241.91/237.98 YES 241.91/237.98 241.91/237.98 DP problem for innermost termination. 241.91/237.98 P = 241.91/237.98 f17#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f16#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 241.91/237.98 f16#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1#(I0, I1, I2, I3, I4, 0, I6, 0, I8, I9) 241.91/237.98 f2#(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f3#(I10, I11, 0, I13, I14, I15, I16, I17, I18, I19) [1 + I15 <= 20] 241.91/237.98 f2#(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f5#(I20, I21, I22, I23, I24, I25, 0, I27, I28, I29) [20 <= I25] 241.91/237.98 f4#(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39) -> f3#(I30, I31, 1 + I32, I33, I34, I35, I36, rnd8, rnd9, I39) [rnd9 = rnd8 /\ rnd8 = rnd8 /\ 1 + I32 <= 20] 241.91/237.98 f4#(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) -> f1#(I40, I41, I42, I43, I44, 1 + I45, I46, I47, I48, I49) [20 <= I42] 241.91/237.98 f9#(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f7#(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 241.91/237.98 f8#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f10#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) 241.91/237.98 f6#(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) -> f14#(I70, I71, I72, 0, I74, I75, I76, I77, I78, I79) [1 + I76 <= 20] 241.91/237.98 f6#(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f11#(I80, I81, I82, I83, 0, I85, I86, I87, I88, I89) [20 <= I86] 241.91/237.98 f15#(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f14#(I90, I91, I92, 1 + I93, I94, I95, I96, I100, I98, rnd10) [rnd10 = I100 /\ I100 = I100 /\ 1 + I93 <= 20] 241.91/237.98 f15#(I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f5#(I101, I102, I103, I104, I105, I106, 1 + I107, I108, I109, I110) [20 <= I104] 241.91/237.98 f11#(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) -> f12#(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) 241.91/237.98 f14#(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) -> f15#(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) 241.91/237.98 f12#(I131, I132, I133, I134, I135, I136, I137, I138, I139, I140) -> f8#(I131, 0, I133, I134, I135, I136, I137, I138, I139, I140) [1 + I135 <= 20] 241.91/237.98 f10#(I151, I152, I153, I154, I155, I156, I157, I158, I159, I160) -> f9#(0, I152, I153, I154, I155, I156, I157, I158, I159, I160) [1 + I152 <= 20] 241.91/237.98 f10#(I161, I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f11#(I161, I162, I163, I164, 1 + I165, I166, I167, I168, I169, I170) [20 <= I162] 241.91/237.98 f7#(I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) -> f9#(1 + I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) [1 + I171 <= 20] 241.91/237.98 f7#(I181, I182, I183, I184, I185, I186, I187, I188, I189, I190) -> f8#(I181, 1 + I182, I183, I184, I185, I186, I187, I188, I189, I190) [20 <= I181] 241.91/237.98 f5#(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200) -> f6#(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200) 241.91/237.98 f3#(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) -> f4#(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) 241.91/237.98 f1#(I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f2#(I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) 241.91/237.98 R = 241.91/237.98 f17(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 241.91/237.98 f16(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, I8, I9) 241.91/237.98 f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f3(I10, I11, 0, I13, I14, I15, I16, I17, I18, I19) [1 + I15 <= 20] 241.91/237.98 f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f5(I20, I21, I22, I23, I24, I25, 0, I27, I28, I29) [20 <= I25] 241.91/237.98 f4(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39) -> f3(I30, I31, 1 + I32, I33, I34, I35, I36, rnd8, rnd9, I39) [rnd9 = rnd8 /\ rnd8 = rnd8 /\ 1 + I32 <= 20] 241.91/237.98 f4(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) -> f1(I40, I41, I42, I43, I44, 1 + I45, I46, I47, I48, I49) [20 <= I42] 241.91/237.98 f9(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f7(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 241.91/237.98 f8(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f10(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) 241.91/237.98 f6(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) -> f14(I70, I71, I72, 0, I74, I75, I76, I77, I78, I79) [1 + I76 <= 20] 241.91/237.98 f6(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f11(I80, I81, I82, I83, 0, I85, I86, I87, I88, I89) [20 <= I86] 241.91/237.98 f15(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f14(I90, I91, I92, 1 + I93, I94, I95, I96, I100, I98, rnd10) [rnd10 = I100 /\ I100 = I100 /\ 1 + I93 <= 20] 241.91/237.98 f15(I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f5(I101, I102, I103, I104, I105, I106, 1 + I107, I108, I109, I110) [20 <= I104] 241.91/237.98 f11(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) -> f12(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) 241.91/237.98 f14(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) -> f15(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) 241.91/237.98 f12(I131, I132, I133, I134, I135, I136, I137, I138, I139, I140) -> f8(I131, 0, I133, I134, I135, I136, I137, I138, I139, I140) [1 + I135 <= 20] 241.91/237.98 f12(I141, I142, I143, I144, I145, I146, I147, I148, I149, I150) -> f13(I141, I142, I143, I144, I145, I146, I147, I148, I149, I150) [20 <= I145] 241.91/237.98 f10(I151, I152, I153, I154, I155, I156, I157, I158, I159, I160) -> f9(0, I152, I153, I154, I155, I156, I157, I158, I159, I160) [1 + I152 <= 20] 241.91/237.98 f10(I161, I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f11(I161, I162, I163, I164, 1 + I165, I166, I167, I168, I169, I170) [20 <= I162] 241.91/237.98 f7(I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) -> f9(1 + I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) [1 + I171 <= 20] 241.91/237.98 f7(I181, I182, I183, I184, I185, I186, I187, I188, I189, I190) -> f8(I181, 1 + I182, I183, I184, I185, I186, I187, I188, I189, I190) [20 <= I181] 241.91/237.98 f5(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200) -> f6(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200) 241.91/237.98 f3(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) -> f4(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) 241.91/237.98 f1(I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f2(I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) 241.91/237.98 241.91/237.98 The dependency graph for this problem is: 241.91/237.98 0 -> 1 241.91/237.98 1 -> 21 241.91/237.98 2 -> 20 241.91/237.98 3 -> 19 241.91/237.98 4 -> 20 241.91/237.98 5 -> 21 241.91/237.98 6 -> 17, 18 241.91/237.98 7 -> 15, 16 241.91/237.98 8 -> 13 241.91/237.98 9 -> 12 241.91/237.98 10 -> 13 241.91/237.98 11 -> 19 241.91/237.98 12 -> 14 241.91/237.98 13 -> 10, 11 241.91/237.98 14 -> 7 241.91/237.98 15 -> 6 241.91/237.98 16 -> 12 241.91/237.98 17 -> 6 241.91/237.98 18 -> 7 241.91/237.98 19 -> 8, 9 241.91/237.98 20 -> 4, 5 241.91/237.98 21 -> 2, 3 241.91/237.98 Where: 241.91/237.98 0) f17#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f16#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 241.91/237.98 1) f16#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1#(I0, I1, I2, I3, I4, 0, I6, 0, I8, I9) 241.91/237.98 2) f2#(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f3#(I10, I11, 0, I13, I14, I15, I16, I17, I18, I19) [1 + I15 <= 20] 241.91/237.98 3) f2#(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f5#(I20, I21, I22, I23, I24, I25, 0, I27, I28, I29) [20 <= I25] 241.91/237.98 4) f4#(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39) -> f3#(I30, I31, 1 + I32, I33, I34, I35, I36, rnd8, rnd9, I39) [rnd9 = rnd8 /\ rnd8 = rnd8 /\ 1 + I32 <= 20] 241.91/237.98 5) f4#(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) -> f1#(I40, I41, I42, I43, I44, 1 + I45, I46, I47, I48, I49) [20 <= I42] 241.91/237.98 6) f9#(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f7#(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 241.91/237.98 7) f8#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f10#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) 241.91/237.98 8) f6#(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) -> f14#(I70, I71, I72, 0, I74, I75, I76, I77, I78, I79) [1 + I76 <= 20] 241.91/237.98 9) f6#(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f11#(I80, I81, I82, I83, 0, I85, I86, I87, I88, I89) [20 <= I86] 241.91/237.98 10) f15#(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f14#(I90, I91, I92, 1 + I93, I94, I95, I96, I100, I98, rnd10) [rnd10 = I100 /\ I100 = I100 /\ 1 + I93 <= 20] 241.91/237.98 11) f15#(I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f5#(I101, I102, I103, I104, I105, I106, 1 + I107, I108, I109, I110) [20 <= I104] 241.91/237.98 12) f11#(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) -> f12#(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) 241.91/237.98 13) f14#(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) -> f15#(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) 241.91/237.98 14) f12#(I131, I132, I133, I134, I135, I136, I137, I138, I139, I140) -> f8#(I131, 0, I133, I134, I135, I136, I137, I138, I139, I140) [1 + I135 <= 20] 241.91/237.98 15) f10#(I151, I152, I153, I154, I155, I156, I157, I158, I159, I160) -> f9#(0, I152, I153, I154, I155, I156, I157, I158, I159, I160) [1 + I152 <= 20] 241.91/237.98 16) f10#(I161, I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f11#(I161, I162, I163, I164, 1 + I165, I166, I167, I168, I169, I170) [20 <= I162] 241.91/237.98 17) f7#(I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) -> f9#(1 + I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) [1 + I171 <= 20] 241.91/237.98 18) f7#(I181, I182, I183, I184, I185, I186, I187, I188, I189, I190) -> f8#(I181, 1 + I182, I183, I184, I185, I186, I187, I188, I189, I190) [20 <= I181] 241.91/237.98 19) f5#(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200) -> f6#(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200) 241.91/237.98 20) f3#(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) -> f4#(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) 241.91/237.98 21) f1#(I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f2#(I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) 241.91/237.98 241.91/237.98 We have the following SCCs. 241.91/237.98 { 2, 4, 5, 20, 21 } 241.91/237.98 { 8, 10, 11, 13, 19 } 241.91/237.98 { 6, 7, 12, 14, 15, 16, 17, 18 } 241.91/237.98 241.91/237.98 DP problem for innermost termination. 