105.17/104.27 YES 105.17/104.27 105.17/104.27 DP problem for innermost termination. 105.17/104.27 P = 105.17/104.27 f19#(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f18#(x1, x2, x3, x4, x5, x6, x7, x8, x9) 105.17/104.27 f18#(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f1#(I0, I1, I2, I3, 0, I5, 0, rnd8, rnd9) [rnd8 = rnd8 /\ rnd9 = rnd9 /\ y1 = 0] 105.17/104.27 f2#(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1#(I9, I10, I11, I12, 1 + I13, I14, I15, I16, I17) [1 + I13 <= 50] 105.17/104.27 f2#(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6#(I18, I19, I20, I21, I22, 0, I24, I25, I26) [50 <= I22 /\ I27 = 0] 105.17/104.27 f5#(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3#(I28, I29, I30, I31, I32, I33, I34, I35, I36) 105.17/104.27 f7#(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6#(I37, I38, I39, I40, I41, 1 + I42, I43, I44, I45) [1 + I42 <= 50] 105.17/104.27 f7#(I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f10#(0, I47, I48, I49, I50, I51, I52, I53, I54) [50 <= I51 /\ I55 = 0] 105.17/104.27 f9#(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8#(I56, I57, I58, I59, I60, I61, I62, I63, I64) 105.17/104.27 f11#(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f10#(1 + I65, I66, I67, I68, I69, I70, I71, I72, I73) [1 + I65 <= 50] 105.17/104.27 f11#(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f14#(I74, I75, I76, I77, I78, I79, 0, I81, I82) [50 <= I74] 105.17/104.27 f13#(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12#(I83, I84, I85, I86, I87, I88, I89, I90, I91) 105.17/104.27 f15#(I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f14#(I92, I93, I94, I95, I96, I97, 1 + I98, I99, I100) [1 + I98 <= 50] 105.17/104.27 f15#(I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f17#(I101, 0, I103, I104, I105, I106, I107, I108, I109) [50 <= I107 /\ I110 = 0] 105.17/104.27 f17#(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16#(I111, I112, I113, I114, I115, I116, I117, I118, I119) 105.17/104.27 f16#(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f17#(I120, 1 + I121, I122, I123, I124, I125, I126, I127, I128) [1 + I121 <= 50] 105.17/104.27 f16#(I129, I130, I131, I132, I133, I134, I135, I136, I137) -> f13#(I129, I130, 0, I132, I133, I134, I135, I136, I137) [50 <= I130 /\ I138 = 0] 105.17/104.27 f14#(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15#(I139, I140, I141, I142, I143, I144, I145, I146, I147) 105.17/104.27 f12#(I148, I149, I150, I151, I152, I153, I154, I155, I156) -> f13#(I148, I149, 1 + I150, I151, I152, I153, I154, I155, I156) [1 + I150 <= 50] 105.17/104.27 f12#(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f9#(I157, I158, I159, 0, I161, I162, I163, I164, I165) [50 <= I159 /\ I166 = 0] 105.17/104.27 f10#(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11#(I167, I168, I169, I170, I171, I172, I173, I174, I175) 105.17/104.27 f8#(I176, I177, I178, I179, I180, I181, I182, I183, I184) -> f9#(I176, I177, I178, 1 + I179, I180, I181, I182, I183, I184) [1 + I179 <= 50] 105.17/104.27 f8#(I185, I186, I187, I188, I189, I190, I191, I192, I193) -> f5#(I185, I186, I187, I188, I189, I190, 0, I192, I193) [50 <= I188] 105.17/104.27 f6#(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7#(I194, I195, I196, I197, I198, I199, I200, I201, I202) 105.17/104.27 f3#(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5#(I203, I204, I205, I206, I207, I208, 1 + I209, I210, I211) [1 + I209 <= 50] 105.17/104.27 f1#(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2#(I221, I222, I223, I224, I225, I226, I227, I228, I229) 105.17/104.27 R = 105.17/104.27 f19(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) 105.17/104.27 f18(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f1(I0, I1, I2, I3, 0, I5, 0, rnd8, rnd9) [rnd8 = rnd8 /\ rnd9 = rnd9 /\ y1 = 0] 105.17/104.27 f2(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, 1 + I13, I14, I15, I16, I17) [1 + I13 <= 50] 105.17/104.27 f2(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, 0, I24, I25, I26) [50 <= I22 /\ I27 = 0] 105.17/104.27 f5(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3(I28, I29, I30, I31, I32, I33, I34, I35, I36) 105.17/104.27 f7(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6(I37, I38, I39, I40, I41, 1 + I42, I43, I44, I45) [1 + I42 <= 50] 105.17/104.27 f7(I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f10(0, I47, I48, I49, I50, I51, I52, I53, I54) [50 <= I51 /\ I55 = 0] 105.17/104.27 f9(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8(I56, I57, I58, I59, I60, I61, I62, I63, I64) 105.17/104.27 f11(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f10(1 + I65, I66, I67, I68, I69, I70, I71, I72, I73) [1 + I65 <= 50] 105.17/104.27 f11(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f14(I74, I75, I76, I77, I78, I79, 0, I81, I82) [50 <= I74] 105.17/104.27 f13(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12(I83, I84, I85, I86, I87, I88, I89, I90, I91) 105.17/104.27 f15(I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f14(I92, I93, I94, I95, I96, I97, 1 + I98, I99, I100) [1 + I98 <= 50] 105.17/104.27 f15(I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f17(I101, 0, I103, I104, I105, I106, I107, I108, I109) [50 <= I107 /\ I110 = 0] 105.17/104.27 f17(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16(I111, I112, I113, I114, I115, I116, I117, I118, I119) 105.17/104.27 f16(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f17(I120, 1 + I121, I122, I123, I124, I125, I126, I127, I128) [1 + I121 <= 50] 105.17/104.27 f16(I129, I130, I131, I132, I133, I134, I135, I136, I137) -> f13(I129, I130, 0, I132, I133, I134, I135, I136, I137) [50 <= I130 /\ I138 = 0] 105.17/104.27 f14(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15(I139, I140, I141, I142, I143, I144, I145, I146, I147) 105.17/104.27 f12(I148, I149, I150, I151, I152, I153, I154, I155, I156) -> f13(I148, I149, 1 + I150, I151, I152, I153, I154, I155, I156) [1 + I150 <= 50] 105.17/104.27 f12(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f9(I157, I158, I159, 0, I161, I162, I163, I164, I165) [50 <= I159 /\ I166 = 0] 105.17/104.27 f10(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11(I167, I168, I169, I170, I171, I172, I173, I174, I175) 105.17/104.27 f8(I176, I177, I178, I179, I180, I181, I182, I183, I184) -> f9(I176, I177, I178, 1 + I179, I180, I181, I182, I183, I184) [1 + I179 <= 50] 105.17/104.27 f8(I185, I186, I187, I188, I189, I190, I191, I192, I193) -> f5(I185, I186, I187, I188, I189, I190, 0, I192, I193) [50 <= I188] 105.17/104.27 f6(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7(I194, I195, I196, I197, I198, I199, I200, I201, I202) 105.17/104.27 f3(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5(I203, I204, I205, I206, I207, I208, 1 + I209, I210, I211) [1 + I209 <= 50] 105.17/104.27 f3(I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f4(I212, I213, I214, I215, I216, I217, I218, I219, I220) [50 <= I218] 105.17/104.27 f1(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2(I221, I222, I223, I224, I225, I226, I227, I228, I229) 105.17/104.27 105.17/104.27 The dependency graph for this problem is: 105.17/104.27 0 -> 1 105.17/104.27 1 -> 24 105.17/104.27 2 -> 24 105.17/104.27 3 -> 22 105.17/104.27 4 -> 23 105.17/104.27 5 -> 22 105.17/104.27 6 -> 19 105.17/104.27 7 -> 20, 21 105.17/104.27 8 -> 19 105.17/104.27 9 -> 16 105.17/104.27 10 -> 17, 18 105.17/104.27 11 -> 16 105.17/104.27 12 -> 13 105.17/104.27 13 -> 14, 15 105.17/104.27 14 -> 13 105.17/104.27 15 -> 10 105.17/104.27 16 -> 11, 12 105.17/104.27 17 -> 10 105.17/104.27 18 -> 7 105.17/104.27 19 -> 8, 9 105.17/104.27 20 -> 7 105.17/104.27 21 -> 4 105.17/104.27 22 -> 5, 6 105.17/104.27 23 -> 4 105.17/104.27 24 -> 2, 3 105.17/104.27 Where: 105.17/104.27 0) f19#(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f18#(x1, x2, x3, x4, x5, x6, x7, x8, x9) 105.17/104.27 1) f18#(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f1#(I0, I1, I2, I3, 0, I5, 0, rnd8, rnd9) [rnd8 = rnd8 /\ rnd9 = rnd9 /\ y1 = 0] 105.17/104.27 2) f2#(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1#(I9, I10, I11, I12, 1 + I13, I14, I15, I16, I17) [1 + I13 <= 50] 105.17/104.27 3) f2#(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6#(I18, I19, I20, I21, I22, 0, I24, I25, I26) [50 <= I22 /\ I27 = 0] 105.17/104.27 4) f5#(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3#(I28, I29, I30, I31, I32, I33, I34, I35, I36) 105.17/104.27 5) f7#(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6#(I37, I38, I39, I40, I41, 1 + I42, I43, I44, I45) [1 + I42 <= 50] 105.17/104.27 6) f7#(I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f10#(0, I47, I48, I49, I50, I51, I52, I53, I54) [50 <= I51 /\ I55 = 0] 105.17/104.27 7) f9#(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8#(I56, I57, I58, I59, I60, I61, I62, I63, I64) 105.17/104.27 8) f11#(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f10#(1 + I65, I66, I67, I68, I69, I70, I71, I72, I73) [1 + I65 <= 50] 105.17/104.27 9) f11#(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f14#(I74, I75, I76, I77, I78, I79, 0, I81, I82) [50 <= I74] 105.17/104.27 10) f13#(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12#(I83, I84, I85, I86, I87, I88, I89, I90, I91) 105.17/104.27 11) f15#(I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f14#(I92, I93, I94, I95, I96, I97, 1 + I98, I99, I100) [1 + I98 <= 50] 105.17/104.27 12) f15#(I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f17#(I101, 0, I103, I104, I105, I106, I107, I108, I109) [50 <= I107 /\ I110 = 0] 105.17/104.27 13) f17#(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16#(I111, I112, I113, I114, I115, I116, I117, I118, I119) 105.17/104.27 14) f16#(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f17#(I120, 1 + I121, I122, I123, I124, I125, I126, I127, I128) [1 + I121 <= 50] 105.17/104.27 15) f16#(I129, I130, I131, I132, I133, I134, I135, I136, I137) -> f13#(I129, I130, 