129.25/127.44 YES 129.25/127.44 129.25/127.44 DP problem for innermost termination. 129.25/127.44 P = 129.25/127.44 f19#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f18#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 129.25/127.44 f18#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1#(I0, I1, I2, I3, I4, 0, I6, 0, rnd9, rnd10) [rnd9 = rnd9 /\ rnd10 = rnd10 /\ y1 = 0] 129.25/127.44 f2#(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1#(I10, I11, I12, I13, I14, 1 + I15, I16, I17, I18, I19) [1 + I15 <= I10] 129.25/127.44 f2#(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f6#(I20, I21, I22, I23, I24, I25, 0, I27, I28, I29) [I20 <= I25 /\ I30 = 0] 129.25/127.44 f5#(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3#(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 129.25/127.44 f7#(I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f6#(I41, I42, I43, I44, I45, I46, 1 + I47, I48, I49, I50) [1 + I47 <= I41] 129.25/127.44 f7#(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60) -> f10#(I51, 0, I53, I54, I55, I56, I57, I58, I59, I60) [I51 <= I57 /\ I61 = 0] 129.25/127.44 f9#(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8#(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 129.25/127.44 f11#(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81) -> f10#(I72, 1 + I73, I74, I75, I76, I77, I78, I79, I80, I81) [1 + I73 <= I72] 129.25/127.44 f11#(I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f14#(I82, I83, I84, I85, I86, I87, I88, 0, I90, I91) [I82 <= I83] 129.25/127.44 f13#(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12#(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 129.25/127.44 f15#(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14#(I102, I103, I104, I105, I106, I107, I108, 1 + I109, I110, I111) [1 + I109 <= I102] 129.25/127.44 f15#(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f17#(I112, I113, 0, I115, I116, I117, I118, I119, I120, I121) [I112 <= I119 /\ I122 = 0] 129.25/127.44 f17#(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16#(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 129.25/127.44 f16#(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f17#(I133, I134, 1 + I135, I136, I137, I138, I139, I140, I141, I142) [1 + I135 <= I133] 129.25/127.44 f16#(I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f13#(I143, I144, I145, 0, I147, I148, I149, I150, I151, I152) [I143 <= I145 /\ I153 = 0] 129.25/127.44 f14#(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15#(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 129.25/127.44 f12#(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f13#(I164, I165, I166, 1 + I167, I168, I169, I170, I171, I172, I173) [1 + I167 <= I164] 129.25/127.44 f12#(I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f9#(I174, I175, I176, I177, 0, I179, I180, I181, I182, I183) [I174 <= I177 /\ I184 = 0] 129.25/127.44 f10#(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11#(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 129.25/127.44 f8#(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204) -> f9#(I195, I196, I197, I198, 1 + I199, I200, I201, I202, I203, I204) [1 + I199 <= I195] 129.25/127.44 f8#(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214) -> f5#(I205, I206, I207, I208, I209, I210, I211, 0, I213, I214) [I205 <= I209] 129.25/127.44 f6#(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7#(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 129.25/127.44 f3#(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234) -> f5#(I225, I226, I227, I228, I229, I230, I231, 1 + I232, I233, I234) [1 + I232 <= I225] 129.25/127.44 f1#(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2#(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 129.25/127.44 R = 129.25/127.44 f19(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 129.25/127.44 f18(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, rnd9, rnd10) [rnd9 = rnd9 /\ rnd10 = rnd10 /\ y1 = 0] 129.25/127.44 f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1(I10, I11, I12, I13, I14, 1 + I15, I16, I17, I18, I19) [1 + I15 <= I10] 129.25/127.44 f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f6(I20, I21, I22, I23, I24, I25, 0, I27, I28, I29) [I20 <= I25 /\ I30 = 0] 129.25/127.44 f5(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 129.25/127.44 f7(I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f6(I41, I42, I43, I44, I45, I46, 1 + I47, I48, I49, I50) [1 + I47 <= I41] 129.25/127.44 f7(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60) -> f10(I51, 0, I53, I54, I55, I56, I57, I58, I59, I60) [I51 <= I57 /\ I61 = 0] 129.25/127.44 f9(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 129.25/127.44 f11(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81) -> f10(I72, 1 + I73, I74, I75, I76, I77, I78, I79, I80, I81) [1 + I73 <= I72] 129.25/127.44 f11(I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f14(I82, I83, I84, I85, I86, I87, I88, 0, I90, I91) [I82 <= I83] 129.25/127.44 f13(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 129.25/127.44 f15(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14(I102, I103, I104, I105, I106, I107, I108, 1 + I109, I110, I111) [1 + I109 <= I102] 129.25/127.44 f15(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f17(I112, I113, 0, I115, I116, I117, I118, I119, I120, I121) [I112 <= I119 /\ I122 = 0] 129.25/127.44 f17(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 129.25/127.44 f16(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f17(I133, I134, 1 + I135, I136, I137, I138, I139, I140, I141, I142) [1 + I135 <= I133] 129.25/127.44 f16(I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f13(I143, I144, I145, 0, I147, I148, I149, I150, I151, I152) [I143 <= I145 /\ I153 = 0] 129.25/127.44 f14(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 129.25/127.44 f12(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f13(I164, I165, I166, 1 + I167, I168, I169, I170, I171, I172, I173) [1 + I167 <= I164] 129.25/127.44 f12(I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f9(I174, I175, I176, I177, 0, I179, I180, I181, I182, I183) [I174 <= I177 /\ I184 = 0] 129.25/127.44 f10(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 129.25/127.44 f8(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204) -> f9(I195, I196, I197, I198, 1 + I199, I200, I201, I202, I203, I204) [1 + I199 <= I195] 129.25/127.44 f8(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214) -> f5(I205, I206, I207, I208, I209, I210, I211, 0, I213, I214) [I205 <= I209] 129.25/127.44 f6(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 129.25/127.44 f3(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234) -> f5(I225, I226, I227, I228, I229, I230, I231, 1 + I232, I233, I234) [1 + I232 <= I225] 129.25/127.44 f3(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) -> f4(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) [I235 <= I242] 129.25/127.44 f1(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 129.25/127.44 129.25/127.44 The dependency graph for this problem is: 129.25/127.44 0 -> 1 129.25/127.44 1 -> 24 129.25/127.44 2 -> 24 129.25/127.44 3 -> 22 129.25/127.44 4 -> 23 129.25/127.44 5 -> 22 129.25/127.44 6 -> 19 129.25/127.44 7 -> 20, 21 129.25/127.44 8 -> 19 129.25/127.44 9 -> 16 129.25/127.44 10 -> 17, 18 129.25/127.44 11 -> 16 129.25/127.44 12 -> 13 129.25/127.44 13 -> 14, 15 129.25/127.44 14 -> 13 129.25/127.44 15 -> 10 129.25/127.44 16 -> 11, 12 129.25/127.44 17 -> 10 129.25/127.44 18 -> 7 129.25/127.44 19 -> 8, 9 129.25/127.44 20 -> 7 129.25/127.44 21 -> 4 129.25/127.44 22 -> 5, 6 129.25/127.44 23 -> 4 129.25/127.44 24 -> 2, 3 129.25/127.44 Where: 129.25/127.44 0) f19#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f18#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 129.25/127.44 1) f18#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1#(I0, I1, I2, I3, I4, 0, I6, 0, rnd9, rnd10) [rnd9 = rnd9 /\ rnd10 = rnd10 /\ y1 = 0] 129.25/127.44 2) f2#(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1#(I10, I11, I12, I13, I14, 1 + I15, I16, I17, I18, I19) [1 + I15 <= I10] 129.25/127.44 3) f2#(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f6#(I20, I21, I22, I23, I24, I25, 0, I27, I28, I29) [I20 <= I25 /\ I30 = 0] 129.25/127.44 4) f5#(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3#(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 129.25/127.44 5) f7#(I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f6#(I41, I42, I43, I44, I45, I46, 1 + I47, I48, I49, I50) [1 + I47 <= I41] 129.25/127.44 6) f7#(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60) -> f10#(I51, 0, I53, I54, I55, I56, I57, I58, I59, I60) [I51 <= I57 /\ I61 = 0] 129.25/127.44 7) f9#(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8#(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 129.25/127.44 8) f11#(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81) -> f10#(I72, 1 + I73, I74, I75, I76, I77, I78, I79, I80, I81) [1 + I73 <= I72] 129.25/127.44 9) f11#(I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f14#(I82, I83, I84, I85, I86, I87, I88, 0, I90, I91) [I82 <= I83] 129.25/127.44 10) f13#(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12#(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 129.25/127.44 11) f15#(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14#(I102, I103, I104, I105, I106, I107, I108, 1 + I109, I110, I111) [1 + I109 <= I102] 129.25/127.44 12) f15#(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f17#(I112, I113, 