/export/starexec/sandbox/solver/bin/starexec_run_Transition /export/starexec/sandbox/benchmark/theBenchmark.smt2 /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- MAYBE DP problem for innermost termination. P = f18#(x1, x2, x3, x4, x5, x6, x7) -> f17#(x1, x2, x3, x4, x5, x6, x7) f17#(I0, I1, I2, I3, I4, I5, I6) -> f10#(I0, 4, 0, 0, I4, I5, I6) f3#(I7, I8, I9, I10, I11, I12, I13) -> f16#(I7, I8, I9, I10, I11, I12, I13) [1 <= I9 /\ I9 <= 1] f3#(I14, I15, I16, I17, I18, I19, I20) -> f15#(I14, I15, I16, I17, I18, I19, I20) [1 + I16 <= 1] f3#(I21, I22, I23, I24, I25, I26, I27) -> f15#(I21, I22, I23, I24, I25, I26, I27) [2 <= I23] f16#(I28, I29, I30, I31, I32, I33, I34) -> f15#(I28, -1 + I29, I30, 1, I32, I33, I34) [0 <= I31 /\ I31 <= 0] f16#(I35, I36, I37, I38, I39, I40, I41) -> f15#(I35, I36, I37, I38, I39, I40, I41) [1 + I38 <= 0] f16#(I42, I43, I44, I45, I46, I47, I48) -> f15#(I42, I43, I44, I45, I46, I47, I48) [1 <= I45] f15#(I49, I50, I51, I52, I53, I54, I55) -> f14#(I49, I50, 2, I52, I53, I54, I50 + I55) f14#(I56, I57, I58, I59, I60, I61, I62) -> f7#(I56, I57, I58, I59, I60, I61, I62) [1 + I56 <= I62] f14#(I63, I64, I65, I66, I67, I68, I69) -> f10#(I63, I64, I65, I66, I67, I68, I69) [I69 <= I63] f2#(I70, I71, I72, I73, I74, I75, I76) -> f13#(I70, I71, I72, I73, I74, I75, I76) [1 + I74 <= I75] f2#(I77, I78, I79, I80, I81, I82, I83) -> f7#(I77, I78, I79, I80, I81, I82, I83) [I82 <= I81] f13#(I84, I85, I86, I87, I88, I89, I90) -> f12#(I84, I85, I86, I87, I88, I89, I90) [2 <= I86 /\ I86 <= 2] f13#(I91, I92, I93, I94, I95, I96, I97) -> f11#(I91, I92, I93, I94, I95, I96, I97) [1 + I93 <= 2] f13#(I98, I99, I100, I101, I102, I103, I104) -> f11#(I98, I99, I100, I101, I102, I103, I104) [3 <= I100] f10#(I105, I106, I107, I108, I109, I110, I111) -> f6#(I105, I106, I107, I108, rnd5, I110, I111) [rnd5 = rnd5] f12#(I112, I113, I114, I115, I116, I117, I118) -> f11#(I112, -1 + I113, I114, 1, I116, I117, I118) [0 <= I115 /\ I115 <= 0] f12#(I119, I120, I121, I122, I123, I124, I125) -> f11#(I119, I120, I121, I122, I123, I124, I125) [1 + I122 <= 0] f12#(I126, I127, I128, I129, I130, I131, I132) -> f11#(I126, I127, I128, I129, I130, I131, I132) [1 <= I129] f11#(I133, I134, I135, I136, I137, I138, I139) -> f9#(I133, I134, 1, I136, I137, I138, -1 * I134 + I139) f9#(I140, I141, I142, I143, I144, I145, I146) -> f7#(I140, I141, I142, I143, I144, I145, I146) [1 + I146 <= 0] f9#(I147, I148, I149, I150, I151, I152, I153) -> f10#(I147, I148, I149, I150, I151, I152, I153) [0 <= I153] f6#(I161, I162, I163, I164, I165, I166, I167) -> f7#(I161, I162, I163, I164, I165, I166, I167) [1 <= I162 /\ I162 <= 1] f6#(I168, I169, I170, I171, I172, I173, I174) -> f5#(I168, I169, I170, I171, I172, I173, I174) [1 + I169 <= 1] f6#(I175, I176, I177, I178, I179, I180, I181) -> f5#(I175, I176, I177, I178, I179, I180, I181) [2 <= I176] f5#(I182, I183, I184, I185, I186, I187, I188) -> f4#(I182, I183, I184, I185, I186, I187, I188) [1 + I185 <= 0] f5#(I189, I190, I191, I192, I193, I194, I195) -> f4#(I189, I190, I191, I192, I193, I194, I195) [1 <= I192] f5#(I196, I197, I198, I199, I200, I201, I202) -> f1#(I196, I197, I198, I199, I200, I201, I202) [0 <= I199 /\ I199 <= 0] f4#(I203, I204, I205, I206, I207, I208, I209) -> f1#(I203, -1 + I204, I205, I206, I207, I208, I209) f1#(I210, I211, I212, I213, I214, I215, I216) -> f3#(I210, I211, I212, I213, I214, I215, I216) [1 + I215 <= I214] f1#(I217, I218, I219, I220, I221, I222, I223) -> f2#(I217, I218, I219, I220, I221, I222, I223) [I221 <= I222] R = f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) f17(I0, I1, I2, I3, I4, I5, I6) -> f10(I0, 4, 0, 0, I4, I5, I6) f3(I7, I8, I9, I10, I11, I12, I13) -> f16(I7, I8, I9, I10, I11, I12, I13) [1 <= I9 /\ I9 <= 1] f3(I14, I15, I16, I17, I18, I19, I20) -> f15(I14, I15, I16, I17, I18, I19, I20) [1 + I16 <= 1] f3(I21, I22, I23, I24, I25, I26, I27) -> f15(I21, I22, I23, I24, I25, I26, I27) [2 <= I23] f16(I28, I29, I30, I31, I32, I33, I34) -> f15(I28, -1 + I29, I30, 1, I32, I33, I34) [0 <= I31 /\ I31 <= 0] f16(I35, I36, I37, I38, I39, I40, I41) -> f15(I35, I36, I37, I38, I39, I40, I41) [1 + I38 <= 0] f16(I42, I43, I44, I45, I46, I47, I48) -> f15(I42, I43, I44, I45, I46, I47, I48) [1 <= I45] f15(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, 2, I52, I53, I54, I50 + I55) f14(I56, I57, I58, I59, I60, I61, I62) -> f7(I56, I57, I58, I59, I60, I61, I62) [1 + I56 <= I62] f14(I63, I64, I65, I66, I67, I68, I69) -> f10(I63, I64, I65, I66, I67, I68, I69) [I69 <= I63] f2(I70, I71, I72, I73, I74, I75, I76) -> f13(I70, I71, I72, I73, I74, I75, I76) [1 + I74 <= I75] f2(I77, I78, I79, I80, I81, I82, I83) -> f7(I77, I78, I79, I80, I81, I82, I83) [I82 <= I81] f13(I84, I85, I86, I87, I88, I89, I90) -> f12(I84, I85, I86, I87, I88, I89, I90) [2 <= I86 /\ I86 <= 2] f13(I91, I92, I93, I94, I95, I96, I97) -> f11(I91, I92, I93, I94, I95, I96, I97) [1 + I93 <= 2] f13(I98, I99, I100, I101, I102, I103, I104) -> f11(I98, I99, I100, I101, I102, I103, I104) [3 <= I100] f10(I105, I106, I107, I108, I109, I110, I111) -> f6(I105, I106, I107, I108, rnd5, I110, I111) [rnd5 = rnd5] f12(I112, I113, I114, I115, I116, I117, I118) -> f11(I112, -1 + I113, I114, 1, I116, I117, I118) [0 <= I115 /\ I115 <= 0] f12(I119, I120, I121, I122, I123, I124, I125) -> f11(I119, I120, I121, I122, I123, I124, I125) [1 + I122 <= 0] f12(I126, I127, I128, I129, I130, I131, I132) -> f11(I126, I127, I128, I129, I130, I131, I132) [1 <= I129] f11(I133, I134, I135, I136, I137, I138, I139) -> f9(I133, I134, 1, I136, I137, I138, -1 * I134 + I139) f9(I140, I141, I142, I143, I144, I145, I146) -> f7(I140, I141, I142, I143, I144, I145, I146) [1 + I146 <= 0] f9(I147, I148, I149, I150, I151, I152, I153) -> f10(I147, I148, I149, I150, I151, I152, I153) [0 <= I153] f7(I154, I155, I156, I157, I158, I159, I160) -> f8(I154, I155, I156, I157, I158, I159, I160) f6(I161, I162, I163, I164, I165, I166, I167) -> f7(I161, I162, I163, I164, I165, I166, I167) [1 <= I162 /\ I162 <= 1] f6(I168, I169, I170, I171, I172, I173, I174) -> f5(I168, I169, I170, I171, I172, I173, I174) [1 + I169 <= 1] f6(I175, I176, I177, I178, I179, I180, I181) -> f5(I175, I176, I177, I178, I179, I180, I181) [2 <= I176] f5(I182, I183, I184, I185, I186, I187, I188) -> f4(I182, I183, I184, I185, I186, I187, I188) [1 + I185 <= 0] f5(I189, I190, I191, I192, I193, I194, I195) -> f4(I189, I190, I191, I192, I193, I194, I195) [1 <= I192] f5(I196, I197, I198, I199, I200, I201, I202) -> f1(I196, I197, I198, I199, I200, I201, I202) [0 <= I199 /\ I199 <= 0] f4(I203, I204, I205, I206, I207, I208, I209) -> f1(I203, -1 + I204, I205, I206, I207, I208, I209) f1(I210, I211, I212, I213, I214, I215, I216) -> f3(I210, I211, I212, I213, I214, I215, I216) [1 + I215 <= I214] f1(I217, I218, I219, I220, I221, I222, I223) -> f2(I217, I218, I219, I220, I221, I222, I223) [I221 <= I222] The dependency graph for this problem is: 0 -> 1 1 -> 16 2 -> 5, 6, 7 3 -> 8 4 -> 8 5 -> 8 6 -> 8 7 -> 8 8 -> 9, 10 9 -> 10 -> 16 11 -> 13, 14, 15 12 -> 13 -> 17, 18, 19 14 -> 20 15 -> 20 16 -> 23, 24, 25 17 -> 20 18 -> 20 19 -> 20 20 -> 21, 22 21 -> 22 -> 16 23 -> 24 -> 26, 27, 28 25 -> 26, 27, 28 26 -> 29 27 -> 29 28 -> 30, 31 29 -> 30, 31 30 -> 2, 3, 4 31 -> 11, 12 Where: 0) f18#(x1, x2, x3, x4, x5, x6, x7) -> f17#(x1, x2, x3, x4, x5, x6, x7) 1) f17#(I0, I1, I2, I3, I4, I5, I6) -> f10#(I0, 4, 0, 0, I4, I5, I6) 2) f3#(I7, I8, I9, I10, I11, I12, I13) -> f16#(I7, I8, I9, I10, I11, I12, I13) [1 <= I9 /\ I9 <= 1] 3) f3#(I14, I15, I16, I17, I18, I19, I20) -> f15#(I14, I15, I16, I17, I18, I19, I20) [1 + I16 <= 1] 4) f3#(I21, I22, I23, I24, I25, I26, I27) -> f15#(I21, I22, I23, I24, I25, I26, I27) [2 <= I23] 5) f16#(I28, I29, I30, I31, I32, I33, I34) -> f15#(I28, -1 + I29, I30, 1, I32, I33, I34) [0 <= I31 /\ I31 <= 0] 6) f16#(I35, I36, I37, I38, I39, I40, I41) -> f15#(I35, I36, I37, I38, I39, I40, I41) [1 + I38 <= 0] 