0, I132, I133, I134, I135, I136, I137) [50 <= I130 /\ I138 = 0] 105.17/104.27 16) f14#(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15#(I139, I140, I141, I142, I143, I144, I145, I146, I147) 105.17/104.27 17) f12#(I148, I149, I150, I151, I152, I153, I154, I155, I156) -> f13#(I148, I149, 1 + I150, I151, I152, I153, I154, I155, I156) [1 + I150 <= 50] 105.17/104.27 18) f12#(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f9#(I157, I158, I159, 0, I161, I162, I163, I164, I165) [50 <= I159 /\ I166 = 0] 105.17/104.27 19) f10#(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11#(I167, I168, I169, I170, I171, I172, I173, I174, I175) 105.17/104.27 20) f8#(I176, I177, I178, I179, I180, I181, I182, I183, I184) -> f9#(I176, I177, I178, 1 + I179, I180, I181, I182, I183, I184) [1 + I179 <= 50] 105.17/104.27 21) f8#(I185, I186, I187, I188, I189, I190, I191, I192, I193) -> f5#(I185, I186, I187, I188, I189, I190, 0, I192, I193) [50 <= I188] 105.17/104.27 22) f6#(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7#(I194, I195, I196, I197, I198, I199, I200, I201, I202) 105.17/104.27 23) f3#(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5#(I203, I204, I205, I206, I207, I208, 1 + I209, I210, I211) [1 + I209 <= 50] 105.17/104.27 24) f1#(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2#(I221, I222, I223, I224, I225, I226, I227, I228, I229) 105.17/104.27 105.17/104.27 We have the following SCCs. 105.17/104.27 { 2, 24 } 105.17/104.27 { 5, 22 } 105.17/104.27 { 8, 19 } 105.17/104.27 { 11, 16 } 105.17/104.27 { 13, 14 } 105.17/104.27 { 10, 17 } 105.17/104.27 { 7, 20 } 105.17/104.27 { 4, 23 } 105.17/104.27 105.17/104.27 DP problem for innermost termination. 105.17/104.27 P = 105.17/104.27 f5#(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3#(I28, I29, I30, I31, I32, I33, I34, I35, I36) 105.17/104.27 f3#(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5#(I203, I204, I205, I206, I207, I208, 1 + I209, I210, I211) [1 + I209 <= 50] 105.17/104.27 R = 105.17/104.27 f19(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) 105.17/104.27 f18(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f1(I0, I1, I2, I3, 0, I5, 0, rnd8, rnd9) [rnd8 = rnd8 /\ rnd9 = rnd9 /\ y1 = 0] 105.17/104.27 f2(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, 1 + I13, I14, I15, I16, I17) [1 + I13 <= 50] 105.17/104.27 f2(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, 0, I24, I25, I26) [50 <= I22 /\ I27 = 0] 105.17/104.27 f5(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3(I28, I29, I30, I31, I32, I33, I34, I35, I36) 105.17/104.27 f7(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6(I37, I38, I39, I40, I41, 1 + I42, I43, I44, I45) [1 + I42 <= 50] 105.17/104.27 f7(I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f10(0, I47, I48, I49, I50, I51, I52, I53, I54) [50 <= I51 /\ I55 = 0] 105.17/104.27 f9(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8(I56, I57, I58, I59, I60, I61, I62, I63, I64) 105.17/104.27 f11(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f10(1 + I65, I66, I67, I68, I69, I70, I71, I72, I73) [1 + I65 <= 50] 105.17/104.27 f11(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f14(I74, I75, I76, I77, I78, I79, 0, I81, I82) [50 <= I74] 105.17/104.27 f13(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12(I83, I84, I85, I86, I87, I88, I89, I90, I91) 105.17/104.27 f15(I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f14(I92, I93, I94, I95, I96, I97, 1 + I98, I99, I100) [1 + I98 <= 50] 105.17/104.27 f15(I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f17(I101, 0, I103, I104, I105, I106, I107, I108, I109) [50 <= I107 /\ I110 = 0] 105.17/104.27 f17(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16(I111, I112, I113, I114, I115, I116, I117, I118, I119) 105.17/104.27 f16(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f17(I120, 1 + I121, I122, I123, I124, I125, I126, I127, I128) [1 + I121 <= 50] 105.17/104.27 f16(I129, I130, I131, I132, I133, I134, I135, I136, I137) -> f13(I129, I130, 0, I132, I133, I134, I135, I136, I137) [50 <= I130 /\ I138 = 0] 105.17/104.27 f14(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15(I139, I140, I141, I142, I143, I144, I145, I146, I147) 105.17/104.27 f12(I148, I149, I150, I151, I152, I153, I154, I155, I156) -> f13(I148, I149, 1 + I150, I151, I152, I153, I154, I155, I156) [1 + I150 <= 50] 105.17/104.27 f12(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f9(I157, I158, I159, 0, I161, I162, I163, I164, I165) [50 <= I159 /\ I166 = 0] 105.17/104.27 f10(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11(I167, I168, I169, I170, I171, I172, I173, I174, I175) 105.17/104.27 f8(I176, I177, I178, I179, I180, I181, I182, I183, I184) -> f9(I176, I177, I178, 1 + I179, I180, I181, I182, I183, I184) [1 + I179 <= 50] 105.17/104.27 f8(I185, I186, I187, I188, I189, I190, I191, I192, I193) -> f5(I185, I186, I187, I188, I189, I190, 0, I192, I193) [50 <= I188] 105.17/104.27 f6(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7(I194, I195, I196, I197, I198, I199, I200, I201, I202) 105.17/104.27 f3(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5(I203, I204, I205, I206, I207, I208, 1 + I209, I210, I211) [1 + I209 <= 50] 105.17/104.27 f3(I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f4(I212, I213, I214, I215, I216, I217, I218, I219, I220) [50 <= I218] 105.17/104.27 f1(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2(I221, I222, I223, I224, I225, I226, I227, I228, I229) 105.17/104.27 105.17/104.27 We use the reverse value criterion with the projection function NU: 105.17/104.27 NU[f3#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = 50 + -1 * (1 + z7) 105.17/104.27 NU[f5#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = 50 + -1 * (1 + z7) 105.17/104.27 105.17/104.27 This gives the following inequalities: 105.17/104.27 ==> 50 + -1 * (1 + I34) >= 50 + -1 * (1 + I34) 105.17/104.27 1 + I209 <= 50 ==> 50 + -1 * (1 + I209) > 50 + -1 * (1 + (1 + I209)) with 50 + -1 * (1 + I209) >= 0 105.17/104.27 105.17/104.27 We remove all the strictly oriented dependency pairs. 105.17/104.27 105.17/104.27 DP problem for innermost termination. 105.17/104.27 P = 105.17/104.27 f5#(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3#(I28, I29, I30, I31, I32, I33, I34, I35, I36) 105.17/104.27 R = 105.17/104.27 f19(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) 105.17/104.27 f18(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f1(I0, I1, I2, I3, 0, I5, 0, rnd8, rnd9) [rnd8 = rnd8 /\ rnd9 = rnd9 /\ y1 = 0] 105.17/104.27 f2(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, 1 + I13, I14, I15, I16, I17) [1 + I13 <= 50] 105.17/104.27 f2(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, 0, I24, I25, I26) [50 <= I22 /\ I27 = 0] 105.17/104.27 f5(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3(I28, I29, I30, I31, I32, I33, I34, I35, I36) 105.17/104.27 f7(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6(I37, I38, I39, I40, I41, 1 + I42, I43, I44, I45) [1 + I42 <= 50] 105.17/104.27 f7(I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f10(0, I47, I48, I49, I50, I51, I52, I53, I54) [50 <= I51 /\ I55 = 0] 105.17/104.27 f9(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8(I56, I57, I58, I59, I60, I61, I62, I63, I64) 105.17/104.27 f11(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f10(1 + I65, I66, I67, I68, I69, I70, I71, I72, I73) [1 + I65 <= 50] 105.17/104.27 f11(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f14(I74, I75, I76, I77, I78, I79, 0, I81, I82) [50 <= I74] 105.17/104.27 f13(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12(I83, I84, I85, I86, I87, I88, I89, I90, I91) 105.17/104.27 f15(I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f14(I92, I93, I94, I95, I96, I97, 1 + I98, I99, I100) [1 + I98 <= 50] 105.17/104.27 f15(I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f17(I101, 0, I103, I104, I105, I106, I107, I108, I109) [50 <= I107 /\ I110 = 0] 105.17/104.27 f17(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16(I111, I112, I113, I114, I115, I116, I117, I118, I119) 105.17/104.27 f16(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f17(I120, 1 + I121, I122, I123, I124, I125, I126, I127, I128) [1 + I121 <= 50] 105.17/104.27 f16(I129, I130, I131, I132, I133, I134, I135, I136, I137) -> f13(I129, I130, 0, I132, I133, I134, I135, I136, I137) [50 <= I130 /\ I138 = 0] 105.17/104.27 f14(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15(I139, I140, I141, I142, I143, I144, I145, I146, I147) 105.17/104.27 f12(I148, I149, I150, I151, I152, I153, I154, I155, I156) -> f13(I148, I149, 1 + I150, I151, I152, I153, I154, I155, I156) [1 + I150 <= 50] 105.17/104.27 f12(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f9(I157, I158, I159, 0, I161, I162, I163, I164, I165) [50 <= I159 /\ I166 = 0] 105.17/104.27 f10(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11(I167, I168, I169, I170, I171, I172, I173, I174, I175) 105.17/104.27 f8(I176, I177, I178, I179, I180, I181, I182, I183, I184) -> f9(I176, I177, I178, 1 + I179, I180, I181, I182, I183, I184) [1 + I179 <= 50] 105.17/104.27 f8(I185, I186, I187, I188, I189, I190, I191, I192, I193) -> f5(I185, I186, I187, I188, I189, I190, 0, I192, I193) [50 <= I188] 105.17/104.27 f6(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7(I194, I195, I196, I197, I198, I199, I200, I201, I202) 105.17/104.27 f3(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5(I203, I204, I205, I206, I207, I208, 1 + I209, I210, I211) [1 + I209 <= 50] 105.17/104.27 f3(I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f4(I212, I213, I214, I215, I216, I217, I218, I219, I220) [50 <= I218] 105.17/104.27 f1(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2(I221, I222, I223, I224, I225, I226, I227, I228, I229) 105.17/104.27 105.17/104.27 The dependency graph for this problem is: 105.17/104.27 4 -> 105.17/104.27 Where: 105.17/104.27 4) f5#(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3#(I28, I29, I30, I31, I32, I33, I34, I35, I36) 105.17/104.27 105.17/104.27 We have the following SCCs. 105.17/104.27 105.17/104.27 105.17/104.27 DP problem for innermost termination. 