0, I115, I116, I117, I118, I119, I120, I121) [I112 <= I119 /\ I122 = 0] 129.25/127.44 13) f17#(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16#(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 129.25/127.44 14) f16#(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f17#(I133, I134, 1 + I135, I136, I137, I138, I139, I140, I141, I142) [1 + I135 <= I133] 129.25/127.44 15) f16#(I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f13#(I143, I144, I145, 0, I147, I148, I149, I150, I151, I152) [I143 <= I145 /\ I153 = 0] 129.25/127.44 16) f14#(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15#(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 129.25/127.44 17) f12#(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f13#(I164, I165, I166, 1 + I167, I168, I169, I170, I171, I172, I173) [1 + I167 <= I164] 129.25/127.44 18) f12#(I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f9#(I174, I175, I176, I177, 0, I179, I180, I181, I182, I183) [I174 <= I177 /\ I184 = 0] 129.25/127.44 19) f10#(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11#(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 129.25/127.44 20) f8#(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204) -> f9#(I195, I196, I197, I198, 1 + I199, I200, I201, I202, I203, I204) [1 + I199 <= I195] 129.25/127.44 21) f8#(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214) -> f5#(I205, I206, I207, I208, I209, I210, I211, 0, I213, I214) [I205 <= I209] 129.25/127.44 22) f6#(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7#(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 129.25/127.44 23) f3#(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234) -> f5#(I225, I226, I227, I228, I229, I230, I231, 1 + I232, I233, I234) [1 + I232 <= I225] 129.25/127.44 24) f1#(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2#(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 129.25/127.44 129.25/127.44 We have the following SCCs. 129.25/127.44 { 2, 24 } 129.25/127.44 { 5, 22 } 129.25/127.44 { 8, 19 } 129.25/127.44 { 11, 16 } 129.25/127.44 { 13, 14 } 129.25/127.44 { 10, 17 } 129.25/127.44 { 7, 20 } 129.25/127.44 { 4, 23 } 129.25/127.44 129.25/127.44 DP problem for innermost termination. 129.25/127.44 P = 129.25/127.44 f5#(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3#(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 129.25/127.44 f3#(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234) -> f5#(I225, I226, I227, I228, I229, I230, I231, 1 + I232, I233, I234) [1 + I232 <= I225] 129.25/127.44 R = 129.25/127.44 f19(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 129.25/127.44 f18(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, rnd9, rnd10) [rnd9 = rnd9 /\ rnd10 = rnd10 /\ y1 = 0] 129.25/127.44 f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1(I10, I11, I12, I13, I14, 1 + I15, I16, I17, I18, I19) [1 + I15 <= I10] 129.25/127.44 f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f6(I20, I21, I22, I23, I24, I25, 0, I27, I28, I29) [I20 <= I25 /\ I30 = 0] 129.25/127.44 f5(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 129.25/127.44 f7(I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f6(I41, I42, I43, I44, I45, I46, 1 + I47, I48, I49, I50) [1 + I47 <= I41] 129.25/127.44 f7(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60) -> f10(I51, 0, I53, I54, I55, I56, I57, I58, I59, I60) [I51 <= I57 /\ I61 = 0] 129.25/127.44 f9(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 129.25/127.44 f11(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81) -> f10(I72, 1 + I73, I74, I75, I76, I77, I78, I79, I80, I81) [1 + I73 <= I72] 129.25/127.44 f11(I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f14(I82, I83, I84, I85, I86, I87, I88, 0, I90, I91) [I82 <= I83] 129.25/127.44 f13(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 129.25/127.44 f15(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14(I102, I103, I104, I105, I106, I107, I108, 1 + I109, I110, I111) [1 + I109 <= I102] 129.25/127.44 f15(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f17(I112, I113, 0, I115, I116, I117, I118, I119, I120, I121) [I112 <= I119 /\ I122 = 0] 129.25/127.44 f17(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 129.25/127.44 f16(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f17(I133, I134, 1 + I135, I136, I137, I138, I139, I140, I141, I142) [1 + I135 <= I133] 129.25/127.44 f16(I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f13(I143, I144, I145, 0, I147, I148, I149, I150, I151, I152) [I143 <= I145 /\ I153 = 0] 129.25/127.44 f14(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 129.25/127.44 f12(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f13(I164, I165, I166, 1 + I167, I168, I169, I170, I171, I172, I173) [1 + I167 <= I164] 129.25/127.44 f12(I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f9(I174, I175, I176, I177, 0, I179, I180, I181, I182, I183) [I174 <= I177 /\ I184 = 0] 129.25/127.44 f10(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 129.25/127.44 f8(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204) -> f9(I195, I196, I197, I198, 1 + I199, I200, I201, I202, I203, I204) [1 + I199 <= I195] 129.25/127.44 f8(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214) -> f5(I205, I206, I207, I208, I209, I210, I211, 0, I213, I214) [I205 <= I209] 129.25/127.44 f6(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 129.25/127.44 f3(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234) -> f5(I225, I226, I227, I228, I229, I230, I231, 1 + I232, I233, I234) [1 + I232 <= I225] 129.25/127.44 f3(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) -> f4(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) [I235 <= I242] 129.25/127.44 f1(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 129.25/127.44 129.25/127.44 We use the reverse value criterion with the projection function NU: 129.25/127.44 NU[f3#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10)] = z1 + -1 * (1 + z8) 129.25/127.44 NU[f5#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10)] = z1 + -1 * (1 + z8) 129.25/127.44 129.25/127.44 This gives the following inequalities: 129.25/127.44 ==> I31 + -1 * (1 + I38) >= I31 + -1 * (1 + I38) 129.25/127.44 1 + I232 <= I225 ==> I225 + -1 * (1 + I232) > I225 + -1 * (1 + (1 + I232)) with I225 + -1 * (1 + I232) >= 0 129.25/127.44 129.25/127.44 We remove all the strictly oriented dependency pairs. 129.25/127.44 129.25/127.44 DP problem for innermost termination. 129.25/127.44 P = 129.25/127.44 f5#(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3#(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 129.25/127.44 R = 129.25/127.44 f19(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 129.25/127.44 f18(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, rnd9, rnd10) [rnd9 = rnd9 /\ rnd10 = rnd10 /\ y1 = 0] 129.25/127.44 f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1(I10, I11, I12, I13, I14, 1 + I15, I16, I17, I18, I19) [1 + I15 <= I10] 129.25/127.44 f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f6(I20, I21, I22, I23, I24, I25, 0, I27, I28, I29) [I20 <= I25 /\ I30 = 0] 129.25/127.44 f5(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 129.25/127.44 f7(I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f6(I41, I42, I43, I44, I45, I46, 1 + I47, I48, I49, I50) [1 + I47 <= I41] 129.25/127.44 f7(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60) -> f10(I51, 0, I53, I54, I55, I56, I57, I58, I59, I60) [I51 <= I57 /\ I61 = 0] 129.25/127.44 f9(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 129.25/127.44 f11(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81) -> f10(I72, 1 + I73, I74, I75, I76, I77, I78, I79, I80, I81) [1 + I73 <= I72] 129.25/127.44 f11(I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f14(I82, I83, I84, I85, I86, I87, I88, 0, I90, I91) [I82 <= I83] 129.25/127.44 f13(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 129.25/127.44 f15(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14(I102, I103, I104, I105, I106, I107, I108, 1 + I109, I110, I111) [1 + I109 <= I102] 129.25/127.44 f15(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f17(I112, I113, 0, I115, I116, I117, I118, I119, I120, I121) [I112 <= I119 /\ I122 = 0] 129.25/127.44 f17(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 129.25/127.44 f16(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f17(I133, I134, 1 + I135, I136, I137, I138, I139, I140, I141, I142) [1 + I135 <= I133] 129.25/127.44 f16(I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f13(I143, I144, I145, 0, I147, I148, I149, I150, I151, I152) [I143 <= I145 /\ I153 = 0] 129.25/127.44 f14(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 129.25/127.44 f12(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f13(I164, I165, I166, 1 + I167, I168, I169, I170, I171, I172, I173) [1 + I167 <= I164] 129.25/127.44 f12(I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f9(I174, I175, I176, I177, 0, I179, I180, I181, I182, I183) [I174 <= I177 /\ I184 = 0] 129.25/127.44 f10(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 129.25/127.44 f8(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204) -> f9(I195, I196, I197, I198, 1 + I199, I200, I201, I202, I203, I204) [1 + I199 <= I195] 129.25/127.44 f8(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214) -> f5(I205, I206, I207, I208, I209, I210, I211, 0, I213, I214) [I205 <= I209] 129.25/127.44 f6(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 129.25/127.44 f3(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234) -> f5(I225, I226, I227, I228, I229, I230, I231, 1 + I232, I233, I234) [1 + I232 <= I225] 129.25/127.44 f3(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) -> f4(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) [I235 <= I242] 129.25/127.44 f1(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 129.25/127.44 129.25/127.44 The dependency graph for this problem is: 129.25/127.44 4 -> 129.25/127.44 Where: 129.25/127.44 4) f5#(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3#(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 129.25/127.44 129.25/127.44 We have the following SCCs. 129.25/127.44 129.25/127.44 129.25/127.44 DP problem for innermost termination. 