/export/starexec/sandbox2/solver/bin/starexec_run_Transition /export/starexec/sandbox2/benchmark/theBenchmark.smt2 /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- MAYBE DP problem for innermost termination. P = f13#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> f9#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) f12#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13) -> f3#(rnd1, rnd2, I2, 0, -2, I5, I6, I7, rnd9, rnd10, rnd11, I11, I12, I13) [y3 = -1 /\ 0 <= 4 - y3 /\ rnd10 = rnd10 /\ y2 = -1 /\ rnd9 = rnd9 /\ rnd2 = 0 /\ y1 = rnd2 /\ rnd11 = y1 /\ rnd1 = rnd1] f11#(I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27) -> f2#(I28, I29, I16, 1, I18, I19, I20, I21, I22, I30, I31, I25, I26, I27) [I32 = I19 /\ 5 - I32 <= 0 /\ I30 = I30 /\ I29 = 1 /\ I33 = I29 /\ I31 = I33 /\ I28 = I28] f11#(I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) -> f3#(I48, I49, I36, 0, I38, I39, -1 + I39, I41, I50, I51, I52, I45, I46, I47) [I53 = I39 /\ 0 <= 4 - I53 /\ I51 = I51 /\ I54 = I39 /\ I50 = I50 /\ I49 = 0 /\ I55 = I49 /\ I52 = I55 /\ I48 = I48] f10#(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f3#(I70, I71, I58, 0, I60, -2, I62, I63, I72, I73, I74, I67, I68, I69) [I75 = -1 /\ 0 <= 4 - I75 /\ I73 = I73 /\ I76 = -1 /\ I72 = I72 /\ I71 = 0 /\ I77 = I71 /\ I74 = I77 /\ I70 = I70] f9#(I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f4#(I78, I79, I80, I81, I82, I83, I84, rnd8, I86, I87, I88, I89, I90, I91) [rnd8 = rnd8] f6#(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105) -> f4#(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, 1 + I103, I104, I105) [-1 * I104 + I105 <= 0] f6#(I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f3#(I120, I121, I108, 0, I110, I111, I112, I113, I122, I123, I124, I117, I118, I119) [0 <= -1 - I118 + I119 /\ I125 = 0 /\ 0 <= 4 - I125 /\ I123 = I123 /\ I126 = 0 /\ I122 = I122 /\ I121 = 0 /\ I127 = I121 /\ I124 = I127 /\ I120 = I120] f8#(I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139, I140, I141) -> f7#(I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139, 1 + I140, I141) f2#(I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) -> f8#(I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) [I144 = I144] f7#(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) -> f4#(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, 1 + I167, I168, I169) [-1 * I168 + I169 <= 0] f7#(I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f3#(I184, I185, I172, 0, I174, I175, I176, I177, I186, I187, I188, I181, I182, I183) [0 <= -1 - I182 + I183 /\ I189 = 0 /\ 0 <= 4 - I189 /\ I187 = I187 /\ I190 = 0 /\ I186 = I186 /\ I185 = 0 /\ I191 = I185 /\ I188 = I191 /\ I184 = I184] f3#(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) -> f1#(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) [0 <= -1 - I204 + I205 /\ 0 <= I202 /\ I202 <= 0] f4#(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) -> f6#(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) [0 <= -1 - I217 + I218] f1#(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248) -> f3#(I249, I250, I237, 0, I239, I240, I241, I242, I251, I252, I253, I246, I247, I248) [I254 = I239 /\ 0 <= 4 - I254 /\ I252 = I252 /\ I255 = I239 /\ I251 = I251 /\ I250 = 0 /\ I256 = I250 /\ I253 = I256 /\ I249 = I249] f1#(I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270) -> f2#(I271, I272, I259, 1, I261, I262, I263, I264, I265, I273, I274, I268, I269, I270) [I275 = I261 /\ 5 - I275 <= 0 /\ I273 = I273 /\ I272 = 1 /\ I276 = I272 /\ I274 = I276 /\ I271 = I271] R = f13(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> f9(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) f12(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13) -> f3(rnd1, rnd2, I2, 0, -2, I5, I6, I7, rnd9, rnd10, rnd11, I11, I12, I13) [y3 = -1 /\ 0 <= 4 - y3 /\ rnd10 = rnd10 /\ y2 = -1 /\ rnd9 = rnd9 /\ rnd2 = 0 /\ y1 = rnd2 /\ rnd11 = y1 /\ rnd1 = rnd1] f11(I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27) -> f2(I28, I29, I16, 1, I18, I19, I20, I21, I22, I30, I31, I25, I26, I27) [I32 = I19 /\ 5 - I32 <= 0 /\ I30 = I30 /\ I29 = 1 /\ I33 = I29 /\ I31 = I33 /\ I28 = I28] f11(I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) -> f3(I48, I49, I36, 0, I38, I39, -1 + I39, I41, I50, I51, I52, I45, I46, I47) [I53 = I39 /\ 0 <= 4 - I53 /\ I51 = I51 /\ I54 = I39 /\ I50 = I50 /\ I49 = 0 /\ I55 = I49 /\ I52 = I55 /\ I48 = I48] f10(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f3(I70, I71, I58, 0, I60, -2, I62, I63, I72, I73, I74, I67, I68, I69) [I75 = -1 /\ 0 <= 4 - I75 /\ I73 = I73 /\ I76 = -1 /\ I72 = I72 /\ I71 = 0 /\ I77 = I71 /\ I74 = I77 /\ I70 = I70] f9(I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f4(I78, I79, I80, I81, I82, I83, I84, rnd8, I86, I87, I88, I89, I90, I91) [rnd8 = rnd8] f6(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105) -> f4(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, 1 + I103, I104, I105) [-1 * I104 + I105 <= 0] f6(I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f3(I120, I121, I108, 0, I110, I111, I112, I113, I122, I123, I124, I117, I118, I119) [0 <= -1 - I118 + I119 /\ I125 = 0 /\ 0 <= 4 - I125 /\ I123 = I123 /\ I126 = 0 /\ I122 = I122 /\ I121 = 0 /\ I127 = I121 /\ I124 = I127 /\ I120 = I120] f8(I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139, I140, I141) -> f7(I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139, 1 + I140, I141) f2(I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) -> f8(I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) [I144 = I144] f7(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) -> f4(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, 1 + I167, I168, I169) [-1 * I168 + I169 <= 0] f7(I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f3(I184, I185, I172, 0, I174, I175, I176, I177, I186, I187, I188, I181, I182, I183) [0 <= -1 - I182 + I183 /\ I189 = 0 /\ 0 <= 4 - I189 /\ I187 = I187 /\ I190 = 0 /\ I186 = I186 /\ I185 = 0 /\ I191 = I185 /\ I188 = I191 /\ I184 = I184] f3(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) -> f1(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) [0 <= -1 - I204 + I205 /\ 0 <= I202 /\ I202 <= 0] f4(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) -> f6(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) [0 <= -1 - I217 + I218] f4(I220, I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233) -> f5(I234, I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233) [I234 = I234 /\ -1 * I231 + I232 <= 0] f1(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248) -> f3(I249, I250, I237, 0, I239, I240, I241, I242, I251, I252, I253, I246, I247, I248) [I254 = I239 /\ 0 <= 4 - I254 /\ I252 = I252 /\ I255 = I239 /\ I251 = I251 /\ I250 = 0 /\ I256 = I250 /\ I253 = I256 /\ I249 = I249] f1(I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270) -> f2(I271, I272, I259, 1, I261, I262, I263, I264, I265, I273, I274, I268, I269, I270) [I275 = I261 /\ 5 - I275 <= 0 /\ I273 = I273 /\ I272 = 1 /\ I276 = I272 /\ I274 = I276 /\ I271 = I271] The dependency graph for this problem is: 0 -> 5 1 -> 12 2 -> 9 3 -> 12 4 -> 12 5 -> 13 6 -> 13 7 -> 12 8 -> 10, 11 9 -> 8 10 -> 13 11 -> 12 12 -> 14, 15 13 -> 6, 7 14 -> 12 15 -> 9 Where: 0) f13#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> f9#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) 1) f12#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13) -> f3#(rnd1, rnd2, I2, 0, -2, I5, I6, I7, rnd9, rnd10, rnd11, I11, I12, I13) [y3 = -1 /\ 0 <= 4 - y3 /\ rnd10 = rnd10 /\ y2 = -1 /\ rnd9 = rnd9 /\ rnd2 = 0 /\ y1 = rnd2 /\ rnd11 = y1 /\ rnd1 = rnd1] 2) f11#(I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27) -> f2#(I28, I29, I16, 1, I18, I19, I20, I21, I22, I30, I31, I25, I26, I27) [I32 = I19 /\ 5 - I32 <= 0 /\ I30 = I30 /\ I29 = 1 /\ I33 = I29 /\ I31 = I33 /\ I28 = I28] 3) f11#(I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) -> f3#(I48, I49, I36, 0, I38, I39, -1 + I39, I41, I50, I51, I52, I45, I46, I47) [I53 = I39 /\ 0 <= 4 - I53 /\ I51 = I51 /\ I54 = I39 /\ I50 = I50 /\ I49 = 0 /\ I55 = I49 /\ I52 = I55 /\ I48 = I48] 4) f10#(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f3#(I70, I71, I58, 0, I60, -2, I62, I63, I72, I73, I74, I67, I68, I69) [I75 = -1 /\ 0 <= 4 - I75 /\ I73 = I73 /\ I76 = -1 /\ I72 = I72 /\ I71 = 0 /\ I77 = I71 /\ I74 = I77 /\ I70 = I70] 5) f9#(I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f4#(I78, I79, I80, I81, I82, I83, I84, rnd8, I86, I87, I88, I89, I90, I91) [rnd8 = rnd8] 6) f6#(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105) -> f4#(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, 1 + I103, I104, I105) [-1 * I104 + I105 <= 0] 7) f6#(I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f3#(I120, I121, I108, 0, I110, I111, I112, I113, I122, I123, I124, I117, I118, I119) [0 <= -1 - I118 + I119 /\ I125 = 0 /\ 0 <= 4 - I125 /\ I123 = I123 /\ I126 = 0 /\ I122 = I122 /\ I121 = 0 /\ I127 = I121 /\ I124 = I127 /\ I120 = I120] 8) f8#(I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139, I140, I141) -> f7#(I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139, 1 + I140, I141) 9) f2#(I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) -> f8#(I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) [I144 = I144] 10) f7#(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) -> f4#(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, 1 + I167, I168, I169) [-1 * I168 + I169 <= 0] 11) f7#(I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f3#(I184, I185, I172, 0, I174, I175, I176, I177, I186, I187, I188, I181, I182, I183) [0 <= -1 - I182 + I183 /\ I189 = 0 /\ 0 <= 4 - I189 /\ I187 = I187 /\ I190 = 0 /\ I186 = I186 /\ I185 = 0 /\ I191 = I185 /\ I188 = I191 /\ I184 = I184] 12) f3#(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) -> f1#(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) [0 <= -1 - I204 + I205 /\ 0 <= I202 /\ I202 <= 0] 13) f4#(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) -> f6#(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) [0 <= -1 - I217 + I218] 14) f1#(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248) -> f3#(I249, I250, I237, 0, I239, I240, I241, I242, I251, I252, I253, I246, I247, I248) [I254 = I239 /\ 0 <= 4 - I254 /\ I252 = I252 /\ I255 = I239 /\ I251 = I251 /\ I250 = 0 /\ I256 = I250 /\ I253 = I256 /\ I249 = I249] 15) f1#(I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270) -> f2#(I271, I272, I259, 1, I261, I262, I263, I264, I265, I273, I274, I268, I269, I270) [I275 = I261 /\ 5 - I275 <= 0 /\ I273 = I273 /\ I272 = 1 /\ I276 = I272 /\ I274 = I276 /\ I271 = I271] We have the following SCCs. { 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 } DP problem for innermost termination. P = f6#(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105) -> f4#(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, 1 + I103, I104, I105) [-1 * I104 + I105 <= 0] f6#(I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f3#(I120, I121, I108, 0, I110, I111, I112, I113, I122, I123, I124, I117, I118, I119) [0 <= -1 - I118 + I119 /\ I125 = 0 /\ 0 <= 4 - I125 /\ I123 = I123 /\ I126 = 0 /\ I122 = I122 /\ I121 = 0 /\ I127 = I121 /\ I124 = I127 /\ I120 = I120] f8#(I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139, I140, I141) -> f7#(I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139, 1 + I140, I141) f2#(I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) -> f8#(I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) [I144 = I144] f7#(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) -> f4#(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, 1 + I167, I168, I169) [-1 * I168 + I169 <= 0] f7#(I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f3#(I184, I185, I172, 0, I174, I175, I176, I177, I186, I187, I188, I181, I182, I183) [0 <= -1 - I182 + I183 /\ I189 = 0 /\ 0 <= 4 - I189 /\ I187 = I187 /\ I190 = 0 /\ I186 = I186 /\ I185 = 0 /\ I191 = I185 /\ I188 = I191 /\ I184 = I184] f3#(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) -> f1#(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) [0 <= -1 - I204 + I205 /\ 0 <= I202 /\ I202 <= 0] f4#(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) -> f6#(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) [0 <= -1 - I217 + I218] f1#(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248) -> f3#(I249, I250, I237, 0, I239, I240, I241, I242, I251, I252, I253, I246, I247, I248) [I254 = I239 /\ 0 <= 4 - I254 /\ I252 = I252 /\ I255 = I239 /\ I251 = I251 /\ I250 = 0 /\ I256 = I250 /\ I253 = I256 /\ I249 = I249] f1#(I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270) -> f2#(I271, I272, I259, 1, I261, I262, I263, I264, I265, I273, I274, I268, I269, I270) [I275 = I261 /\ 5 - I275 <= 0 /\ I273 = I273 /\ I272 = 1 /\ I276 = I272 /\ I274 = I276 /\ I271 = I271] R = f13(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> f9(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) f12(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13) -> f3(rnd1, rnd2, I2, 0, -2, I5, I6, I7, rnd9, rnd10, rnd11, I11, I12, I13) [y3 = -1 /\ 0 <= 4 - y3 /\ rnd10 = rnd10 /\ y2 = -1 /\ rnd9 = rnd9 /\ rnd2 = 0 /\ y1 = rnd2 /\ rnd11 = y1 /\ rnd1 = rnd1] f11(I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27) -> f2(I28, I29, I16, 1, I18, I19, I20, I21, I22, I30, I31, I25, I26, I27) [I32 = I19 /\ 5 - I32 <= 0 /\ I30 = I30 /\ I29 = 1 /\ I33 = I29 /\ I31 = I33 /\ I28 = I28] f11(I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) -> f3(I48, I49, I36, 0, I38, I39, -1 + I39, I41, I50, I51, I52, I45, I46, I47) [I53 = I39 /\ 0 <= 4 - I53 /\ I51 = I51 /\ I54 = I39 /\ I50 = I50 /\ I49 = 0 /\ I55 = I49 /\ I52 = I55 /\ I48 = I48] f10(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f3(I70, I71, I58, 0, I60, -2, I62, I63, I72, I73, I74, I67, I68, I69) [I75 = -1 /\ 0 <= 4 - I75 /\ I73 = I73 /\ I76 = -1 /\ I72 = I72 /\ I71 = 0 /\ I77 = I71 /\ I74 = I77 /\ I70 = I70] f9(I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f4(I78, I79, I80, I81, I82, I83, I84, rnd8, I86, I87, I88, I89, I90, I91) [rnd8 = rnd8] f6(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105) -> f4(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, 1 + I103, I104, I105) [-1 * I104 + I105 <= 0] f6(I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f3(I120, I121, I108, 0, I110, I111, I112, I113, I122, I123, I124, I117, I118, I119) [0 <= -1 - I118 + I119 /\ I125 = 0 /\ 0 <= 4 - I125 /\ I123 = I123 /\ I126 = 0 /\ I122 = I122 /\ I121 = 0 /\ I127 = I121 /\ I124 = I127 /\ I120 = I120] f8(I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139, I140, I141) -> f7(I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139, 1 + I140, I141) f2(I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) -> f8(I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) [I144 = I144] f7(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) -> f4(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, 1 + I167, I168, I169) [-1 * I168 + I169 <= 0] f7(I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f3(I184, I185, I172, 0, I174, I175, I176, I177, I186, I187, I188, I181, I182, I183) [0 <= -1 - I182 + I183 /\ I189 = 0 /\ 0 <= 4 - I189 /\ I187 = I187 /\ I190 = 0 /\ I186 = I186 /\ I185 = 0 /\ I191 = I185 /\ I188 = I191 /\ I184 = I184] f3(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) -> f1(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) [0 <= -1 - I204 + I205 /\ 0 <= I202 /\ I202 <= 0] f4(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) -> f6(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) [0 <= -1 - I217 + I218] f4(I220, I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233) -> f5(I234, I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233) [I234 = I234 /\ -1 * I231 + I232 <= 0] f1(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248) -> f3(I249, I250, I237, 0, I239, I240, I241, I242, I251, I252, I253, I246, I247, I248) [I254 = I239 /\ 0 <= 4 - I254 /\ I252 = I252 /\ I255 = I239 /\ I251 = I251 /\ I250 = 0 /\ I256 = I250 /\ I253 = I256 /\ I249 = I249] f1(I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270) -> f2(I271, I272, I259, 1, I261, I262, I263, I264, I265, I273, I274, I268, I269, I270) [I275 = I261 /\ 5 - I275 <= 0 /\ I273 = I273 /\ I272 = 1 /\ I276 = I272 /\ I274 = I276 /\ I271 = I271] We use the extended value criterion with the projection function NU: NU[f1#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13)] = -1 NU[f2#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13)] = -1 NU[f7#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13)] = -1 NU[f8#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13)] = -1 NU[f3#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13)] = -1 NU[f4#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13)] = -x12 + x13 - 1 NU[f6#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13)] = -x12 + x13 - 1 This gives the following inequalities: -1 * I104 + I105 <= 0 ==> -I104 + I105 - 1 >= -I104 + I105 - 1 0 <= -1 - I118 + I119 /\ I125 = 0 /\ 0 <= 4 - I125 /\ I123 = I123 /\ I126 = 0 /\ I122 = I122 /\ I121 = 0 /\ I127 = I121 /\ I124 = I127 /\ I120 = I120 ==> -I118 + I119 - 1 > -1 with -I118 + I119 - 1 >= 0 ==> -1 >= -1 I144 = I144 ==> -1 >= -1 -1 * I168 + I169 <= 0 ==> -1 >= -I168 + I169 - 1 0 <= -1 - I182 + I183 /\ I189 = 0 /\ 0 <= 4 - I189 /\ I187 = I187 /\ I190 = 0 /\ I186 = I186 /\ I185 = 0 /\ I191 = I185 /\ I188 = I191 /\ I184 = I184 ==> -1 >= -1 0 <= -1 - I204 + I205 /\ 0 <= I202 /\ I202 <= 0 ==> -1 >= -1 0 <= -1 - I217 + I218 ==> -I218 + I219 - 1 >= -I218 + I219 - 1 I254 = I239 /\ 0 <= 4 - I254 /\ I252 = I252 /\ I255 = I239 /\ I251 = I251 /\ I250 = 0 /\ I256 = I250 /\ I253 = I256 /\ I249 = I249 ==> -1 >= -1 I275 = I261 /\ 5 - I275 <= 0 /\ I273 = I273 /\ I272 = 1 /\ I276 = I272 /\ I274 = I276 /\ I271 = I271 ==> -1 >= -1 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f6#(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105) -> f4#(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, 1 + I103, I104, I105) [-1 * I104 + I105 <= 0] f8#(I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139, I140, I141) -> f7#(I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139, 1 + I140, I141) f2#(I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) -> f8#(I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) [I144 = I144] f7#(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) -> f4#(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, 1 + I167, I168, I169) [-1 * I168 + I169 <= 0] f7#(I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f3#(I184, I185, I172, 0, I174, I175, I176, I177, I186, I187, I188, I181, I182, I183) [0 <= -1 - I182 + I183 /\ I189 = 0 /\ 0 <= 4 - I189 /\ I187 = I187 /\ I190 = 0 /\ I186 = I186 /\ I185 = 0 /\ I191 = I185 /\ I188 = I191 /\ I184 = I184] f3#(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) -> f1#(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) [0 <= -1 - I204 + I205 /\ 0 <= I202 /\ I202 <= 0] f4#(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) -> f6#(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) [0 <= -1 - I217 + I218] f1#(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248) -> f3#(I249, I250, I237, 0, I239, I240, I241, I242, I251, I252, I253, I246, I247, I248) [I254 = I239 /\ 0 <= 4 - I254 /\ I252 = I252 /\ I255 = I239 /\ I251 = I251 /\ I250 = 0 /\ I256 = I250 /\ I253 = I256 /\ I249 = I249] f1#(I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270) -> f2#(I271, I272, I259, 1, I261, I262, I263, I264, I265, I273, I274, I268, I269, I270) [I275 = I261 /\ 5 - I275 <= 0 /\ I273 = I273 /\ I272 = 1 /\ I276 = I272 /\ I274 = I276 /\ I271 = I271] R = f13(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> f9(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) f12(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13) -> f3(rnd1, rnd2, I2, 0, -2, I5, I6, I7, rnd9, rnd10, rnd11, I11, I12, I13) [y3 = -1 /\ 0 <= 4 - y3 /\ rnd10 = rnd10 /\ y2 = -1 /\ rnd9 = rnd9 /\ rnd2 = 0 /\ y1 = rnd2 /\ rnd11 = y1 /\ rnd1 = rnd1] f11(I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27) -> f2(I28, I29, I16, 1, I18, I19, I20, I21, I22, I30, I31, I25, I26, I27) [I32 = I19 /\ 5 - I32 <= 0 /\ I30 = I30 /\ I29 = 1 /\ I33 = I29 /\ I31 = I33 /\ I28 = I28] f11(I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) -> f3(I48, I49, I36, 0, I38, I39, -1 + I39, I41, I50, I51, I52, I45, I46, I47) [I53 = I39 /\ 0 <= 4 - I53 /\ I51 = I51 /\ I54 = I39 /\ I50 = I50 /\ I49 = 0 /\ I55 = I49 /\ I52 = I55 /\ I48 = I48] f10(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f3(I70, I71, I58, 0, I60, -2, I62, I63, I72, I73, I74, I67, I68, I69) [I75 = -1 /\ 0 <= 4 - I75 /\ I73 = I73 /\ I76 = -1 /\ I72 = I72 /\ I71 = 0 /\ I77 = I71 /\ I74 = I77 /\ I70 = I70] f9(I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f4(I78, I79, I80, I81, I82, I83, I84, rnd8, I86, I87, I88, I89, I90, I91) [rnd8 = rnd8] f6(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105) -> f4(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, 1 + I103, I104, I105) [-1 * I104 + I105 <= 0] f6(I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f3(I120, I121, I108, 0, I110, I111, I112, I113, I122, I123, I124, I117, I118, I119) [0 <= -1 - I118 + I119 /\ I125 = 0 /\ 0 <= 4 - I125 /\ I123 = I123 /\ I126 = 0 /\ I122 = I122 /\ I121 = 0 /\ I127 = I121 /\ I124 = I127 /\ I120 = I120] f8(I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139, I140, I141) -> f7(I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139, 1 + I140, I141) f2(I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) -> f8(I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) [I144 = I144] f7(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) -> f4(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, 1 + I167, I168, I169) [-1 * I168 + I169 <= 0] f7(I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f3(I184, I185, I172, 0, I174, I175, I176, I177, I186, I187, I188, I181, I182, I183) [0 <= -1 - I182 + I183 /\ I189 = 0 /\ 0 <= 4 - I189 /\ I187 = I187 /\ I190 = 0 /\ I186 = I186 /\ I185 = 0 /\ I191 = I185 /\ I188 = I191 /\ I184 = I184] f3(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) -> f1(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) [0 <= -1 - I204 + I205 /\ 0 <= I202 /\ I202 <= 0] f4(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) -> f6(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) [0 <= -1 - I217 + I218] f4(I220, I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233) -> f5(I234, I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233) [I234 = I234 /\ -1 * I231 + I232 <= 0] f1(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248) -> f3(I249, I250, I237, 0, I239, I240, I241, I242, I251, I252, I253, I246, I247, I248) [I254 = I239 /\ 0 <= 4 - I254 /\ I252 = I252 /\ I255 = I239 /\ I251 = I251 /\ I250 = 0 /\ I256 = I250 /\ I253 = I256 /\ I249 = I249] f1(I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270) -> f2(I271, I272, I259, 1, I261, I262, I263, I264, I265, I273, I274, I268, I269, I270) [I275 = I261 /\ 5 - I275 <= 0 /\ I273 = I273 /\ I272 = 1 /\ I276 = I272 /\ I274 = I276 /\ I271 = I271] The dependency graph for this problem is: 6 -> 13 8 -> 10, 11 9 -> 8 10 -> 13 11 -> 12 12 -> 14, 15 13 -> 6 14 -> 12 15 -> 9 Where: 6) f6#(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105) -> f4#(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, 1 + I103, I104, I105) [-1 * I104 + I105 <= 0] 8) f8#(I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139, I140, I141) -> f7#(I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139, 1 + I140, I141) 9) f2#(I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) -> f8#(I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) [I144 = I144] 10) f7#(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) -> f4#(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, 1 + I167, I168, I169) [-1 * I168 + I169 <= 0] 11) f7#(I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f3#(I184, I185, I172, 0, I174, I175, I176, I177, I186, I187, I188, I181, I182, I183) [0 <= -1 - I182 + I183 /\ I189 = 0 /\ 0 <= 4 - I189 /\ I187 = I187 /\ I190 = 0 /\ I186 = I186 /\ I185 = 0 /\ I191 = I185 /\ I188 = I191 /\ I184 = I184] 12) f3#(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) -> f1#(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) [0 <= -1 - I204 + I205 /\ 0 <= I202 /\ I202 <= 0] 13) f4#(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) -> f6#(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) [0 <= -1 - I217 + I218] 14) f1#(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248) -> f3#(I249, I250, I237, 