105.17/104.27 P = 105.17/104.27 f9#(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8#(I56, I57, I58, I59, I60, I61, I62, I63, I64) 105.17/104.27 f8#(I176, I177, I178, I179, I180, I181, I182, I183, I184) -> f9#(I176, I177, I178, 1 + I179, I180, I181, I182, I183, I184) [1 + I179 <= 50] 105.17/104.27 R = 105.17/104.27 f19(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) 105.17/104.27 f18(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f1(I0, I1, I2, I3, 0, I5, 0, rnd8, rnd9) [rnd8 = rnd8 /\ rnd9 = rnd9 /\ y1 = 0] 105.17/104.27 f2(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, 1 + I13, I14, I15, I16, I17) [1 + I13 <= 50] 105.17/104.27 f2(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, 0, I24, I25, I26) [50 <= I22 /\ I27 = 0] 105.17/104.27 f5(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3(I28, I29, I30, I31, I32, I33, I34, I35, I36) 105.17/104.27 f7(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6(I37, I38, I39, I40, I41, 1 + I42, I43, I44, I45) [1 + I42 <= 50] 105.17/104.27 f7(I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f10(0, I47, I48, I49, I50, I51, I52, I53, I54) [50 <= I51 /\ I55 = 0] 105.17/104.27 f9(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8(I56, I57, I58, I59, I60, I61, I62, I63, I64) 105.17/104.27 f11(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f10(1 + I65, I66, I67, I68, I69, I70, I71, I72, I73) [1 + I65 <= 50] 105.17/104.27 f11(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f14(I74, I75, I76, I77, I78, I79, 0, I81, I82) [50 <= I74] 105.17/104.27 f13(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12(I83, I84, I85, I86, I87, I88, I89, I90, I91) 105.17/104.27 f15(I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f14(I92, I93, I94, I95, I96, I97, 1 + I98, I99, I100) [1 + I98 <= 50] 105.17/104.27 f15(I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f17(I101, 0, I103, I104, I105, I106, I107, I108, I109) [50 <= I107 /\ I110 = 0] 105.17/104.27 f17(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16(I111, I112, I113, I114, I115, I116, I117, I118, I119) 105.17/104.27 f16(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f17(I120, 1 + I121, I122, I123, I124, I125, I126, I127, I128) [1 + I121 <= 50] 105.17/104.27 f16(I129, I130, I131, I132, I133, I134, I135, I136, I137) -> f13(I129, I130, 0, I132, I133, I134, I135, I136, I137) [50 <= I130 /\ I138 = 0] 105.17/104.27 f14(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15(I139, I140, I141, I142, I143, I144, I145, I146, I147) 105.17/104.27 f12(I148, I149, I150, I151, I152, I153, I154, I155, I156) -> f13(I148, I149, 1 + I150, I151, I152, I153, I154, I155, I156) [1 + I150 <= 50] 105.17/104.27 f12(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f9(I157, I158, I159, 0, I161, I162, I163, I164, I165) [50 <= I159 /\ I166 = 0] 105.17/104.27 f10(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11(I167, I168, I169, I170, I171, I172, I173, I174, I175) 105.17/104.27 f8(I176, I177, I178, I179, I180, I181, I182, I183, I184) -> f9(I176, I177, I178, 1 + I179, I180, I181, I182, I183, I184) [1 + I179 <= 50] 105.17/104.27 f8(I185, I186, I187, I188, I189, I190, I191, I192, I193) -> f5(I185, I186, I187, I188, I189, I190, 0, I192, I193) [50 <= I188] 105.17/104.27 f6(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7(I194, I195, I196, I197, I198, I199, I200, I201, I202) 105.17/104.27 f3(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5(I203, I204, I205, I206, I207, I208, 1 + I209, I210, I211) [1 + I209 <= 50] 105.17/104.27 f3(I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f4(I212, I213, I214, I215, I216, I217, I218, I219, I220) [50 <= I218] 105.17/104.27 f1(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2(I221, I222, I223, I224, I225, I226, I227, I228, I229) 105.17/104.27 105.17/104.27 We use the reverse value criterion with the projection function NU: 105.17/104.27 NU[f8#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = 50 + -1 * (1 + z4) 105.17/104.27 NU[f9#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = 50 + -1 * (1 + z4) 105.17/104.27 105.17/104.27 This gives the following inequalities: 105.17/104.27 ==> 50 + -1 * (1 + I59) >= 50 + -1 * (1 + I59) 105.17/104.27 1 + I179 <= 50 ==> 50 + -1 * (1 + I179) > 50 + -1 * (1 + (1 + I179)) with 50 + -1 * (1 + I179) >= 0 105.17/104.27 105.17/104.27 We remove all the strictly oriented dependency pairs. 105.17/104.27 105.17/104.27 DP problem for innermost termination. 105.17/104.27 P = 105.17/104.27 f9#(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8#(I56, I57, I58, I59, I60, I61, I62, I63, I64) 105.17/104.27 R = 105.17/104.27 f19(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) 105.17/104.27 f18(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f1(I0, I1, I2, I3, 0, I5, 0, rnd8, rnd9) [rnd8 = rnd8 /\ rnd9 = rnd9 /\ y1 = 0] 105.17/104.27 f2(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, 1 + I13, I14, I15, I16, I17) [1 + I13 <= 50] 105.17/104.27 f2(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, 0, I24, I25, I26) [50 <= I22 /\ I27 = 0] 105.17/104.27 f5(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3(I28, I29, I30, I31, I32, I33, I34, I35, I36) 105.17/104.27 f7(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6(I37, I38, I39, I40, I41, 1 + I42, I43, I44, I45) [1 + I42 <= 50] 105.17/104.27 f7(I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f10(0, I47, I48, I49, I50, I51, I52, I53, I54) [50 <= I51 /\ I55 = 0] 105.17/104.27 f9(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8(I56, I57, I58, I59, I60, I61, I62, I63, I64) 105.17/104.27 f11(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f10(1 + I65, I66, I67, I68, I69, I70, I71, I72, I73) [1 + I65 <= 50] 105.17/104.27 f11(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f14(I74, I75, I76, I77, I78, I79, 0, I81, I82) [50 <= I74] 105.17/104.27 f13(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12(I83, I84, I85, I86, I87, I88, I89, I90, I91) 105.17/104.27 f15(I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f14(I92, I93, I94, I95, I96, I97, 1 + I98, I99, I100) [1 + I98 <= 50] 105.17/104.27 f15(I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f17(I101, 0, I103, I104, I105, I106, I107, I108, I109) [50 <= I107 /\ I110 = 0] 105.17/104.27 f17(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16(I111, I112, I113, I114, I115, I116, I117, I118, I119) 105.17/104.27 f16(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f17(I120, 1 + I121, I122, I123, I124, I125, I126, I127, I128) [1 + I121 <= 50] 105.17/104.27 f16(I129, I130, I131, I132, I133, I134, I135, I136, I137) -> f13(I129, I130, 0, I132, I133, I134, I135, I136, I137) [50 <= I130 /\ I138 = 0] 105.17/104.27 f14(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15(I139, I140, I141, I142, I143, I144, I145, I146, I147) 105.17/104.27 f12(I148, I149, I150, I151, I152, I153, I154, I155, I156) -> f13(I148, I149, 1 + I150, I151, I152, I153, I154, I155, I156) [1 + I150 <= 50] 105.17/104.27 f12(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f9(I157, I158, I159, 0, I161, I162, I163, I164, I165) [50 <= I159 /\ I166 = 0] 105.17/104.27 f10(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11(I167, I168, I169, I170, I171, I172, I173, I174, I175) 105.17/104.27 f8(I176, I177, I178, I179, I180, I181, I182, I183, I184) -> f9(I176, I177, I178, 1 + I179, I180, I181, I182, I183, I184) [1 + I179 <= 50] 105.17/104.27 f8(I185, I186, I187, I188, I189, I190, I191, I192, I193) -> f5(I185, I186, I187, I188, I189, I190, 0, I192, I193) [50 <= I188] 105.17/104.27 f6(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7(I194, I195, I196, I197, I198, I199, I200, I201, I202) 105.17/104.27 f3(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5(I203, I204, I205, I206, I207, I208, 1 + I209, I210, I211) [1 + I209 <= 50] 105.17/104.27 f3(I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f4(I212, I213, I214, I215, I216, I217, I218, I219, I220) [50 <= I218] 105.17/104.27 f1(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2(I221, I222, I223, I224, I225, I226, I227, I228, I229) 105.17/104.27 105.17/104.27 The dependency graph for this problem is: 105.17/104.27 7 -> 105.17/104.27 Where: 105.17/104.27 7) f9#(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8#(I56, I57, I58, I59, I60, I61, I62, I63, I64) 105.17/104.27 105.17/104.27 We have the following SCCs. 105.17/104.27 105.17/104.27 105.17/104.27 DP problem for innermost termination. 