129.25/127.44 P = 129.25/127.44 f9#(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8#(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 129.25/127.44 f8#(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204) -> f9#(I195, I196, I197, I198, 1 + I199, I200, I201, I202, I203, I204) [1 + I199 <= I195] 129.25/127.44 R = 129.25/127.44 f19(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 129.25/127.44 f18(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, rnd9, rnd10) [rnd9 = rnd9 /\ rnd10 = rnd10 /\ y1 = 0] 129.25/127.44 f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1(I10, I11, I12, I13, I14, 1 + I15, I16, I17, I18, I19) [1 + I15 <= I10] 129.25/127.44 f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f6(I20, I21, I22, I23, I24, I25, 0, I27, I28, I29) [I20 <= I25 /\ I30 = 0] 129.25/127.44 f5(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 129.25/127.44 f7(I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f6(I41, I42, I43, I44, I45, I46, 1 + I47, I48, I49, I50) [1 + I47 <= I41] 129.25/127.44 f7(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60) -> f10(I51, 0, I53, I54, I55, I56, I57, I58, I59, I60) [I51 <= I57 /\ I61 = 0] 129.25/127.44 f9(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 129.25/127.44 f11(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81) -> f10(I72, 1 + I73, I74, I75, I76, I77, I78, I79, I80, I81) [1 + I73 <= I72] 129.25/127.44 f11(I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f14(I82, I83, I84, I85, I86, I87, I88, 0, I90, I91) [I82 <= I83] 129.25/127.44 f13(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 129.25/127.44 f15(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14(I102, I103, I104, I105, I106, I107, I108, 1 + I109, I110, I111) [1 + I109 <= I102] 129.25/127.44 f15(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f17(I112, I113, 0, I115, I116, I117, I118, I119, I120, I121) [I112 <= I119 /\ I122 = 0] 129.25/127.44 f17(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 129.25/127.44 f16(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f17(I133, I134, 1 + I135, I136, I137, I138, I139, I140, I141, I142) [1 + I135 <= I133] 129.25/127.44 f16(I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f13(I143, I144, I145, 0, I147, I148, I149, I150, I151, I152) [I143 <= I145 /\ I153 = 0] 129.25/127.44 f14(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 129.25/127.44 f12(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f13(I164, I165, I166, 1 + I167, I168, I169, I170, I171, I172, I173) [1 + I167 <= I164] 129.25/127.44 f12(I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f9(I174, I175, I176, I177, 0, I179, I180, I181, I182, I183) [I174 <= I177 /\ I184 = 0] 129.25/127.44 f10(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 129.25/127.44 f8(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204) -> f9(I195, I196, I197, I198, 1 + I199, I200, I201, I202, I203, I204) [1 + I199 <= I195] 129.25/127.44 f8(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214) -> f5(I205, I206, I207, I208, I209, I210, I211, 0, I213, I214) [I205 <= I209] 129.25/127.44 f6(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 129.25/127.44 f3(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234) -> f5(I225, I226, I227, I228, I229, I230, I231, 1 + I232, I233, I234) [1 + I232 <= I225] 129.25/127.44 f3(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) -> f4(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) [I235 <= I242] 129.25/127.44 f1(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 129.25/127.44 129.25/127.44 We use the reverse value criterion with the projection function NU: 129.25/127.44 NU[f8#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10)] = z1 + -1 * (1 + z5) 129.25/127.44 NU[f9#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10)] = z1 + -1 * (1 + z5) 129.25/127.44 129.25/127.44 This gives the following inequalities: 129.25/127.44 ==> I62 + -1 * (1 + I66) >= I62 + -1 * (1 + I66) 129.25/127.44 1 + I199 <= I195 ==> I195 + -1 * (1 + I199) > I195 + -1 * (1 + (1 + I199)) with I195 + -1 * (1 + I199) >= 0 129.25/127.44 129.25/127.44 We remove all the strictly oriented dependency pairs. 129.25/127.44 129.25/127.44 DP problem for innermost termination. 129.25/127.44 P = 129.25/127.44 f9#(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8#(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 129.25/127.44 R = 129.25/127.44 f19(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 129.25/127.44 f18(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, rnd9, rnd10) [rnd9 = rnd9 /\ rnd10 = rnd10 /\ y1 = 0] 129.25/127.44 f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1(I10, I11, I12, I13, I14, 1 + I15, I16, I17, I18, I19) [1 + I15 <= I10] 129.25/127.44 f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f6(I20, I21, I22, I23, I24, I25, 0, I27, I28, I29) [I20 <= I25 /\ I30 = 0] 129.25/127.44 f5(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 129.25/127.44 f7(I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f6(I41, I42, I43, I44, I45, I46, 1 + I47, I48, I49, I50) [1 + I47 <= I41] 129.25/127.44 f7(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60) -> f10(I51, 0, I53, I54, I55, I56, I57, I58, I59, I60) [I51 <= I57 /\ I61 = 0] 129.25/127.44 f9(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 129.25/127.44 f11(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81) -> f10(I72, 1 + I73, I74, I75, I76, I77, I78, I79, I80, I81) [1 + I73 <= I72] 129.25/127.44 f11(I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f14(I82, I83, I84, I85, I86, I87, I88, 0, I90, I91) [I82 <= I83] 129.25/127.44 f13(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 129.25/127.44 f15(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14(I102, I103, I104, I105, I106, I107, I108, 1 + I109, I110, I111) [1 + I109 <= I102] 129.25/127.44 f15(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f17(I112, I113, 0, I115, I116, I117, I118, I119, I120, I121) [I112 <= I119 /\ I122 = 0] 129.25/127.44 f17(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 129.25/127.44 f16(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f17(I133, I134, 1 + I135, I136, I137, I138, I139, I140, I141, I142) [1 + I135 <= I133] 129.25/127.44 f16(I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f13(I143, I144, I145, 0, I147, I148, I149, I150, I151, I152) [I143 <= I145 /\ I153 = 0] 129.25/127.44 f14(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 129.25/127.44 f12(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f13(I164, I165, I166, 1 + I167, I168, I169, I170, I171, I172, I173) [1 + I167 <= I164] 129.25/127.44 f12(I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f9(I174, I175, I176, I177, 0, I179, I180, I181, I182, I183) [I174 <= I177 /\ I184 = 0] 129.25/127.44 f10(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 129.25/127.44 f8(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204) -> f9(I195, I196, I197, I198, 1 + I199, I200, I201, I202, I203, I204) [1 + I199 <= I195] 129.25/127.44 f8(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214) -> f5(I205, I206, I207, I208, I209, I210, I211, 0, I213, I214) [I205 <= I209] 129.25/127.44 f6(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 129.25/127.44 f3(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234) -> f5(I225, I226, I227, I228, I229, I230, I231, 1 + I232, I233, I234) [1 + I232 <= I225] 129.25/127.44 f3(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) -> f4(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) [I235 <= I242] 129.25/127.44 f1(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 129.25/127.44 129.25/127.44 The dependency graph for this problem is: 129.25/127.44 7 -> 129.25/127.44 Where: 129.25/127.44 7) f9#(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8#(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 129.25/127.44 129.25/127.44 We have the following SCCs. 129.25/127.44 129.25/127.44 129.25/127.44 DP problem for innermost termination. 