241.91/237.98 P = 241.91/237.98 f9#(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f7#(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 241.91/237.98 f8#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f10#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) 241.91/237.98 f11#(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) -> f12#(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) 241.91/237.98 f12#(I131, I132, I133, I134, I135, I136, I137, I138, I139, I140) -> f8#(I131, 0, I133, I134, I135, I136, I137, I138, I139, I140) [1 + I135 <= 20] 241.91/237.98 f10#(I151, I152, I153, I154, I155, I156, I157, I158, I159, I160) -> f9#(0, I152, I153, I154, I155, I156, I157, I158, I159, I160) [1 + I152 <= 20] 241.91/237.98 f10#(I161, I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f11#(I161, I162, I163, I164, 1 + I165, I166, I167, I168, I169, I170) [20 <= I162] 241.91/237.98 f7#(I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) -> f9#(1 + I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) [1 + I171 <= 20] 241.91/237.98 f7#(I181, I182, I183, I184, I185, I186, I187, I188, I189, I190) -> f8#(I181, 1 + I182, I183, I184, I185, I186, I187, I188, I189, I190) [20 <= I181] 241.91/237.98 R = 241.91/237.98 f17(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 241.91/237.98 f16(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, I8, I9) 241.91/237.98 f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f3(I10, I11, 0, I13, I14, I15, I16, I17, I18, I19) [1 + I15 <= 20] 241.91/237.98 f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f5(I20, I21, I22, I23, I24, I25, 0, I27, I28, I29) [20 <= I25] 241.91/237.98 f4(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39) -> f3(I30, I31, 1 + I32, I33, I34, I35, I36, rnd8, rnd9, I39) [rnd9 = rnd8 /\ rnd8 = rnd8 /\ 1 + I32 <= 20] 241.91/237.98 f4(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) -> f1(I40, I41, I42, I43, I44, 1 + I45, I46, I47, I48, I49) [20 <= I42] 241.91/237.98 f9(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f7(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 241.91/237.98 f8(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f10(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) 241.91/237.98 f6(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) -> f14(I70, I71, I72, 0, I74, I75, I76, I77, I78, I79) [1 + I76 <= 20] 241.91/237.98 f6(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f11(I80, I81, I82, I83, 0, I85, I86, I87, I88, I89) [20 <= I86] 241.91/237.98 f15(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f14(I90, I91, I92, 1 + I93, I94, I95, I96, I100, I98, rnd10) [rnd10 = I100 /\ I100 = I100 /\ 1 + I93 <= 20] 241.91/237.98 f15(I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f5(I101, I102, I103, I104, I105, I106, 1 + I107, I108, I109, I110) [20 <= I104] 241.91/237.98 f11(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) -> f12(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) 241.91/237.98 f14(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) -> f15(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) 241.91/237.98 f12(I131, I132, I133, I134, I135, I136, I137, I138, I139, I140) -> f8(I131, 0, I133, I134, I135, I136, I137, I138, I139, I140) [1 + I135 <= 20] 241.91/237.98 f12(I141, I142, I143, I144, I145, I146, I147, I148, I149, I150) -> f13(I141, I142, I143, I144, I145, I146, I147, I148, I149, I150) [20 <= I145] 241.91/237.98 f10(I151, I152, I153, I154, I155, I156, I157, I158, I159, I160) -> f9(0, I152, I153, I154, I155, I156, I157, I158, I159, I160) [1 + I152 <= 20] 241.91/237.98 f10(I161, I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f11(I161, I162, I163, I164, 1 + I165, I166, I167, I168, I169, I170) [20 <= I162] 241.91/237.98 f7(I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) -> f9(1 + I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) [1 + I171 <= 20] 241.91/237.98 f7(I181, I182, I183, I184, I185, I186, I187, I188, I189, I190) -> f8(I181, 1 + I182, I183, I184, I185, I186, I187, I188, I189, I190) [20 <= I181] 241.91/237.98 f5(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200) -> f6(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200) 241.91/237.98 f3(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) -> f4(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) 241.91/237.98 f1(I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f2(I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) 241.91/237.98 241.91/237.98 We use the extended value criterion with the projection function NU: 241.91/237.98 NU[f12#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9)] = -x4 + 19 241.91/237.98 NU[f11#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9)] = -x4 + 19 241.91/237.98 NU[f10#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9)] = -x4 + 18 241.91/237.98 NU[f8#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9)] = -x4 + 18 241.91/237.98 NU[f7#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9)] = -x4 + 18 241.91/237.98 NU[f9#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9)] = -x4 + 18 241.91/237.98 241.91/237.98 This gives the following inequalities: 241.91/237.98 ==> -I54 + 18 >= -I54 + 18 241.91/237.98 ==> -I64 + 18 >= -I64 + 18 241.91/237.98 ==> -I115 + 19 >= -I115 + 19 241.91/237.98 1 + I135 <= 20 ==> -I135 + 19 > -I135 + 18 with -I135 + 19 >= 0 241.91/237.99 1 + I152 <= 20 ==> -I155 + 18 >= -I155 + 18 241.91/237.99 20 <= I162 ==> -I165 + 18 >= -(1 + I165) + 19 241.91/237.99 1 + I171 <= 20 ==> -I175 + 18 >= -I175 + 18 241.91/237.99 20 <= I181 ==> -I185 + 18 >= -I185 + 18 241.91/237.99 241.91/237.99 We remove all the strictly oriented dependency pairs. 241.91/237.99 241.91/237.99 DP problem for innermost termination. 241.91/237.99 P = 241.91/237.99 f9#(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f7#(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 241.91/237.99 f8#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f10#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) 241.91/237.99 f11#(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) -> f12#(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) 241.91/237.99 f10#(I151, I152, I153, I154, I155, I156, I157, I158, I159, I160) -> f9#(0, I152, I153, I154, I155, I156, I157, I158, I159, I160) [1 + I152 <= 20] 241.91/237.99 f10#(I161, I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f11#(I161, I162, I163, I164, 1 + I165, I166, I167, I168, I169, I170) [20 <= I162] 241.91/237.99 f7#(I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) -> f9#(1 + I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) [1 + I171 <= 20] 241.91/237.99 f7#(I181, I182, I183, I184, I185, I186, I187, I188, I189, I190) -> f8#(I181, 1 + I182, I183, I184, I185, I186, I187, I188, I189, I190) [20 <= I181] 241.91/237.99 R = 241.91/237.99 f17(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 241.91/237.99 f16(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, I8, I9) 241.91/237.99 f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f3(I10, I11, 0, I13, I14, I15, I16, I17, I18, I19) [1 + I15 <= 20] 241.91/237.99 f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f5(I20, I21, I22, I23, I24, I25, 0, I27, I28, I29) [20 <= I25] 241.91/237.99 f4(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39) -> f3(I30, I31, 1 + I32, I33, I34, I35, I36, rnd8, rnd9, I39) [rnd9 = rnd8 /\ rnd8 = rnd8 /\ 1 + I32 <= 20] 241.91/237.99 f4(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) -> f1(I40, I41, I42, I43, I44, 1 + I45, I46, I47, I48, I49) [20 <= I42] 241.91/237.99 f9(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f7(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 241.91/237.99 f8(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f10(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) 241.91/237.99 f6(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) -> f14(I70, I71, I72, 0, I74, I75, I76, I77, I78, I79) [1 + I76 <= 20] 241.91/237.99 f6(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f11(I80, I81, I82, I83, 0, I85, I86, I87, I88, I89) [20 <= I86] 241.91/237.99 f15(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f14(I90, I91, I92, 1 + I93, I94, I95, I96, I100, I98, rnd10) [rnd10 = I100 /\ I100 = I100 /\ 1 + I93 <= 20] 241.91/237.99 f15(I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f5(I101, I102, I103, I104, I105, I106, 1 + I107, I108, I109, I110) [20 <= I104] 241.91/237.99 f11(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) -> f12(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) 241.91/237.99 f14(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) -> f15(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) 241.91/237.99 f12(I131, I132, I133, I134, I135, I136, I137, I138, I139, I140) -> f8(I131, 0, I133, I134, I135, I136, I137, I138, I139, I140) [1 + I135 <= 20] 241.91/237.99 f12(I141, I142, I143, I144, I145, I146, I147, I148, I149, I150) -> f13(I141, I142, I143, I144, I145, I146, I147, I148, I149, I150) [20 <= I145] 241.91/237.99 f10(I151, I152, I153, I154, I155, I156, I157, I158, I159, I160) -> f9(0, I152, I153, I154, I155, I156, I157, I158, I159, I160) [1 + I152 <= 20] 241.91/237.99 f10(I161, I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f11(I161, I162, I163, I164, 1 + I165, I166, I167, I168, I169, I170) [20 <= I162] 241.91/237.99 f7(I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) -> f9(1 + I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) [1 + I171 <= 20] 241.91/237.99 f7(I181, I182, I183, I184, I185, I186, I187, I188, I189, I190) -> f8(I181, 1 + I182, I183, I184, I185, I186, I187, I188, I189, I190) [20 <= I181] 241.91/237.99 f5(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200) -> f6(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200) 241.91/237.99 f3(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) -> f4(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) 241.91/237.99 f1(I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f2(I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) 241.91/237.99 241.91/237.99 The dependency graph for this problem is: 241.91/237.99 6 -> 17, 18 241.91/237.99 7 -> 15, 16 241.91/237.99 12 -> 241.91/237.99 15 -> 6 241.91/237.99 16 -> 12 241.91/237.99 17 -> 6 241.91/237.99 18 -> 7 241.91/237.99 Where: 241.91/237.99 6) f9#(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f7#(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 241.91/237.99 7) f8#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f10#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) 241.91/237.99 12) f11#(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) -> f12#(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) 241.91/237.99 15) f10#(I151, I152, I153, I154, I155, I156, I157, I158, I159, I160) -> f9#(0, I152, I153, I154, I155, I156, I157, I158, I159, I160) [1 + I152 <= 20] 241.91/237.99 16) f10#(I161, I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f11#(I161, I162, I163, I164, 1 + I165, I166, I167, I168, I169, I170) [20 <= I162] 241.91/237.99 17) f7#(I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) -> f9#(1 + I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) [1 + I171 <= 20] 241.91/237.99 18) f7#(I181, I182, I183, I184, I185, I186, I187, I188, I189, I190) -> f8#(I181, 1 + I182, I183, I184, I185, I186, I187, I188, I189, I190) [20 <= I181] 241.91/237.99 241.91/237.99 We have the following SCCs. 241.91/237.99 { 6, 7, 15, 17, 18 } 241.91/237.99 241.91/237.99 DP problem for innermost termination. 241.91/237.99 P = 241.91/237.99 f9#(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f7#(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 241.91/237.99 f8#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f10#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) 241.91/237.99 f10#(I151, I152, I153, I154, I155, I156, I157, I158, I159, I160) -> f9#(0, I152, I153, I154, I155, I156, I157, I158, I159, I160) [1 + I152 <= 20] 241.91/237.99 f7#(I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) -> f9#(1 + I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) [1 + I171 <= 20] 241.91/237.99 f7#(I181, I182, I183, I184, I185, I186, I187, I188, I189, I190) -> f8#(I181, 1 + I182, I183, I184, I185, I186, I187, I188, I189, I190) [20 <= I181] 241.91/237.99 R = 241.91/237.99 f17(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 241.91/237.99 f16(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, I8, I9) 241.91/237.99 f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f3(I10, I11, 0, I13, I14, I15, I16, I17, I18, I19) [1 + I15 <= 20] 241.91/237.99 f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f5(I20, I21, I22, I23, I24, I25, 0, I27, I28, I29) [20 <= I25] 241.91/237.99 f4(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39) -> f3(I30, I31, 1 + I32, I33, I34, I35, I36, rnd8, rnd9, I39) [rnd9 = rnd8 /\ rnd8 = rnd8 /\ 1 + I32 <= 20] 241.91/237.99 f4(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) -> f1(I40, I41, I42, I43, I44, 1 + I45, I46, I47, I48, I49) [20 <= I42] 241.91/237.99 f9(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f7(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 241.91/237.99 f8(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f10(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) 241.91/237.99 f6(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) -> f14(I70, I71, I72, 0, I74, I75, I76, I77, I78, I79) [1 + I76 <= 20] 241.91/237.99 f6(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f11(I80, I81, I82, I83, 0, I85, I86, I87, I88, I89) [20 <= I86] 241.91/237.99 f15(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f14(I90, I91, I92, 1 + I93, I94, I95, I96, I100, I98, rnd10) [rnd10 = I100 /\ I100 = I100 /\ 1 + I93 <= 20] 241.91/237.99 f15(I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f5(I101, I102, I103, I104, I105, I106, 1 + I107, I108, I109, I110) [20 <= I104] 241.91/237.99 f11(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) -> f12(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) 241.91/237.99 f14(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) -> f15(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) 241.91/237.99 f12(I131, I132, I133, I134, I135, I136, I137, I138, I139, I140) -> f8(I131, 0, I133, I134, I135, I136, I137, I138, I139, I140) [1 + I135 <= 20] 241.91/237.99 f12(I141, I142, I143, I144, I145, I146, I147, I148, I149, I150) -> f13(I141, I142, I143, I144, I145, I146, I147, I148, I149, I150) [20 <= I145] 241.91/237.99 f10(I151, I152, I153, I154, I155, I156, I157, I158, I159, I160) -> f9(0, I152, I153, I154, I155, I156, I157, I158, I159, I160) [1 + I152 <= 20] 241.91/237.99 f10(I161, I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f11(I161, I162, I163, I164, 1 + I165, I166, I167, I168, I169, I170) [20 <= I162] 241.91/237.99 f7(I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) -> f9(1 + I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) [1 + I171 <= 20] 241.91/237.99 f7(I181, I182, I183, I184, I185, I186, I187, I188, I189, I190) -> f8(I181, 1 + I182, I183, I184, I185, I186, I187, I188, I189, I190) [20 <= I181] 241.91/237.99 f5(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200) -> f6(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200) 241.91/237.99 f3(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) -> f4(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) 241.91/237.99 f1(I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f2(I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) 241.91/237.99 241.91/237.99 We use the extended value criterion with the projection function NU: 241.91/237.99 NU[f10#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9)] = -x1 + 19 241.91/237.99 NU[f8#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9)] = -x1 + 19 241.91/237.99 NU[f7#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9)] = -x1 + 18 241.91/237.99 NU[f9#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9)] = -x1 + 18 241.91/237.99 241.91/237.99 This gives the following inequalities: 241.91/237.99 ==> -I51 + 18 >= -I51 + 18 241.91/237.99 ==> -I61 + 19 >= -I61 + 19 241.91/237.99 1 + I152 <= 20 ==> -I152 + 19 > -I152 + 18 with -I152 + 19 >= 0 241.91/237.99 1 + I171 <= 20 ==> -I172 + 18 >= -I172 + 18 241.91/237.99 20 <= I181 ==> -I182 + 18 >= -(1 + I182) + 19 241.91/237.99 241.91/237.99 We remove all the strictly oriented dependency pairs. 241.91/237.99 241.91/237.99 DP problem for innermost termination. 