105.17/104.27 P = 105.17/104.27 f13#(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12#(I83, I84, I85, I86, I87, I88, I89, I90, I91) 105.17/104.27 f12#(I148, I149, I150, I151, I152, I153, I154, I155, I156) -> f13#(I148, I149, 1 + I150, I151, I152, I153, I154, I155, I156) [1 + I150 <= 50] 105.17/104.27 R = 105.17/104.27 f19(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) 105.17/104.27 f18(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f1(I0, I1, I2, I3, 0, I5, 0, rnd8, rnd9) [rnd8 = rnd8 /\ rnd9 = rnd9 /\ y1 = 0] 105.17/104.27 f2(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, 1 + I13, I14, I15, I16, I17) [1 + I13 <= 50] 105.17/104.27 f2(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, 0, I24, I25, I26) [50 <= I22 /\ I27 = 0] 105.17/104.27 f5(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3(I28, I29, I30, I31, I32, I33, I34, I35, I36) 105.17/104.27 f7(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6(I37, I38, I39, I40, I41, 1 + I42, I43, I44, I45) [1 + I42 <= 50] 105.17/104.27 f7(I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f10(0, I47, I48, I49, I50, I51, I52, I53, I54) [50 <= I51 /\ I55 = 0] 105.17/104.27 f9(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8(I56, I57, I58, I59, I60, I61, I62, I63, I64) 105.17/104.27 f11(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f10(1 + I65, I66, I67, I68, I69, I70, I71, I72, I73) [1 + I65 <= 50] 105.17/104.27 f11(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f14(I74, I75, I76, I77, I78, I79, 0, I81, I82) [50 <= I74] 105.17/104.27 f13(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12(I83, I84, I85, I86, I87, I88, I89, I90, I91) 105.17/104.27 f15(I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f14(I92, I93, I94, I95, I96, I97, 1 + I98, I99, I100) [1 + I98 <= 50] 105.17/104.27 f15(I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f17(I101, 0, I103, I104, I105, I106, I107, I108, I109) [50 <= I107 /\ I110 = 0] 105.17/104.27 f17(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16(I111, I112, I113, I114, I115, I116, I117, I118, I119) 105.17/104.27 f16(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f17(I120, 1 + I121, I122, I123, I124, I125, I126, I127, I128) [1 + I121 <= 50] 105.17/104.27 f16(I129, I130, I131, I132, I133, I134, I135, I136, I137) -> f13(I129, I130, 0, I132, I133, I134, I135, I136, I137) [50 <= I130 /\ I138 = 0] 105.17/104.27 f14(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15(I139, I140, I141, I142, I143, I144, I145, I146, I147) 105.17/104.27 f12(I148, I149, I150, I151, I152, I153, I154, I155, I156) -> f13(I148, I149, 1 + I150, I151, I152, I153, I154, I155, I156) [1 + I150 <= 50] 105.17/104.27 f12(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f9(I157, I158, I159, 0, I161, I162, I163, I164, I165) [50 <= I159 /\ I166 = 0] 105.17/104.27 f10(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11(I167, I168, I169, I170, I171, I172, I173, I174, I175) 105.17/104.27 f8(I176, I177, I178, I179, I180, I181, I182, I183, I184) -> f9(I176, I177, I178, 1 + I179, I180, I181, I182, I183, I184) [1 + I179 <= 50] 105.17/104.27 f8(I185, I186, I187, I188, I189, I190, I191, I192, I193) -> f5(I185, I186, I187, I188, I189, I190, 0, I192, I193) [50 <= I188] 105.17/104.27 f6(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7(I194, I195, I196, I197, I198, I199, I200, I201, I202) 105.17/104.27 f3(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5(I203, I204, I205, I206, I207, I208, 1 + I209, I210, I211) [1 + I209 <= 50] 105.17/104.27 f3(I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f4(I212, I213, I214, I215, I216, I217, I218, I219, I220) [50 <= I218] 105.17/104.27 f1(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2(I221, I222, I223, I224, I225, I226, I227, I228, I229) 105.17/104.27 105.17/104.27 We use the reverse value criterion with the projection function NU: 105.17/104.27 NU[f12#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = 50 + -1 * (1 + z3) 105.17/104.27 NU[f13#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = 50 + -1 * (1 + z3) 105.17/104.27 105.17/104.27 This gives the following inequalities: 105.17/104.27 ==> 50 + -1 * (1 + I85) >= 50 + -1 * (1 + I85) 105.17/104.27 1 + I150 <= 50 ==> 50 + -1 * (1 + I150) > 50 + -1 * (1 + (1 + I150)) with 50 + -1 * (1 + I150) >= 0 105.17/104.27 105.17/104.27 We remove all the strictly oriented dependency pairs. 105.17/104.27 105.17/104.27 DP problem for innermost termination. 105.17/104.27 P = 105.17/104.27 f13#(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12#(I83, I84, I85, I86, I87, I88, I89, I90, I91) 105.17/104.27 R = 105.17/104.27 f19(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) 105.17/104.27 f18(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f1(I0, I1, I2, I3, 0, I5, 0, rnd8, rnd9) [rnd8 = rnd8 /\ rnd9 = rnd9 /\ y1 = 0] 105.17/104.27 f2(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, 1 + I13, I14, I15, I16, I17) [1 + I13 <= 50] 105.17/104.27 f2(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, 0, I24, I25, I26) [50 <= I22 /\ I27 = 0] 105.17/104.27 f5(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3(I28, I29, I30, I31, I32, I33, I34, I35, I36) 105.17/104.27 f7(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6(I37, I38, I39, I40, I41, 1 + I42, I43, I44, I45) [1 + I42 <= 50] 105.17/104.27 f7(I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f10(0, I47, I48, I49, I50, I51, I52, I53, I54) [50 <= I51 /\ I55 = 0] 105.17/104.27 f9(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8(I56, I57, I58, I59, I60, I61, I62, I63, I64) 105.17/104.27 f11(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f10(1 + I65, I66, I67, I68, I69, I70, I71, I72, I73) [1 + I65 <= 50] 105.17/104.27 f11(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f14(I74, I75, I76, I77, I78, I79, 0, I81, I82) [50 <= I74] 105.17/104.27 f13(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12(I83, I84, I85, I86, I87, I88, I89, I90, I91) 105.17/104.27 f15(I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f14(I92, I93, I94, I95, I96, I97, 1 + I98, I99, I100) [1 + I98 <= 50] 105.17/104.27 f15(I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f17(I101, 0, I103, I104, I105, I106, I107, I108, I109) [50 <= I107 /\ I110 = 0] 105.17/104.27 f17(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16(I111, I112, I113, I114, I115, I116, I117, I118, I119) 105.17/104.27 f16(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f17(I120, 1 + I121, I122, I123, I124, I125, I126, I127, I128) [1 + I121 <= 50] 105.17/104.27 f16(I129, I130, I131, I132, I133, I134, I135, I136, I137) -> f13(I129, I130, 0, I132, I133, I134, I135, I136, I137) [50 <= I130 /\ I138 = 0] 105.17/104.27 f14(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15(I139, I140, I141, I142, I143, I144, I145, I146, I147) 105.17/104.27 f12(I148, I149, I150, I151, I152, I153, I154, I155, I156) -> f13(I148, I149, 1 + I150, I151, I152, I153, I154, I155, I156) [1 + I150 <= 50] 105.17/104.27 f12(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f9(I157, I158, I159, 0, I161, I162, I163, I164, I165) [50 <= I159 /\ I166 = 0] 105.17/104.27 f10(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11(I167, I168, I169, I170, I171, I172, I173, I174, I175) 105.17/104.27 f8(I176, I177, I178, I179, I180, I181, I182, I183, I184) -> f9(I176, I177, I178, 1 + I179, I180, I181, I182, I183, I184) [1 + I179 <= 50] 105.17/104.27 f8(I185, I186, I187, I188, I189, I190, I191, I192, I193) -> f5(I185, I186, I187, I188, I189, I190, 0, I192, I193) [50 <= I188] 105.17/104.27 f6(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7(I194, I195, I196, I197, I198, I199, I200, I201, I202) 105.17/104.27 f3(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5(I203, I204, I205, I206, I207, I208, 1 + I209, I210, I211) [1 + I209 <= 50] 105.17/104.27 f3(I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f4(I212, I213, I214, I215, I216, I217, I218, I219, I220) [50 <= I218] 105.17/104.27 f1(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2(I221, I222, I223, I224, I225, I226, I227, I228, I229) 105.17/104.27 105.17/104.27 The dependency graph for this problem is: 105.17/104.27 10 -> 105.17/104.27 Where: 105.17/104.27 10) f13#(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12#(I83, I84, I85, I86, I87, I88, I89, I90, I91) 105.17/104.27 105.17/104.27 We have the following SCCs. 105.17/104.27 105.17/104.27 105.17/104.27 DP problem for innermost termination. 105.17/104.27 P = 105.17/104.27 f17#(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16#(I111, I112, I113, I114, I115, I116, I117, I118, I119) 105.17/104.27 f16#(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f17#(I120, 1 + I121, I122, I123, I124, I125, I126, I127, I128) [1 + I121 <= 50] 105.17/104.27 R = 105.17/104.27 f19(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) 105.17/104.27 f18(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f1(I0, I1, I2, I3, 0, I5, 0, rnd8, rnd9) [rnd8 = rnd8 /\ rnd9 = rnd9 /\ y1 = 0] 105.17/104.27 f2(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, 1 + I13, I14, I15, I16, I17) [1 + I13 <= 50] 105.17/104.27 f2(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, 0, I24, I25, I26) [50 <= I22 /\ I27 = 0] 105.17/104.27 f5(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3(I28, I29, I30, I31, I32, I33, I34, I35, I36) 105.17/104.27 f7(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6(I37, I38, I39, I40, I41, 1 + I42, I43, I44, I45) [1 + I42 <= 50] 105.17/104.27 f7(I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f10(0, I47, I48, I49, I50, I51, I52, I53, I54) [50 <= I51 /\ I55 = 0] 105.17/104.27 f9(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8(I56, I57, I58, I59, I60, I61, I62, I63, I64) 105.17/104.27 f11(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f10(1 + I65, I66, I67, I68, I69, I70, I71, I72, I73) [1 + I65 <= 50] 105.17/104.27 f11(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f14(I74, I75, I76, I77, I78, I79, 0, I81, I82) [50 <= I74] 105.17/104.27 f13(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12(I83, I84, I85, I86, I87, I88, I89, I90, I91) 105.17/104.27 f15(I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f14(I92, I93, I94, I95, I96, I97, 1 + I98, I99, I100) [1 + I98 <= 50] 105.17/104.27 f15(I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f17(I101, 0, I103, I104, I105, I106, I107, I108, I109) [50 <= I107 /\ I110 = 0] 105.17/104.27 f17(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16(I111, I112, I113, I114, I115, I116, I117, I118, I119) 105.17/104.27 f16(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f17(I120, 1 + I121, I122, I123, I124, I125, I126, I127, I128) [1 + I121 <= 50] 105.17/104.27 f16(I129, I130, I131, I132, I133, I134, I135, I136, I137) -> f13(I129, I130, 0, I132, I133, I134, I135, I136, I137) [50 <= I130 /\ I138 = 0] 105.17/104.27 f14(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15(I139, I140, I141, I142, I143, I144, I145, I146, I147) 105.17/104.27 f12(I148, I149, I150, I151, I152, I153, I154, I155, I156) -> f13(I148, I149, 1 + I150, I151, I152, I153, I154, I155, I156) [1 + I150 <= 50] 