129.25/127.44 P = 129.25/127.44 f13#(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12#(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 129.25/127.44 f12#(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f13#(I164, I165, I166, 1 + I167, I168, I169, I170, I171, I172, I173) [1 + I167 <= I164] 129.25/127.44 R = 129.25/127.44 f19(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 129.25/127.44 f18(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, rnd9, rnd10) [rnd9 = rnd9 /\ rnd10 = rnd10 /\ y1 = 0] 129.25/127.44 f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1(I10, I11, I12, I13, I14, 1 + I15, I16, I17, I18, I19) [1 + I15 <= I10] 129.25/127.44 f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f6(I20, I21, I22, I23, I24, I25, 0, I27, I28, I29) [I20 <= I25 /\ I30 = 0] 129.25/127.44 f5(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 129.25/127.44 f7(I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f6(I41, I42, I43, I44, I45, I46, 1 + I47, I48, I49, I50) [1 + I47 <= I41] 129.25/127.44 f7(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60) -> f10(I51, 0, I53, I54, I55, I56, I57, I58, I59, I60) [I51 <= I57 /\ I61 = 0] 129.25/127.44 f9(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 129.25/127.44 f11(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81) -> f10(I72, 1 + I73, I74, I75, I76, I77, I78, I79, I80, I81) [1 + I73 <= I72] 129.25/127.44 f11(I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f14(I82, I83, I84, I85, I86, I87, I88, 0, I90, I91) [I82 <= I83] 129.25/127.44 f13(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 129.25/127.44 f15(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14(I102, I103, I104, I105, I106, I107, I108, 1 + I109, I110, I111) [1 + I109 <= I102] 129.25/127.44 f15(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f17(I112, I113, 0, I115, I116, I117, I118, I119, I120, I121) [I112 <= I119 /\ I122 = 0] 129.25/127.44 f17(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 129.25/127.44 f16(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f17(I133, I134, 1 + I135, I136, I137, I138, I139, I140, I141, I142) [1 + I135 <= I133] 129.25/127.44 f16(I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f13(I143, I144, I145, 0, I147, I148, I149, I150, I151, I152) [I143 <= I145 /\ I153 = 0] 129.25/127.44 f14(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 129.25/127.44 f12(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f13(I164, I165, I166, 1 + I167, I168, I169, I170, I171, I172, I173) [1 + I167 <= I164] 129.25/127.44 f12(I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f9(I174, I175, I176, I177, 0, I179, I180, I181, I182, I183) [I174 <= I177 /\ I184 = 0] 129.25/127.44 f10(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 129.25/127.44 f8(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204) -> f9(I195, I196, I197, I198, 1 + I199, I200, I201, I202, I203, I204) [1 + I199 <= I195] 129.25/127.44 f8(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214) -> f5(I205, I206, I207, I208, I209, I210, I211, 0, I213, I214) [I205 <= I209] 129.25/127.44 f6(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 129.25/127.44 f3(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234) -> f5(I225, I226, I227, I228, I229, I230, I231, 1 + I232, I233, I234) [1 + I232 <= I225] 129.25/127.44 f3(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) -> f4(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) [I235 <= I242] 129.25/127.44 f1(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 129.25/127.44 129.25/127.44 We use the reverse value criterion with the projection function NU: 129.25/127.44 NU[f12#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10)] = z1 + -1 * (1 + z4) 129.25/127.44 NU[f13#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10)] = z1 + -1 * (1 + z4) 129.25/127.44 129.25/127.44 This gives the following inequalities: 129.25/127.44 ==> I92 + -1 * (1 + I95) >= I92 + -1 * (1 + I95) 129.25/127.44 1 + I167 <= I164 ==> I164 + -1 * (1 + I167) > I164 + -1 * (1 + (1 + I167)) with I164 + -1 * (1 + I167) >= 0 129.25/127.44 129.25/127.44 We remove all the strictly oriented dependency pairs. 129.25/127.44 129.25/127.44 DP problem for innermost termination. 129.25/127.44 P = 129.25/127.44 f13#(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12#(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 129.25/127.44 R = 129.25/127.44 f19(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 129.25/127.44 f18(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, rnd9, rnd10) [rnd9 = rnd9 /\ rnd10 = rnd10 /\ y1 = 0] 129.25/127.44 f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1(I10, I11, I12, I13, I14, 1 + I15, I16, I17, I18, I19) [1 + I15 <= I10] 129.25/127.44 f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f6(I20, I21, I22, I23, I24, I25, 0, I27, I28, I29) [I20 <= I25 /\ I30 = 0] 129.25/127.44 f5(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 129.25/127.44 f7(I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f6(I41, I42, I43, I44, I45, I46, 1 + I47, I48, I49, I50) [1 + I47 <= I41] 129.25/127.44 f7(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60) -> f10(I51, 0, I53, I54, I55, I56, I57, I58, I59, I60) [I51 <= I57 /\ I61 = 0] 129.25/127.44 f9(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 129.25/127.44 f11(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81) -> f10(I72, 1 + I73, I74, I75, I76, I77, I78, I79, I80, I81) [1 + I73 <= I72] 129.25/127.44 f11(I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f14(I82, I83, I84, I85, I86, I87, I88, 0, I90, I91) [I82 <= I83] 129.25/127.44 f13(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 129.25/127.44 f15(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14(I102, I103, I104, I105, I106, I107, I108, 1 + I109, I110, I111) [1 + I109 <= I102] 129.25/127.44 f15(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f17(I112, I113, 0, I115, I116, I117, I118, I119, I120, I121) [I112 <= I119 /\ I122 = 0] 129.25/127.44 f17(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 129.25/127.44 f16(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f17(I133, I134, 1 + I135, I136, I137, I138, I139, I140, I141, I142) [1 + I135 <= I133] 129.25/127.44 f16(I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f13(I143, I144, I145, 0, I147, I148, I149, I150, I151, I152) [I143 <= I145 /\ I153 = 0] 129.25/127.44 f14(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 129.25/127.44 f12(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f13(I164, I165, I166, 1 + I167, I168, I169, I170, I171, I172, I173) [1 + I167 <= I164] 129.25/127.44 f12(I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f9(I174, I175, I176, I177, 0, I179, I180, I181, I182, I183) [I174 <= I177 /\ I184 = 0] 129.25/127.44 f10(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 129.25/127.44 f8(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204) -> f9(I195, I196, I197, I198, 1 + I199, I200, I201, I202, I203, I204) [1 + I199 <= I195] 129.25/127.44 f8(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214) -> f5(I205, I206, I207, I208, I209, I210, I211, 0, I213, I214) [I205 <= I209] 129.25/127.44 f6(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 129.25/127.44 f3(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234) -> f5(I225, I226, I227, I228, I229, I230, I231, 1 + I232, I233, I234) [1 + I232 <= I225] 129.25/127.44 f3(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) -> f4(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) [I235 <= I242] 129.25/127.44 f1(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 129.25/127.44 129.25/127.44 The dependency graph for this problem is: 129.25/127.44 10 -> 129.25/127.44 Where: 129.25/127.44 10) f13#(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12#(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 129.25/127.44 129.25/127.44 We have the following SCCs. 129.25/127.44 129.25/127.44 129.25/127.44 DP problem for innermost termination. 129.25/127.44 P = 129.25/127.44 f17#(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16#(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 129.25/127.44 f16#(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f17#(I133, I134, 1 + I135, I136, I137, I138, I139, I140, I141, I142) [1 + I135 <= I133] 129.25/127.44 R = 129.25/127.44 f19(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 129.25/127.44 f18(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, rnd9, rnd10) [rnd9 = rnd9 /\ rnd10 = rnd10 /\ y1 = 0] 129.25/127.44 f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1(I10, I11, I12, I13, I14, 1 + I15, I16, I17, I18, I19) [1 + I15 <= I10] 129.25/127.44 f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f6(I20, I21, I22, I23, I24, I25, 0, I27, I28, I29) [I20 <= I25 /\ I30 = 0] 129.25/127.44 f5(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 129.25/127.44 f7(I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f6(I41, I42, I43, I44, I45, I46, 1 + I47, I48, I49, I50) [1 + I47 <= I41] 129.25/127.44 f7(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60) -> f10(I51, 0, I53, I54, I55, I56, I57, I58, I59, I60) [I51 <= I57 /\ I61 = 0] 129.25/127.44 f9(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 129.25/127.44 f11(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81) -> f10(I72, 1 + I73, I74, I75, I76, I77, I78, I79, I80, I81) [1 + I73 <= I72] 129.25/127.44 f11(I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f14(I82, I83, I84, I85, I86, I87, I88, 0, I90, I91) [I82 <= I83] 129.25/127.44 f13(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 129.25/127.44 f15(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14(I102, I103, I104, I105, I106, I107, I108, 1 + I109, I110, I111) [1 + I109 <= I102] 129.25/127.44 f15(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f17(I112, I113, 0, I115, I116, I117, I118, I119, I120, I121) [I112 <= I119 /\ I122 = 0] 129.25/127.44 f17(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 129.25/127.44 f16(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f17(I133, I134, 1 + I135, I136, I137, I138, I139, I140, I141, I142) [1 + I135 <= I133] 129.25/127.44 f16(I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f13(I143, I144, I145, 0, I147, I148, I149, I150, I151, I152) [I143 <= I145 /\ I153 = 0] 