0, I239, I240, I241, I242, I251, I252, I253, I246, I247, I248) [I254 = I239 /\ 0 <= 4 - I254 /\ I252 = I252 /\ I255 = I239 /\ I251 = I251 /\ I250 = 0 /\ I256 = I250 /\ I253 = I256 /\ I249 = I249] 15) f1#(I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270) -> f2#(I271, I272, I259, 1, I261, I262, I263, I264, I265, I273, I274, I268, I269, I270) [I275 = I261 /\ 5 - I275 <= 0 /\ I273 = I273 /\ I272 = 1 /\ I276 = I272 /\ I274 = I276 /\ I271 = I271] We have the following SCCs. { 8, 9, 11, 12, 14, 15 } { 6, 13 } DP problem for innermost termination. P = f6#(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105) -> f4#(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, 1 + I103, I104, I105) [-1 * I104 + I105 <= 0] f4#(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) -> f6#(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) [0 <= -1 - I217 + I218] R = f13(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> f9(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) f12(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13) -> f3(rnd1, rnd2, I2, 0, -2, I5, I6, I7, rnd9, rnd10, rnd11, I11, I12, I13) [y3 = -1 /\ 0 <= 4 - y3 /\ rnd10 = rnd10 /\ y2 = -1 /\ rnd9 = rnd9 /\ rnd2 = 0 /\ y1 = rnd2 /\ rnd11 = y1 /\ rnd1 = rnd1] f11(I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27) -> f2(I28, I29, I16, 1, I18, I19, I20, I21, I22, I30, I31, I25, I26, I27) [I32 = I19 /\ 5 - I32 <= 0 /\ I30 = I30 /\ I29 = 1 /\ I33 = I29 /\ I31 = I33 /\ I28 = I28] f11(I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) -> f3(I48, I49, I36, 0, I38, I39, -1 + I39, I41, I50, I51, I52, I45, I46, I47) [I53 = I39 /\ 0 <= 4 - I53 /\ I51 = I51 /\ I54 = I39 /\ I50 = I50 /\ I49 = 0 /\ I55 = I49 /\ I52 = I55 /\ I48 = I48] f10(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f3(I70, I71, I58, 0, I60, -2, I62, I63, I72, I73, I74, I67, I68, I69) [I75 = -1 /\ 0 <= 4 - I75 /\ I73 = I73 /\ I76 = -1 /\ I72 = I72 /\ I71 = 0 /\ I77 = I71 /\ I74 = I77 /\ I70 = I70] f9(I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f4(I78, I79, I80, I81, I82, I83, I84, rnd8, I86, I87, I88, I89, I90, I91) [rnd8 = rnd8] f6(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105) -> f4(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, 1 + I103, I104, I105) [-1 * I104 + I105 <= 0] f6(I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f3(I120, I121, I108, 0, I110, I111, I112, I113, I122, I123, I124, I117, I118, I119) [0 <= -1 - I118 + I119 /\ I125 = 0 /\ 0 <= 4 - I125 /\ I123 = I123 /\ I126 = 0 /\ I122 = I122 /\ I121 = 0 /\ I127 = I121 /\ I124 = I127 /\ I120 = I120] f8(I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139, I140, I141) -> f7(I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139, 1 + I140, I141) f2(I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) -> f8(I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) [I144 = I144] f7(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) -> f4(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, 1 + I167, I168, I169) [-1 * I168 + I169 <= 0] f7(I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f3(I184, I185, I172, 0, I174, I175, I176, I177, I186, I187, I188, I181, I182, I183) [0 <= -1 - I182 + I183 /\ I189 = 0 /\ 0 <= 4 - I189 /\ I187 = I187 /\ I190 = 0 /\ I186 = I186 /\ I185 = 0 /\ I191 = I185 /\ I188 = I191 /\ I184 = I184] f3(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) -> f1(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) [0 <= -1 - I204 + I205 /\ 0 <= I202 /\ I202 <= 0] f4(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) -> f6(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) [0 <= -1 - I217 + I218] f4(I220, I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233) -> f5(I234, I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233) [I234 = I234 /\ -1 * I231 + I232 <= 0] f1(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248) -> f3(I249, I250, I237, 0, I239, I240, I241, I242, I251, I252, I253, I246, I247, I248) [I254 = I239 /\ 0 <= 4 - I254 /\ I252 = I252 /\ I255 = I239 /\ I251 = I251 /\ I250 = 0 /\ I256 = I250 /\ I253 = I256 /\ I249 = I249] f1(I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270) -> f2(I271, I272, I259, 1, I261, I262, I263, I264, I265, I273, I274, I268, I269, I270) [I275 = I261 /\ 5 - I275 <= 0 /\ I273 = I273 /\ I272 = 1 /\ I276 = I272 /\ I274 = I276 /\ I271 = I271] We use the reverse value criterion with the projection function NU: NU[f4#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14)] = -1 - z12 + z13 + -1 * 0 NU[f6#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14)] = -1 - (1 + z12) + z13 + -1 * 0 This gives the following inequalities: -1 * I104 + I105 <= 0 ==> -1 - (1 + I103) + I104 + -1 * 0 >= -1 - (1 + I103) + I104 + -1 * 0 0 <= -1 - I217 + I218 ==> -1 - I217 + I218 + -1 * 0 > -1 - (1 + I217) + I218 + -1 * 0 with -1 - I217 + I218 + -1 * 0 >= 0 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f6#(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105) -> f4#(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, 1 + I103, I104, I105) [-1 * I104 + I105 <= 0] R = f13(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> f9(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) f12(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13) -> f3(rnd1, rnd2, I2, 0, -2, I5, I6, I7, rnd9, rnd10, rnd11, I11, I12, I13) [y3 = -1 /\ 0 <= 4 - y3 /\ rnd10 = rnd10 /\ y2 = -1 /\ rnd9 = rnd9 /\ rnd2 = 0 /\ y1 = rnd2 /\ rnd11 = y1 /\ rnd1 = rnd1] f11(I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27) -> f2(I28, I29, I16, 1, I18, I19, I20, I21, I22, I30, I31, I25, I26, I27) [I32 = I19 /\ 5 - I32 <= 0 /\ I30 = I30 /\ I29 = 1 /\ I33 = I29 /\ I31 = I33 /\ I28 = I28] f11(I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) -> f3(I48, I49, I36, 0, I38, I39, -1 + I39, I41, I50, I51, I52, I45, I46, I47) [I53 = I39 /\ 0 <= 4 - I53 /\ I51 = I51 /\ I54 = I39 /\ I50 = I50 /\ I49 = 0 /\ I55 = I49 /\ I52 = I55 /\ I48 = I48] f10(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f3(I70, I71, I58, 0, I60, -2, I62, I63, I72, I73, I74, I67, I68, I69) [I75 = -1 /\ 0 <= 4 - I75 /\ I73 = I73 /\ I76 = -1 /\ I72 = I72 /\ I71 = 0 /\ I77 = I71 /\ I74 = I77 /\ I70 = I70] f9(I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f4(I78, I79, I80, I81, I82, I83, I84, rnd8, I86, I87, I88, I89, I90, I91) [rnd8 = rnd8] f6(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105) -> f4(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, 1 + I103, I104, I105) [-1 * I104 + I105 <= 0] f6(I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f3(I120, I121, I108, 0, I110, I111, I112, I113, I122, I123, I124, I117, I118, I119) [0 <= -1 - I118 + I119 /\ I125 = 0 /\ 0 <= 4 - I125 /\ I123 = I123 /\ I126 = 0 /\ I122 = I122 /\ I121 = 0 /\ I127 = I121 /\ I124 = I127 /\ I120 = I120] f8(I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139, I140, I141) -> f7(I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139, 1 + I140, I141) f2(I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) -> f8(I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) [I144 = I144] f7(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) -> f4(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, 1 + I167, I168, I169) [-1 * I168 + I169 <= 0] f7(I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f3(I184, I185, I172, 0, I174, I175, I176, I177, I186, I187, I188, I181, I182, I183) [0 <= -1 - I182 + I183 /\ I189 = 0 /\ 0 <= 4 - I189 /\ I187 = I187 /\ I190 = 0 /\ I186 = I186 /\ I185 = 0 /\ I191 = I185 /\ I188 = I191 /\ I184 = I184] f3(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) -> f1(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) [0 <= -1 - I204 + I205 /\ 0 <= I202 /\ I202 <= 0] f4(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) -> f6(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) [0 <= -1 - I217 + I218] f4(I220, I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233) -> f5(I234, I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233) [I234 = I234 /\ -1 * I231 + I232 <= 0] f1(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248) -> f3(I249, I250, I237, 0, I239, I240, I241, I242, I251, I252, I253, I246, I247, I248) [I254 = I239 /\ 0 <= 4 - I254 /\ I252 = I252 /\ I255 = I239 /\ I251 = I251 /\ I250 = 0 /\ I256 = I250 /\ I253 = I256 /\ I249 = I249] f1(I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270) -> f2(I271, I272, I259, 1, I261, I262, I263, I264, I265, I273, I274, I268, I269, I270) [I275 = I261 /\ 5 - I275 <= 0 /\ I273 = I273 /\ I272 = 1 /\ I276 = I272 /\ I274 = I276 /\ I271 = I271] The dependency graph for this problem is: 6 -> Where: 6) f6#(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105) -> f4#(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, 1 + I103, I104, I105) [-1 * I104 + I105 <= 0] We have the following SCCs. DP problem for innermost termination. P = f8#(I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139, I140, I141) -> f7#(I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139, 1 + I140, I141) f2#(I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) -> f8#(I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) [I144 = I144] f7#(I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f3#(I184, I185, I172, 0, I174, I175, I176, I177, I186, I187, I188, I181, I182, I183) [0 <= -1 - I182 + I183 /\ I189 = 0 /\ 0 <= 4 - I189 /\ I187 = I187 /\ I190 = 0 /\ I186 = I186 /\ I185 = 0 /\ I191 = I185 /\ I188 = I191 /\ I184 = I184] f3#(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) -> f1#(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) [0 <= -1 - I204 + I205 /\ 0 <= I202 /\ I202 <= 0] f1#(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248) -> f3#(I249, I250, I237, 0, I239, I240, I241, I242, I251, I252, I253, I246, I247, I248) [I254 = I239 /\ 0 <= 4 - I254 /\ I252 = I252 /\ I255 = I239 /\ I251 = I251 /\ I250 = 0 /\ I256 = I250 /\ I253 = I256 /\ I249 = I249] f1#(I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270) -> f2#(I271, I272, I259, 1, I261, I262, I263, I264, I265, I273, I274, I268, I269, I270) [I275 = I261 /\ 5 - I275 <= 0 /\ I273 = I273 /\ I272 = 1 /\ I276 = I272 /\ I274 = I276 /\ I271 = I271] R = f13(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> f9(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) f12(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13) -> f3(rnd1, rnd2, I2, 0, -2, I5, I6, I7, rnd9, rnd10, rnd11, I11, I12, I13) [y3 = -1 /\ 0 <= 4 - y3 /\ rnd10 = rnd10 /\ y2 = -1 /\ rnd9 = rnd9 /\ rnd2 = 0 /\ y1 = rnd2 /\ rnd11 = y1 /\ rnd1 = rnd1] f11(I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27) -> f2(I28, I29, I16, 1, I18, I19, I20, I21, I22, I30, I31, I25, I26, I27) [I32 = I19 /\ 5 - I32 <= 0 /\ I30 = I30 /\ I29 = 1 /\ I33 = I29 /\ I31 = I33 /\ I28 = I28] f11(I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) -> f3(I48, I49, I36, 0, I38, I39, -1 + I39, I41, I50, I51, I52, I45, I46, I47) [I53 = I39 /\ 0 <= 4 - I53 /\ I51 = I51 /\ I54 = I39 /\ I50 = I50 /\ I49 = 0 /\ I55 = I49 /\ I52 = I55 /\ I48 = I48] f10(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f3(I70, I71, I58, 0, I60, -2, I62, I63, I72, I73, I74, I67, I68, I69) [I75 = -1 /\ 0 <= 4 - I75 /\ I73 = I73 /\ I76 = -1 /\ I72 = I72 /\ I71 = 0 /\ I77 = I71 /\ I74 = I77 /\ I70 = I70] f9(I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f4(I78, I79, I80, I81, I82, I83, I84, rnd8, I86, I87, I88, I89, I90, I91) [rnd8 = rnd8] f6(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105) -> f4(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, 1 + I103, I104, I105) [-1 * I104 + I105 <= 0] f6(I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f3(I120, I121, I108, 0, I110, I111, I112, I113, I122, I123, I124, I117, I118, I119) [0 <= -1 - I118 + I119 /\ I125 = 0 /\ 0 <= 4 - I125 /\ I123 = I123 /\ I126 = 0 /\ I122 = I122 /\ I121 = 0 /\ I127 = I121 /\ I124 = I127 /\ I120 = I120] f8(I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139, I140, I141) -> f7(I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139, 1 + I140, I141) f2(I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) -> f8(I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) [I144 = I144] f7(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) -> f4(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, 