(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154) -> f8(I144, 0, I146, I147, I148, I149, I150, I151, I152, I153, I154) [1 + I148 <= I152] f12(I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f13(I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165) [I163 <= I159] f10(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176) -> f9(0, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176) [1 + I167 <= I174] f10(I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187) -> f11(I177, I178, I179, I180, 1 + I181, I182, I183, I184, I185, I186, I187) [I185 <= I178] f7(I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f9(1 + I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) [1 + I188 <= I196] f7(I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f8(I199, 1 + I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) [I207 <= I199] f5(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f6(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) f3(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) -> f4(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) f1(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242) -> f2(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242) We use the extended value criterion with the projection function NU: NU[f12#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)] = -x4 + x8 + 1 NU[f11#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)] = -x4 + x8 + 1 NU[f10#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)] = -x4 + x8 NU[f8#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)] = -x4 + x8 NU[f7#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)] = -x4 + x8 NU[f9#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)] = -x4 + x8 This gives the following inequalities: ==> -I59 + I63 >= -I59 + I63 ==> -I70 + I74 >= -I70 + I74 ==> -I126 + I130 + 1 >= -I126 + I130 + 1 1 + I148 <= I152 ==> -I148 + I152 + 1 > -I148 + I152 with -I148 + I152 + 1 >= 0 1 + I167 <= I174 ==> -I170 + I174 >= -I170 + I174 I185 <= I178 ==> -I181 + I185 >= -(1 + I181) + I185 + 1 1 + I188 <= I196 ==> -I192 + I196 >= -I192 + I196 I207 <= I199 ==> -I203 + I207 >= -I203 + I207 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f9#(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f7#(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) f8#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f10#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) f11#(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f12#(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) f10#(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176) -> f9#(0, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176) [1 + I167 <= I174] f10#(I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187) -> f11#(I177, I178, I179, I180, 1 + I181, I182, I183, I184, I185, I186, I187) [I185 <= I178] f7#(I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f9#(1 + I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) [1 + I188 <= I196] f7#(I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f8#(I199, 1 + I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) [I207 <= I199] R = f17(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> f16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) f16(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, I8, I9, I10) f2(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f3(I11, I12, 0, I14, I15, I16, I17, I18, I19, I20, I21) [1 + I16 <= I19] f2(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f5(I22, I23, I24, I25, I26, I27, 0, I29, I30, I31, I32) [I30 <= I27] f4(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f3(I33, I34, 1 + I35, I36, I37, I38, I39, rnd8, I41, rnd10, I43) [rnd10 = rnd8 /\ rnd8 = rnd8 /\ 1 + I35 <= I41] f4(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f1(I44, I45, I46, I47, I48, 1 + I49, I50, I51, I52, I53, I54) [I52 <= I46] f9(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f7(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) f8(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f10(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) f6(I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f14(I77, I78, I79, 0, I81, I82, I83, I84, I85, I86, I87) [1 + I83 <= I85] f6(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f11(I88, I89, I90, I91, 0, I93, I94, I95, I96, I97, I98) [I96 <= I94] f15(I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f14(I99, I100, I101, 1 + I102, I103, I104, I105, I110, I107, I108, rnd11) [rnd11 = I110 /\ I110 = I110 /\ 1 + I102 <= I107] f15(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f5(I111, I112, I113, I114, I115, I116, 1 + I117, I118, I119, I120, I121) [I119 <= I114] f11(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f12(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) f14(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f15(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) f12(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154) -> f8(I144, 0, I146, I147, I148, I149, I150, I151, I152, I153, I154) [1 + I148 <= I152] f12(I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f13(I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165) [I163 <= I159] f10(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176) -> f9(0, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176) [1 + I167 <= I174] f10(I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187) -> f11(I177, I178, I179, I180, 1 + I181, I182, I183, I184, I185, I186, I187) [I185 <= I178] f7(I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f9(1 + I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) [1 + I188 <= I196] f7(I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f8(I199, 1 + I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) [I207 <= I199] f5(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f6(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) f3(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) -> f4(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) f1(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242) -> f2(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242) The dependency graph for this problem is: 6 -> 17, 18 7 -> 15, 16 12 -> 15 -> 6 16 -> 12 17 -> 6 18 -> 7 Where: 6) f9#(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f7#(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) 7) f8#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f10#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) 12) f11#(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f12#(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 15) f10#(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176) -> f9#(0, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176) [1 + I167 <= I174] 16) f10#(I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187) -> f11#(I177, I178, I179, I180, 