129.25/127.44 f14(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 129.25/127.44 f12(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f13(I164, I165, I166, 1 + I167, I168, I169, I170, I171, I172, I173) [1 + I167 <= I164] 129.25/127.44 f12(I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f9(I174, I175, I176, I177, 0, I179, I180, I181, I182, I183) [I174 <= I177 /\ I184 = 0] 129.25/127.44 f10(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 129.25/127.44 f8(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204) -> f9(I195, I196, I197, I198, 1 + I199, I200, I201, I202, I203, I204) [1 + I199 <= I195] 129.25/127.44 f8(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214) -> f5(I205, I206, I207, I208, I209, I210, I211, 0, I213, I214) [I205 <= I209] 129.25/127.44 f6(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 129.25/127.44 f3(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234) -> f5(I225, I226, I227, I228, I229, I230, I231, 1 + I232, I233, I234) [1 + I232 <= I225] 129.25/127.44 f3(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) -> f4(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) [I235 <= I242] 129.25/127.44 f1(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 129.25/127.44 129.25/127.44 We use the reverse value criterion with the projection function NU: 129.25/127.44 NU[f16#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10)] = z1 + -1 * (1 + z3) 129.25/127.44 NU[f17#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10)] = z1 + -1 * (1 + z3) 129.25/127.44 129.25/127.44 This gives the following inequalities: 129.25/127.44 ==> I123 + -1 * (1 + I125) >= I123 + -1 * (1 + I125) 129.25/127.44 1 + I135 <= I133 ==> I133 + -1 * (1 + I135) > I133 + -1 * (1 + (1 + I135)) with I133 + -1 * (1 + I135) >= 0 129.25/127.44 129.25/127.44 We remove all the strictly oriented dependency pairs. 129.25/127.44 129.25/127.44 DP problem for innermost termination. 129.25/127.44 P = 129.25/127.44 f17#(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16#(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 129.25/127.44 R = 129.25/127.44 f19(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 129.25/127.44 f18(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, rnd9, rnd10) [rnd9 = rnd9 /\ rnd10 = rnd10 /\ y1 = 0] 129.25/127.44 f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1(I10, I11, I12, I13, I14, 1 + I15, I16, I17, I18, I19) [1 + I15 <= I10] 129.25/127.44 f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f6(I20, I21, I22, I23, I24, I25, 0, I27, I28, I29) [I20 <= I25 /\ I30 = 0] 129.25/127.44 f5(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 129.25/127.44 f7(I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f6(I41, I42, I43, I44, I45, I46, 1 + I47, I48, I49, I50) [1 + I47 <= I41] 129.25/127.44 f7(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60) -> f10(I51, 0, I53, I54, I55, I56, I57, I58, I59, I60) [I51 <= I57 /\ I61 = 0] 129.25/127.44 f9(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 129.25/127.44 f11(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81) -> f10(I72, 1 + I73, I74, I75, I76, I77, I78, I79, I80, I81) [1 + I73 <= I72] 129.25/127.44 f11(I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f14(I82, I83, I84, I85, I86, I87, I88, 0, I90, I91) [I82 <= I83] 129.25/127.44 f13(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 129.25/127.44 f15(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14(I102, I103, I104, I105, I106, I107, I108, 1 + I109, I110, I111) [1 + I109 <= I102] 129.25/127.44 f15(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f17(I112, I113, 0, I115, I116, I117, I118, I119, I120, I121) [I112 <= I119 /\ I122 = 0] 129.25/127.44 f17(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 129.25/127.44 f16(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f17(I133, I134, 1 + I135, I136, I137, I138, I139, I140, I141, I142) [1 + I135 <= I133] 129.25/127.44 f16(I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f13(I143, I144, I145, 0, I147, I148, I149, I150, I151, I152) [I143 <= I145 /\ I153 = 0] 129.25/127.44 f14(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 129.25/127.44 f12(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f13(I164, I165, I166, 1 + I167, I168, I169, I170, I171, I172, I173) [1 + I167 <= I164] 129.25/127.44 f12(I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f9(I174, I175, I176, I177, 0, I179, I180, I181, I182, I183) [I174 <= I177 /\ I184 = 0] 129.25/127.44 f10(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 129.25/127.44 f8(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204) -> f9(I195, I196, I197, I198, 1 + I199, I200, I201, I202, I203, I204) [1 + I199 <= I195] 129.25/127.44 f8(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214) -> f5(I205, I206, I207, I208, I209, I210, I211, 0, I213, I214) [I205 <= I209] 129.25/127.44 f6(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 129.25/127.44 f3(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234) -> f5(I225, I226, I227, I228, I229, I230, I231, 1 + I232, I233, I234) [1 + I232 <= I225] 129.25/127.44 f3(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) -> f4(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) [I235 <= I242] 129.25/127.44 f1(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 129.25/127.44 129.25/127.44 The dependency graph for this problem is: 129.25/127.44 13 -> 129.25/127.44 Where: 129.25/127.44 13) f17#(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16#(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 129.25/127.44 129.25/127.44 We have the following SCCs. 129.25/127.44 129.25/127.44 129.25/127.44 DP problem for innermost termination. 129.25/127.44 P = 129.25/127.44 f15#(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14#(I102, I103, I104, I105, I106, I107, I108, 1 + I109, I110, I111) [1 + I109 <= I102] 129.25/127.44 f14#(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15#(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 129.25/127.44 R = 129.25/127.44 f19(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 129.25/127.44 f18(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, rnd9, rnd10) [rnd9 = rnd9 /\ rnd10 = rnd10 /\ y1 = 0] 129.25/127.44 f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1(I10, I11, I12, I13, I14, 1 + I15, I16, I17, I18, I19) [1 + I15 <= I10] 129.25/127.44 f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f6(I20, I21, I22, I23, I24, I25, 0, I27, I28, I29) [I20 <= I25 /\ I30 = 0] 129.25/127.44 f5(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 129.25/127.44 f7(I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f6(I41, I42, I43, I44, I45, I46, 1 + I47, I48, I49, I50) [1 + I47 <= I41] 129.25/127.44 f7(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60) -> f10(I51, 0, I53, I54, I55, I56, I57, I58, I59, I60) [I51 <= I57 /\ I61 = 0] 129.25/127.44 f9(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 129.25/127.44 f11(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81) -> f10(I72, 1 + I73, I74, I75, I76, I77, I78, I79, I80, I81) [1 + I73 <= I72] 129.25/127.44 f11(I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f14(I82, I83, I84, I85, I86, I87, I88, 0, I90, I91) [I82 <= I83] 129.25/127.44 f13(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 129.25/127.44 f15(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14(I102, I103, I104, I105, I106, I107, I108, 1 + I109, I110, I111) [1 + I109 <= I102] 129.25/127.44 f15(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f17(I112, I113, 0, I115, I116, I117, I118, I119, I120, I121) [I112 <= I119 /\ I122 = 0] 129.25/127.44 f17(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 129.25/127.44 f16(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f17(I133, I134, 1 + I135, I136, I137, I138, I139, I140, I141, I142) [1 + I135 <= I133] 129.25/127.44 f16(I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f13(I143, I144, I145, 0, I147, I148, I149, I150, I151, I152) [I143 <= I145 /\ I153 = 0] 129.25/127.44 f14(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 129.25/127.44 f12(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f13(I164, I165, I166, 1 + I167, I168, I169, I170, I171, I172, I173) [1 + I167 <= I164] 129.25/127.44 f12(I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f9(I174, I175, I176, I177, 0, I179, I180, I181, I182, I183) [I174 <= I177 /\ I184 = 0] 129.25/127.44 f10(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 129.25/127.44 f8(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204) -> f9(I195, I196, I197, I198, 1 + I199, I200, I201, I202, I203, I204) [1 + I199 <= I195] 129.25/127.44 f8(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214) -> f5(I205, I206, I207, I208, I209, I210, I211, 0, I213, I214) [I205 <= I209] 129.25/127.44 f6(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 129.25/127.44 f3(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234) -> f5(I225, I226, I227, I228, I229, I230, I231, 1 + I232, I233, I234) [1 + I232 <= I225] 129.25/127.44 f3(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) -> f4(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) [I235 <= I242] 129.25/127.44 f1(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 129.25/127.44 129.25/127.44 We use the reverse value criterion with the projection function NU: 129.25/127.44 NU[f14#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10)] = z1 + -1 * (1 + z8) 129.25/127.44 NU[f15#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10)] = z1 + -1 * (1 + z8) 129.25/127.44 129.25/127.44 This gives the following inequalities: 129.25/127.44 1 + I109 <= I102 ==> I102 + -1 * (1 + I109) > I102 + -1 * (1 + (1 + I109)) with I102 + -1 * (1 + I109) >= 0 129.25/127.44 ==> I154 + -1 * (1 + I161) >= I154 + -1 * (1 + I161) 129.25/127.44 129.25/127.44 We remove all the strictly oriented dependency pairs. 