241.91/237.99 P = 241.91/237.99 f9#(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f7#(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 241.91/237.99 f8#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f10#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) 241.91/237.99 f7#(I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) -> f9#(1 + I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) [1 + I171 <= 20] 241.91/237.99 f7#(I181, I182, I183, I184, I185, I186, I187, I188, I189, I190) -> f8#(I181, 1 + I182, I183, I184, I185, I186, I187, I188, I189, I190) [20 <= I181] 241.91/237.99 R = 241.91/237.99 f17(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 241.91/237.99 f16(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, I8, I9) 241.91/237.99 f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f3(I10, I11, 0, I13, I14, I15, I16, I17, I18, I19) [1 + I15 <= 20] 241.91/237.99 f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f5(I20, I21, I22, I23, I24, I25, 0, I27, I28, I29) [20 <= I25] 241.91/237.99 f4(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39) -> f3(I30, I31, 1 + I32, I33, I34, I35, I36, rnd8, rnd9, I39) [rnd9 = rnd8 /\ rnd8 = rnd8 /\ 1 + I32 <= 20] 241.91/237.99 f4(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) -> f1(I40, I41, I42, I43, I44, 1 + I45, I46, I47, I48, I49) [20 <= I42] 241.91/237.99 f9(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f7(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 241.91/237.99 f8(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f10(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) 241.91/237.99 f6(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) -> f14(I70, I71, I72, 0, I74, I75, I76, I77, I78, I79) [1 + I76 <= 20] 241.91/237.99 f6(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f11(I80, I81, I82, I83, 0, I85, I86, I87, I88, I89) [20 <= I86] 241.91/237.99 f15(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f14(I90, I91, I92, 1 + I93, I94, I95, I96, I100, I98, rnd10) [rnd10 = I100 /\ I100 = I100 /\ 1 + I93 <= 20] 241.91/237.99 f15(I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f5(I101, I102, I103, I104, I105, I106, 1 + I107, I108, I109, I110) [20 <= I104] 241.91/237.99 f11(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) -> f12(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) 241.91/237.99 f14(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) -> f15(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) 241.91/237.99 f12(I131, I132, I133, I134, I135, I136, I137, I138, I139, I140) -> f8(I131, 0, I133, I134, I135, I136, I137, I138, I139, I140) [1 + I135 <= 20] 241.91/237.99 f12(I141, I142, I143, I144, I145, I146, I147, I148, I149, I150) -> f13(I141, I142, I143, I144, I145, I146, I147, I148, I149, I150) [20 <= I145] 241.91/237.99 f10(I151, I152, I153, I154, I155, I156, I157, I158, I159, I160) -> f9(0, I152, I153, I154, I155, I156, I157, I158, I159, I160) [1 + I152 <= 20] 241.91/237.99 f10(I161, I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f11(I161, I162, I163, I164, 1 + I165, I166, I167, I168, I169, I170) [20 <= I162] 241.91/237.99 f7(I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) -> f9(1 + I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) [1 + I171 <= 20] 241.91/237.99 f7(I181, I182, I183, I184, I185, I186, I187, I188, I189, I190) -> f8(I181, 1 + I182, I183, I184, I185, I186, I187, I188, I189, I190) [20 <= I181] 241.91/237.99 f5(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200) -> f6(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200) 241.91/237.99 f3(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) -> f4(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) 241.91/237.99 f1(I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f2(I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) 241.91/237.99 241.91/237.99 The dependency graph for this problem is: 241.91/237.99 6 -> 17, 18 241.91/237.99 7 -> 241.91/237.99 17 -> 6 241.91/237.99 18 -> 7 241.91/237.99 Where: 241.91/237.99 6) f9#(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f7#(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 241.91/237.99 7) f8#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f10#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) 241.91/237.99 17) f7#(I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) -> f9#(1 + I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) [1 + I171 <= 20] 241.91/237.99 18) f7#(I181, I182, I183, I184, I185, I186, I187, I188, I189, I190) -> f8#(I181, 1 + I182, I183, I184, I185, I186, I187, I188, I189, I190) [20 <= I181] 241.91/237.99 241.91/237.99 We have the following SCCs. 241.91/237.99 { 6, 17 } 241.91/237.99 241.91/237.99 DP problem for innermost termination. 241.91/237.99 P = 241.91/237.99 f9#(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f7#(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 241.91/237.99 f7#(I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) -> f9#(1 + I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) [1 + I171 <= 20] 241.91/237.99 R = 241.91/237.99 f17(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 241.91/237.99 f16(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, I8, I9) 241.91/237.99 f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f3(I10, I11, 0, I13, I14, I15, I16, I17, I18, I19) [1 + I15 <= 20] 241.91/237.99 f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f5(I20, I21, I22, I23, I24, I25, 0, I27, I28, I29) [20 <= I25] 241.91/237.99 f4(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39) -> f3(I30, I31, 1 + I32, I33, I34, I35, I36, rnd8, rnd9, I39) [rnd9 = rnd8 /\ rnd8 = rnd8 /\ 1 + I32 <= 20] 241.91/237.99 f4(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) -> f1(I40, I41, I42, I43, I44, 1 + I45, I46, I47, I48, I49) [20 <= I42] 241.91/237.99 f9(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f7(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 241.91/237.99 f8(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f10(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) 241.91/237.99 f6(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) -> f14(I70, I71, I72, 0, I74, I75, I76, I77, I78, I79) [1 + I76 <= 20] 241.91/237.99 f6(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f11(I80, I81, I82, I83, 0, I85, I86, I87, I88, I89) [20 <= I86] 241.91/237.99 f15(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f14(I90, I91, I92, 1 + I93, I94, I95, I96, I100, I98, rnd10) [rnd10 = I100 /\ I100 = I100 /\ 1 + I93 <= 20] 241.91/237.99 f15(I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f5(I101, I102, I103, I104, I105, I106, 1 + I107, I108, I109, I110) [20 <= I104] 241.91/237.99 f11(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) -> f12(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) 241.91/237.99 f14(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) -> f15(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) 241.91/237.99 f12(I131, I132, I133, I134, I135, I136, I137, I138, I139, I140) -> f8(I131, 0, I133, I134, I135, I136, I137, I138, I139, I140) [1 + I135 <= 20] 241.91/237.99 f12(I141, I142, I143, I144, I145, I146, I147, I148, I149, I150) -> f13(I141, I142, I143, I144, I145, I146, I147, I148, I149, I150) [20 <= I145] 241.91/237.99 f10(I151, I152, I153, I154, I155, I156, I157, I158, I159, I160) -> f9(0, I152, I153, I154, I155, I156, I157, I158, I159, I160) [1 + I152 <= 20] 241.91/237.99 f10(I161, I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f11(I161, I162, I163, I164, 1 + I165, I166, I167, I168, I169, I170) [20 <= I162] 241.91/237.99 f7(I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) -> f9(1 + I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) [1 + I171 <= 20] 241.91/237.99 f7(I181, I182, I183, I184, I185, I186, I187, I188, I189, I190) -> f8(I181, 1 + I182, I183, I184, I185, I186, I187, I188, I189, I190) [20 <= I181] 241.91/237.99 f5(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200) -> f6(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200) 241.91/237.99 f3(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) -> f4(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) 241.91/237.99 f1(I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f2(I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) 241.91/237.99 241.91/237.99 We use the reverse value criterion with the projection function NU: 241.91/237.99 NU[f7#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10)] = 20 + -1 * (1 + z1) 241.91/237.99 NU[f9#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10)] = 20 + -1 * (1 + z1) 241.91/237.99 241.91/237.99 This gives the following inequalities: 241.91/237.99 ==> 20 + -1 * (1 + I50) >= 20 + -1 * (1 + I50) 241.91/237.99 1 + I171 <= 20 ==> 20 + -1 * (1 + I171) > 20 + -1 * (1 + (1 + I171)) with 20 + -1 * (1 + I171) >= 0 241.91/237.99 241.91/237.99 We remove all the strictly oriented dependency pairs. 241.91/237.99 241.91/237.99 DP problem for innermost termination. 241.91/237.99 P = 241.91/237.99 f9#(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f7#(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 241.91/237.99 R = 241.91/237.99 f17(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 241.91/237.99 f16(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, I8, I9) 241.91/237.99 f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f3(I10, I11, 0, I13, I14, I15, I16, I17, I18, I19) [1 + I15 <= 20] 241.91/237.99 f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f5(I20, I21, I22, I23, I24, I25, 0, I27, I28, I29) [20 <= I25] 241.91/237.99 f4(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39) -> f3(I30, I31, 1 + I32, I33, I34, I35, I36, rnd8, rnd9, I39) [rnd9 = rnd8 /\ rnd8 = rnd8 /\ 1 + I32 <= 20] 241.91/237.99 f4(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) -> f1(I40, I41, I42, I43, I44, 1 + I45, I46, I47, I48, I49) [20 <= I42] 241.91/237.99 f9(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f7(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 241.91/237.99 f8(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f10(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) 241.91/237.99 f6(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) -> f14(I70, I71, I72, 0, I74, I75, I76, I77, I78, I79) [1 + I76 <= 20] 241.91/237.99 f6(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f11(I80, I81, I82, I83, 0, I85, I86, I87, I88, I89) [20 <= I86] 241.91/237.99 f15(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f14(I90, I91, I92, 1 + I93, I94, I95, I96, I100, I98, rnd10) [rnd10 = I100 /\ I100 = I100 /\ 1 + I93 <= 20] 241.91/237.99 f15(I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f5(I101, I102, I103, I104, I105, I106, 