1 + I181, I182, I183, I184, I185, I186, I187) [I185 <= I178] 17) f7#(I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f9#(1 + I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) [1 + I188 <= I196] 18) f7#(I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f8#(I199, 1 + I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) [I207 <= I199] We have the following SCCs. { 6, 7, 15, 17, 18 } DP problem for innermost termination. P = f9#(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f7#(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) f8#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f10#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) f10#(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176) -> f9#(0, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176) [1 + I167 <= I174] f7#(I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f9#(1 + I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) [1 + I188 <= I196] f7#(I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f8#(I199, 1 + I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) [I207 <= I199] R = f17(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> f16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) f16(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, I8, I9, I10) f2(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f3(I11, I12, 0, I14, I15, I16, I17, I18, I19, I20, I21) [1 + I16 <= I19] f2(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f5(I22, I23, I24, I25, I26, I27, 0, I29, I30, I31, I32) [I30 <= I27] f4(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f3(I33, I34, 1 + I35, I36, I37, I38, I39, rnd8, I41, rnd10, I43) [rnd10 = rnd8 /\ rnd8 = rnd8 /\ 1 + I35 <= I41] f4(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f1(I44, I45, I46, I47, I48, 1 + I49, I50, I51, I52, I53, I54) [I52 <= I46] f9(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f7(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) f8(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f10(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) f6(I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f14(I77, I78, I79, 0, I81, I82, I83, I84, I85, I86, I87) [1 + I83 <= I85] f6(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f11(I88, I89, I90, I91, 0, I93, I94, I95, I96, I97, I98) [I96 <= I94] f15(I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f14(I99, I100, I101, 1 + I102, I103, I104, I105, I110, I107, I108, rnd11) [rnd11 = I110 /\ I110 = I110 /\ 1 + I102 <= I107] f15(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f5(I111, I112, I113, I114, I115, I116, 1 + I117, I118, I119, I120, I121) [I119 <= I114] f11(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f12(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) f14(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f15(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) f12(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154) -> f8(I144, 0, I146, I147, I148, I149, I150, I151, I152, I153, I154) [1 + I148 <= I152] f12(I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f13(I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165) [I163 <= I159] f10(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176) -> f9(0, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176) [1 + I167 <= I174] f10(I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187) -> f11(I177, I178, I179, I180, 1 + I181, I182, I183, I184, I185, I186, I187) [I185 <= I178] f7(I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f9(1 + I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) [1 + I188 <= I196] f7(I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f8(I199, 1 + I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) [I207 <= I199] f5(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f6(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) f3(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) -> f4(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) f1(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242) -> f2(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242) We use the extended value criterion with the projection function NU: NU[f10#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)] = -x1 + x8 - 1 NU[f8#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)] = -x1 + x8 - 1 NU[f7#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)] = -x1 + x8 - 2 NU[f9#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)] = -x1 + x8 - 2 This gives the following inequalities: ==> -I56 + I63 - 2 >= -I56 + I63 - 2 ==> -I67 + I74 - 1 >= -I67 + I74 - 1 1 + I167 <= I174 ==> -I167 + I174 - 1 > -I167 + I174 - 2 with -I167 + I174 - 1 >= 0 1 + I188 <= I196 ==> -I189 + I196 - 2 >= -I189 + I196 - 2 I207 <= I199 ==> -I200 + I207 - 2 >= -(1 + I200) + I207 - 1 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f9#(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f7#(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) f8#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f10#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) f7#(I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f9#(1 + I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) [1 + I188 <= I196] f7#(I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f8#(I199, 1 + I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) [I207 <= I199] R = f17(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> f16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) f16(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, I8, I9, I10) f2(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f3(I11, I12, 0, I14, I15, I16, I17, I18, I19, I20, I21) [1 + I16 <= I19] f2(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f5(I22, I23, I24, I25, I26, I27, 0, I29, I30, I31, I32) [I30 <= I27] f4(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f3(I33, I34, 1 + I35, I36, I37, I38, I39, rnd8, I41, rnd10, I43) [rnd10 = rnd8 /\ rnd8 = rnd8 /\ 1 + I35 <= I41] f4(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f1(I44, I45, I46, I47, I48, 1 + I49, I50, I51, I52, I53, I54) [I52 <= I46] f9(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f7(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) f8(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f10(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) f6(I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f14(I77, I78, I79, 0, I81, I82, I83, I84, I85, I86, I87) [1 + I83 <= I85] f6(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f11(I88, I89, I90, I91, 0, I93, I94, I95, I96, I97, I98) [I96 <= I94] f15(I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f14(I99, I100, I101, 1 + I102, I103, I104, I105, I110, I107, I108, rnd11) [rnd11 = I110 /\ I110 = I110 /\ 1 + I102 <= I107] f15(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f5(I111, I112, I113, I114, I115, I116, 