129.25/127.44 129.25/127.44 DP problem for innermost termination. 129.25/127.44 P = 129.25/127.44 f14#(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15#(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 129.25/127.44 R = 129.25/127.44 f19(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 129.25/127.44 f18(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, rnd9, rnd10) [rnd9 = rnd9 /\ rnd10 = rnd10 /\ y1 = 0] 129.25/127.44 f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1(I10, I11, I12, I13, I14, 1 + I15, I16, I17, I18, I19) [1 + I15 <= I10] 129.25/127.44 f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f6(I20, I21, I22, I23, I24, I25, 0, I27, I28, I29) [I20 <= I25 /\ I30 = 0] 129.25/127.44 f5(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 129.25/127.44 f7(I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f6(I41, I42, I43, I44, I45, I46, 1 + I47, I48, I49, I50) [1 + I47 <= I41] 129.25/127.44 f7(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60) -> f10(I51, 0, I53, I54, I55, I56, I57, I58, I59, I60) [I51 <= I57 /\ I61 = 0] 129.25/127.44 f9(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 129.25/127.44 f11(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81) -> f10(I72, 1 + I73, I74, I75, I76, I77, I78, I79, I80, I81) [1 + I73 <= I72] 129.25/127.44 f11(I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f14(I82, I83, I84, I85, I86, I87, I88, 0, I90, I91) [I82 <= I83] 129.25/127.44 f13(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 129.25/127.44 f15(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14(I102, I103, I104, I105, I106, I107, I108, 1 + I109, I110, I111) [1 + I109 <= I102] 129.25/127.44 f15(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f17(I112, I113, 0, I115, I116, I117, I118, I119, I120, I121) [I112 <= I119 /\ I122 = 0] 129.25/127.44 f17(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 129.25/127.44 f16(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f17(I133, I134, 1 + I135, I136, I137, I138, I139, I140, I141, I142) [1 + I135 <= I133] 129.25/127.44 f16(I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f13(I143, I144, I145, 0, I147, I148, I149, I150, I151, I152) [I143 <= I145 /\ I153 = 0] 129.25/127.44 f14(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 129.25/127.44 f12(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f13(I164, I165, I166, 1 + I167, I168, I169, I170, I171, I172, I173) [1 + I167 <= I164] 129.25/127.44 f12(I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f9(I174, I175, I176, I177, 0, I179, I180, I181, I182, I183) [I174 <= I177 /\ I184 = 0] 129.25/127.44 f10(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 129.25/127.44 f8(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204) -> f9(I195, I196, I197, I198, 1 + I199, I200, I201, I202, I203, I204) [1 + I199 <= I195] 129.25/127.44 f8(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214) -> f5(I205, I206, I207, I208, I209, I210, I211, 0, I213, I214) [I205 <= I209] 129.25/127.44 f6(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 129.25/127.44 f3(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234) -> f5(I225, I226, I227, I228, I229, I230, I231, 1 + I232, I233, I234) [1 + I232 <= I225] 129.25/127.44 f3(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) -> f4(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) [I235 <= I242] 129.25/127.44 f1(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 129.25/127.44 129.25/127.44 The dependency graph for this problem is: 129.25/127.44 16 -> 129.25/127.44 Where: 129.25/127.44 16) f14#(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15#(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 129.25/127.44 129.25/127.44 We have the following SCCs. 129.25/127.44 129.25/127.44 129.25/127.44 DP problem for innermost termination. 129.25/127.44 P = 129.25/127.44 f11#(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81) -> f10#(I72, 1 + I73, I74, I75, I76, I77, I78, I79, I80, I81) [1 + I73 <= I72] 129.25/127.44 f10#(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11#(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 129.25/127.44 R = 129.25/127.44 f19(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 129.25/127.44 f18(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, rnd9, rnd10) [rnd9 = rnd9 /\ rnd10 = rnd10 /\ y1 = 0] 129.25/127.44 f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1(I10, I11, I12, I13, I14, 1 + I15, I16, I17, I18, I19) [1 + I15 <= I10] 129.25/127.45 f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f6(I20, I21, I22, I23, I24, I25, 0, I27, I28, I29) [I20 <= I25 /\ I30 = 0] 129.25/127.45 f5(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 129.25/127.45 f7(I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f6(I41, I42, I43, I44, I45, I46, 1 + I47, I48, I49, I50) [1 + I47 <= I41] 129.25/127.45 f7(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60) -> f10(I51, 0, I53, I54, I55, I56, I57, I58, I59, I60) [I51 <= I57 /\ I61 = 0] 129.25/127.45 f9(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 129.25/127.45 f11(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81) -> f10(I72, 1 + I73, I74, I75, I76, I77, I78, I79, I80, I81) [1 + I73 <= I72] 129.25/127.45 f11(I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f14(I82, I83, I84, I85, I86, I87, I88, 0, I90, I91) [I82 <= I83] 129.25/127.45 f13(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 129.25/127.45 f15(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14(I102, I103, I104, I105, I106, I107, I108, 1 + I109, I110, I111) [1 + I109 <= I102] 129.25/127.45 f15(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f17(I112, I113, 0, I115, I116, I117, I118, I119, I120, I121) [I112 <= I119 /\ I122 = 0] 129.25/127.45 f17(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 129.25/127.45 f16(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f17(I133, I134, 1 + I135, I136, I137, I138, I139, I140, I141, I142) [1 + I135 <= I133] 129.25/127.45 f16(I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f13(I143, I144, I145, 0, I147, I148, I149, I150, I151, I152) [I143 <= I145 /\ I153 = 0] 129.25/127.45 f14(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 129.25/127.45 f12(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f13(I164, I165, I166, 1 + I167, I168, I169, I170, I171, I172, I173) [1 + I167 <= I164] 129.25/127.45 f12(I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f9(I174, I175, I176, I177, 0, I179, I180, I181, I182, I183) [I174 <= I177 /\ I184 = 0] 129.25/127.45 f10(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 129.25/127.45 f8(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204) -> f9(I195, I196, I197, I198, 1 + I199, I200, I201, I202, I203, I204) [1 + I199 <= I195] 129.25/127.45 f8(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214) -> f5(I205, I206, I207, I208, I209, I210, I211, 0, I213, I214) [I205 <= I209] 129.25/127.45 f6(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 129.25/127.45 f3(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234) -> f5(I225, I226, I227, I228, I229, I230, I231, 1 + I232, I233, I234) [1 + I232 <= I225] 129.25/127.45 f3(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) -> f4(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) [I235 <= I242] 129.25/127.45 f1(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 129.25/127.45 129.25/127.45 We use the reverse value criterion with the projection function NU: 129.25/127.45 NU[f10#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10)] = z1 + -1 * (1 + z2) 129.25/127.45 NU[f11#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10)] = z1 + -1 * (1 + z2) 129.25/127.45 129.25/127.45 This gives the following inequalities: 129.25/127.45 1 + I73 <= I72 ==> I72 + -1 * (1 + I73) > I72 + -1 * (1 + (1 + I73)) with I72 + -1 * (1 + I73) >= 0 129.25/127.45 ==> I185 + -1 * (1 + I186) >= I185 + -1 * (1 + I186) 129.25/127.45 129.25/127.45 We remove all the strictly oriented dependency pairs. 129.25/127.45 129.25/127.45 DP problem for innermost termination. 