34.11/33.91 MAYBE 34.11/33.91 34.11/33.91 DP problem for innermost termination. 34.11/33.91 P = 34.11/33.91 f13#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) -> f12#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) 34.11/33.91 f12#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14) -> f1#(I0, I1, I2, I3, I4, rnd6, I6, I7, I8, I9, I10, I11, I12, I13, 1) [y1 = 1 /\ rnd6 = rnd6] 34.11/33.91 f3#(I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f6#(I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) [I28 <= 0] 34.11/33.91 f3#(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f2#(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44) [1 <= I43] 34.11/33.91 f11#(I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f7#(I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 34.11/33.91 f7#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74) -> f11#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, 1) 34.11/33.91 f2#(I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f10#(I75, I76, 0, I78, I79, I80, rnd7, I82, I83, rnd10, I85, rnd12, I87, I88, 0) [rnd7 = rnd10 /\ rnd10 = rnd12 /\ rnd12 = rnd12 /\ 1 <= I89] 34.11/33.91 f2#(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) -> f10#(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) [I104 <= 0] 34.11/33.91 f10#(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f9#(I105, I106, I107, 0, rnd5, I110, I111, I112, rnd9, I114, I115, I116, rnd13, I118, I119) [rnd5 = rnd9 /\ rnd9 = rnd13 /\ rnd13 = rnd13 /\ I119 <= 0] 34.11/33.91 f10#(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f8#(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) [1 <= I134] 34.11/33.91 f9#(I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) -> f8#(I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, 1) [1000 <= I139 - I141] 34.11/33.91 f9#(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164) -> f8#(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164) [1 + I154 - I156 <= 1000] 34.11/33.91 f8#(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f6#(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) 34.11/33.91 f6#(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f7#(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 34.11/33.91 f1#(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f3#(rnd1, 1, I212, I213, I214, 0, I216, rnd8, I218, I219, rnd11, I221, I222, rnd14, I224) [rnd14 = rnd11 /\ rnd11 = rnd8 /\ rnd8 = rnd1 /\ rnd1 = rnd1 /\ 1 <= I215] 34.11/33.91 f1#(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f2#(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) [I230 <= 0] 34.11/33.91 R = 34.11/33.91 f13(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) -> f12(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) 34.11/33.91 f12(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14) -> f1(I0, I1, I2, I3, I4, rnd6, I6, I7, I8, I9, I10, I11, I12, I13, 1) [y1 = 1 /\ rnd6 = rnd6] 34.11/33.91 f3(I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f6(I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) [I28 <= 0] 34.11/33.91 f3(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f2(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44) [1 <= I43] 34.11/33.91 f11(I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f7(I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 34.11/33.91 f7(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74) -> f11(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, 1) 34.11/33.91 f2(I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f10(I75, I76, 0, I78, I79, I80, rnd7, I82, I83, rnd10, I85, rnd12, I87, I88, 0) [rnd7 = rnd10 /\ rnd10 = rnd12 /\ rnd12 = rnd12 /\ 1 <= I89] 34.11/33.91 f2(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) -> f10(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) [I104 <= 0] 34.11/33.91 f10(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f9(I105, I106, I107, 0, rnd5, I110, I111, I112, rnd9, I114, I115, I116, rnd13, I118, I119) [rnd5 = rnd9 /\ rnd9 = rnd13 /\ rnd13 = rnd13 /\ I119 <= 0] 34.11/33.91 f10(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f8(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) [1 <= I134] 34.11/33.91 f9(I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) -> f8(I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, 1) [1000 <= I139 - I141] 34.11/33.91 f9(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164) -> f8(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164) [1 + I154 - I156 <= 1000] 34.11/33.91 f8(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f6(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) 34.11/33.91 f6(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f7(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 34.11/33.91 f4(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f5(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) 34.11/33.91 f1(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f3(rnd1, 1, I212, I213, I214, 0, I216, rnd8, I218, I219, rnd11, I221, I222, rnd14, I224) [rnd14 = rnd11 /\ rnd11 = rnd8 /\ rnd8 = rnd1 /\ rnd1 = rnd1 /\ 1 <= I215] 34.11/33.91 f1(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f2(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) [I230 <= 0] 34.11/33.91 34.11/33.91 The dependency graph for this problem is: 34.11/33.91 0 -> 1 34.11/33.91 1 -> 14, 15 34.11/33.91 2 -> 13 34.11/33.91 3 -> 6, 7 34.11/33.91 4 -> 5 34.11/33.91 5 -> 4 34.11/33.91 6 -> 8 34.11/33.91 7 -> 8 34.11/33.91 8 -> 10, 11 34.11/33.91 9 -> 12 34.11/33.91 10 -> 12 34.11/33.91 11 -> 12 34.11/33.91 12 -> 13 34.11/33.91 13 -> 5 34.11/33.91 14 -> 2, 3 34.11/33.91 15 -> 6, 7 34.11/33.91 