1 + I117, I118, I119, I120, I121) [I119 <= I114] f11(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f12(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) f14(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f15(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) f12(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154) -> f8(I144, 0, I146, I147, I148, I149, I150, I151, I152, I153, I154) [1 + I148 <= I152] f12(I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f13(I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165) [I163 <= I159] f10(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176) -> f9(0, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176) [1 + I167 <= I174] f10(I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187) -> f11(I177, I178, I179, I180, 1 + I181, I182, I183, I184, I185, I186, I187) [I185 <= I178] f7(I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f9(1 + I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) [1 + I188 <= I196] f7(I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f8(I199, 1 + I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) [I207 <= I199] f5(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f6(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) f3(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) -> f4(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) f1(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242) -> f2(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242) The dependency graph for this problem is: 6 -> 17, 18 7 -> 17 -> 6 18 -> 7 Where: 6) f9#(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f7#(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) 7) f8#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f10#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) 17) f7#(I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f9#(1 + I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) [1 + I188 <= I196] 18) f7#(I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f8#(I199, 1 + I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) [I207 <= I199] We have the following SCCs. { 6, 17 } DP problem for innermost termination. P = f9#(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f7#(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) f7#(I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f9#(1 + I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) [1 + I188 <= I196] R = f17(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> f16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) f16(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, I8, I9, I10) f2(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f3(I11, I12, 0, I14, I15, I16, I17, I18, I19, I20, I21) [1 + I16 <= I19] f2(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f5(I22, I23, I24, I25, I26, I27, 0, I29, I30, I31, I32) [I30 <= I27] f4(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f3(I33, I34, 1 + I35, I36, I37, I38, I39, rnd8, I41, rnd10, I43) [rnd10 = rnd8 /\ rnd8 = rnd8 /\ 1 + I35 <= I41] f4(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f1(I44, I45, I46, I47, I48, 1 + I49, I50, I51, I52, I53, I54) [I52 <= I46] f9(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f7(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) f8(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f10(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) f6(I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f14(I77, I78, I79, 0, I81, I82, I83, I84, I85, I86, I87) [1 + I83 <= I85] f6(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f11(I88, I89, I90, I91, 0, I93, I94, I95, I96, I97, I98) [I96 <= I94] f15(I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f14(I99, I100, I101, 1 + I102, I103, I104, I105, I110, I107, I108, rnd11) [rnd11 = I110 /\ I110 = I110 /\ 1 + I102 <= I107] f15(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f5(I111, I112, I113, I114, I115, I116, 1 + I117, I118, I119, I120, I121) [I119 <= I114] f11(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f12(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) f14(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f15(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) f12(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154) -> f8(I144, 0, I146, I147, I148, I149, I150, I151, I152, I153, I154) [1 + I148 <= I152] f12(I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f13(I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165) [I163 <= I159] f10(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176) -> f9(0, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176) [1 + I167 <= I174] f10(I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187) -> f11(I177, I178, I179, I180, 1 + I181, I182, I183, I184, I185, I186, I187) [I185 <= I178] f7(I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f9(1 + I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) [1 + I188 <= I196] f7(I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f8(I199, 1 + I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) [I207 <= I199] f5(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f6(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) f3(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) -> f4(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) f1(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242) -> f2(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242) We use the reverse value criterion with the projection function NU: NU[f7#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11)] = z9 + -1 * (1 + z1) NU[f9#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11)] = z9 + -1 * (1 + z1) This gives the following inequalities: ==> I63 + -1 * (1 + I55) >= I63 + -1 * (1 + I55) 1 + I188 <= I196 ==> I196 + -1 * (1 + I188) > I196 + -1 * (1 + (1 + I188)) with I196 + -1 * (1 + I188) >= 0 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f9#(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f7#(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) R = f17(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> f16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) f16(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, I8, I9, I10) f2(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f3(I11, I12, 0, I14, I15, I16, I17, I18, I19, I20, I21) [1 + I16 <= I19] f2(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f5(I22, I23, I24, I25, I26, I27, 0, I29, I30, I31, I32) [I30 <= I27] f4(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f3(I33, I34, 1 + I35, I36, I37, I38, I39, rnd8, I41, rnd10, I43) [rnd10 = rnd8 /\ rnd8 = rnd8 /\ 1 + I35 <= I41] f4(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f1(I44, I45, I46, I47, I48, 1 + I49, I50, I51, I52, I53, I54) [I52 <= I46] f9(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f7(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) f8(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f10(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) f6(I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f14(I77, I78, I79, 0, I81, I82, I83, I84, I85, I86, I87) [1 + I83 <= I85] f6(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f11(I88, I89, I90, I91, 0, I93, I94, I95, I96, I97, I98) [I96 <= I94] f15(I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f14(I99, I100, I101, 1 + I102, I103, I104, I105, I110, I107, I108, rnd11) [rnd11 = I110 /\ I110 = I110 /\ 1 + I102 <= I107] f15(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f5(I111, I112, I113, I114, I115, I116, 1 + I117, I118, I119, I120, I121) [I119 <= I114] f11(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f12(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) f14(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f15(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) f12(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154) -> f8(I144, 0, I146, I147, I148, I149, I150, I151, I152, I153, I154) [1 + I148 <= I152] f12(I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f13(I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165) [I163 <= I159] f10(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176) -> f9(0, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176) [1 + I167 <= I174] f10(I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187) -> f11(I177, I178, I179, I180, 1 + I181, I182, I183, I184, I185, I186, I187) [I185 <= I178] f7(I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f9(1 + I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) [1 + I188 <= I196] f7(I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f8(I199, 1 + I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) [I207 <= I199] f5(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f6(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) f3(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) -> f4(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) f1(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242) -> f2(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242) The dependency graph for this problem is: 6 -> Where: 6) f9#(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f7#(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) We have the following SCCs. DP problem for innermost termination. P = f6#(I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f14#(I77, I78, I79, 0, I81, I82, I83, I84, I85, I86, I87) [1 + I83 <= I85] f15#(I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f14#(I99, I100, I101, 1 + I102, I103, I104, I105, I110, I107, I108, rnd11) [rnd11 = I110 /\ I110 = I110 /\ 1 + I102 <= I107] f15#(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f5#(I111, I112, I113, I114, I115, I116, 1 + I117, I118, I119, I120, I121) [I119 <= I114] f14#(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f15#(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) f5#(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f6#(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) R = f17(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> f16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) f16(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, I8, I9, I10) f2(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f3(I11, I12, 0, I14, I15, I16, I17, I18, I19, I20, I21) [1 + I16 <= I19] f2(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f5(I22, I23, I24, I25, I26, I27, 0, I29, I30, I31, I32) [I30 <= I27] f4(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f3(I33, I34, 1 + I35, I36, I37, I38, I39, rnd8, I41, rnd10, I43) [rnd10 = rnd8 /\ rnd8 = rnd8 /\ 1 + I35 <= I41] f4(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f1(I44, I45, I46, I47, I48, 1 + I49, I50, I51, I52, I53, I54) [I52 <= I46] f9(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f7(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) f8(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f10(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) f6(I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f14(I77, I78, I79, 0, I81, I82, I83, I84, I85, I86, I87) [1 + I83 <= I85] f6(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f11(I88, I89, I90, I91, 0, I93, I94, I95, I96, I97, I98) [I96 <= I94] f15(I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f14(I99, I100, I101, 1 + I102, I103, I104, I105, I110, I107, I108, rnd11) [rnd11 = I110 /\ I110 = I110 /\ 1 + I102 <= I107] f15(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f5(I111, I112, I113, I114, I115, I116, 1 + I117, I118, I119, I120, I121) [I119 <= I114] f11(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f12(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) f14(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f15(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) f12(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154) -> f8(I144, 0, I146, I147, I148, I149, I150, I151, I152, I153, I154) [1 + I148 <= I152] f12(I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f13(I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165) [I163 <= I159] f10(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176) -> f9(0, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176) [1 + I167 <= I174] f10(I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187) -> f11(I177, I178, I179, I180, 1 + I181, I182, I183, I184, I185, I186, I187) [I185 <= I178] f7(I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f9(1 + I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) [1 + I188 <= I196] f7(I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f8(I199, 1 + I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) [I207 <= I199] f5(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f6(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) f3(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) -> f4(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) f1(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242) -> f2(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242) We use the extended value criterion with the projection function NU: NU[f5#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)] = -x6 + x8 - 1 NU[f15#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)] = -x6 + x8 - 2 NU[f14#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)] = -x6 + x8 - 2 NU[f6#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)] = -x6 + x8 - 1 This gives the following inequalities: 1 + I83 <= I85 ==> -I83 + I85 - 1 > -I83 + I85 - 2 with -I83 + I85 - 1 >= 0 rnd11 = I110 /\ I110 = I110 /\ 1 + I102 <= I107 ==> -I105 + I107 - 2 >= -I105 + I107 - 2 I119 <= I114 ==> -I117 + I119 - 2 >= -(1 + I117) + I119 - 1 ==> -I139 + I141 - 2 >= -I139 + I141 - 2 ==> -I216 + I218 - 1 >= -I216 + I218 - 1 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f15#(I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f14#(I99, I100, I101, 1 + I102, I103, I104, I105, I110, I107, I108, rnd11) [rnd11 = I110 /\ I110 = I110 /\ 1 + I102 <= I107] f15#(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f5#(I111, I112, I113, I114, I115, I116, 1 + I117, I118, I119, I120, I121) [I119 <= I114] f14#(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f15#(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) f5#(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f6#(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) R = f17(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> f16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) f16(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, I8, I9, I10) f2(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f3(I11, I12, 0, I14, I15, I16, I17, I18, I19, I20, I21) [1 + I16 <= I19] f2(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f5(I22, I23, I24, I25, I26, I27, 0, I29, I30, I31, I32) [I30 <= I27] f4(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f3(I33, I34, 1 + I35, I36, I37, I38, I39, rnd8, I41, rnd10, I43) [rnd10 = rnd8 /\ rnd8 = rnd8 /\ 1 + I35 <= I41] f4(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f1(I44, I45, I46, I47, I48, 1 + I49, I50, I51, I52, I53, I54) [I52 <= I46] f9(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f7(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) f8(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f10(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) f6(I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f14(I77, I78, I79, 0, I81, I82, I83, I84, I85, I86, I87) [1 + I83 <= I85] f6(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f11(I88, I89, I90, I91, 0, I93, I94, I95, I96, I97, I98) [I96 <= I94] f15(I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f14(I99, I100, I101, 1 + I102, I103, I104, I105, I110, I107, I108, rnd11) [rnd11 = I110 /\ I110 = I110 /\ 1 + I102 <= I107] f15(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f5(I111, I112, I113, I114, I115, I116, 1 + I117, I118, I119, I120, I121) [I119 <= I114] f11(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f12(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) f14(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f15(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) f12(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154) -> f8(I144, 0, I146, I147, I148, I149, I150, I151, I152, I153, I154) [1 + I148 <= I152] f12(I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f13(I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165) [I163 <= I159] f10(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176) -> f9(0, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176) [1 + I167 <= I174] f10(I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187) -> f11(I177, I178, I179, I180, 1 + I181, I182, I183, I184, I185, I186, I187) [I185 <= I178] f7(I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f9(1 + I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) [1 + I188 <= I196] f7(I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f8(I199, 1 + I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) [I207 <= I199] f5(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f6(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) f3(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) -> f4(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) f1(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242) -> f2(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242) The dependency graph for this problem is: 10 -> 13 11 -> 19 13 -> 10, 11 19 -> Where: 10) f15#(I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f14#(I99, I100, I101, 1 + I102, I103, I104, I105, I110, I107, I108, rnd11) [rnd11 = I110 /\ I110 = I110 /\ 1 + I102 <= I107] 11) f15#(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f5#(I111, I112, I113, I114, I115, I116, 1 + I117, I118, I119, I120, I121) [I119 <= I114] 13) f14#(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f15#(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) 19) f5#(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f6#(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) We have the following SCCs. { 10, 13 } DP problem for innermost termination. P = f15#(I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f14#(I99, I100, I101, 1 + I102, I103, I104, I105, I110, I107, I108, rnd11) [rnd11 = I110 /\ I110 = I110 /\ 1 + I102 <= I107] f14#(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f15#(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) R = f17(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> f16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) f16(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, I8, I9, I10) f2(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f3(I11, I12, 0, I14, I15, I16, I17, I18, I19, I20, I21) [1 + I16 <= I19] f2(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f5(I22, I23, I24, I25, I26, I27, 0, I29, I30, I31, I32) [I30 <= I27] f4(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f3(I33, I34, 1 + I35, I36, I37, I38, I39, rnd8, I41, rnd10, I43) [rnd10 = rnd8 /\ rnd8 = rnd8 /\ 1 + I35 <= I41] f4(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f1(I44, I45, I46, I47, I48, 1 + I49, I50, I51, I52, I53, I54) [I52 <= I46] f9(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f7(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) f8(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f10(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) f6(I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f14(I77, I78, I79, 0, I81, I82, I83, I84, I85, I86, I87) [1 + I83 <= I85] f6(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f11(I88, I89, I90, I91, 0, I93, I94, I95, I96, I97, I98) [I96 <= I94] f15(I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f14(I99, I100, I101, 1 + I102, I103, I104, I105, I110, I107, I108, rnd11) [rnd11 = I110 /\ I110 = I110 /\ 1 + I102 <= I107] f15(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f5(I111, I112, I113, I114, I115, I116, 1 + I117, I118, I119, I120, I121) [I119 <= I114] f11(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f12(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) f14(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f15(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) f12(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154) -> f8(I144, 0, I146, I147, I148, I149, I150, I151, I152, I153, I154) [1 + I148 <= I152] f12(I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f13(I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165) [I163 <= I159] f10(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176) -> f9(0, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176) [1 + I167 <= I174] f10(I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187) -> f11(I177, I178, I179, I180, 1 + I181, I182, I183, I184, I185, I186, I187) [I185 <= I178] f7(I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f9(1 + I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) [1 + I188 <= I196] f7(I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f8(I199, 1 + I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) [I207 <= I199] f5(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f6(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) f3(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) -> f4(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) f1(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242) -> f2(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242) We use the reverse value criterion with the projection function NU: NU[f14#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11)] = z9 + -1 * (1 + z4) NU[f15#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11)] = z9 + -1 * (1 + z4) This gives the following inequalities: rnd11 = I110 /\ I110 = I110 /\ 1 + I102 <= I107 ==> I107 + -1 * (1 + I102) > I107 + -1 * (1 + (1 + I102)) with I107 + -1 * (1 + I102) >= 0 ==> I141 + -1 * (1 + I136) >= I141 + -1 * (1 + I136) We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f14#(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f15#(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) R = f17(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> f16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) f16(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, I8, I9, I10) f2(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f3(I11, I12, 0, I14, I15, I16, I17, I18, I19, I20, I21) [1 + I16 <= I19] f2(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f5(I22, I23, I24, I25, I26, I27, 0, I29, I30, I31, I32) [I30 <= I27] f4(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f3(I33, I34, 1 + I35, I36, I37, I38, I39, rnd8, I41, rnd10, I43) [rnd10 = rnd8 /\ rnd8 = rnd8 /\ 1 + I35 <= I41] f4(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f1(I44, I45, I46, I47, I48, 1 + I49, I50, I51, I52, I53, I54) [I52 <= I46] f9(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f7(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) f8(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f10(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) f6(I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f14(I77, I78, I79, 0, I81, I82, I83, I84, I85, I86, I87) [1 + I83 <= I85] f6(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f11(I88, I89, I90, I91, 0, I93, I94, I95, I96, I97, I98) [I96 <= I94] f15(I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f14(I99, I100, I101, 1 + I102, I103, I104, I105, I110, I107, I108, rnd11) [rnd11 = I110 /\ I110 = I110 /\ 1 + I102 <= I107] f15(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f5(I111, I112, I113, I114, I115, I116, 1 + I117, I118, I119, I120, I121) [I119 <= I114] f11(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f12(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) f14(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f15(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) f12(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154) -> f8(I144, 0, I146, I147, I148, I149, I150, I151, I152, I153, I154) [1 + I148 <= I152] f12(I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f13(I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165) [I163 <= I159] f10(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176) -> f9(0, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176) [1 + I167 <= I174] f10(I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187) -> f11(I177, I178, I179, I180, 1 + I181, I182, I183, I184, I185, I186, I187) [I185 <= I178] f7(I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f9(1 + I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) [1 + I188 <= I196] f7(I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f8(I199, 1 + I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) [I207 <= I199] f5(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f6(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) f3(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) -> f4(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) f1(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242) -> f2(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242) The dependency graph for this problem is: 13 -> Where: 13) f14#(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f15#(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) We have the following SCCs. DP problem for innermost termination. P = f2#(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f3#(I11, I12, 0, I14, I15, I16, I17, I18, I19, I20, I21) [1 + I16 <= I19] f4#(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f3#(I33, I34, 1 + I35, I36, I37, I38, I39, rnd8, I41, rnd10, I43) [rnd10 = rnd8 /\ rnd8 = rnd8 /\ 1 + I35 <= I41] f4#(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f1#(I44, I45, I46, I47, I48, 1 + I49, I50, I51, I52, I53, I54) [I52 <= I46] f3#(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) -> f4#(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) f1#(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242) -> f2#(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242) R = f17(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> f16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) f16(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, I8, I9, I10) f2(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f3(I11, I12, 0, I14, I15, I16, I17, I18, I19, I20, I21) [1 + I16 <= I19] f2(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f5(I22, I23, I24, I25, I26, I27, 0, I29, I30, I31, I32) [I30 <= I27] f4(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f3(I33, I34, 1 + I35, I36, I37, I38, I39, rnd8, I41, rnd10, I43) [rnd10 = rnd8 /\ rnd8 = rnd8 /\ 1 + I35 <= I41] f4(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f1(I44, I45, I46, I47, I48, 1 + I49, I50, I51, I52, I53, I54) [I52 <= I46] f9(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f7(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) f8(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f10(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) f6(I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f14(I77, I78, I79, 0, I81, I82, I83, I84, I85, I86, I87) [1 + I83 <= I85] f6(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f11(I88, I89, I90, I91, 0, I93, I94, I95, I96, I97, I98) [I96 <= I94] f15(I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f14(I99, I100, I101, 1 + I102, I103, I104, I105, I110, I107, I108, rnd11) [rnd11 = I110 /\ I110 = I110 /\ 1 + I102 <= I107] f15(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f5(I111, I112, I113, I114, I115, I116, 