129.25/127.45 P = 129.25/127.45 f10#(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11#(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 129.25/127.45 R = 129.25/127.45 f19(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 129.25/127.45 f18(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, rnd9, rnd10) [rnd9 = rnd9 /\ rnd10 = rnd10 /\ y1 = 0] 129.25/127.45 f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1(I10, I11, I12, I13, I14, 1 + I15, I16, I17, I18, I19) [1 + I15 <= I10] 129.25/127.45 f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f6(I20, I21, I22, I23, I24, I25, 0, I27, I28, I29) [I20 <= I25 /\ I30 = 0] 129.25/127.45 f5(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 129.25/127.45 f7(I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f6(I41, I42, I43, I44, I45, I46, 1 + I47, I48, I49, I50) [1 + I47 <= I41] 129.25/127.45 f7(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60) -> f10(I51, 0, I53, I54, I55, I56, I57, I58, I59, I60) [I51 <= I57 /\ I61 = 0] 129.25/127.45 f9(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 129.25/127.45 f11(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81) -> f10(I72, 1 + I73, I74, I75, I76, I77, I78, I79, I80, I81) [1 + I73 <= I72] 129.25/127.45 f11(I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f14(I82, I83, I84, I85, I86, I87, I88, 0, I90, I91) [I82 <= I83] 129.25/127.45 f13(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 129.25/127.45 f15(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14(I102, I103, I104, I105, I106, I107, I108, 1 + I109, I110, I111) [1 + I109 <= I102] 129.25/127.45 f15(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f17(I112, I113, 0, I115, I116, I117, I118, I119, I120, I121) [I112 <= I119 /\ I122 = 0] 129.25/127.45 f17(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 129.25/127.45 f16(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f17(I133, I134, 1 + I135, I136, I137, I138, I139, I140, I141, I142) [1 + I135 <= I133] 129.25/127.45 f16(I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f13(I143, I144, I145, 0, I147, I148, I149, I150, I151, I152) [I143 <= I145 /\ I153 = 0] 129.25/127.45 f14(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 129.25/127.45 f12(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f13(I164, I165, I166, 1 + I167, I168, I169, I170, I171, I172, I173) [1 + I167 <= I164] 129.25/127.45 f12(I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f9(I174, I175, I176, I177, 0, I179, I180, I181, I182, I183) [I174 <= I177 /\ I184 = 0] 129.25/127.45 f10(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 129.25/127.45 f8(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204) -> f9(I195, I196, I197, I198, 1 + I199, I200, I201, I202, I203, I204) [1 + I199 <= I195] 129.25/127.45 f8(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214) -> f5(I205, I206, I207, I208, I209, I210, I211, 0, I213, I214) [I205 <= I209] 129.25/127.45 f6(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 129.25/127.45 f3(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234) -> f5(I225, I226, I227, I228, I229, I230, I231, 1 + I232, I233, I234) [1 + I232 <= I225] 129.25/127.45 f3(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) -> f4(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) [I235 <= I242] 129.25/127.45 f1(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 129.25/127.45 129.25/127.45 The dependency graph for this problem is: 129.25/127.45 19 -> 129.25/127.45 Where: 129.25/127.45 19) f10#(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11#(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 129.25/127.45 129.25/127.45 We have the following SCCs. 129.25/127.45 129.25/127.45 129.25/127.45 DP problem for innermost termination. 129.25/127.45 P = 129.25/127.45 f7#(I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f6#(I41, I42, I43, I44, I45, I46, 1 + I47, I48, I49, I50) [1 + I47 <= I41] 129.25/127.45 f6#(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7#(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 129.25/127.45 R = 129.25/127.45 f19(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 129.25/127.45 f18(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, rnd9, rnd10) [rnd9 = rnd9 /\ rnd10 = rnd10 /\ y1 = 0] 129.25/127.45 f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1(I10, I11, I12, I13, I14, 1 + I15, I16, I17, I18, I19) [1 + I15 <= I10] 129.25/127.45 f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f6(I20, I21, I22, I23, I24, I25, 0, I27, I28, I29) [I20 <= I25 /\ I30 = 0] 129.25/127.45 f5(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 129.25/127.45 f7(I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f6(I41, I42, I43, I44, I45, I46, 1 + I47, I48, I49, I50) [1 + I47 <= I41] 129.25/127.45 f7(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60) -> f10(I51, 0, I53, I54, I55, I56, I57, I58, I59, I60) [I51 <= I57 /\ I61 = 0] 129.25/127.45 f9(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 129.25/127.45 f11(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81) -> f10(I72, 1 + I73, I74, I75, I76, I77, I78, I79, I80, I81) [1 + I73 <= I72] 129.25/127.45 f11(I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f14(I82, I83, I84, I85, I86, I87, I88, 0, I90, I91) [I82 <= I83] 129.25/127.45 f13(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 129.25/127.45 f15(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14(I102, I103, I104, I105, I106, I107, I108, 1 + I109, I110, I111) [1 + I109 <= I102] 129.25/127.45 f15(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f17(I112, I113, 0, I115, I116, I117, I118, I119, I120, I121) [I112 <= I119 /\ I122 = 0] 129.25/127.45 f17(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 129.25/127.45 f16(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f17(I133, I134, 1 + I135, I136, I137, I138, I139, I140, I141, I142) [1 + I135 <= I133] 129.25/127.45 f16(I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f13(I143, I144, I145, 0, I147, I148, I149, I150, I151, I152) [I143 <= I145 /\ I153 = 0] 129.25/127.45 f14(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 129.25/127.45 f12(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f13(I164, I165, I166, 1 + I167, I168, I169, I170, I171, I172, I173) [1 + I167 <= I164] 129.25/127.45 f12(I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f9(I174, I175, I176, I177, 0, I179, I180, I181, I182, I183) [I174 <= I177 /\ I184 = 0] 129.25/127.45 f10(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 129.25/127.45 f8(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204) -> f9(I195, I196, I197, I198, 1 + I199, I200, I201, I202, I203, I204) [1 + I199 <= I195] 129.25/127.45 f8(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214) -> f5(I205, I206, I207, I208, I209, I210, I211, 0, I213, I214) [I205 <= I209] 129.25/127.45 f6(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 129.25/127.45 f3(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234) -> f5(I225, I226, I227, I228, I229, I230, I231, 1 + I232, I233, I234) [1 + I232 <= I225] 129.25/127.45 f3(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) -> f4(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) [I235 <= I242] 129.25/127.45 f1(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 129.25/127.45 129.25/127.45 We use the reverse value criterion with the projection function NU: 129.25/127.45 NU[f6#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10)] = z1 + -1 * (1 + z7) 129.25/127.45 NU[f7#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10)] = z1 + -1 * (1 + z7) 129.25/127.45 129.25/127.45 This gives the following inequalities: 129.25/127.45 1 + I47 <= I41 ==> I41 + -1 * (1 + I47) > I41 + -1 * (1 + (1 + I47)) with I41 + -1 * (1 + I47) >= 0 129.25/127.45 ==> I215 + -1 * (1 + I221) >= I215 + -1 * (1 + I221) 129.25/127.45 129.25/127.45 We remove all the strictly oriented dependency pairs. 129.25/127.45 129.25/127.45 DP problem for innermost termination. 129.25/127.45 P = 129.25/127.45 f6#(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7#(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 129.25/127.45 R = 129.25/127.45 f19(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 129.25/127.45 f18(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, rnd9, rnd10) [rnd9 = rnd9 /\ rnd10 = rnd10 /\ y1 = 0] 129.25/127.45 f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1(I10, I11, I12, I13, I14, 1 + I15, I16, I17, I18, I19) [1 + I15 <= I10] 129.25/127.45 f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f6(I20, I21, I22, I23, I24, I25, 0, I27, I28, I29) [I20 <= I25 /\ I30 = 0] 129.25/127.45 f5(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 129.25/127.45 f7(I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f6(I41, I42, I43, I44, I45, I46, 1 + I47, I48, I49, I50) [1 + I47 <= I41] 129.25/127.45 f7(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60) -> f10(I51, 0, I53, I54, I55, I56, I57, I58, I59, I60) [I51 <= I57 /\ I61 = 0] 129.25/127.45 f9(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 129.25/127.45 f11(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81) -> f10(I72, 1 + I73, I74, I75, I76, I77, I78, I79, I80, I81) [1 + I73 <= I72] 129.25/127.45 f11(I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f14(I82, I83, I84, I85, I86, I87, I88, 0, I90, I91) [I82 <= I83] 129.25/127.45 f13(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 129.25/127.45 f15(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14(I102, I103, I104, I105, I106, I107, I108, 1 + I109, I110, I111) [1 + I109 <= I102] 129.25/127.45 f15(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f17(I112, I113, 0, I115, I116, I117, I118, I119, I120, I121) [I112 <= I119 /\ I122 = 0] 129.25/127.45 f17(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 129.25/127.45 f16(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f17(I133, I134, 1 + I135, I136, I137, I138, I139, I140, I141, I142) [1 + I135 <= I133] 129.25/127.45 f16(I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f13(I143, I144, I145, 0, I147, I148, I149, I150, I151, I152) [I143 <= I145 /\ I153 = 0] 129.25/127.45 f14(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 129.25/127.45 f12(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f13(I164, I165, I166, 1 + I167, I168, I169, I170, I171, I172, I173) [1 + I167 <= I164] 129.25/127.45 f12(I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f9(I174, I175, I176, I177, 0, I179, I180, I181, I182, I183) [I174 <= I177 /\ I184 = 0] 129.25/127.45 f10(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 129.25/127.45 f8(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204) -> f9(I195, I196, I197, I198, 1 + I199, I200, I201, I202, I203, I204) [1 + I199 <= I195] 129.25/127.45 f8(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214) -> f5(I205, I206, I207, I208, I209, I210, I211, 0, I213, I214) [I205 <= I209] 129.25/127.45 f6(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 129.25/127.45 f3(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234) -> f5(I225, I226, I227, I228, I229, I230, I231, 1 + I232, I233, I234) [1 + I232 <= I225] 129.25/127.45 f3(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) -> f4(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) [I235 <= I242] 129.25/127.45 f1(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 129.25/127.45 129.25/127.45 The dependency graph for this problem is: 129.25/127.45 22 -> 129.25/127.45 Where: 129.25/127.45 22) f6#(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7#(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 129.25/127.45 129.25/127.45 We have the following SCCs. 129.25/127.45 129.25/127.45 129.25/127.45 DP problem for innermost termination. 