1 + I107, I108, I109, I110) [20 <= I104] 241.91/237.99 f11(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) -> f12(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) 241.91/237.99 f14(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) -> f15(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) 241.91/237.99 f12(I131, I132, I133, I134, I135, I136, I137, I138, I139, I140) -> f8(I131, 0, I133, I134, I135, I136, I137, I138, I139, I140) [1 + I135 <= 20] 241.91/237.99 f12(I141, I142, I143, I144, I145, I146, I147, I148, I149, I150) -> f13(I141, I142, I143, I144, I145, I146, I147, I148, I149, I150) [20 <= I145] 241.91/237.99 f10(I151, I152, I153, I154, I155, I156, I157, I158, I159, I160) -> f9(0, I152, I153, I154, I155, I156, I157, I158, I159, I160) [1 + I152 <= 20] 241.91/237.99 f10(I161, I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f11(I161, I162, I163, I164, 1 + I165, I166, I167, I168, I169, I170) [20 <= I162] 241.91/237.99 f7(I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) -> f9(1 + I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) [1 + I171 <= 20] 241.91/237.99 f7(I181, I182, I183, I184, I185, I186, I187, I188, I189, I190) -> f8(I181, 1 + I182, I183, I184, I185, I186, I187, I188, I189, I190) [20 <= I181] 241.91/237.99 f5(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200) -> f6(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200) 241.91/237.99 f3(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) -> f4(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) 241.91/237.99 f1(I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f2(I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) 241.91/237.99 241.91/237.99 The dependency graph for this problem is: 241.91/237.99 6 -> 241.91/237.99 Where: 241.91/237.99 6) f9#(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f7#(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 241.91/237.99 241.91/237.99 We have the following SCCs. 241.91/237.99 241.91/237.99 241.91/237.99 DP problem for innermost termination. 241.91/237.99 P = 241.91/237.99 f6#(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) -> f14#(I70, I71, I72, 0, I74, I75, I76, I77, I78, I79) [1 + I76 <= 20] 241.91/237.99 f15#(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f14#(I90, I91, I92, 1 + I93, I94, I95, I96, I100, I98, rnd10) [rnd10 = I100 /\ I100 = I100 /\ 1 + I93 <= 20] 241.91/237.99 f15#(I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f5#(I101, I102, I103, I104, I105, I106, 1 + I107, I108, I109, I110) [20 <= I104] 241.91/237.99 f14#(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) -> f15#(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) 241.91/237.99 f5#(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200) -> f6#(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200) 241.91/237.99 R = 241.91/237.99 f17(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 241.91/237.99 f16(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, I8, I9) 241.91/237.99 f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f3(I10, I11, 0, I13, I14, I15, I16, I17, I18, I19) [1 + I15 <= 20] 241.91/237.99 f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f5(I20, I21, I22, I23, I24, I25, 0, I27, I28, I29) [20 <= I25] 241.91/237.99 f4(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39) -> f3(I30, I31, 1 + I32, I33, I34, I35, I36, rnd8, rnd9, I39) [rnd9 = rnd8 /\ rnd8 = rnd8 /\ 1 + I32 <= 20] 241.91/237.99 f4(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) -> f1(I40, I41, I42, I43, I44, 1 + I45, I46, I47, I48, I49) [20 <= I42] 241.91/237.99 f9(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f7(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 241.91/237.99 f8(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f10(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) 241.91/237.99 f6(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) -> f14(I70, I71, I72, 0, I74, I75, I76, I77, I78, I79) [1 + I76 <= 20] 241.91/237.99 f6(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f11(I80, I81, I82, I83, 0, I85, I86, I87, I88, I89) [20 <= I86] 241.91/237.99 f15(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f14(I90, I91, I92, 1 + I93, I94, I95, I96, I100, I98, rnd10) [rnd10 = I100 /\ I100 = I100 /\ 1 + I93 <= 20] 241.91/237.99 f15(I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f5(I101, I102, I103, I104, I105, I106, 1 + I107, I108, I109, I110) [20 <= I104] 241.91/237.99 f11(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) -> f12(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) 241.91/237.99 f14(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) -> f15(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) 241.91/237.99 f12(I131, I132, I133, I134, I135, I136, I137, I138, I139, I140) -> f8(I131, 0, I133, I134, I135, I136, I137, I138, I139, I140) [1 + I135 <= 20] 241.91/237.99 f12(I141, I142, I143, I144, I145, I146, I147, I148, I149, I150) -> f13(I141, I142, I143, I144, I145, I146, I147, I148, I149, I150) [20 <= I145] 241.91/237.99 f10(I151, I152, I153, I154, I155, I156, I157, I158, I159, I160) -> f9(0, I152, I153, I154, I155, I156, I157, I158, I159, I160) [1 + I152 <= 20] 241.91/237.99 f10(I161, I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f11(I161, I162, I163, I164, 1 + I165, I166, I167, I168, I169, I170) [20 <= I162] 241.91/237.99 f7(I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) -> f9(1 + I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) [1 + I171 <= 20] 241.91/237.99 f7(I181, I182, I183, I184, I185, I186, I187, I188, I189, I190) -> f8(I181, 1 + I182, I183, I184, I185, I186, I187, I188, I189, I190) [20 <= I181] 241.91/237.99 f5(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200) -> f6(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200) 241.91/237.99 f3(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) -> f4(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) 241.91/237.99 f1(I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f2(I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) 241.91/237.99 241.91/237.99 We use the extended value criterion with the projection function NU: 241.91/237.99 NU[f5#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9)] = -x6 + 19 241.91/237.99 NU[f15#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9)] = -x6 + 18 241.91/237.99 NU[f14#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9)] = -x6 + 18 241.91/237.99 NU[f6#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9)] = -x6 + 19 241.91/237.99 241.91/237.99 This gives the following inequalities: 241.91/237.99 1 + I76 <= 20 ==> -I76 + 19 > -I76 + 18 with -I76 + 19 >= 0 241.91/237.99 rnd10 = I100 /\ I100 = I100 /\ 1 + I93 <= 20 ==> -I96 + 18 >= -I96 + 18 241.91/237.99 20 <= I104 ==> -I107 + 18 >= -(1 + I107) + 19 241.91/237.99 ==> -I127 + 18 >= -I127 + 18 241.91/237.99 ==> -I197 + 19 >= -I197 + 19 241.91/237.99 241.91/237.99 We remove all the strictly oriented dependency pairs. 241.91/237.99 241.91/237.99 DP problem for innermost termination. 241.91/237.99 P = 241.91/237.99 f15#(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f14#(I90, I91, I92, 1 + I93, I94, I95, I96, I100, I98, rnd10) [rnd10 = I100 /\ I100 = I100 /\ 1 + I93 <= 20] 241.91/237.99 f15#(I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f5#(I101, I102, I103, I104, I105, I106, 1 + I107, I108, I109, I110) [20 <= I104] 241.91/237.99 f14#(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) -> f15#(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) 241.91/237.99 f5#(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200) -> f6#(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200) 241.91/237.99 R = 241.91/237.99 f17(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 241.91/237.99 f16(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, I8, I9) 241.91/237.99 f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f3(I10, I11, 0, I13, I14, I15, I16, I17, I18, I19) [1 + I15 <= 20] 241.91/237.99 f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f5(I20, I21, I22, I23, I24, I25, 0, I27, I28, I29) [20 <= I25] 241.91/237.99 f4(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39) -> f3(I30, I31, 1 + I32, I33, I34, I35, I36, rnd8, rnd9, I39) [rnd9 = rnd8 /\ rnd8 = rnd8 /\ 1 + I32 <= 20] 241.91/237.99 f4(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) -> f1(I40, I41, I42, I43, I44, 1 + I45, I46, I47, I48, I49) [20 <= I42] 241.91/237.99 f9(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f7(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 241.91/237.99 f8(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f10(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) 241.91/237.99 f6(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) -> f14(I70, I71, I72, 0, I74, I75, I76, I77, I78, I79) [1 + I76 <= 20] 241.91/237.99 f6(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f11(I80, I81, I82, I83, 0, I85, I86, I87, I88, I89) [20 <= I86] 241.91/237.99 f15(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f14(I90, I91, I92, 1 + I93, I94, I95, I96, I100, I98, rnd10) [rnd10 = I100 /\ I100 = I100 /\ 1 + I93 <= 20] 241.91/237.99 f15(I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f5(I101, I102, I103, I104, I105, I106, 1 + I107, I108, I109, I110) [20 <= I104] 241.91/237.99 f11(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) -> f12(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) 241.91/237.99 