1 + I167, I168, I169) [-1 * I168 + I169 <= 0] f7(I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f3(I184, I185, I172, 0, I174, I175, I176, I177, I186, I187, I188, I181, I182, I183) [0 <= -1 - I182 + I183 /\ I189 = 0 /\ 0 <= 4 - I189 /\ I187 = I187 /\ I190 = 0 /\ I186 = I186 /\ I185 = 0 /\ I191 = I185 /\ I188 = I191 /\ I184 = I184] f3(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) -> f1(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) [0 <= -1 - I204 + I205 /\ 0 <= I202 /\ I202 <= 0] f4(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) -> f6(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) [0 <= -1 - I217 + I218] f4(I220, I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233) -> f5(I234, I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233) [I234 = I234 /\ -1 * I231 + I232 <= 0] f1(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248) -> f3(I249, I250, I237, 0, I239, I240, I241, I242, I251, I252, I253, I246, I247, I248) [I254 = I239 /\ 0 <= 4 - I254 /\ I252 = I252 /\ I255 = I239 /\ I251 = I251 /\ I250 = 0 /\ I256 = I250 /\ I253 = I256 /\ I249 = I249] f1(I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270) -> f2(I271, I272, I259, 1, I261, I262, I263, I264, I265, I273, I274, I268, I269, I270) [I275 = I261 /\ 5 - I275 <= 0 /\ I273 = I273 /\ I272 = 1 /\ I276 = I272 /\ I274 = I276 /\ I271 = I271] We use the extended value criterion with the projection function NU: NU[f1#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13)] = -x12 + x13 - 2 NU[f3#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13)] = -x12 + x13 - 2 NU[f2#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13)] = -x12 + x13 - 2 NU[f7#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13)] = -x12 + x13 - 1 NU[f8#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13)] = -x12 + x13 - 2 This gives the following inequalities: ==> -I140 + I141 - 2 >= -(1 + I140) + I141 - 1 I144 = I144 ==> -I154 + I155 - 2 >= -I154 + I155 - 2 0 <= -1 - I182 + I183 /\ I189 = 0 /\ 0 <= 4 - I189 /\ I187 = I187 /\ I190 = 0 /\ I186 = I186 /\ I185 = 0 /\ I191 = I185 /\ I188 = I191 /\ I184 = I184 ==> -I182 + I183 - 1 > -I182 + I183 - 2 with -I182 + I183 - 1 >= 0 0 <= -1 - I204 + I205 /\ 0 <= I202 /\ I202 <= 0 ==> -I204 + I205 - 2 >= -I204 + I205 - 2 I254 = I239 /\ 0 <= 4 - I254 /\ I252 = I252 /\ I255 = I239 /\ I251 = I251 /\ I250 = 0 /\ I256 = I250 /\ I253 = I256 /\ I249 = I249 ==> -I247 + I248 - 2 >= -I247 + I248 - 2 I275 = I261 /\ 5 - I275 <= 0 /\ I273 = I273 /\ I272 = 1 /\ I276 = I272 /\ I274 = I276 /\ I271 = I271 ==> -I269 + I270 - 2 >= -I269 + I270 - 2 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f8#(I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139, I140, I141) -> f7#(I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139, 1 + I140, I141) f2#(I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) -> f8#(I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) [I144 = I144] f3#(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) -> f1#(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) [0 <= -1 - I204 + I205 /\ 0 <= I202 /\ I202 <= 0] f1#(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248) -> f3#(I249, I250, I237, 0, I239, I240, I241, I242, I251, I252, I253, I246, I247, I248) [I254 = I239 /\ 0 <= 4 - I254 /\ I252 = I252 /\ I255 = I239 /\ I251 = I251 /\ I250 = 0 /\ I256 = I250 /\ I253 = I256 /\ I249 = I249] f1#(I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270) -> f2#(I271, I272, I259, 1, I261, I262, I263, I264, I265, I273, I274, I268, I269, I270) [I275 = I261 /\ 5 - I275 <= 0 /\ I273 = I273 /\ I272 = 1 /\ I276 = I272 /\ I274 = I276 /\ I271 = I271] R = f13(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> f9(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) f12(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13) -> f3(rnd1, rnd2, I2, 0, -2, I5, I6, I7, rnd9, rnd10, rnd11, I11, I12, I13) [y3 = -1 /\ 0 <= 4 - y3 /\ rnd10 = rnd10 /\ y2 = -1 /\ rnd9 = rnd9 /\ rnd2 = 0 /\ y1 = rnd2 /\ rnd11 = y1 /\ rnd1 = rnd1] f11(I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27) -> f2(I28, I29, I16, 1, I18, I19, I20, I21, I22, I30, I31, I25, I26, I27) [I32 = I19 /\ 5 - I32 <= 0 /\ I30 = I30 /\ I29 = 1 /\ I33 = I29 /\ I31 = I33 /\ I28 = I28] f11(I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) -> f3(I48, I49, I36, 0, I38, I39, -1 + I39, I41, I50, I51, I52, I45, I46, I47) [I53 = I39 /\ 0 <= 4 - I53 /\ I51 = I51 /\ I54 = I39 /\ I50 = I50 /\ I49 = 0 /\ I55 = I49 /\ I52 = I55 /\ I48 = I48] f10(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f3(I70, I71, I58, 0, I60, -2, I62, I63, I72, I73, I74, I67, I68, I69) [I75 = -1 /\ 0 <= 4 - I75 /\ I73 = I73 /\ I76 = -1 /\ I72 = I72 /\ I71 = 0 /\ I77 = I71 /\ I74 = I77 /\ I70 = I70] f9(I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f4(I78, I79, I80, I81, I82, I83, I84, rnd8, I86, I87, I88, I89, I90, I91) [rnd8 = rnd8] f6(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105) -> f4(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, 1 + I103, I104, I105) [-1 * I104 + I105 <= 0] f6(I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f3(I120, I121, I108, 0, I110, I111, I112, I113, I122, I123, I124, I117, I118, I119) [0 <= -1 - I118 + I119 /\ I125 = 0 /\ 0 <= 4 - I125 /\ I123 = I123 /\ I126 = 0 /\ I122 = I122 /\ I121 = 0 /\ I127 = I121 /\ I124 = I127 /\ I120 = I120] f8(I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139, I140, I141) -> f7(I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139, 1 + I140, I141) f2(I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) -> f8(I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) [I144 = I144] f7(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) -> f4(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, 1 + I167, I168, I169) [-1 * I168 + I169 <= 0] f7(I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f3(I184, I185, I172, 0, I174, I175, I176, I177, I186, I187, I188, I181, I182, I183) [0 <= -1 - I182 + I183 /\ I189 = 0 /\ 0 <= 4 - I189 /\ I187 = I187 /\ I190 = 0 /\ I186 = I186 /\ I185 = 0 /\ I191 = I185 /\ I188 = I191 /\ I184 = I184] f3(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) -> f1(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) [0 <= -1 - I204 + I205 /\ 0 <= I202 /\ I202 <= 0] f4(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) -> f6(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) [0 <= -1 - I217 + I218] f4(I220, I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233) -> f5(I234, I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233) [I234 = I234 /\ -1 * I231 + I232 <= 0] f1(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248) -> f3(I249, I250, I237, 0, I239, I240, I241, I242, I251, I252, I253, I246, I247, I248) [I254 = I239 /\ 0 <= 4 - I254 /\ I252 = I252 /\ I255 = I239 /\ I251 = I251 /\ I250 = 0 /\ I256 = I250 /\ I253 = I256 /\ I249 = I249] f1(I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270) -> f2(I271, I272, I259, 1, I261, I262, I263, I264, I265, I273, I274, I268, I269, I270) [I275 = I261 /\ 5 - I275 <= 0 /\ I273 = I273 /\ I272 = 1 /\ I276 = I272 /\ I274 = I276 /\ I271 = I271] The dependency graph for this problem is: 8 -> 9 -> 8 12 -> 14, 15 14 -> 12 15 -> 9 Where: 8) f8#(I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139, I140, I141) -> f7#(I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139, 1 + I140, I141) 9) f2#(I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) -> f8#(I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) [I144 = I144] 12) f3#(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) -> f1#(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) [0 <= -1 - I204 + I205 /\ 0 <= I202 /\ I202 <= 0] 14) f1#(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248) -> f3#(I249, I250, I237, 0, I239, I240, I241, I242, I251, I252, I253, I246, I247, I248) [I254 = I239 /\ 0 <= 4 - I254 /\ I252 = I252 /\ I255 = I239 /\ I251 = I251 /\ I250 = 0 /\ I256 = I250 /\ I253 = I256 /\ I249 = I249] 15) f1#(I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270) -> f2#(I271, I272, I259, 1, I261, I262, I263, I264, I265, I273, I274, I268, I269, I270) [I275 = I261 /\ 5 - I275 <= 0 /\ I273 = I273 /\ I272 = 1 /\ I276 = I272 /\ I274 = I276 /\ I271 = I271] We have the following SCCs. { 12, 14 } DP problem for innermost termination. P = f3#(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) -> f1#(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) [0 <= -1 - I204 + I205 /\ 0 <= I202 /\ I202 <= 0] f1#(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248) -> f3#(I249, I250, I237, 0, I239, I240, I241, I242, I251, I252, I253, I246, I247, I248) [I254 = I239 /\ 0 <= 4 - I254 /\ I252 = I252 /\ I255 = I239 /\ I251 = I251 /\ I250 = 0 /\ I256 = I250 /\ I253 = I256 /\ I249 = I249] R = f13(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> f9(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) f12(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13) -> f3(rnd1, rnd2, I2, 0, -2, I5, I6, I7, rnd9, rnd10, rnd11, I11, I12, I13) [y3 = -1 /\ 0 <= 4 - y3 /\ rnd10 = rnd10 /\ y2 = -1 /\ rnd9 = rnd9 /\ rnd2 = 0 /\ y1 = rnd2 /\ rnd11 = y1 /\ rnd1 = rnd1] f11(I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27) -> f2(I28, I29, I16, 1, I18, I19, I20, I21, I22, I30, I31, I25, I26, I27) [I32 = I19 /\ 5 - I32 <= 0 /\ I30 = I30 /\ I29 = 1 /\ I33 = I29 /\ I31 = I33 /\ I28 = I28] f11(I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) -> f3(I48, I49, I36, 0, I38, I39, -1 + I39, I41, I50, I51, I52, I45, I46, I47) [I53 = I39 /\ 0 <= 4 - I53 /\ I51 = I51 /\ I54 = I39 /\ I50 = I50 /\ I49 = 0 /\ I55 = I49 /\ I52 = I55 /\ I48 = I48] f10(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f3(I70, I71, I58, 0, I60, -2, I62, I63, I72, I73, I74, I67, I68, I69) [I75 = -1 /\ 0 <= 4 - I75 /\ I73 = I73 /\ I76 = -1 /\ I72 = I72 /\ I71 = 0 /\ I77 = I71 /\ I74 = I77 /\ I70 = I70] f9(I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f4(I78, I79, I80, I81, I82, I83, I84, rnd8, I86, I87, I88, I89, I90, I91) [rnd8 = rnd8] f6(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105) -> f4(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, 1 + I103, I104, I105) [-1 * I104 + I105 <= 0] f6(I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f3(I120, I121, I108, 0, I110, I111, I112, I113, I122, I123, I124, I117, I118, I119) [0 <= -1 - I118 + I119 /\ I125 = 0 /\ 0 <= 4 - I125 /\ I123 = I123 /\ I126 = 0 /\ I122 = I122 /\ I121 = 0 /\ I127 = I121 /\ I124 = I127 /\ I120 = I120] f8(I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139, I140, I141) -> f7(I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138, I139, 1 + I140, I141) f2(I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) -> f8(I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) [I144 = I144] f7(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169) -> f4(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, 1 + I167, I168, I169) [-1 * I168 + I169 <= 0] f7(I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f3(I184, I185, I172, 0, I174, I175, I176, I177, I186, I187, I188, I181, I182, I183) [0 <= -1 - I182 + I183 /\ I189 = 0 /\ 0 <= 4 - I189 /\ I187 = I187 /\ I190 = 0 /\ I186 = I186 /\ I185 = 0 /\ I191 = I185 /\ I188 = I191 /\ I184 = I184] f3(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) -> f1(I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) [0 <= -1 - I204 + I205 /\ 0 <= I202 /\ I202 <= 0] f4(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) -> f6(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) [0 <= -1 - I217 + I218] f4(I220, I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233) -> f5(I234, I221, I222, I223, I224, I225, I226, I227, I228, I229, I230, I231, I232, I233) [I234 = I234 /\ -1 * I231 + I232 <= 0] f1(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248) -> f3(I249, I250, I237, 0, I239, I240, I241, I242, I251, I252, I253, I246, I247, I248) [I254 = I239 /\ 0 <= 4 - I254 /\ I252 = I252 /\ I255 = I239 /\ I251 = I251 /\ I250 = 0 /\ I256 = I250 /\ I253 = I256 /\ I249 = I249] f1(I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270) -> f2(I271, I272, I259, 1, I261, I262, I263, I264, I265, I273, I274, I268, I269, I270) [I275 = I261 /\ 5 - I275 <= 0 /\ I273 = I273 /\ I272 = 1 /\ I276 = I272 /\ I274 = I276 /\ I271 = I271]