7) f16#(I42, I43, I44, I45, I46, I47, I48) -> f15#(I42, I43, I44, I45, I46, I47, I48) [1 <= I45] 8) f15#(I49, I50, I51, I52, I53, I54, I55) -> f14#(I49, I50, 2, I52, I53, I54, I50 + I55) 9) f14#(I56, I57, I58, I59, I60, I61, I62) -> f7#(I56, I57, I58, I59, I60, I61, I62) [1 + I56 <= I62] 10) f14#(I63, I64, I65, I66, I67, I68, I69) -> f10#(I63, I64, I65, I66, I67, I68, I69) [I69 <= I63] 11) f2#(I70, I71, I72, I73, I74, I75, I76) -> f13#(I70, I71, I72, I73, I74, I75, I76) [1 + I74 <= I75] 12) f2#(I77, I78, I79, I80, I81, I82, I83) -> f7#(I77, I78, I79, I80, I81, I82, I83) [I82 <= I81] 13) f13#(I84, I85, I86, I87, I88, I89, I90) -> f12#(I84, I85, I86, I87, I88, I89, I90) [2 <= I86 /\ I86 <= 2] 14) f13#(I91, I92, I93, I94, I95, I96, I97) -> f11#(I91, I92, I93, I94, I95, I96, I97) [1 + I93 <= 2] 15) f13#(I98, I99, I100, I101, I102, I103, I104) -> f11#(I98, I99, I100, I101, I102, I103, I104) [3 <= I100] 16) f10#(I105, I106, I107, I108, I109, I110, I111) -> f6#(I105, I106, I107, I108, rnd5, I110, I111) [rnd5 = rnd5] 17) f12#(I112, I113, I114, I115, I116, I117, I118) -> f11#(I112, -1 + I113, I114, 1, I116, I117, I118) [0 <= I115 /\ I115 <= 0] 18) f12#(I119, I120, I121, I122, I123, I124, I125) -> f11#(I119, I120, I121, I122, I123, I124, I125) [1 + I122 <= 0] 19) f12#(I126, I127, I128, I129, I130, I131, I132) -> f11#(I126, I127, I128, I129, I130, I131, I132) [1 <= I129] 20) f11#(I133, I134, I135, I136, I137, I138, I139) -> f9#(I133, I134, 1, I136, I137, I138, -1 * I134 + I139) 21) f9#(I140, I141, I142, I143, I144, I145, I146) -> f7#(I140, I141, I142, I143, I144, I145, I146) [1 + I146 <= 0] 22) f9#(I147, I148, I149, I150, I151, I152, I153) -> f10#(I147, I148, I149, I150, I151, I152, I153) [0 <= I153] 23) f6#(I161, I162, I163, I164, I165, I166, I167) -> f7#(I161, I162, I163, I164, I165, I166, I167) [1 <= I162 /\ I162 <= 1] 24) f6#(I168, I169, I170, I171, I172, I173, I174) -> f5#(I168, I169, I170, I171, I172, I173, I174) [1 + I169 <= 1] 25) f6#(I175, I176, I177, I178, I179, I180, I181) -> f5#(I175, I176, I177, I178, I179, I180, I181) [2 <= I176] 26) f5#(I182, I183, I184, I185, I186, I187, I188) -> f4#(I182, I183, I184, I185, I186, I187, I188) [1 + I185 <= 0] 27) f5#(I189, I190, I191, I192, I193, I194, I195) -> f4#(I189, I190, I191, I192, I193, I194, I195) [1 <= I192] 28) f5#(I196, I197, I198, I199, I200, I201, I202) -> f1#(I196, I197, I198, I199, I200, I201, I202) [0 <= I199 /\ I199 <= 0] 29) f4#(I203, I204, I205, I206, I207, I208, I209) -> f1#(I203, -1 + I204, I205, I206, I207, I208, I209) 30) f1#(I210, I211, I212, I213, I214, I215, I216) -> f3#(I210, I211, I212, I213, I214, I215, I216) [1 + I215 <= I214] 31) f1#(I217, I218, I219, I220, I221, I222, I223) -> f2#(I217, I218, I219, I220, I221, I222, I223) [I221 <= I222] We have the following SCCs. { 2, 3, 4, 5, 6, 7, 8, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 22, 24, 25, 26, 27, 28, 29, 30, 31 } DP problem for innermost termination. P = f3#(I7, I8, I9, I10, I11, I12, I13) -> f16#(I7, I8, I9, I10, I11, I12, I13) [1 <= I9 /\ I9 <= 1] f3#(I14, I15, I16, I17, I18, I19, I20) -> f15#(I14, I15, I16, I17, I18, I19, I20) [1 + I16 <= 1] f3#(I21, I22, I23, I24, I25, I26, I27) -> f15#(I21, I22, I23, I24, I25, I26, I27) [2 <= I23] f16#(I28, I29, I30, I31, I32, I33, I34) -> f15#(I28, -1 + I29, I30, 1, I32, I33, I34) [0 <= I31 /\ I31 <= 0] f16#(I35, I36, I37, I38, I39, I40, I41) -> f15#(I35, I36, I37, I38, I39, I40, I41) [1 + I38 <= 0] f16#(I42, I43, I44, I45, I46, I47, I48) -> f15#(I42, I43, I44, I45, I46, I47, I48) [1 <= I45] f15#(I49, I50, I51, I52, I53, I54, I55) -> f14#(I49, I50, 2, I52, I53, I54, I50 + I55) f14#(I63, I64, I65, I66, I67, I68, I69) -> f10#(I63, I64, I65, I66, I67, I68, I69) [I69 <= I63] f2#(I70, I71, I72, I73, I74, I75, I76) -> f13#(I70, I71, I72, I73, I74, I75, I76) [1 + I74 <= I75] f13#(I84, I85, I86, I87, I88, I89, I90) -> f12#(I84, I85, I86, I87, I88, I89, I90) [2 <= I86 /\ I86 <= 