f14(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) -> f15(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) 241.91/237.99 f12(I131, I132, I133, I134, I135, I136, I137, I138, I139, I140) -> f8(I131, 0, I133, I134, I135, I136, I137, I138, I139, I140) [1 + I135 <= 20] 241.91/237.99 f12(I141, I142, I143, I144, I145, I146, I147, I148, I149, I150) -> f13(I141, I142, I143, I144, I145, I146, I147, I148, I149, I150) [20 <= I145] 241.91/237.99 f10(I151, I152, I153, I154, I155, I156, I157, I158, I159, I160) -> f9(0, I152, I153, I154, I155, I156, I157, I158, I159, I160) [1 + I152 <= 20] 241.91/237.99 f10(I161, I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f11(I161, I162, I163, I164, 1 + I165, I166, I167, I168, I169, I170) [20 <= I162] 241.91/237.99 f7(I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) -> f9(1 + I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) [1 + I171 <= 20] 241.91/237.99 f7(I181, I182, I183, I184, I185, I186, I187, I188, I189, I190) -> f8(I181, 1 + I182, I183, I184, I185, I186, I187, I188, I189, I190) [20 <= I181] 241.91/237.99 f5(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200) -> f6(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200) 241.91/237.99 f3(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) -> f4(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) 241.91/237.99 f1(I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f2(I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) 241.91/237.99 241.91/237.99 The dependency graph for this problem is: 241.91/237.99 10 -> 13 241.91/237.99 11 -> 19 241.91/237.99 13 -> 10, 11 241.91/237.99 19 -> 241.91/237.99 Where: 241.91/237.99 10) f15#(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f14#(I90, I91, I92, 1 + I93, I94, I95, I96, I100, I98, rnd10) [rnd10 = I100 /\ I100 = I100 /\ 1 + I93 <= 20] 241.91/237.99 11) f15#(I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f5#(I101, I102, I103, I104, I105, I106, 1 + I107, I108, I109, I110) [20 <= I104] 241.91/237.99 13) f14#(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) -> f15#(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) 241.91/237.99 19) f5#(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200) -> f6#(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200) 241.91/237.99 241.91/237.99 We have the following SCCs. 241.91/237.99 { 10, 13 } 241.91/237.99 241.91/237.99 DP problem for innermost termination. 241.91/237.99 P = 241.91/237.99 f15#(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f14#(I90, I91, I92, 1 + I93, I94, I95, I96, I100, I98, rnd10) [rnd10 = I100 /\ I100 = I100 /\ 1 + I93 <= 20] 241.91/237.99 f14#(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) -> f15#(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) 241.91/237.99 R = 241.91/237.99 f17(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 241.91/237.99 f16(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, I8, I9) 241.91/237.99 f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f3(I10, I11, 0, I13, I14, I15, I16, I17, I18, I19) [1 + I15 <= 20] 241.91/237.99 f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f5(I20, I21, I22, I23, I24, I25, 0, I27, I28, I29) [20 <= I25] 241.91/237.99 f4(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39) -> f3(I30, I31, 1 + I32, I33, I34, I35, I36, rnd8, rnd9, I39) [rnd9 = rnd8 /\ rnd8 = rnd8 /\ 1 + I32 <= 20] 241.91/237.99 f4(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) -> f1(I40, I41, I42, I43, I44, 1 + I45, I46, I47, I48, I49) [20 <= I42] 241.91/237.99 f9(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f7(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 241.91/237.99 f8(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f10(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) 241.91/237.99 f6(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) -> f14(I70, I71, I72, 0, I74, I75, I76, I77, I78, I79) [1 + I76 <= 20] 241.91/237.99 f6(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f11(I80, I81, I82, I83, 0, I85, I86, I87, I88, I89) [20 <= I86] 241.91/237.99 f15(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f14(I90, I91, I92, 1 + I93, I94, I95, I96, I100, I98, rnd10) [rnd10 = I100 /\ I100 = I100 /\ 1 + I93 <= 20] 241.91/237.99 f15(I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f5(I101, I102, I103, I104, I105, I106, 1 + I107, I108, I109, I110) [20 <= I104] 241.91/237.99 f11(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) -> f12(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) 241.91/237.99 f14(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) -> f15(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) 241.91/237.99 f12(I131, I132, I133, I134, I135, I136, I137, I138, I139, I140) -> f8(I131, 0, I133, I134, I135, I136, I137, I138, I139, I140) [1 + I135 <= 20] 241.91/237.99 f12(I141, I142, I143, I144, I145, I146, I147, I148, I149, I150) -> f13(I141, I142, I143, I144, I145, I146, I147, I148, I149, I150) [20 <= I145] 241.91/237.99 f10(I151, I152, I153, I154, I155, I156, I157, I158, I159, I160) -> f9(0, I152, I153, I154, I155, I156, I157, I158, I159, I160) [1 + I152 <= 20] 241.91/237.99 f10(I161, I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f11(I161, I162, I163, I164, 1 + I165, I166, I167, I168, I169, I170) [20 <= I162] 241.91/237.99 f7(I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) -> f9(1 + I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) [1 + I171 <= 20] 241.91/237.99 f7(I181, I182, I183, I184, I185, I186, I187, I188, I189, I190) -> f8(I181, 1 + I182, I183, I184, I185, I186, I187, I188, I189, I190) [20 <= I181] 241.91/237.99 f5(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200) -> f6(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200) 241.91/237.99 f3(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) -> f4(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) 241.91/237.99 f1(I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f2(I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) 241.91/237.99 241.91/237.99 We use the reverse value criterion with the projection function NU: 241.91/237.99 NU[f14#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10)] = 20 + -1 * (1 + z4) 241.91/237.99 NU[f15#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10)] = 20 + -1 * (1 + z4) 241.91/237.99 241.91/237.99 This gives the following inequalities: 241.91/237.99 rnd10 = I100 /\ I100 = I100 /\ 1 + I93 <= 20 ==> 20 + -1 * (1 + I93) > 20 + -1 * (1 + (1 + I93)) with 20 + -1 * (1 + I93) >= 0 241.91/237.99 ==> 20 + -1 * (1 + I124) >= 20 + -1 * (1 + I124) 241.91/237.99 241.91/237.99 We remove all the strictly oriented dependency pairs. 241.91/237.99 241.91/237.99 DP problem for innermost termination. 241.91/237.99 P = 241.91/237.99 f14#(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) -> f15#(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) 241.91/237.99 R = 241.91/237.99 f17(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 241.91/237.99 f16(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, I8, I9) 241.91/237.99 f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f3(I10, I11, 0, I13, I14, I15, I16, I17, I18, I19) [1 + I15 <= 20] 241.91/237.99 f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f5(I20, I21, I22, I23, I24, I25, 0, I27, I28, I29) [20 <= I25] 241.91/237.99 f4(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39) -> f3(I30, I31, 1 + I32, I33, I34, I35, I36, rnd8, rnd9, I39) [rnd9 = rnd8 /\ rnd8 = rnd8 /\ 1 + I32 <= 20] 241.91/237.99 f4(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) -> f1(I40, I41, I42, I43, I44, 1 + I45, I46, I47, I48, I49) [20 <= I42] 241.91/237.99 f9(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f7(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 241.91/237.99 f8(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f10(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) 241.91/237.99 f6(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) -> f14(I70, I71, I72, 0, I74, I75, I76, I77, I78, I79) [1 + I76 <= 20] 241.91/237.99 f6(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f11(I80, I81, I82, I83, 0, I85, I86, I87, I88, I89) [20 <= I86] 241.91/237.99 f15(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f14(I90, I91, I92, 1 + I93, I94, I95, I96, I100, I98, rnd10) [rnd10 = I100 /\ I100 = I100 /\ 1 + I93 <= 20] 241.91/237.99 f15(I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f5(I101, I102, I103, I104, I105, I106, 1 + I107, I108, I109, I110) [20 <= I104] 241.91/237.99 f11(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) -> f12(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) 241.91/237.99 f14(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) -> f15(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) 241.91/237.99 f12(I131, I132, I133, I134, I135, I136, I137, I138, I139, I140) -> f8(I131, 0, I133, I134, I135, I136, I137, I138, I139, I140) [1 + I135 <= 20] 241.91/237.99 f12(I141, I142, I143, I144, I145, I146, I147, I148, I149, I150) -> f13(I141, I142, I143, I144, I145, I146, I147, I148, I149, I150) [20 <= I145] 241.91/237.99 f10(I151, I152, I153, I154, I155, I156, I157, I158, I159, I160) -> f9(0, I152, I153, I154, I155, I156, I157, I158, I159, I160) [1 + I152 <= 20] 241.91/237.99 f10(I161, I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f11(I161, I162, I163, I164, 1 + I165, I166, I167, I168, I169, I170) [20 <= I162] 241.91/237.99 f7(I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) -> f9(1 + I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) [1 + I171 <= 20] 241.91/237.99 f7(I181, I182, I183, I184, I185, I186, I187, I188, I189, I190) -> f8(I181, 1 + I182, I183, I184, I185, I186, I187, I188, I189, I190) [20 <= I181] 241.91/237.99 f5(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200) -> f6(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200) 241.91/237.99 f3(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) -> f4(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) 241.91/237.99 f1(I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f2(I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) 241.91/237.99 241.91/237.99 The dependency graph for this problem is: 241.91/237.99 13 -> 241.91/237.99 Where: 241.91/237.99 13) f14#(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) -> f15#(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) 241.91/237.99 241.91/237.99 We have the following SCCs. 241.91/237.99 241.91/237.99 241.91/237.99 DP problem for innermost termination. 