105.17/104.27 f12(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f9(I157, I158, I159, 0, I161, I162, I163, I164, I165) [50 <= I159 /\ I166 = 0] 105.17/104.27 f10(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11(I167, I168, I169, I170, I171, I172, I173, I174, I175) 105.17/104.27 f8(I176, I177, I178, I179, I180, I181, I182, I183, I184) -> f9(I176, I177, I178, 1 + I179, I180, I181, I182, I183, I184) [1 + I179 <= 50] 105.17/104.27 f8(I185, I186, I187, I188, I189, I190, I191, I192, I193) -> f5(I185, I186, I187, I188, I189, I190, 0, I192, I193) [50 <= I188] 105.17/104.27 f6(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7(I194, I195, I196, I197, I198, I199, I200, I201, I202) 105.17/104.27 f3(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5(I203, I204, I205, I206, I207, I208, 1 + I209, I210, I211) [1 + I209 <= 50] 105.17/104.27 f3(I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f4(I212, I213, I214, I215, I216, I217, I218, I219, I220) [50 <= I218] 105.17/104.27 f1(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2(I221, I222, I223, I224, I225, I226, I227, I228, I229) 105.17/104.27 105.17/104.27 We use the reverse value criterion with the projection function NU: 105.17/104.27 NU[f16#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = 50 + -1 * (1 + z2) 105.17/104.27 NU[f17#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = 50 + -1 * (1 + z2) 105.17/104.27 105.17/104.27 This gives the following inequalities: 105.17/104.27 ==> 50 + -1 * (1 + I112) >= 50 + -1 * (1 + I112) 105.17/104.27 1 + I121 <= 50 ==> 50 + -1 * (1 + I121) > 50 + -1 * (1 + (1 + I121)) with 50 + -1 * (1 + I121) >= 0 105.17/104.27 105.17/104.27 We remove all the strictly oriented dependency pairs. 105.17/104.27 105.17/104.27 DP problem for innermost termination. 105.17/104.27 P = 105.17/104.27 f17#(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16#(I111, I112, I113, I114, I115, I116, I117, I118, I119) 105.17/104.27 R = 105.17/104.27 f19(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) 105.17/104.27 f18(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f1(I0, I1, I2, I3, 0, I5, 0, rnd8, rnd9) [rnd8 = rnd8 /\ rnd9 = rnd9 /\ y1 = 0] 105.17/104.27 f2(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, 1 + I13, I14, I15, I16, I17) [1 + I13 <= 50] 105.17/104.27 f2(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, 0, I24, I25, I26) [50 <= I22 /\ I27 = 0] 105.17/104.27 f5(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3(I28, I29, I30, I31, I32, I33, I34, I35, I36) 105.17/104.27 f7(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6(I37, I38, I39, I40, I41, 1 + I42, I43, I44, I45) [1 + I42 <= 50] 105.17/104.27 f7(I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f10(0, I47, I48, I49, I50, I51, I52, I53, I54) [50 <= I51 /\ I55 = 0] 105.17/104.27 f9(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8(I56, I57, I58, I59, I60, I61, I62, I63, I64) 105.17/104.27 f11(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f10(1 + I65, I66, I67, I68, I69, I70, I71, I72, I73) [1 + I65 <= 50] 105.17/104.27 f11(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f14(I74, I75, I76, I77, I78, I79, 0, I81, I82) [50 <= I74] 105.17/104.27 f13(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12(I83, I84, I85, I86, I87, I88, I89, I90, I91) 105.17/104.27 f15(I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f14(I92, I93, I94, I95, I96, I97, 1 + I98, I99, I100) [1 + I98 <= 50] 105.17/104.27 f15(I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f17(I101, 0, I103, I104, I105, I106, I107, I108, I109) [50 <= I107 /\ I110 = 0] 105.17/104.27 f17(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16(I111, I112, I113, I114, I115, I116, I117, I118, I119) 105.17/104.27 f16(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f17(I120, 1 + I121, I122, I123, I124, I125, I126, I127, I128) [1 + I121 <= 50] 105.17/104.27 f16(I129, I130, I131, I132, I133, I134, I135, I136, I137) -> f13(I129, I130, 0, I132, I133, I134, I135, I136, I137) [50 <= I130 /\ I138 = 0] 105.17/104.27 f14(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15(I139, I140, I141, I142, I143, I144, I145, I146, I147) 105.17/104.27 f12(I148, I149, I150, I151, I152, I153, I154, I155, I156) -> f13(I148, I149, 1 + I150, I151, I152, I153, I154, I155, I156) [1 + I150 <= 50] 105.17/104.27 f12(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f9(I157, I158, I159, 0, I161, I162, I163, I164, I165) [50 <= I159 /\ I166 = 0] 105.17/104.27 f10(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11(I167, I168, I169, I170, I171, I172, I173, I174, I175) 105.17/104.27 f8(I176, I177, I178, I179, I180, I181, I182, I183, I184) -> f9(I176, I177, I178, 1 + I179, I180, I181, I182, I183, I184) [1 + I179 <= 50] 105.17/104.27 f8(I185, I186, I187, I188, I189, I190, I191, I192, I193) -> f5(I185, I186, I187, I188, I189, I190, 0, I192, I193) [50 <= I188] 105.17/104.27 f6(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7(I194, I195, I196, I197, I198, I199, I200, I201, I202) 105.17/104.27 f3(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5(I203, I204, I205, I206, I207, I208, 1 + I209, I210, I211) [1 + I209 <= 50] 105.17/104.27 f3(I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f4(I212, I213, I214, I215, I216, I217, I218, I219, I220) [50 <= I218] 105.17/104.27 f1(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2(I221, I222, I223, I224, I225, I226, I227, I228, I229) 105.17/104.27 105.17/104.27 The dependency graph for this problem is: 105.17/104.27 13 -> 105.17/104.27 Where: 105.17/104.27 13) f17#(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16#(I111, I112, I113, I114, I115, I116, I117, I118, I119) 105.17/104.27 105.17/104.27 We have the following SCCs. 105.17/104.27 105.17/104.27 105.17/104.27 DP problem for innermost termination. 105.17/104.27 P = 105.17/104.27 f15#(I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f14#(I92, I93, I94, I95, I96, I97, 1 + I98, I99, I100) [1 + I98 <= 50] 105.17/104.27 f14#(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15#(I139, I140, I141, I142, I143, I144, I145, I146, I147) 105.17/104.27 R = 105.17/104.27 f19(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) 105.17/104.27 f18(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f1(I0, I1, I2, I3, 0, I5, 0, rnd8, rnd9) [rnd8 = rnd8 /\ rnd9 = rnd9 /\ y1 = 0] 105.17/104.27 f2(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, 1 + I13, I14, I15, I16, I17) [1 + I13 <= 50] 105.17/104.27 f2(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, 0, I24, I25, I26) [50 <= I22 /\ I27 = 0] 105.17/104.27 f5(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3(I28, I29, I30, I31, I32, I33, I34, I35, I36) 105.17/104.27 f7(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6(I37, I38, I39, I40, I41, 1 + I42, I43, I44, I45) [1 + I42 <= 50] 105.17/104.27 f7(I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f10(0, I47, I48, I49, I50, I51, I52, I53, I54) [50 <= I51 /\ I55 = 0] 105.17/104.27 f9(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8(I56, I57, I58, I59, I60, I61, I62, I63, I64) 105.17/104.27 f11(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f10(1 + I65, I66, I67, I68, I69, I70, I71, I72, I73) [1 + I65 <= 50] 105.17/104.27 f11(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f14(I74, I75, I76, I77, I78, I79, 0, I81, I82) [50 <= I74] 105.17/104.27 f13(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12(I83, I84, I85, I86, I87, I88, I89, I90, I91) 105.17/104.27 f15(I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f14(I92, I93, I94, I95, I96, I97, 1 + I98, I99, I100) [1 + I98 <= 50] 105.17/104.27 f15(I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f17(I101, 0, I103, I104, I105, I106, I107, I108, I109) [50 <= I107 /\ I110 = 0] 105.17/104.27 f17(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16(I111, I112, I113, I114, I115, I116, I117, I118, I119) 105.17/104.27 f16(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f17(I120, 1 + I121, I122, I123, I124, I125, I126, I127, I128) [1 + I121 <= 50] 105.17/104.27 f16(I129, I130, I131, I132, I133, I134, I135, I136, I137) -> f13(I129, I130, 0, I132, I133, I134, I135, I136, I137) [50 <= I130 /\ I138 = 0] 105.17/104.27 f14(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15(I139, I140, I141, I142, I143, I144, I145, I146, I147) 105.17/104.27 f12(I148, I149, I150, I151, I152, I153, I154, I155, I156) -> f13(I148, I149, 1 + I150, I151, I152, I153, I154, I155, I156) [1 + I150 <= 50] 105.17/104.27 f12(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f9(I157, I158, I159, 0, I161, I162, I163, I164, I165) [50 <= I159 /\ I166 = 0] 105.17/104.27 f10(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11(I167, I168, I169, I170, I171, I172, I173, I174, I175) 105.17/104.27 f8(I176, I177, I178, I179, I180, I181, I182, I183, I184) -> f9(I176, I177, I178, 1 + I179, I180, I181, I182, I183, I184) [1 + I179 <= 50] 105.17/104.27 f8(I185, I186, I187, I188, I189, I190, I191, I192, I193) -> f5(I185, I186, I187, I188, I189, I190, 0, I192, I193) [50 <= I188] 105.17/104.27 f6(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7(I194, I195, I196, I197, I198, I199, I200, I201, I202) 105.17/104.27 f3(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5(I203, I204, I205, I206, I207, I208, 1 + I209, I210, I211) [1 + I209 <= 50] 105.17/104.27 f3(I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f4(I212, I213, I214, I215, I216, I217, I218, I219, I220) [50 <= I218] 105.17/104.27 f1(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2(I221, I222, I223, I224, I225, I226, I227, I228, I229) 105.17/104.27 105.17/104.27 We use the reverse value criterion with the projection function NU: 105.17/104.27 NU[f14#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = 50 + -1 * (1 + z7) 105.17/104.27 NU[f15#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = 50 + -1 * (1 + z7) 105.17/104.27 105.17/104.27 This gives the following inequalities: 105.17/104.27 1 + I98 <= 50 ==> 50 + -1 * (1 + I98) > 50 + -1 * (1 + (1 + I98)) with 50 + -1 * (1 + I98) >= 0 105.17/104.27 ==> 50 + -1 * (1 + I145) >= 50 + -1 * (1 + I145) 105.17/104.27 105.17/104.27 We remove all the strictly oriented dependency pairs. 