Where: 34.11/33.91 0) f13#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) -> f12#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) 34.11/33.91 1) f12#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14) -> f1#(I0, I1, I2, I3, I4, rnd6, I6, I7, I8, I9, I10, I11, I12, I13, 1) [y1 = 1 /\ rnd6 = rnd6] 34.11/33.91 2) f3#(I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f6#(I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) [I28 <= 0] 34.11/33.91 3) f3#(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f2#(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44) [1 <= I43] 34.11/33.91 4) f11#(I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f7#(I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 34.11/33.91 5) f7#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74) -> f11#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, 1) 34.11/33.91 6) f2#(I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f10#(I75, I76, 0, I78, I79, I80, rnd7, I82, I83, rnd10, I85, rnd12, I87, I88, 0) [rnd7 = rnd10 /\ rnd10 = rnd12 /\ rnd12 = rnd12 /\ 1 <= I89] 34.11/33.91 7) f2#(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) -> f10#(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) [I104 <= 0] 34.11/33.91 8) f10#(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f9#(I105, I106, I107, 0, rnd5, I110, I111, I112, rnd9, I114, I115, I116, rnd13, I118, I119) [rnd5 = rnd9 /\ rnd9 = rnd13 /\ rnd13 = rnd13 /\ I119 <= 0] 34.11/33.91 9) f10#(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f8#(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) [1 <= I134] 34.11/33.91 10) f9#(I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) -> f8#(I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, 1) [1000 <= I139 - I141] 34.11/33.91 11) f9#(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164) -> f8#(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164) [1 + I154 - I156 <= 1000] 34.11/33.91 12) f8#(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f6#(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) 34.11/33.91 13) f6#(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f7#(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 34.11/33.91 14) f1#(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f3#(rnd1, 1, I212, I213, I214, 0, I216, rnd8, I218, I219, rnd11, I221, I222, rnd14, I224) [rnd14 = rnd11 /\ rnd11 = rnd8 /\ rnd8 = rnd1 /\ rnd1 = rnd1 /\ 1 <= I215] 34.11/33.91 15) f1#(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f2#(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) [I230 <= 0] 34.11/33.91 34.11/33.91 We have the following SCCs. 34.11/33.91 { 4, 5 } 34.11/33.91 34.11/33.91 DP problem for innermost termination. 34.11/33.91 P = 34.11/33.91 f11#(I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f7#(I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 34.11/33.91 f7#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74) -> f11#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, 1) 34.11/33.91 R = 34.11/33.91 f13(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) -> f12(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) 34.11/33.91 f12(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14) -> f1(I0, I1, I2, I3, I4, rnd6, I6, I7, I8, I9, I10, I11, I12, I13, 1) [y1 = 1 /\ rnd6 = rnd6] 34.11/33.91 f3(I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f6(I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) [I28 <= 0] 34.11/33.91 f3(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f2(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44) [1 <= I43] 34.11/33.91 f11(I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f7(I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 34.11/33.91 f7(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74) -> f11(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, 1) 34.11/33.91 f2(I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f10(I75, I76, 0, I78, I79, I80, rnd7, I82, I83, rnd10, I85, rnd12, I87, I88, 0) [rnd7 = rnd10 /\ rnd10 = rnd12 /\ rnd12 = rnd12 /\ 1 <= I89] 34.11/33.91 f2(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) -> f10(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) [I104 <= 0] 34.11/33.91 f10(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f9(I105, I106, I107, 0, rnd5, I110, I111, I112, rnd9, I114, I115, I116, rnd13, I118, I119) [rnd5 = rnd9 /\ rnd9 = rnd13 /\ rnd13 = rnd13 /\ I119 <= 0] 34.11/33.91 f10(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f8(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) [1 <= I134] 34.11/33.91 f9(I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) -> f8(I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, 1) [1000 <= I139 - I141] 34.11/33.91 f9(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164) -> f8(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164) [1 + I154 - I156 <= 1000] 34.11/33.91 f8(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f6(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) 34.11/33.91 f6(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f7(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 34.11/33.91 f4(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f5(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) 34.11/33.91 f1(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f3(rnd1, 1, I212, I213, I214, 0, I216, rnd8, I218, I219, rnd11, I221, I222, rnd14, I224) [rnd14 = rnd11 /\ rnd11 = rnd8 /\ rnd8 = rnd1 /\ rnd1 = rnd1 /\ 1 <= I215] 34.11/33.91 f1(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f2(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) [I230 <= 0] 34.11/33.91 34.11/36.89 EOF