241.91/237.99 P = 241.91/237.99 f2#(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f3#(I10, I11, 0, I13, I14, I15, I16, I17, I18, I19) [1 + I15 <= 20] 241.91/237.99 f4#(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39) -> f3#(I30, I31, 1 + I32, I33, I34, I35, I36, rnd8, rnd9, I39) [rnd9 = rnd8 /\ rnd8 = rnd8 /\ 1 + I32 <= 20] 241.91/237.99 f4#(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) -> f1#(I40, I41, I42, I43, I44, 1 + I45, I46, I47, I48, I49) [20 <= I42] 241.91/237.99 f3#(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) -> f4#(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) 241.91/237.99 f1#(I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f2#(I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) 241.91/237.99 R = 241.91/237.99 f17(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 241.91/237.99 f16(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, I8, I9) 241.91/237.99 f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f3(I10, I11, 0, I13, I14, I15, I16, I17, I18, I19) [1 + I15 <= 20] 241.91/237.99 f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f5(I20, I21, I22, I23, I24, I25, 0, I27, I28, I29) [20 <= I25] 241.91/237.99 f4(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39) -> f3(I30, I31, 1 + I32, I33, I34, I35, I36, rnd8, rnd9, I39) [rnd9 = rnd8 /\ rnd8 = rnd8 /\ 1 + I32 <= 20] 241.91/237.99 f4(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) -> f1(I40, I41, I42, I43, I44, 1 + I45, I46, I47, I48, I49) [20 <= I42] 241.91/237.99 f9(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f7(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 241.91/237.99 f8(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f10(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) 241.91/237.99 f6(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) -> f14(I70, I71, I72, 0, I74, I75, I76, I77, I78, I79) [1 + I76 <= 20] 241.91/237.99 f6(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f11(I80, I81, I82, I83, 0, I85, I86, I87, I88, I89) [20 <= I86] 241.91/237.99 f15(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f14(I90, I91, I92, 1 + I93, I94, I95, I96, I100, I98, rnd10) [rnd10 = I100 /\ I100 = I100 /\ 1 + I93 <= 20] 241.91/237.99 f15(I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f5(I101, I102, I103, I104, I105, I106, 1 + I107, I108, I109, I110) [20 <= I104] 241.91/237.99 f11(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) -> f12(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) 241.91/237.99 f14(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) -> f15(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) 241.91/237.99 f12(I131, I132, I133, I134, I135, I136, I137, I138, I139, I140) -> f8(I131, 0, I133, I134, I135, I136, I137, I138, I139, I140) [1 + I135 <= 20] 241.91/237.99 f12(I141, I142, I143, I144, I145, I146, I147, I148, I149, I150) -> f13(I141, I142, I143, I144, I145, I146, I147, I148, I149, I150) [20 <= I145] 241.91/237.99 f10(I151, I152, I153, I154, I155, I156, I157, I158, I159, I160) -> f9(0, I152, I153, I154, I155, I156, I157, I158, I159, I160) [1 + I152 <= 20] 241.91/237.99 f10(I161, I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f11(I161, I162, I163, I164, 1 + I165, I166, I167, I168, I169, I170) [20 <= I162] 241.91/237.99 f7(I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) -> f9(1 + I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) [1 + I171 <= 20] 241.91/237.99 f7(I181, I182, I183, I184, I185, I186, I187, I188, I189, I190) -> f8(I181, 1 + I182, I183, I184, I185, I186, I187, I188, I189, I190) [20 <= I181] 241.91/237.99 f5(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200) -> f6(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200) 241.91/237.99 f3(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) -> f4(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) 241.91/237.99 f1(I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f2(I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) 241.91/237.99 241.91/237.99 We use the extended value criterion with the projection function NU: 241.91/237.99 NU[f1#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9)] = -x5 + 19 241.91/237.99 NU[f4#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9)] = -x5 + 18 241.91/237.99 NU[f3#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9)] = -x5 + 18 241.91/237.99 NU[f2#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9)] = -x5 + 19 241.91/237.99 241.91/237.99 This gives the following inequalities: 241.91/237.99 1 + I15 <= 20 ==> -I15 + 19 > -I15 + 18 with -I15 + 19 >= 0 241.91/237.99 rnd9 = rnd8 /\ rnd8 = rnd8 /\ 1 + I32 <= 20 ==> -I35 + 18 >= -I35 + 18 241.91/237.99 20 <= I42 ==> -I45 + 18 >= -(1 + I45) + 19 241.91/237.99 ==> -I206 + 18 >= -I206 + 18 241.91/237.99 ==> -I216 + 19 >= -I216 + 19 241.91/237.99 241.91/237.99 We remove all the strictly oriented dependency pairs. 241.91/237.99 241.91/237.99 DP problem for innermost termination. 241.91/237.99 P = 241.91/237.99 f4#(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39) -> f3#(I30, I31, 1 + I32, I33, I34, I35, I36, rnd8, rnd9, I39) [rnd9 = rnd8 /\ rnd8 = rnd8 /\ 1 + I32 <= 20] 241.91/237.99 f4#(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) -> f1#(I40, I41, I42, I43, I44, 1 + I45, I46, I47, I48, I49) [20 <= I42] 241.91/237.99 f3#(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) -> f4#(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) 241.91/237.99 f1#(I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f2#(I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) 241.91/237.99 R = 241.91/237.99 f17(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 241.91/237.99 f16(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, I8, I9) 241.91/237.99 f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f3(I10, I11, 0, I13, I14, I15, I16, I17, I18, I19) [1 + I15 <= 20] 241.91/237.99 f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f5(I20, I21, I22, I23, I24, I25, 0, I27, I28, I29) [20 <= I25] 241.91/237.99 f4(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39) -> f3(I30, I31, 1 + I32, I33, I34, I35, I36, rnd8, rnd9, I39) [rnd9 = rnd8 /\ rnd8 = rnd8 /\ 1 + I32 <= 20] 241.91/237.99 f4(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) -> f1(I40, I41, I42, I43, I44, 1 + I45, I46, I47, I48, I49) [20 <= I42] 241.91/237.99 f9(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f7(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 241.91/237.99 f8(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f10(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) 241.91/237.99 f6(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) -> f14(I70, I71, I72, 0, I74, I75, I76, I77, I78, I79) [1 + I76 <= 20] 241.91/237.99 f6(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f11(I80, I81, I82, I83, 0, I85, I86, I87, I88, I89) [20 <= I86] 241.91/237.99 f15(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f14(I90, I91, I92, 1 + I93, I94, I95, I96, I100, I98, rnd10) [rnd10 = I100 /\ I100 = I100 /\ 1 + I93 <= 20] 241.91/237.99 f15(I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f5(I101, I102, I103, I104, I105, I106, 1 + I107, I108, I109, I110) [20 <= I104] 241.91/237.99 f11(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) -> f12(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) 241.91/237.99 f14(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) -> f15(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) 241.91/237.99 f12(I131, I132, I133, I134, I135, I136, I137, I138, I139, I140) -> f8(I131, 0, I133, I134, I135, I136, I137, I138, I139, I140) [1 + I135 <= 20] 241.91/237.99 f12(I141, I142, I143, I144, I145, I146, I147, I148, I149, I150) -> f13(I141, I142, I143, I144, I145, I146, I147, I148, I149, I150) [20 <= I145] 241.91/237.99 f10(I151, I152, I153, I154, I155, I156, I157, I158, I159, I160) -> f9(0, I152, I153, I154, I155, I156, I157, I158, I159, I160) [1 + I152 <= 20] 241.91/237.99 f10(I161, I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f11(I161, I162, I163, I164, 1 + I165, I166, I167, I168, I169, I170) [20 <= I162] 241.91/237.99 f7(I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) -> f9(1 + I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) [1 + I171 <= 20] 241.91/237.99 f7(I181, I182, I183, I184, I185, I186, I187, I188, I189, I190) -> f8(I181, 1 + I182, I183, I184, I185, I186, I187, I188, I189, I190) [20 <= I181] 241.91/237.99 f5(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200) -> f6(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200) 241.91/237.99 f3(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) -> f4(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) 241.91/237.99 f1(I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f2(I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) 241.91/237.99 241.91/237.99 The dependency graph for this problem is: 241.91/237.99 4 -> 20 241.91/237.99 5 -> 21 241.91/237.99 20 -> 4, 5 241.91/237.99 21 -> 241.91/237.99 Where: 241.91/237.99 4) f4#(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39) -> f3#(I30, I31, 1 + I32, I33, I34, I35, I36, rnd8, rnd9, I39) [rnd9 = rnd8 /\ rnd8 = rnd8 /\ 1 + I32 <= 20] 241.91/237.99 5) f4#(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) -> f1#(I40, I41, I42, I43, I44, 1 + I45, I46, I47, I48, I49) [20 <= I42] 241.91/237.99 20) f3#(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) -> f4#(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) 241.91/237.99 21) f1#(I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f2#(I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) 241.91/237.99 241.91/237.99 We have the following SCCs. 241.91/237.99 { 4, 20 } 241.91/237.99 241.91/237.99 DP problem for innermost termination. 