105.17/104.27 105.17/104.27 DP problem for innermost termination. 105.17/104.27 P = 105.17/104.27 f14#(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15#(I139, I140, I141, I142, I143, I144, I145, I146, I147) 105.17/104.27 R = 105.17/104.27 f19(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) 105.17/104.27 f18(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f1(I0, I1, I2, I3, 0, I5, 0, rnd8, rnd9) [rnd8 = rnd8 /\ rnd9 = rnd9 /\ y1 = 0] 105.17/104.27 f2(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, 1 + I13, I14, I15, I16, I17) [1 + I13 <= 50] 105.17/104.27 f2(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, 0, I24, I25, I26) [50 <= I22 /\ I27 = 0] 105.17/104.27 f5(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3(I28, I29, I30, I31, I32, I33, I34, I35, I36) 105.17/104.27 f7(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6(I37, I38, I39, I40, I41, 1 + I42, I43, I44, I45) [1 + I42 <= 50] 105.17/104.27 f7(I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f10(0, I47, I48, I49, I50, I51, I52, I53, I54) [50 <= I51 /\ I55 = 0] 105.17/104.27 f9(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8(I56, I57, I58, I59, I60, I61, I62, I63, I64) 105.17/104.27 f11(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f10(1 + I65, I66, I67, I68, I69, I70, I71, I72, I73) [1 + I65 <= 50] 105.17/104.27 f11(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f14(I74, I75, I76, I77, I78, I79, 0, I81, I82) [50 <= I74] 105.17/104.27 f13(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12(I83, I84, I85, I86, I87, I88, I89, I90, I91) 105.17/104.27 f15(I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f14(I92, I93, I94, I95, I96, I97, 1 + I98, I99, I100) [1 + I98 <= 50] 105.17/104.27 f15(I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f17(I101, 0, I103, I104, I105, I106, I107, I108, I109) [50 <= I107 /\ I110 = 0] 105.17/104.27 f17(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16(I111, I112, I113, I114, I115, I116, I117, I118, I119) 105.17/104.27 f16(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f17(I120, 1 + I121, I122, I123, I124, I125, I126, I127, I128) [1 + I121 <= 50] 105.17/104.27 f16(I129, I130, I131, I132, I133, I134, I135, I136, I137) -> f13(I129, I130, 0, I132, I133, I134, I135, I136, I137) [50 <= I130 /\ I138 = 0] 105.17/104.27 f14(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15(I139, I140, I141, I142, I143, I144, I145, I146, I147) 105.17/104.27 f12(I148, I149, I150, I151, I152, I153, I154, I155, I156) -> f13(I148, I149, 1 + I150, I151, I152, I153, I154, I155, I156) [1 + I150 <= 50] 105.17/104.27 f12(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f9(I157, I158, I159, 0, I161, I162, I163, I164, I165) [50 <= I159 /\ I166 = 0] 105.17/104.27 f10(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11(I167, I168, I169, I170, I171, I172, I173, I174, I175) 105.17/104.27 f8(I176, I177, I178, I179, I180, I181, I182, I183, I184) -> f9(I176, I177, I178, 1 + I179, I180, I181, I182, I183, I184) [1 + I179 <= 50] 105.17/104.27 f8(I185, I186, I187, I188, I189, I190, I191, I192, I193) -> f5(I185, I186, I187, I188, I189, I190, 0, I192, I193) [50 <= I188] 105.17/104.27 f6(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7(I194, I195, I196, I197, I198, I199, I200, I201, I202) 105.17/104.27 f3(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5(I203, I204, I205, I206, I207, I208, 1 + I209, I210, I211) [1 + I209 <= 50] 105.17/104.27 f3(I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f4(I212, I213, I214, I215, I216, I217, I218, I219, I220) [50 <= I218] 105.17/104.27 f1(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2(I221, I222, I223, I224, I225, I226, I227, I228, I229) 105.17/104.27 105.17/104.27 The dependency graph for this problem is: 105.17/104.27 16 -> 105.17/104.27 Where: 105.17/104.27 16) f14#(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15#(I139, I140, I141, I142, I143, I144, I145, I146, I147) 105.17/104.27 105.17/104.27 We have the following SCCs. 105.17/104.27 105.17/104.27 105.17/104.27 DP problem for innermost termination. 105.17/104.27 P = 105.17/104.27 f11#(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f10#(1 + I65, I66, I67, I68, I69, I70, I71, I72, I73) [1 + I65 <= 50] 105.17/104.27 f10#(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11#(I167, I168, I169, I170, I171, I172, I173, I174, I175) 105.17/104.27 R = 105.17/104.27 f19(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) 105.17/104.27 f18(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f1(I0, I1, I2, I3, 0, I5, 0, rnd8, rnd9) [rnd8 = rnd8 /\ rnd9 = rnd9 /\ y1 = 0] 105.17/104.27 f2(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, 1 + I13, I14, I15, I16, I17) [1 + I13 <= 50] 105.17/104.27 f2(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, 0, I24, I25, I26) [50 <= I22 /\ I27 = 0] 105.17/104.27 f5(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3(I28, I29, I30, I31, I32, I33, I34, I35, I36) 105.17/104.27 f7(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6(I37, I38, I39, I40, I41, 1 + I42, I43, I44, I45) [1 + I42 <= 50] 105.17/104.27 f7(I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f10(0, I47, I48, I49, I50, I51, I52, I53, I54) [50 <= I51 /\ I55 = 0] 105.17/104.27 f9(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8(I56, I57, I58, I59, I60, I61, I62, I63, I64) 105.17/104.27 f11(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f10(1 + I65, I66, I67, I68, I69, I70, I71, I72, I73) [1 + I65 <= 50] 105.17/104.27 f11(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f14(I74, I75, I76, I77, I78, I79, 0, I81, I82) [50 <= I74] 105.17/104.27 f13(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12(I83, I84, I85, I86, I87, I88, I89, I90, I91) 105.17/104.27 f15(I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f14(I92, I93, I94, I95, I96, I97, 1 + I98, I99, I100) [1 + I98 <= 50] 105.17/104.27 f15(I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f17(I101, 0, I103, I104, I105, I106, I107, I108, I109) [50 <= I107 /\ I110 = 0] 105.17/104.27 f17(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16(I111, I112, I113, I114, I115, I116, I117, I118, I119) 105.17/104.27 f16(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f17(I120, 1 + I121, I122, I123, I124, I125, I126, I127, I128) [1 + I121 <= 50] 105.17/104.27 f16(I129, I130, I131, I132, I133, I134, I135, I136, I137) -> f13(I129, I130, 0, I132, I133, I134, I135, I136, I137) [50 <= I130 /\ I138 = 0] 105.17/104.27 f14(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15(I139, I140, I141, I142, I143, I144, I145, I146, I147) 105.17/104.27 f12(I148, I149, I150, I151, I152, I153, I154, I155, I156) -> f13(I148, I149, 1 + I150, I151, I152, I153, I154, I155, I156) [1 + I150 <= 50] 105.17/104.27 f12(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f9(I157, I158, I159, 0, I161, I162, I163, I164, I165) [50 <= I159 /\ I166 = 0] 105.17/104.27 f10(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11(I167, I168, I169, I170, I171, I172, I173, I174, I175) 105.17/104.27 f8(I176, I177, I178, I179, I180, I181, I182, I183, I184) -> f9(I176, I177, I178, 1 + I179, I180, I181, I182, I183, I184) [1 + I179 <= 50] 105.17/104.27 f8(I185, I186, I187, I188, I189, I190, I191, I192, I193) -> f5(I185, I186, I187, I188, I189, I190, 0, I192, I193) [50 <= I188] 105.17/104.27 f6(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7(I194, I195, I196, I197, I198, I199, I200, I201, I202) 105.17/104.27 f3(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5(I203, I204, I205, I206, I207, I208, 1 + I209, I210, I211) [1 + I209 <= 50] 105.17/104.27 f3(I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f4(I212, I213, I214, I215, I216, I217, I218, I219, I220) [50 <= I218] 105.17/104.27 f1(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2(I221, I222, I223, I224, I225, I226, I227, I228, I229) 105.17/104.27 105.17/104.27 We use the reverse value criterion with the projection function NU: 105.17/104.27 NU[f10#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = 50 + -1 * (1 + z1) 105.17/104.27 NU[f11#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = 50 + -1 * (1 + z1) 105.17/104.27 105.17/104.27 This gives the following inequalities: 105.17/104.27 1 + I65 <= 50 ==> 50 + -1 * (1 + I65) > 50 + -1 * (1 + (1 + I65)) with 50 + -1 * (1 + I65) >= 0 105.17/104.27 ==> 50 + -1 * (1 + I167) >= 50 + -1 * (1 + I167) 105.17/104.27 105.17/104.27 We remove all the strictly oriented dependency pairs. 105.17/104.27 105.17/104.27 DP problem for innermost termination. 