2] f13#(I91, I92, I93, I94, I95, I96, I97) -> f11#(I91, I92, I93, I94, I95, I96, I97) [1 + I93 <= 2] f13#(I98, I99, I100, I101, I102, I103, I104) -> f11#(I98, I99, I100, I101, I102, I103, I104) [3 <= I100] f10#(I105, I106, I107, I108, I109, I110, I111) -> f6#(I105, I106, I107, I108, rnd5, I110, I111) [rnd5 = rnd5] f12#(I112, I113, I114, I115, I116, I117, I118) -> f11#(I112, -1 + I113, I114, 1, I116, I117, I118) [0 <= I115 /\ I115 <= 0] f12#(I119, I120, I121, I122, I123, I124, I125) -> f11#(I119, I120, I121, I122, I123, I124, I125) [1 + I122 <= 0] f12#(I126, I127, I128, I129, I130, I131, I132) -> f11#(I126, I127, I128, I129, I130, I131, I132) [1 <= I129] f11#(I133, I134, I135, I136, I137, I138, I139) -> f9#(I133, I134, 1, I136, I137, I138, -1 * I134 + I139) f9#(I147, I148, I149, I150, I151, I152, I153) -> f10#(I147, I148, I149, I150, I151, I152, I153) [0 <= I153] f6#(I168, I169, I170, I171, I172, I173, I174) -> f5#(I168, I169, I170, I171, I172, I173, I174) [1 + I169 <= 1] f6#(I175, I176, I177, I178, I179, I180, I181) -> f5#(I175, I176, I177, I178, I179, I180, I181) [2 <= I176] f5#(I182, I183, I184, I185, I186, I187, I188) -> f4#(I182, I183, I184, I185, I186, I187, I188) [1 + I185 <= 0] f5#(I189, I190, I191, I192, I193, I194, I195) -> f4#(I189, I190, I191, I192, I193, I194, I195) [1 <= I192] f5#(I196, I197, I198, I199, I200, I201, I202) -> f1#(I196, I197, I198, I199, I200, I201, I202) [0 <= I199 /\ I199 <= 0] f4#(I203, I204, I205, I206, I207, I208, I209) -> f1#(I203, -1 + I204, I205, I206, I207, I208, I209) f1#(I210, I211, I212, I213, I214, I215, I216) -> f3#(I210, I211, I212, I213, I214, I215, I216) [1 + I215 <= I214] f1#(I217, I218, I219, I220, I221, I222, I223) -> f2#(I217, I218, I219, I220, I221, I222, I223) [I221 <= I222] R = f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) f17(I0, I1, I2, I3, I4, I5, I6) -> f10(I0, 4, 0, 0, I4, I5, I6) f3(I7, I8, I9, I10, I11, I12, I13) -> f16(I7, I8, I9, I10, I11, I12, I13) [1 <= I9 /\ I9 <= 1] f3(I14, I15, I16, I17, I18, I19, I20) -> f15(I14, I15, I16, I17, I18, I19, I20) [1 + I16 <= 1] f3(I21, I22, I23, I24, I25, I26, I27) -> f15(I21, I22, I23, I24, I25, I26, I27) [2 <= I23] f16(I28, I29, I30, I31, I32, I33, I34) -> f15(I28, -1 + I29, I30, 1, I32, I33, I34) [0 <= I31 /\ I31 <= 0] f16(I35, I36, I37, I38, I39, I40, I41) -> f15(I35, I36, I37, I38, I39, I40, I41) [1 + I38 <= 0] f16(I42, I43, I44, I45, I46, I47, I48) -> f15(I42, I43, I44, I45, I46, I47, I48) [1 <= I45] f15(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, 2, I52, I53, I54, I50 + I55) f14(I56, I57, I58, I59, I60, I61, I62) -> f7(I56, I57, I58, I59, I60, I61, I62) [1 + I56 <= I62] f14(I63, I64, I65, I66, I67, I68, I69) -> f10(I63, I64, I65, I66, I67, I68, I69) [I69 <= I63] f2(I70, I71, I72, I73, I74, I75, I76) -> f13(I70, I71, I72, I73, I74, I75, I76) [1 + I74 <= I75] f2(I77, I78, I79, I80, I81, I82, I83) -> f7(I77, I78, I79, I80, I81, I82, I83) [I82 <= I81] f13(I84, I85, I86, I87, I88, I89, I90) -> f12(I84, I85, I86, I87, I88, I89, I90) [2 <= I86 /\ I86 <= 2] f13(I91, I92, I93, I94, I95, I96, I97) -> f11(I91, I92, I93, I94, I95, I96, I97) [1 + I93 <= 2] f13(I98, I99, I100, I101, I102, I103, I104) -> f11(I98, I99, I100, I101, I102, I103, I104) [3 <= I100] f10(I105, I106, I107, I108, I109, I110, I111) -> f6(I105, I106, I107, I108, rnd5, I110, I111) [rnd5 = rnd5] f12(I112, I113, I114, I115, I116, I117, I118) -> f11(I112, -1 + I113, I114, 1, I116, I117, I118) [0 <= I115 /\ I115 <= 0] f12(I119, I120, I121, I122, I123, I124, I125) -> f11(I119, I120, I121, I122, I123, I124, I125) [1 + I122 <= 0] f12(I126, I127, I128, I129, I130, I131, I132) -> f11(I126, I127, I128, I129, I130, I131, I132) [1 <= I129] f11(I133, I134, I135, I136, I137, I138, I139) -> f9(I133, I134, 1, I136, I137, I138, -1 * I134 + I139) f9(I140, I141, I142, I143, I144, I145, I146) -> f7(I140, I141, I142, I143, I144, I145, I146) [1 + I146 <= 0] f9(I147, I148, I149, I150, I151, I152, I153) -> f10(I147, I148, I149, I150, I151, I152, I153) [0 <= I153] f7(I154, I155, I156, I157, I158, I159, I160) -> f8(I154, I155, I156, I157, I158, I159, I160) f6(I161, I162, I163, I164, I165, I166, I167) -> f7(I161, I162, I163, I164, I165, I166, I167) [1 <= I162 /\ I162 <= 1] f6(I168, I169, I170, I171, I172, I173, I174) -> f5(I168, I169, I170, I171, I172, I173, I174) [1 + I169 <= 1] f6(I175, I176, I177, I178, I179, I180, I181) -> f5(I175, I176, I177, I178, I179, I180, I181) [2 <= I176] f5(I182, I183, I184, I185, I186, I187, I188) -> f4(I182, I183, I184, I185, I186, I187, I188) [1 + I185 <= 0] f5(I189, I190, I191, I192, I193, I194, I195) -> f4(I189, I190, I191, I192, I193, I194, I195) [1 <= I192] f5(I196, I197, I198, I199, I200, I201, I202) -> f1(I196, I197, I198, I199, I200, I201, I202) [0 <= I199 /\ I199 <= 0] f4(I203, I204, I205, I206, I207, I208, I209) -> f1(I203, -1 + I204, I205, I206, I207, I208, I209) f1(I210, I211, I212, I213, I214, I215, I216) -> f3(I210, I211, I212, I213, I214, I215, I216) [1 + I215 <= I214] f1(I217, I218, I219, I220, I221, I222, I223) -> f2(I217, I218, I219, I220, I221, I222, I223) [I221 <= I222] We use the extended value criterion with the projection function NU: NU[f1#(x0,x1,x2,x3,x4,x5,x6)] = -x3 NU[f4#(x0,x1,x2,x3,x4,x5,x6)] = -x3 NU[f5#(x0,x1,x2,x3,x4,x5,x6)] = -x3 NU[f9#(x0,x1,x2,x3,x4,x5,x6)] = -x3 NU[f6#(x0,x1,x2,x3,x4,x5,x6)] = -x3 NU[f11#(x0,x1,x2,x3,x4,x5,x6)] = -x3 NU[f12#(x0,x1,x2,x3,x4,x5,x6)] = -x3 NU[f13#(x0,x1,x2,x3,x4,x5,x6)] = -x3 NU[f2#(x0,x1,x2,x3,x4,x5,x6)] = -x3 NU[f10#(x0,x1,x2,x3,x4,x5,x6)] = -x3 NU[f14#(x0,x1,x2,x3,x4,x5,x6)] = -x3 NU[f15#(x0,x1,x2,x3,x4,x5,x6)] = -x3 NU[f16#(x0,x1,x2,x3,x4,x5,x6)] = -x3 NU[f3#(x0,x1,x2,x3,x4,x5,x6)] = -x3 This gives the following inequalities: 1 <= I9 /\ I9 <= 1 ==> -I10 >= -I10 1 + I16 <= 1 ==> -I17 >= -I17 2 <= I23 ==> -I24 >= -I24 0 <= I31 /\ I31 <= 0 ==> -I31 >= -1 1 + I38 <= 0 ==> -I38 >= -I38 1 <= I45 ==> -I45 >= -I45 ==> -I52 >= -I52 I69 <= I63 ==> -I66 >= -I66 1 + I74 <= I75 ==> -I73 >= -I73 2 <= I86 /\ I86 <= 2 ==> -I87 >= -I87 1 + I93 <= 2 ==> -I94 >= -I94 3 <= I100 ==> -I101 >= -I101 rnd5 = rnd5 ==> -I108 >= -I108 0 <= I115 /\ I115 <= 0 ==> -I115 > -1 with -I115 >= 0 1 + I122 <= 0 ==> -I122 >= -I122 1 <= I129 ==> -I129 >= -I129 ==> -I136 >= -I136 0 <= I153 ==> -I150 >= -I150 1 + I169 <= 1 ==> -I171 >= -I171 2 <= I176 ==> -I178 >= -I178 1 + I185 <= 0 ==> -I185 >= -I185 1 <= I192 ==> -I192 >= -I192 0 <= I199 /\ I199 <= 0 ==> -I199 >= -I199 ==> -I206 >= -I206 1 + I215 <= I214 ==> -I213 >= -I213 I221 <= I222 ==> -I220 >= -I220 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f3#(I7, I8, I9, I10, I11, I12, I13) -> f16#(I7, I8, I9, I10, I11, I12, I13) [1 <= I9 /\ I9 <= 1] f3#(I14, I15, I16, I17, I18, I19, I20) -> f15#(I14, I15, I16, I17, I18, I19, I20) [1 + I16 <= 1] f3#(I21, I22, I23, I24, I25, I26, I27) -> f15#(I21, I22, I23, I24, I25, I26, I27) [2 <= I23] f16#(I28, I29, I30, I31, I32, I33, I34) -> f15#(I28, -1 + I29, I30, 1, I32, I33, I34) [0 <= I31 /\ I31 <= 0] f16#(I35, I36, I37, I38, I39, I40, I41) -> f15#(I35, I36, I37, I38, I39, I40, I41) [1 + I38 <= 0] f16#(I42, I43, I44, I45, I46, I47, I48) -> f15#(I42, I43, I44, I45, I46, I47, I48) [1 <= I45] f15#(I49, I50, I51, I52, I53, I54, I55) -> f14#(I49, I50, 2, I52, I53, I54, I50 + I55) f14#(I63, I64, I65, I66, I67, I68, I69) -> f10#(I63, I64, I65, I66, I67, I68, I69) [I69 <= I63] f2#(I70, I71, I72, I73, I74, I75, I76) -> f13#(I70, I71, I72, I73, I74, I75, I76) [1 + I74 <= I75] f13#(I84, I85, I86, I87, I88, I89, I90) -> f12#(I84, I85, I86, I87, I88, I89, I90) [2 <= I86 /\ I86 <= 2] f13#(I91, I92, I93, I94, I95, I96, I97) -> f11#(I91, I92, I93, I94, I95, I96, I97) [1 + I93 <= 2] f13#(I98, I99, I100, I101, I102, I103, I104) -> f11#(I98, I99, I100, I101, I102, I103, I104) [3 <= I100] f10#(I105, I106, I107, I108, I109, I110, I111) -> f6#(I105, I106, I107, I108, rnd5, I110, I111) [rnd5 = rnd5] f12#(I119, I120, I121, I122, I123, I124, I125) -> f11#(I119, I120, I121, I122, I123, I124, I125) [1 + I122 <= 0] f12#(I126, I127, I128, I129, I130, I131, I132) -> f11#(I126, I127, I128, I129, I130, I131, I132) [1 <= I129] f11#(I133, I134, I135, I136, I137, I138, I139) -> f9#(I133, I134, 1, I136, I137, I138, -1 * I134 + I139) f9#(I147, I148, I149, I150, I151, I152, I153) -> f10#(I147, I148, I149, I150, I151, I152, I153) [0 <= I153] f6#(I168, I169, I170, I171, I172, I173, I174) -> f5#(I168, I169, I170, I171, I172, I173, I174) [1 + I169 <= 1] f6#(I175, I176, I177, I178, I179, I180, I181) -> f5#(I175, I176, I177, I178, I179, I180, I181) [2 <= I176] f5#(I182, I183, I184, I185, I186, I187, I188) -> f4#(I182, I183, I184, I185, I186, I187, I188) [1 + I185 <= 0] f5#(I189, I190, I191, I192, I193, I194, I195) -> f4#(I189, I190, I191, I192, I193, I194, I195) [1 <= I192] f5#(I196, I197, I198, I199, I200, I201, I202) -> f1#(I196, I197, I198, I199, I200, I201, I202) [0 <= I199 /\ I199 <= 0] f4#(I203, I204, I205, I206, I207, I208, I209) -> f1#(I203, -1 + I204, I205, I206, I207, I208, I209) f1#(I210, I211, I212, I213, I214, I215, I216) -> f3#(I210, I211, I212, I213, I214, I215, I216) [1 + I215 <= I214] f1#(I217, I218, I219, I220, I221, I222, I223) -> f2#(I217, I218, I219, I220, I221, I222, I223) [I221 <= I222] R = f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) f17(I0, I1, I2, I3, I4, I5, I6) -> f10(I0, 4, 0, 0, I4, I5, I6) f3(I7, I8, I9, I10, I11, I12, I13) -> f16(I7, I8, I9, I10, I11, I12, I13) [1 <= I9 /\ I9 <= 1] f3(I14, I15, I16, I17, I18, I19, I20) -> f15(I14, I15, I16, I17, I18, I19, I20) [1 + I16 <= 1] f3(I21, I22, I23, I24, I25, I26, I27) -> f15(I21, I22, I23, I24, I25, I26, I27) [2 <= I23] f16(I28, I29, I30, I31, I32, I33, I34) -> f15(I28, -1 + I29, I30, 1, I32, I33, I34) [0 <= I31 /\ I31 <= 0] f16(I35, I36, I37, I38, I39, I40, I41) -> f15(I35, I36, I37, I38, I39, I40, I41) [1 + I38 <= 0] f16(I42, I43, I44, I45, I46, I47, I48) -> f15(I42, I43, I44, I45, I46, I47, I48) [1 <= I45] f15(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, 2, I52, I53, I54, I50 + I55) f14(I56, I57, I58, I59, I60, I61, I62) -> f7(I56, I57, I58, I59, I60, I61, I62) [1 + I56 <= I62] f14(I63, I64, I65, I66, I67, I68, I69) -> f10(I63, I64, I65, I66, I67, I68, I69) [I69 <= I63] f2(I70, I71, I72, I73, I74, I75, I76) -> f13(I70, I71, I72, I73, I74, I75, I76) [1 + I74 <= I75] f2(I77, I78, I79, I80, I81, I82, I83) -> f7(I77, I78, I79, I80, I81, I82, I83) [I82 <= I81] f13(I84, I85, I86, I87, I88, I89, I90) -> f12(I84, I85, I86, I87, I88, I89, I90) [2 <= I86 /\ I86 <= 2] f13(I91, I92, I93, I94, I95, I96, I97) -> f11(I91, I92, I93, I94, I95, I96, I97) [1 + I93 <= 2] f13(I98, I99, I100, I101, I102, I103, I104) -> f11(I98, I99, I100, I101, I102, I103, I104) [3 <= I100] f10(I105, I106, I107, I108, I109, I110, I111) -> f6(I105, I106, I107, I108, rnd5, I110, I111) [rnd5 = rnd5] f12(I112, I113, I114, I115, I116, I117, I118) -> f11(I112, -1 + I113, I114, 1, I116, I117, I118) [0 <= I115 /\ I115 <= 0] f12(I119, I120, I121, I122, I123, I124, I125) -> f11(I119, I120, I121, I122, I123, I124, I125) [1 + I122 <= 0] f12(I126, I127, I128, I129, I130, I131, I132) -> f11(I126, I127, I128, I129, I130, I131, I132) [1 <= I129] f11(I133, I134, I135, I136, I137, I138, I139) -> f9(I133, I134, 1, I136, I137, I138, -1 * I134 + I139) f9(I140, I141, I142, I143, I144, I145, I146) -> f7(I140, I141, I142, I143, I144, I145, I146) [1 + I146 <= 0] f9(I147, I148, I149, I150, I151, I152, I153) -> f10(I147, I148, I149, I150, I151, I152, I153) [0 <= I153] f7(I154, I155, I156, I157, I158, I159, I160) -> f8(I154, I155, I156, I157, I158, I159, I160) f6(I161, I162, I163, I164, I165, I166, I167) -> f7(I161, I162, I163, I164, I165, I166, I167) [1 <= I162 /\ I162 <= 1] f6(I168, I169, I170, I171, I172, I173, I174) -> f5(I168, I169, I170, I171, I172, I173, I174) [1 + I169 <= 1] f6(I175, I176, I177, I178, I179, I180, I181) -> f5(I175, I176, I177, I178, I179, I180, I181) [2 <= I176] f5(I182, I183, I184, I185, I186, I187, I188) -> f4(I182, I183, I184, I185, I186, I187, I188) [1 + I185 <= 0] f5(I189, I190, I191, I192, I193, I194, I195) -> f4(I189, I190, I191, I192, I193, I194, I195) [1 <= I192] f5(I196, I197, I198, I199, I200, I201, I202) -> f1(I196, I197, I198, I199, I200, I201, I202) [0 <= I199 /\ I199 <= 0] f4(I203, I204, I205, I206, I207, I208, I209) -> f1(I203, -1 + I204, I205, I206, I207, I208, I209) f1(I210, I211, I212, I213, I214, I215, I216) -> f3(I210, I211, I212, I213, I214, I215, I216) [1 + I215 <= I214] f1(I217, I218, I219, I220, I221, I222, I223) -> f2(I217, I218, I219, I220, I221, I222, I223) [I221 <= I222] We use the extended value criterion with the projection function NU: NU[f1#(x0,x1,x2,x3,x4,x5,x6)] = -x3 NU[f4#(x0,x1,x2,x3,x4,x5,x6)] = -x3 NU[f5#(x0,x1,x2,x3,x4,x5,x6)] = -x3 NU[f9#(x0,x1,x2,x3,x4,x5,x6)] = -x3 NU[f6#(x0,x1,x2,x3,x4,x5,x6)] = -x3 NU[f11#(x0,x1,x2,x3,x4,x5,x6)] = -x3 NU[f12#(x0,x1,x2,x3,x4,x5,x6)] = -x3 NU[f13#(x0,x1,x2,x3,x4,x5,x6)] = -x3 NU[f2#(x0,x1,x2,x3,x4,x5,x6)] = -x3 NU[f10#(x0,x1,x2,x3,x4,x5,x6)] = -x3 NU[f14#(x0,x1,x2,x3,x4,x5,x6)] = -x3 NU[f15#(x0,x1,x2,x3,x4,x5,x6)] = -x3 NU[f16#(x0,x1,x2,x3,x4,x5,x6)] = -x3 NU[f3#(x0,x1,x2,x3,x4,x5,x6)] = -x3 This gives the following inequalities: 1 <= I9 /\ I9 <= 1 ==> -I10 >= -I10 1 + I16 <= 1 ==> -I17 >= -I17 2 <= I23 ==> -I24 >= -I24 0 <= I31 /\ I31 <= 0 ==> -I31 > -1 with -I31 >= 0 1 + I38 <= 0 ==> -I38 >= -I38 1 <= I45 ==> -I45 >= -I45 ==> -I52 >= -I52 I69 <= I63 ==> -I66 >= -I66 1 + I74 <= I75 ==> -I73 >= -I73 2 <= I86 /\ I86 <= 2 ==> -I87 >= -I87 1 + I93 <= 2 ==> -I94 >= -I94 3 <= I100 ==> -I101 >= -I101 rnd5 = rnd5 ==> -I108 >= -I108 1 + I122 <= 0 ==> -I122 >= -I122 1 <= I129 ==> -I129 >= -I129 ==> -I136 >= -I136 0 <= I153 ==> -I150 >= -I150 1 + I169 <= 1 ==> -I171 >= -I171 2 <= I176 ==> -I178 >= -I178 1 + I185 <= 0 ==> -I185 >= -I185 1 <= I192 ==> -I192 >= -I192 0 <= I199 /\ I199 <= 0 ==> -I199 >= -I199 ==> -I206 >= -I206 1 + I215 <= I214 ==> -I213 >= -I213 I221 <= I222 ==> -I220 >= -I220 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f3#(I7, I8, I9, I10, I11, I12, I13) -> f16#(I7, I8, I9, I10, I11, I12, I13) [1 <= I9 /\ I9 <= 1] f3#(I14, I15, I16, I17, I18, I19, I20) -> f15#(I14, I15, I16, I17, I18, I19, I20) [1 + I16 <= 1] f3#(I21, I22, I23, I24, I25, I26, I27) -> f15#(I21, I22, I23, I24, I25, I26, I27) [2 <= I23] f16#(I35, I36, I37, I38, I39, I40, I41) -> f15#(I35, I36, I37, I38, I39, I40, I41) [1 + I38 <= 0] f16#(I42, I43, I44, I45, I46, I47, I48) -> f15#(I42, I43, I44, I45, I46, I47, I48) [1 <= I45] f15#(I49, I50, I51, I52, I53, I54, I55) -> f14#(I49, I50, 2, I52, I53, I54, I50 + I55) f14#(I63, I64, I65, I66, I67, I68, I69) -> f10#(I63, I64, I65, I66, I67, I68, I69) [I69 <= I63] f2#(I70, I71, I72, I73, I74, I75, I76) -> f13#(I70, I71, I72, I73, I74, I75, I76) [1 + I74 <= I75] f13#(I84, I85, I86, I87, I88, I89, I90) -> f12#(I84, I85, I86, I87, I88, I89, I90) [2 <= I86 /\ I86 <= 2] f13#(I91, I92, I93, I94, I95, I96, I97) -> f11#(I91, I92, I93, I94, I95, I96, I97) [1 + I93 <= 2] f13#(I98, I99, I100, I101, I102, I103, I104) -> f11#(I98, I99, I100, I101, I102, I103, I104) [3 <= I100] f10#(I105, I106, I107, I108, I109, I110, I111) -> f6#(I105, I106, I107, I108, rnd5, I110, I111) [rnd5 = rnd5] f12#(I119, I120, I121, I122, I123, I124, I125) -> f11#(I119, I120, I121, I122, I123, I124, I125) [1 + I122 <= 0] f12#(I126, I127, I128, I129, I130, I131, I132) -> f11#(I126, I127, I128, I129, I130, I131, I132) [1 <= I129] f11#(I133, I134, I135, I136, I137, I138, I139) -> f9#(I133, I134, 1, I136, I137, I138, -1 * I134 + I139) f9#(I147, I148, I149, I150, I151, I152, I153) -> f10#(I147, I148, I149, I150, I151, I152, I153) [0 <= I153] f6#(I168, I169, I170, I171, I172, I173, I174) -> f5#(I168, I169, I170, I171, I172, I173, I174) [1 + I169 <= 1] f6#(I175, I176, I177, I178, I179, I180, I181) -> f5#(I175, I176, I177, I178, I179, I180, I181) [2 <= I176] f5#(I182, I183, I184, I185, I186, I187, I188) -> f4#(I182, I183, I184, I185, I186, I187, I188) [1 + I185 <= 0] f5#(I189, I190, I191, I192, I193, I194, I195) -> f4#(I189, I190, I191, I192, I193, I194, I195) [1 <= I192] f5#(I196, I197, I198, I199, I200, I201, I202) -> f1#(I196, I197, I198, I199, I200, I201, I202) [0 <= I199 /\ I199 <= 0] f4#(I203, I204, I205, I206, I207, I208, I209) -> f1#(I203, -1 + I204, I205, I206, I207, I208, I209) f1#(I210, I211, I212, I213, I214, I215, I216) -> f3#(I210, I211, I212, I213, I214, I215, I216) [1 + I215 <= I214] f1#(I217, I218, I219, I220, I221, I222, I223) -> f2#(I217, I218, I219, I220, I221, I222, I223) [I221 <= I222] R = f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) f17(I0, I1, I2, I3, I4, I5, I6) -> f10(I0, 4, 0, 0, I4, I5, I6) f3(I7, I8, I9, I10, I11, I12, I13) -> f16(I7, I8, I9, I10, I11, I12, I13) [1 <= I9 /\ I9 <= 1] f3(I14, I15, I16, I17, I18, I19, I20) -> f15(I14, I15, I16, I17, I18, I19, I20) [1 + I16 <= 1] f3(I21, I22, I23, I24, I25, I26, I27) -> f15(I21, I22, I23, I24, I25, I26, I27) [2 <= I23] f16(I28, I29, I30, I31, I32, I33, I34) -> f15(I28, -1 + I29, I30, 1, I32, I33, I34) [0 <= I31 /\ I31 <= 0] f16(I35, I36, I37, I38, I39, I40, I41) -> f15(I35, I36, I37, I38, I39, I40, I41) [1 + I38 <= 0] f16(I42, I43, I44, I45, I46, I47, I48) -> f15(I42, I43, I44, I45, I46, I47, I48) [1 <= I45] f15(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, 2, I52, I53, I54, I50 + I55) f14(I56, I57, I58, I59, I60, I61, I62) -> f7(I56, I57, I58, I59, I60, I61, I62) [1 + I56 <= I62] f14(I63, I64, I65, I66, I67, I68, I69) -> f10(I63, I64, I65, I66, I67, I68, I69) [I69 <= I63] f2(I70, I71, I72, I73, I74, I75, I76) -> f13(I70, I71, I72, I73, I74, I75, I76) [1 + I74 <= I75] f2(I77, I78, I79, I80, I81, I82, I83) -> f7(I77, I78, I79, I80, I81, I82, I83) [I82 <= I81] f13(I84, I85, I86, I87, I88, I89, I90) -> f12(I84, I85, I86, I87, I88, I89, I90) [2 <= I86 /\ I86 <= 2] f13(I91, I92, I93, I94, I95, I96, I97) -> f11(I91, I92, I93, I94, I95, I96, I97) [1 + I93 <= 2] f13(I98, I99, I100, I101, I102, I103, I104) -> f11(I98, I99, I100, I101, I102, I103, I104) [3 <= I100] f10(I105, I106, I107, I108, I109, I110, I111) -> f6(I105, I106, I107, I108, rnd5, I110, I111) [rnd5 = rnd5] f12(I112, I113, I114, I115, I116, I117, I118) -> f11(I112, -1 + I113, I114, 1, I116, I117, I118) [0 <= I115 /\ I115 <= 0] f12(I119, I120, I121, I122, I123, I124, I125) -> f11(I119, I120, I121, I122, I123, I124, I125) [1 + I122 <= 0] f12(I126, I127, I128, I129, I130, I131, I132) -> f11(I126, I127, I128, I129, I130, I131, I132) [1 <= I129] f11(I133, I134, I135, I136, I137, I138, I139) -> f9(I133, I134, 1, I136, I137, I138, -1 * I134 + I139) f9(I140, I141, I142, I143, I144, I145, I146) -> f7(I140, I141, I142, I143, I144, I145, I146) [1 + I146 <= 0] f9(I147, I148, I149, I150, I151, I152, I153) -> f10(I147, I148, I149, I150, I151, I152, I153) [0 <= I153] f7(I154, I155, I156, I157, I158, I159, I160) -> f8(I154, I155, I156, I157, I158, I159, I160) f6(I161, I162, I163, I164, I165, I166, I167) -> f7(I161, I162, I163, I164, I165, I166, I167) [1 <= I162 /\ I162 <= 1] f6(I168, I169, I170, I171, I172, I173, I174) -> f5(I168, I169, I170, I171, I172, I173, I174) [1 + I169 <= 1] f6(I175, I176, I177, I178, I179, I180, I181) -> f5(I175, I176, I177, I178, I179, I180, I181) [2 <= I176] f5(I182, I183, I184, I185, I186, I187, I188) -> f4(I182, I183, I184, I185, I186, I187, I188) [1 + I185 <= 0] f5(I189, I190, I191, I192, I193, I194, I195) -> f4(I189, I190, I191, I192, I193, I194, I195) [1 <= I192] f5(I196, I197, I198, I199, I200, I201, I202) -> f1(I196, I197, I198, I199, I200, I201, I202) [0 <= I199 /\ I199 <= 0] f4(I203, I204, I205, I206, I207, I208, I209) -> f1(I203, -1 + I204, I205, I206, I207, I208, I209) f1(I210, I211, I212, I213, I214, I215, I216) -> f3(I210, I211, I212, I213, I214, I215, I216) [1 + I215 <= I214] f1(I217, I218, I219, I220, I221, I222, I223) -> f2(I217, I218, I219, I220, I221, I222, I223) [I221 <= I222]