129.25/127.45 P = 129.25/127.45 f2#(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1#(I10, I11, I12, I13, I14, 1 + I15, I16, I17, I18, I19) [1 + I15 <= I10] 129.25/127.45 f1#(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2#(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 129.25/127.45 R = 129.25/127.45 f19(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 129.25/127.45 f18(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, rnd9, rnd10) [rnd9 = rnd9 /\ rnd10 = rnd10 /\ y1 = 0] 129.25/127.45 f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1(I10, I11, I12, I13, I14, 1 + I15, I16, I17, I18, I19) [1 + I15 <= I10] 129.25/127.45 f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f6(I20, I21, I22, I23, I24, I25, 0, I27, I28, I29) [I20 <= I25 /\ I30 = 0] 129.25/127.45 f5(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 129.25/127.45 f7(I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f6(I41, I42, I43, I44, I45, I46, 1 + I47, I48, I49, I50) [1 + I47 <= I41] 129.25/127.45 f7(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60) -> f10(I51, 0, I53, I54, I55, I56, I57, I58, I59, I60) [I51 <= I57 /\ I61 = 0] 129.25/127.45 f9(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 129.25/127.45 f11(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81) -> f10(I72, 1 + I73, I74, I75, I76, I77, I78, I79, I80, I81) [1 + I73 <= I72] 129.25/127.45 f11(I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f14(I82, I83, I84, I85, I86, I87, I88, 0, I90, I91) [I82 <= I83] 129.25/127.45 f13(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 129.25/127.45 f15(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14(I102, I103, I104, I105, I106, I107, I108, 1 + I109, I110, I111) [1 + I109 <= I102] 129.25/127.45 f15(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f17(I112, I113, 0, I115, I116, I117, I118, I119, I120, I121) [I112 <= I119 /\ I122 = 0] 129.25/127.45 f17(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 129.25/127.45 f16(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f17(I133, I134, 1 + I135, I136, I137, I138, I139, I140, I141, I142) [1 + I135 <= I133] 129.25/127.45 f16(I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f13(I143, I144, I145, 0, I147, I148, I149, I150, I151, I152) [I143 <= I145 /\ I153 = 0] 129.25/127.45 f14(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 129.25/127.45 f12(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f13(I164, I165, I166, 1 + I167, I168, I169, I170, I171, I172, I173) [1 + I167 <= I164] 129.25/127.45 f12(I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f9(I174, I175, I176, I177, 0, I179, I180, I181, I182, I183) [I174 <= I177 /\ I184 = 0] 129.25/127.45 f10(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 129.25/127.45 f8(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204) -> f9(I195, I196, I197, I198, 1 + I199, I200, I201, I202, I203, I204) [1 + I199 <= I195] 129.25/127.45 f8(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214) -> f5(I205, I206, I207, I208, I209, I210, I211, 0, I213, I214) [I205 <= I209] 129.25/127.45 f6(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 129.25/127.45 f3(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234) -> f5(I225, I226, I227, I228, I229, I230, I231, 1 + I232, I233, I234) [1 + I232 <= I225] 129.25/127.45 f3(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) -> f4(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) [I235 <= I242] 129.25/127.45 f1(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 129.25/127.45 129.25/127.45 We use the reverse value criterion with the projection function NU: 129.25/127.45 NU[f1#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10)] = z1 + -1 * (1 + z6) 129.25/127.45 NU[f2#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10)] = z1 + -1 * (1 + z6) 129.25/127.45 129.25/127.45 This gives the following inequalities: 129.25/127.45 1 + I15 <= I10 ==> I10 + -1 * (1 + I15) > I10 + -1 * (1 + (1 + I15)) with I10 + -1 * (1 + I15) >= 0 129.25/127.45 ==> I245 + -1 * (1 + I250) >= I245 + -1 * (1 + I250) 129.25/127.45 129.25/127.45 We remove all the strictly oriented dependency pairs. 129.25/127.45 129.25/127.45 DP problem for innermost termination. 129.25/127.45 P = 129.25/127.45 f1#(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2#(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 129.25/127.45 R = 129.25/127.45 f19(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 129.25/127.45 f18(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, rnd9, rnd10) [rnd9 = rnd9 /\ rnd10 = rnd10 /\ y1 = 0] 129.25/127.45 f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1(I10, I11, I12, I13, I14, 1 + I15, I16, I17, I18, I19) [1 + I15 <= I10] 129.25/127.45 f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f6(I20, I21, I22, I23, I24, I25, 0, I27, I28, I29) [I20 <= I25 /\ I30 = 0] 129.25/127.45 f5(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) -> f3(I31, I32, I33, I34, I35, I36, I37, I38, I39, I40) 129.25/127.45 f7(I41, I42, I43, I44, I45, I46, I47, I48, I49, I50) -> f6(I41, I42, I43, I44, I45, I46, 1 + I47, I48, I49, I50) [1 + I47 <= I41] 129.25/127.45 f7(I51, I52, I53, I54, I55, I56, I57, I58, I59, I60) -> f10(I51, 0, I53, I54, I55, I56, I57, I58, I59, I60) [I51 <= I57 /\ I61 = 0] 129.25/127.45 f9(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f8(I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 129.25/127.45 f11(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81) -> f10(I72, 1 + I73, I74, I75, I76, I77, I78, I79, I80, I81) [1 + I73 <= I72] 129.25/127.45 f11(I82, I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f14(I82, I83, I84, I85, I86, I87, I88, 0, I90, I91) [I82 <= I83] 129.25/127.45 f13(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) -> f12(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101) 129.25/127.45 f15(I102, I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f14(I102, I103, I104, I105, I106, I107, I108, 1 + I109, I110, I111) [1 + I109 <= I102] 129.25/127.45 f15(I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f17(I112, I113, 0, I115, I116, I117, I118, I119, I120, I121) [I112 <= I119 /\ I122 = 0] 129.25/127.45 f17(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f16(I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) 129.25/127.45 f16(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f17(I133, I134, 1 + I135, I136, I137, I138, I139, I140, I141, I142) [1 + I135 <= I133] 129.25/127.45 f16(I143, I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f13(I143, I144, I145, 0, I147, I148, I149, I150, I151, I152) [I143 <= I145 /\ I153 = 0] 129.25/127.45 f14(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) -> f15(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163) 129.25/127.45 f12(I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f13(I164, I165, I166, 1 + I167, I168, I169, I170, I171, I172, I173) [1 + I167 <= I164] 129.25/127.45 f12(I174, I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f9(I174, I175, I176, I177, 0, I179, I180, I181, I182, I183) [I174 <= I177 /\ I184 = 0] 129.25/127.45 f10(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f11(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) 129.25/127.45 f8(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204) -> f9(I195, I196, I197, I198, 1 + I199, I200, I201, I202, I203, I204) [1 + I199 <= I195] 129.25/127.45 f8(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214) -> f5(I205, I206, I207, I208, I209, I210, I211, 0, I213, I214) [I205 <= I209] 129.25/127.45 f6(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f7(I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 129.25/127.45 f3(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234) -> f5(I225, I226, I227, I228, I229, I230, I231, 1 + I232, I233, I234) [1 + I232 <= I225] 129.25/127.45 f3(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) -> f4(I235, I236, I237, I238, I239, I240, I241, I242, I243, I244) [I235 <= I242] 129.25/127.45 f1(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 129.25/127.45 129.25/127.45 The dependency graph for this problem is: 129.25/127.45 24 -> 129.25/127.45 Where: 129.25/127.45 24) f1#(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f2#(I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 129.25/127.45 129.25/127.45 We have the following SCCs. 129.25/127.45 129.25/130.41 EOF