105.17/104.27 P = 105.17/104.27 f10#(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11#(I167, I168, I169, I170, I171, I172, I173, I174, I175) 105.17/104.27 R = 105.17/104.27 f19(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) 105.17/104.27 f18(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f1(I0, I1, I2, I3, 0, I5, 0, rnd8, rnd9) [rnd8 = rnd8 /\ rnd9 = rnd9 /\ y1 = 0] 105.17/104.27 f2(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, 1 + I13, I14, I15, I16, I17) [1 + I13 <= 50] 105.17/104.27 f2(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, 0, I24, I25, I26) [50 <= I22 /\ I27 = 0] 105.17/104.27 f5(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3(I28, I29, I30, I31, I32, I33, I34, I35, I36) 105.17/104.27 f7(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6(I37, I38, I39, I40, I41, 1 + I42, I43, I44, I45) [1 + I42 <= 50] 105.17/104.27 f7(I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f10(0, I47, I48, I49, I50, I51, I52, I53, I54) [50 <= I51 /\ I55 = 0] 105.17/104.27 f9(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8(I56, I57, I58, I59, I60, I61, I62, I63, I64) 105.17/104.27 f11(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f10(1 + I65, I66, I67, I68, I69, I70, I71, I72, I73) [1 + I65 <= 50] 105.17/104.27 f11(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f14(I74, I75, I76, I77, I78, I79, 0, I81, I82) [50 <= I74] 105.17/104.27 f13(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12(I83, I84, I85, I86, I87, I88, I89, I90, I91) 105.17/104.27 f15(I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f14(I92, I93, I94, I95, I96, I97, 1 + I98, I99, I100) [1 + I98 <= 50] 105.17/104.27 f15(I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f17(I101, 0, I103, I104, I105, I106, I107, I108, I109) [50 <= I107 /\ I110 = 0] 105.17/104.27 f17(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16(I111, I112, I113, I114, I115, I116, I117, I118, I119) 105.17/104.27 f16(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f17(I120, 1 + I121, I122, I123, I124, I125, I126, I127, I128) [1 + I121 <= 50] 105.17/104.27 f16(I129, I130, I131, I132, I133, I134, I135, I136, I137) -> f13(I129, I130, 0, I132, I133, I134, I135, I136, I137) [50 <= I130 /\ I138 = 0] 105.17/104.27 f14(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15(I139, I140, I141, I142, I143, I144, I145, I146, I147) 105.17/104.27 f12(I148, I149, I150, I151, I152, I153, I154, I155, I156) -> f13(I148, I149, 1 + I150, I151, I152, I153, I154, I155, I156) [1 + I150 <= 50] 105.17/104.27 f12(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f9(I157, I158, I159, 0, I161, I162, I163, I164, I165) [50 <= I159 /\ I166 = 0] 105.17/104.27 f10(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11(I167, I168, I169, I170, I171, I172, I173, I174, I175) 105.17/104.27 f8(I176, I177, I178, I179, I180, I181, I182, I183, I184) -> f9(I176, I177, I178, 1 + I179, I180, I181, I182, I183, I184) [1 + I179 <= 50] 105.17/104.27 f8(I185, I186, I187, I188, I189, I190, I191, I192, I193) -> f5(I185, I186, I187, I188, I189, I190, 0, I192, I193) [50 <= I188] 105.17/104.27 f6(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7(I194, I195, I196, I197, I198, I199, I200, I201, I202) 105.17/104.27 f3(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5(I203, I204, I205, I206, I207, I208, 1 + I209, I210, I211) [1 + I209 <= 50] 105.17/104.27 f3(I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f4(I212, I213, I214, I215, I216, I217, I218, I219, I220) [50 <= I218] 105.17/104.27 f1(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2(I221, I222, I223, I224, I225, I226, I227, I228, I229) 105.17/104.27 105.17/104.27 The dependency graph for this problem is: 105.17/104.27 19 -> 105.17/104.27 Where: 105.17/104.27 19) f10#(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11#(I167, I168, I169, I170, I171, I172, I173, I174, I175) 105.17/104.27 105.17/104.27 We have the following SCCs. 105.17/104.27 105.17/104.27 105.17/104.27 DP problem for innermost termination. 105.17/104.27 P = 105.17/104.27 f7#(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6#(I37, I38, I39, I40, I41, 1 + I42, I43, I44, I45) [1 + I42 <= 50] 105.17/104.27 f6#(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7#(I194, I195, I196, I197, I198, I199, I200, I201, I202) 105.17/104.27 R = 105.17/104.27 f19(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) 105.17/104.27 f18(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f1(I0, I1, I2, I3, 0, I5, 0, rnd8, rnd9) [rnd8 = rnd8 /\ rnd9 = rnd9 /\ y1 = 0] 105.17/104.27 f2(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, 1 + I13, I14, I15, I16, I17) [1 + I13 <= 50] 105.17/104.27 f2(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, 0, I24, I25, I26) [50 <= I22 /\ I27 = 0] 105.17/104.27 f5(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3(I28, I29, I30, I31, I32, I33, I34, I35, I36) 105.17/104.27 f7(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6(I37, I38, I39, I40, I41, 1 + I42, I43, I44, I45) [1 + I42 <= 50] 105.17/104.27 f7(I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f10(0, I47, I48, I49, I50, I51, I52, I53, I54) [50 <= I51 /\ I55 = 0] 105.17/104.27 f9(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8(I56, I57, I58, I59, I60, I61, I62, I63, I64) 105.17/104.27 f11(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f10(1 + I65, I66, I67, I68, I69, I70, I71, I72, I73) [1 + I65 <= 50] 105.17/104.27 f11(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f14(I74, I75, I76, I77, I78, I79, 0, I81, I82) [50 <= I74] 105.17/104.27 f13(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12(I83, I84, I85, I86, I87, I88, I89, I90, I91) 105.17/104.27 f15(I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f14(I92, I93, I94, I95, I96, I97, 1 + I98, I99, I100) [1 + I98 <= 50] 105.17/104.27 f15(I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f17(I101, 0, I103, I104, I105, I106, I107, I108, I109) [50 <= I107 /\ I110 = 0] 105.17/104.27 f17(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16(I111, I112, I113, I114, I115, I116, I117, I118, I119) 105.17/104.27 f16(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f17(I120, 1 + I121, I122, I123, I124, I125, I126, I127, I128) [1 + I121 <= 50] 105.17/104.27 f16(I129, I130, I131, I132, I133, I134, I135, I136, I137) -> f13(I129, I130, 0, I132, I133, I134, I135, I136, I137) [50 <= I130 /\ I138 = 0] 105.17/104.27 f14(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15(I139, I140, I141, I142, I143, I144, I145, I146, I147) 105.17/104.27 f12(I148, I149, I150, I151, I152, I153, I154, I155, I156) -> f13(I148, I149, 1 + I150, I151, I152, I153, I154, I155, I156) [1 + I150 <= 50] 105.17/104.27 f12(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f9(I157, I158, I159, 0, I161, I162, I163, I164, I165) [50 <= I159 /\ I166 = 0] 105.17/104.27 f10(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11(I167, I168, I169, I170, I171, I172, I173, I174, I175) 105.17/104.27 f8(I176, I177, I178, I179, I180, I181, I182, I183, I184) -> f9(I176, I177, I178, 1 + I179, I180, I181, I182, I183, I184) [1 + I179 <= 50] 105.17/104.27 f8(I185, I186, I187, I188, I189, I190, I191, I192, I193) -> f5(I185, I186, I187, I188, I189, I190, 0, I192, I193) [50 <= I188] 105.17/104.27 f6(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7(I194, I195, I196, I197, I198, I199, I200, I201, I202) 105.17/104.27 f3(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5(I203, I204, I205, I206, I207, I208, 1 + I209, I210, I211) [1 + I209 <= 50] 105.17/104.27 f3(I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f4(I212, I213, I214, I215, I216, I217, I218, I219, I220) [50 <= I218] 105.17/104.27 f1(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2(I221, I222, I223, I224, I225, I226, I227, I228, I229) 105.17/104.27 105.17/104.27 We use the reverse value criterion with the projection function NU: 105.17/104.27 NU[f6#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = 50 + -1 * (1 + z6) 105.17/104.27 NU[f7#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = 50 + -1 * (1 + z6) 105.17/104.27 105.17/104.27 This gives the following inequalities: 105.17/104.27 1 + I42 <= 50 ==> 50 + -1 * (1 + I42) > 50 + -1 * (1 + (1 + I42)) with 50 + -1 * (1 + I42) >= 0 105.17/104.27 ==> 50 + -1 * (1 + I199) >= 50 + -1 * (1 + I199) 105.17/104.27 105.17/104.27 We remove all the strictly oriented dependency pairs. 105.17/104.27 105.17/104.27 DP problem for innermost termination. 105.17/104.27 P = 105.17/104.27 f6#(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7#(I194, I195, I196, I197, I198, I199, I200, I201, I202) 105.17/104.27 R = 105.17/104.27 f19(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) 105.17/104.27 f18(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f1(I0, I1, I2, I3, 0, I5, 0, rnd8, rnd9) [rnd8 = rnd8 /\ rnd9 = rnd9 /\ y1 = 0] 105.17/104.27 f2(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, 1 + I13, I14, I15, I16, I17) [1 + I13 <= 50] 105.17/104.27 f2(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, 0, I24, I25, I26) [50 <= I22 /\ I27 = 0] 105.17/104.27 f5(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3(I28, I29, I30, I31, I32, I33, I34, I35, I36) 105.17/104.27 f7(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6(I37, I38, I39, I40, I41, 1 + I42, I43, I44, I45) [1 + I42 <= 50] 105.17/104.27 f7(I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f10(0, I47, I48, I49, I50, I51, I52, I53, I54) [50 <= I51 /\ I55 = 0] 105.17/104.27 f9(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8(I56, I57, I58, I59, I60, I61, I62, I63, I64) 105.17/104.27 f11(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f10(1 + I65, I66, I67, I68, I69, I70, I71, I72, I73) [1 + I65 <= 50] 105.17/104.27 f11(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f14(I74, I75, I76, I77, I78, I79, 0, I81, I82) [50 <= I74] 105.17/104.27 f13(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12(I83, I84, I85, I86, I87, I88, I89, I90, I91) 105.17/104.27 f15(I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f14(I92, I93, I94, I95, I96, I97, 1 + I98, I99, I100) [1 + I98 <= 50] 105.17/104.27 f15(I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f17(I101, 0, I103, I104, I105, I106, I107, I108, I109) [50 <= I107 /\ I110 = 0] 105.17/104.27 f17(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16(I111, I112, I113, I114, I115, I116, I117, I118, I119) 105.17/104.27 f16(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f17(I120, 1 + I121, I122, I123, I124, I125, I126, I127, I128) [1 + I121 <= 50] 105.17/104.27 f16(I129, I130, I131, I132, I133, I134, I135, I136, I137) -> f13(I129, I130, 0, I132, I133, I134, I135, I136, I137) [50 <= I130 /\ I138 = 0] 105.17/104.27 f14(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15(I139, I140, I141, I142, I143, I144, I145, I146, I147) 105.17/104.27 f12(I148, I149, I150, I151, I152, I153, I154, I155, I156) -> f13(I148, I149, 1 + I150, I151, I152, I153, I154, I155, I156) [1 + I150 <= 50] 105.17/104.27 f12(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f9(I157, I158, I159, 0, I161, I162, I163, I164, I165) [50 <= I159 /\ I166 = 0] 105.17/104.27 f10(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11(I167, I168, I169, I170, I171, I172, I173, I174, I175) 105.17/104.27 f8(I176, I177, I178, I179, I180, I181, I182, I183, I184) -> f9(I176, I177, I178, 1 + I179, I180, I181, I182, I183, I184) [1 + I179 <= 50] 105.17/104.27 f8(I185, I186, I187, I188, I189, I190, I191, I192, I193) -> f5(I185, I186, I187, I188, I189, I190, 0, I192, I193) [50 <= I188] 105.17/104.27 f6(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7(I194, I195, I196, I197, I198, I199, I200, I201, I202) 105.17/104.27 f3(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5(I203, I204, I205, I206, I207, I208, 1 + I209, I210, I211) [1 + I209 <= 50] 105.17/104.27 f3(I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f4(I212, I213, I214, I215, I216, I217, I218, I219, I220) [50 <= I218] 105.17/104.27 f1(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2(I221, I222, I223, I224, I225, I226, I227, I228, I229) 105.17/104.27 105.17/104.27 The dependency graph for this problem is: 105.17/104.27 22 -> 105.17/104.27 Where: 105.17/104.27 22) f6#(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7#(I194, I195, I196, I197, I198, I199, I200, I201, I202) 105.17/104.27 105.17/104.27 We have the following SCCs. 105.17/104.27 105.17/104.27 105.17/104.27 DP problem for innermost termination. 