1 + I117, I118, I119, I120, I121) [I119 <= I114] f11(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f12(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) f14(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f15(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) f12(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154) -> f8(I144, 0, I146, I147, I148, I149, I150, I151, I152, I153, I154) [1 + I148 <= I152] f12(I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f13(I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165) [I163 <= I159] f10(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176) -> f9(0, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176) [1 + I167 <= I174] f10(I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187) -> f11(I177, I178, I179, I180, 1 + I181, I182, I183, I184, I185, I186, I187) [I185 <= I178] f7(I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f9(1 + I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) [1 + I188 <= I196] f7(I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f8(I199, 1 + I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) [I207 <= I199] f5(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f6(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) f3(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) -> f4(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) f1(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242) -> f2(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242) We use the extended value criterion with the projection function NU: NU[f1#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)] = -x5 + x8 - 1 NU[f4#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)] = -x5 + x8 - 2 NU[f3#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)] = -x5 + x8 - 2 NU[f2#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)] = -x5 + x8 - 1 This gives the following inequalities: 1 + I16 <= I19 ==> -I16 + I19 - 1 > -I16 + I19 - 2 with -I16 + I19 - 1 >= 0 rnd10 = rnd8 /\ rnd8 = rnd8 /\ 1 + I35 <= I41 ==> -I38 + I41 - 2 >= -I38 + I41 - 2 I52 <= I46 ==> -I49 + I52 - 2 >= -(1 + I49) + I52 - 1 ==> -I226 + I229 - 2 >= -I226 + I229 - 2 ==> -I237 + I240 - 1 >= -I237 + I240 - 1 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f4#(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f3#(I33, I34, 1 + I35, I36, I37, I38, I39, rnd8, I41, rnd10, I43) [rnd10 = rnd8 /\ rnd8 = rnd8 /\ 1 + I35 <= I41] f4#(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f1#(I44, I45, I46, I47, I48, 1 + I49, I50, I51, I52, I53, I54) [I52 <= I46] f3#(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) -> f4#(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) f1#(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242) -> f2#(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242) R = f17(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> f16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) f16(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, I8, I9, I10) f2(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f3(I11, I12, 0, I14, I15, I16, I17, I18, I19, I20, I21) [1 + I16 <= I19] f2(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f5(I22, I23, I24, I25, I26, I27, 0, I29, I30, I31, I32) [I30 <= I27] f4(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f3(I33, I34, 1 + I35, I36, I37, I38, I39, rnd8, I41, rnd10, I43) [rnd10 = rnd8 /\ rnd8 = rnd8 /\ 1 + I35 <= I41] f4(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f1(I44, I45, I46, I47, I48, 1 + I49, I50, I51, I52, I53, I54) [I52 <= I46] f9(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f7(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) f8(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f10(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) f6(I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f14(I77, I78, I79, 0, I81, I82, I83, I84, I85, I86, I87) [1 + I83 <= I85] f6(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f11(I88, I89, I90, I91, 0, I93, I94, I95, I96, I97, I98) [I96 <= I94] f15(I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f14(I99, I100, I101, 1 + I102, I103, I104, I105, I110, I107, I108, rnd11) [rnd11 = I110 /\ I110 = I110 /\ 1 + I102 <= I107] f15(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f5(I111, I112, I113, I114, I115, I116, 1 + I117, I118, I119, I120, I121) [I119 <= I114] f11(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f12(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) f14(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f15(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) f12(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154) -> f8(I144, 0, I146, I147, I148, I149, I150, I151, I152, I153, I154) [1 + I148 <= I152] f12(I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f13(I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165) [I163 <= I159] f10(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176) -> f9(0, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176) [1 + I167 <= I174] f10(I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187) -> f11(I177, I178, I179, I180, 1 + I181, I182, I183, I184, I185, I186, I187) [I185 <= I178] f7(I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f9(1 + I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) [1 + I188 <= I196] f7(I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f8(I199, 1 + I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) [I207 <= I199] f5(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f6(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) f3(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) -> f4(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) f1(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242) -> f2(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242) The dependency graph for this problem is: 4 -> 20 5 -> 21 20 -> 4, 5 21 -> Where: 4) f4#(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f3#(I33, I34, 1 + I35, I36, I37, I38, I39, rnd8, I41, rnd10, I43) [rnd10 = rnd8 /\ rnd8 = rnd8 /\ 1 + I35 <= I41] 5) f4#(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f1#(I44, I45, I46, I47, I48, 1 + I49, I50, I51, I52, I53, I54) [I52 <= I46] 20) f3#(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) -> f4#(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) 21) f1#(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242) -> f2#(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242) We have the following SCCs. { 4, 20 } DP problem for innermost termination. P = f4#(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f3#(I33, I34, 1 + I35, I36, I37, I38, I39, rnd8, I41, rnd10, I43) [rnd10 = rnd8 /\ rnd8 = rnd8 /\ 1 + I35 <= I41] f3#(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) -> f4#(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) R = f17(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> f16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) f16(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, I8, I9, I10) f2(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f3(I11, I12, 0, I14, I15, I16, I17, I18, I19, I20, I21) [1 + I16 <= I19] f2(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f5(I22, I23, I24, I25, I26, I27, 0, I29, I30, I31, I32) [I30 <= I27] f4(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f3(I33, I34, 1 + I35, I36, I37, I38, I39, rnd8, I41, rnd10, I43) [rnd10 = rnd8 /\ rnd8 = rnd8 /\ 1 + I35 <= I41] f4(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f1(I44, I45, I46, I47, I48, 1 + I49, I50, I51, I52, I53, I54) [I52 <= I46] f9(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f7(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) f8(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f10(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) f6(I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f14(I77, I78, I79, 0, I81, I82, I83, I84, I85, I86, I87) [1 + I83 <= I85] f6(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f11(I88, I89, I90, I91, 0, I93, I94, I95, I96, I97, I98) [I96 <= I94] f15(I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f14(I99, I100, I101, 1 + I102, I103, I104, I105, I110, I107, I108, rnd11) [rnd11 = I110 /\ I110 = I110 /\ 1 + I102 <= I107] f15(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f5(I111, I112, I113, I114, I115, I116, 1 + I117, I118, I119, I120, I121) [I119 <= I114] f11(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f12(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) f14(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f15(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) f12(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154) -> f8(I144, 0, I146, I147, I148, I149, I150, I151, I152, I153, I154) [1 + I148 <= I152] f12(I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f13(I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165) [I163 <= I159] f10(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176) -> f9(0, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176) [1 + I167 <= I174] f10(I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187) -> f11(I177, I178, I179, I180, 1 + I181, I182, I183, I184, I185, I186, I187) [I185 <= I178] f7(I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f9(1 + I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) [1 + I188 <= I196] f7(I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f8(I199, 1 + I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) [I207 <= I199] f5(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f6(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) f3(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) -> f4(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) f1(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242) -> f2(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242) We use the reverse value criterion with the projection function NU: NU[f3#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11)] = z9 + -1 * (1 + z3) NU[f4#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11)] = z9 + -1 * (1 + z3) This gives the following inequalities: rnd10 = rnd8 /\ rnd8 = rnd8 /\ 1 + I35 <= I41 ==> I41 + -1 * (1 + I35) > I41 + -1 * (1 + (1 + I35)) with I41 + -1 * (1 + I35) >= 0 ==> I229 + -1 * (1 + I223) >= I229 + -1 * (1 + I223) We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f3#(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) -> f4#(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) R = f17(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> f16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) f16(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, I8, I9, I10) f2(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f3(I11, I12, 0, I14, I15, I16, I17, I18, I19, I20, I21) [1 + I16 <= I19] f2(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f5(I22, I23, I24, I25, I26, I27, 0, I29, I30, I31, I32) [I30 <= I27] f4(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f3(I33, I34, 1 + I35, I36, I37, I38, I39, rnd8, I41, rnd10, I43) [rnd10 = rnd8 /\ rnd8 = rnd8 /\ 1 + I35 <= I41] f4(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f1(I44, I45, I46, I47, I48, 1 + I49, I50, I51, I52, I53, I54) [I52 <= I46] f9(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f7(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) f8(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f10(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) f6(I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f14(I77, I78, I79, 0, I81, I82, I83, I84, I85, I86, I87) [1 + I83 <= I85] f6(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f11(I88, I89, I90, I91, 0, I93, I94, I95, I96, I97, I98) [I96 <= I94] f15(I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f14(I99, I100, I101, 1 + I102, I103, I104, I105, I110, I107, I108, rnd11) [rnd11 = I110 /\ I110 = I110 /\ 1 + I102 <= I107] f15(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f5(I111, I112, I113, I114, I115, I116, 1 + I117, I118, I119, I120, I121) [I119 <= I114] f11(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f12(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) f14(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f15(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) f12(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154) -> f8(I144, 0, I146, I147, I148, I149, I150, I151, I152, I153, I154) [1 + I148 <= I152] f12(I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f13(I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165) [I163 <= I159] f10(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176) -> f9(0, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176) [1 + I167 <= I174] f10(I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187) -> f11(I177, I178, I179, I180, 1 + I181, I182, I183, I184, I185, I186, I187) [I185 <= I178] f7(I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f9(1 + I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) [1 + I188 <= I196] f7(I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f8(I199, 1 + I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) [I207 <= I199] f5(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f6(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) f3(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) -> f4(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) f1(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242) -> f2(I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242) The dependency graph for this problem is: 20 -> Where: 20) f3#(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) -> f4#(I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231) We have the following SCCs.