241.91/237.99 P = 241.91/237.99 f4#(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39) -> f3#(I30, I31, 1 + I32, I33, I34, I35, I36, rnd8, rnd9, I39) [rnd9 = rnd8 /\ rnd8 = rnd8 /\ 1 + I32 <= 20] 241.91/237.99 f3#(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) -> f4#(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) 241.91/237.99 R = 241.91/237.99 f17(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 241.91/237.99 f16(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, I8, I9) 241.91/237.99 f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f3(I10, I11, 0, I13, I14, I15, I16, I17, I18, I19) [1 + I15 <= 20] 241.91/237.99 f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f5(I20, I21, I22, I23, I24, I25, 0, I27, I28, I29) [20 <= I25] 241.91/237.99 f4(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39) -> f3(I30, I31, 1 + I32, I33, I34, I35, I36, rnd8, rnd9, I39) [rnd9 = rnd8 /\ rnd8 = rnd8 /\ 1 + I32 <= 20] 241.91/237.99 f4(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) -> f1(I40, I41, I42, I43, I44, 1 + I45, I46, I47, I48, I49) [20 <= I42] 241.91/237.99 f9(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f7(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 241.91/237.99 f8(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f10(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) 241.91/237.99 f6(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) -> f14(I70, I71, I72, 0, I74, I75, I76, I77, I78, I79) [1 + I76 <= 20] 241.91/237.99 f6(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f11(I80, I81, I82, I83, 0, I85, I86, I87, I88, I89) [20 <= I86] 241.91/237.99 f15(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f14(I90, I91, I92, 1 + I93, I94, I95, I96, I100, I98, rnd10) [rnd10 = I100 /\ I100 = I100 /\ 1 + I93 <= 20] 241.91/237.99 f15(I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f5(I101, I102, I103, I104, I105, I106, 1 + I107, I108, I109, I110) [20 <= I104] 241.91/237.99 f11(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) -> f12(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) 241.91/237.99 f14(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) -> f15(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) 241.91/237.99 f12(I131, I132, I133, I134, I135, I136, I137, I138, I139, I140) -> f8(I131, 0, I133, I134, I135, I136, I137, I138, I139, I140) [1 + I135 <= 20] 241.91/237.99 f12(I141, I142, I143, I144, I145, I146, I147, I148, I149, I150) -> f13(I141, I142, I143, I144, I145, I146, I147, I148, I149, I150) [20 <= I145] 241.91/237.99 f10(I151, I152, I153, I154, I155, I156, I157, I158, I159, I160) -> f9(0, I152, I153, I154, I155, I156, I157, I158, I159, I160) [1 + I152 <= 20] 241.91/237.99 f10(I161, I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f11(I161, I162, I163, I164, 1 + I165, I166, I167, I168, I169, I170) [20 <= I162] 241.91/237.99 f7(I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) -> f9(1 + I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) [1 + I171 <= 20] 241.91/237.99 f7(I181, I182, I183, I184, I185, I186, I187, I188, I189, I190) -> f8(I181, 1 + I182, I183, I184, I185, I186, I187, I188, I189, I190) [20 <= I181] 241.91/237.99 f5(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200) -> f6(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200) 241.91/237.99 f3(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) -> f4(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) 241.91/237.99 f1(I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f2(I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) 241.91/237.99 241.91/237.99 We use the reverse value criterion with the projection function NU: 241.91/237.99 NU[f3#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10)] = 20 + -1 * (1 + z3) 241.91/237.99 NU[f4#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10)] = 20 + -1 * (1 + z3) 241.91/237.99 241.91/237.99 This gives the following inequalities: 241.91/237.99 rnd9 = rnd8 /\ rnd8 = rnd8 /\ 1 + I32 <= 20 ==> 20 + -1 * (1 + I32) > 20 + -1 * (1 + (1 + I32)) with 20 + -1 * (1 + I32) >= 0 241.91/237.99 ==> 20 + -1 * (1 + I203) >= 20 + -1 * (1 + I203) 241.91/237.99 241.91/237.99 We remove all the strictly oriented dependency pairs. 241.91/237.99 241.91/237.99 DP problem for innermost termination. 241.91/237.99 P = 241.91/237.99 f3#(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) -> f4#(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) 241.91/237.99 R = 241.91/237.99 f17(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 241.91/237.99 f16(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f1(I0, I1, I2, I3, I4, 0, I6, 0, I8, I9) 241.91/237.99 f2(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f3(I10, I11, 0, I13, I14, I15, I16, I17, I18, I19) [1 + I15 <= 20] 241.91/237.99 f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f5(I20, I21, I22, I23, I24, I25, 0, I27, I28, I29) [20 <= I25] 241.91/237.99 f4(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39) -> f3(I30, I31, 1 + I32, I33, I34, I35, I36, rnd8, rnd9, I39) [rnd9 = rnd8 /\ rnd8 = rnd8 /\ 1 + I32 <= 20] 241.91/237.99 f4(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) -> f1(I40, I41, I42, I43, I44, 1 + I45, I46, I47, I48, I49) [20 <= I42] 241.91/237.99 f9(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f7(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 241.91/237.99 f8(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f10(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) 241.91/237.99 f6(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) -> f14(I70, I71, I72, 0, I74, I75, I76, I77, I78, I79) [1 + I76 <= 20] 241.91/237.99 f6(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f11(I80, I81, I82, I83, 0, I85, I86, I87, I88, I89) [20 <= I86] 241.91/237.99 f15(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f14(I90, I91, I92, 1 + I93, I94, I95, I96, I100, I98, rnd10) [rnd10 = I100 /\ I100 = I100 /\ 1 + I93 <= 20] 241.91/237.99 f15(I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f5(I101, I102, I103, I104, I105, I106, 1 + I107, I108, I109, I110) [20 <= I104] 241.91/237.99 f11(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) -> f12(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) 241.91/237.99 f14(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) -> f15(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) 241.91/237.99 f12(I131, I132, I133, I134, I135, I136, I137, I138, I139, I140) -> f8(I131, 0, I133, I134, I135, I136, I137, I138, I139, I140) [1 + I135 <= 20] 241.91/237.99 f12(I141, I142, I143, I144, I145, I146, I147, I148, I149, I150) -> f13(I141, I142, I143, I144, I145, I146, I147, I148, I149, I150) [20 <= I145] 241.91/237.99 f10(I151, I152, I153, I154, I155, I156, I157, I158, I159, I160) -> f9(0, I152, I153, I154, I155, I156, I157, I158, I159, I160) [1 + I152 <= 20] 241.91/237.99 f10(I161, I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f11(I161, I162, I163, I164, 1 + I165, I166, I167, I168, I169, I170) [20 <= I162] 241.91/237.99 f7(I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) -> f9(1 + I171, I172, I173, I174, I175, I176, I177, I178, I179, I180) [1 + I171 <= 20] 241.91/237.99 f7(I181, I182, I183, I184, I185, I186, I187, I188, I189, I190) -> f8(I181, 1 + I182, I183, I184, I185, I186, I187, I188, I189, I190) [20 <= I181] 241.91/237.99 f5(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200) -> f6(I191, I192, I193, I194, I195, I196, I197, I198, I199, I200) 241.91/237.99 f3(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) -> f4(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) 241.91/237.99 f1(I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) -> f2(I211, I212, I213, I214, I215, I216, I217, I218, I219, I220) 241.91/237.99 241.91/237.99 The dependency graph for this problem is: 241.91/237.99 20 -> 241.91/237.99 Where: 241.91/237.99 20) f3#(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) -> f4#(I201, I202, I203, I204, I205, I206, I207, I208, I209, I210) 241.91/237.99 241.91/237.99 We have the following SCCs. 241.91/237.99 241.91/240.95 EOF