105.17/104.27 P = 105.17/104.27 f2#(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1#(I9, I10, I11, I12, 1 + I13, I14, I15, I16, I17) [1 + I13 <= 50] 105.17/104.27 f1#(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2#(I221, I222, I223, I224, I225, I226, I227, I228, I229) 105.17/104.27 R = 105.17/104.27 f19(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) 105.17/104.27 f18(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f1(I0, I1, I2, I3, 0, I5, 0, rnd8, rnd9) [rnd8 = rnd8 /\ rnd9 = rnd9 /\ y1 = 0] 105.17/104.27 f2(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, 1 + I13, I14, I15, I16, I17) [1 + I13 <= 50] 105.17/104.27 f2(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, 0, I24, I25, I26) [50 <= I22 /\ I27 = 0] 105.17/104.27 f5(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3(I28, I29, I30, I31, I32, I33, I34, I35, I36) 105.17/104.27 f7(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6(I37, I38, I39, I40, I41, 1 + I42, I43, I44, I45) [1 + I42 <= 50] 105.17/104.27 f7(I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f10(0, I47, I48, I49, I50, I51, I52, I53, I54) [50 <= I51 /\ I55 = 0] 105.17/104.27 f9(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8(I56, I57, I58, I59, I60, I61, I62, I63, I64) 105.17/104.27 f11(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f10(1 + I65, I66, I67, I68, I69, I70, I71, I72, I73) [1 + I65 <= 50] 105.17/104.27 f11(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f14(I74, I75, I76, I77, I78, I79, 0, I81, I82) [50 <= I74] 105.17/104.27 f13(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12(I83, I84, I85, I86, I87, I88, I89, I90, I91) 105.17/104.27 f15(I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f14(I92, I93, I94, I95, I96, I97, 1 + I98, I99, I100) [1 + I98 <= 50] 105.17/104.27 f15(I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f17(I101, 0, I103, I104, I105, I106, I107, I108, I109) [50 <= I107 /\ I110 = 0] 105.17/104.27 f17(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16(I111, I112, I113, I114, I115, I116, I117, I118, I119) 105.17/104.27 f16(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f17(I120, 1 + I121, I122, I123, I124, I125, I126, I127, I128) [1 + I121 <= 50] 105.17/104.27 f16(I129, I130, I131, I132, I133, I134, I135, I136, I137) -> f13(I129, I130, 0, I132, I133, I134, I135, I136, I137) [50 <= I130 /\ I138 = 0] 105.17/104.27 f14(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15(I139, I140, I141, I142, I143, I144, I145, I146, I147) 105.17/104.27 f12(I148, I149, I150, I151, I152, I153, I154, I155, I156) -> f13(I148, I149, 1 + I150, I151, I152, I153, I154, I155, I156) [1 + I150 <= 50] 105.17/104.27 f12(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f9(I157, I158, I159, 0, I161, I162, I163, I164, I165) [50 <= I159 /\ I166 = 0] 105.17/104.27 f10(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11(I167, I168, I169, I170, I171, I172, I173, I174, I175) 105.17/104.27 f8(I176, I177, I178, I179, I180, I181, I182, I183, I184) -> f9(I176, I177, I178, 1 + I179, I180, I181, I182, I183, I184) [1 + I179 <= 50] 105.17/104.27 f8(I185, I186, I187, I188, I189, I190, I191, I192, I193) -> f5(I185, I186, I187, I188, I189, I190, 0, I192, I193) [50 <= I188] 105.17/104.27 f6(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7(I194, I195, I196, I197, I198, I199, I200, I201, I202) 105.17/104.27 f3(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5(I203, I204, I205, I206, I207, I208, 1 + I209, I210, I211) [1 + I209 <= 50] 105.17/104.27 f3(I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f4(I212, I213, I214, I215, I216, I217, I218, I219, I220) [50 <= I218] 105.17/104.27 f1(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2(I221, I222, I223, I224, I225, I226, I227, I228, I229) 105.17/104.27 105.17/104.27 We use the reverse value criterion with the projection function NU: 105.17/104.27 NU[f1#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = 50 + -1 * (1 + z5) 105.17/104.27 NU[f2#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = 50 + -1 * (1 + z5) 105.17/104.27 105.17/104.27 This gives the following inequalities: 105.17/104.27 1 + I13 <= 50 ==> 50 + -1 * (1 + I13) > 50 + -1 * (1 + (1 + I13)) with 50 + -1 * (1 + I13) >= 0 105.17/104.27 ==> 50 + -1 * (1 + I225) >= 50 + -1 * (1 + I225) 105.17/104.27 105.17/104.27 We remove all the strictly oriented dependency pairs. 105.17/104.27 105.17/104.27 DP problem for innermost termination. 105.17/104.27 P = 105.17/104.27 f1#(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2#(I221, I222, I223, I224, I225, I226, I227, I228, I229) 105.17/104.27 R = 105.17/104.27 f19(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) 105.17/104.27 f18(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f1(I0, I1, I2, I3, 0, I5, 0, rnd8, rnd9) [rnd8 = rnd8 /\ rnd9 = rnd9 /\ y1 = 0] 105.17/104.27 f2(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, 1 + I13, I14, I15, I16, I17) [1 + I13 <= 50] 105.17/104.27 f2(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, 0, I24, I25, I26) [50 <= I22 /\ I27 = 0] 105.17/104.27 f5(I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f3(I28, I29, I30, I31, I32, I33, I34, I35, I36) 105.17/104.27 f7(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6(I37, I38, I39, I40, I41, 1 + I42, I43, I44, I45) [1 + I42 <= 50] 105.17/104.27 f7(I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f10(0, I47, I48, I49, I50, I51, I52, I53, I54) [50 <= I51 /\ I55 = 0] 105.17/104.27 f9(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f8(I56, I57, I58, I59, I60, I61, I62, I63, I64) 105.17/104.27 f11(I65, I66, I67, I68, I69, I70, I71, I72, I73) -> f10(1 + I65, I66, I67, I68, I69, I70, I71, I72, I73) [1 + I65 <= 50] 105.17/104.27 f11(I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f14(I74, I75, I76, I77, I78, I79, 0, I81, I82) [50 <= I74] 105.17/104.27 f13(I83, I84, I85, I86, I87, I88, I89, I90, I91) -> f12(I83, I84, I85, I86, I87, I88, I89, I90, I91) 105.17/104.27 f15(I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f14(I92, I93, I94, I95, I96, I97, 1 + I98, I99, I100) [1 + I98 <= 50] 105.17/104.27 f15(I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f17(I101, 0, I103, I104, I105, I106, I107, I108, I109) [50 <= I107 /\ I110 = 0] 105.17/104.27 f17(I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f16(I111, I112, I113, I114, I115, I116, I117, I118, I119) 105.17/104.27 f16(I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f17(I120, 1 + I121, I122, I123, I124, I125, I126, I127, I128) [1 + I121 <= 50] 105.17/104.27 f16(I129, I130, I131, I132, I133, I134, I135, I136, I137) -> f13(I129, I130, 0, I132, I133, I134, I135, I136, I137) [50 <= I130 /\ I138 = 0] 105.17/104.27 f14(I139, I140, I141, I142, I143, I144, I145, I146, I147) -> f15(I139, I140, I141, I142, I143, I144, I145, I146, I147) 105.17/104.27 f12(I148, I149, I150, I151, I152, I153, I154, I155, I156) -> f13(I148, I149, 1 + I150, I151, I152, I153, I154, I155, I156) [1 + I150 <= 50] 105.17/104.27 f12(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f9(I157, I158, I159, 0, I161, I162, I163, I164, I165) [50 <= I159 /\ I166 = 0] 105.17/104.27 f10(I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f11(I167, I168, I169, I170, I171, I172, I173, I174, I175) 105.17/104.27 f8(I176, I177, I178, I179, I180, I181, I182, I183, I184) -> f9(I176, I177, I178, 1 + I179, I180, I181, I182, I183, I184) [1 + I179 <= 50] 105.17/104.27 f8(I185, I186, I187, I188, I189, I190, I191, I192, I193) -> f5(I185, I186, I187, I188, I189, I190, 0, I192, I193) [50 <= I188] 105.17/104.27 f6(I194, I195, I196, I197, I198, I199, I200, I201, I202) -> f7(I194, I195, I196, I197, I198, I199, I200, I201, I202) 105.17/104.27 f3(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f5(I203, I204, I205, I206, I207, I208, 1 + I209, I210, I211) [1 + I209 <= 50] 105.17/104.27 f3(I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f4(I212, I213, I214, I215, I216, I217, I218, I219, I220) [50 <= I218] 105.17/104.27 f1(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2(I221, I222, I223, I224, I225, I226, I227, I228, I229) 105.17/104.27 105.17/104.27 The dependency graph for this problem is: 105.17/104.27 24 -> 105.17/104.27 Where: 105.17/104.27 24) f1#(I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f2#(I221, I222, I223, I224, I225, I226, I227, I228, I229) 105.17/104.27 105.17/104.27 We have the following SCCs. 105.17/104.27 105.17/104.28 EOF