31.62/31.47 MAYBE 31.62/31.47 31.62/31.47 DP problem for innermost termination. 31.62/31.47 P = 31.62/31.47 f19#(x1, x2, x3, x4, x5, x6, x7, x8) -> f18#(x1, x2, x3, x4, x5, x6, x7, x8) 31.62/31.47 f18#(I0, I1, I2, I3, I4, I5, I6, I7) -> f3#(I0, 0, I2, I3, I4, I5, I6, I7) 31.62/31.47 f2#(I16, I17, I18, I19, I20, I21, I22, I23) -> f11#(I16, I17, I18, I20, I20, I21, I22, I23) [1 + I17 <= 0] 31.62/31.47 f12#(I24, I25, I26, I27, I28, I29, I30, I31) -> f17#(I24, I25, I26, I27, I28, I29, I30, I31) 31.62/31.47 f12#(I32, I33, I34, I35, I36, I37, I38, I39) -> f14#(I32, I33, I34, I35, rnd5, I37, I35, rnd8) [rnd8 = rnd8 /\ rnd5 = I35] 31.62/31.47 f17#(I40, I41, I42, I43, I44, I45, I46, I47) -> f16#(I40, I41, I42, I43, I44, I45, I46, I47) 31.62/31.47 f17#(I48, I49, I50, I51, I52, I53, I54, I55) -> f15#(I48, I49, I50, I51, I52, I53, I54, I55) 31.62/31.47 f17#(I56, I57, I58, I59, I60, I61, I62, I63) -> f16#(I56, I57, I58, I59, I60, I61, I62, I63) 31.62/31.47 f7#(I64, I65, I66, I67, I68, I69, I70, I71) -> f10#(I64, I65, I66, I67, I68, I69, I70, I71) 31.62/31.47 f16#(I72, I73, I74, I75, I76, I77, I78, I79) -> f15#(I72, I73, I74, 1 + I75, I76, I77, I78, I79) 31.62/31.47 f15#(I80, I81, I82, I83, I84, I85, I86, I87) -> f11#(I80, I81, I82, I83, I84, I85, I86, I87) 31.62/31.47 f14#(I88, I89, I90, I91, I92, I93, I94, I95) -> f13#(I88, I89, I90, I91, I92, I93, I94, I95) 31.62/31.47 f14#(I96, I97, I98, I99, I100, I101, I102, I103) -> f4#(I96, I97, I98, I99, I100, I101, I102, I103) 31.62/31.47 f14#(I104, I105, I106, I107, I108, I109, I110, I111) -> f13#(I104, I105, I106, I107, I108, I109, I110, I111) 31.62/31.47 f13#(I112, I113, I114, I115, I116, I117, I118, I119) -> f7#(I112, I113, I116, I115, I116, I117, I118, I119) 31.62/31.47 f11#(I120, I121, I122, I123, I124, I125, I126, I127) -> f12#(I120, I121, I122, I123, I124, I125, I126, I127) 31.62/31.47 f10#(I128, I129, I130, I131, I132, I133, I134, I135) -> f9#(I128, I129, I130, I131, I132, I133, I134, I135) 31.62/31.47 f10#(I136, I137, I138, I139, I140, I141, I142, I143) -> f4#(I136, I137, I138, I139, I144, I138, I142, I143) [I144 = I138] 31.62/31.47 f9#(I145, I146, I147, I148, I149, I150, I151, I152) -> f8#(I145, I146, I147, I148, I149, I150, I151, I152) 31.62/31.47 f9#(I153, I154, I155, I156, I157, I158, I159, I160) -> f6#(I153, I154, I155, I156, I157, I158, I159, I160) 31.62/31.47 f9#(I161, I162, I163, I164, I165, I166, I167, I168) -> f8#(I161, I162, I163, I164, I165, I166, I167, I168) 31.62/31.47 f8#(I169, I170, I171, I172, I173, I174, I175, I176) -> f6#(I169, I170, 1 + I171, I172, I173, I174, I175, I176) 31.62/31.47 f6#(I177, I178, I179, I180, I181, I182, I183, I184) -> f7#(I177, I178, I179, I180, I181, I182, I183, I184) 31.62/31.47 f3#(I185, I186, I187, I188, I189, I190, I191, I192) -> f1#(I185, I186, I187, I188, I189, I190, I191, I192) 31.62/31.47 f1#(I201, I202, I203, I204, I205, I206, I207, I208) -> f3#(I201, 1 + I202, I203, I204, I205, I206, I207, I208) [1 + I202 <= I201] 31.62/31.47 f1#(I209, I210, I211, I212, I213, I214, I215, I216) -> f2#(I209, I210, I211, I212, -2 + I210, I214, I215, I216) [I209 <= I210] 31.62/31.47 R = 31.62/31.47 f19(x1, x2, x3, x4, x5, x6, x7, x8) -> f18(x1, x2, x3, x4, x5, x6, x7, x8) 31.62/31.47 f18(I0, I1, I2, I3, I4, I5, I6, I7) -> f3(I0, 0, I2, I3, I4, I5, I6, I7) 31.62/31.47 f2(I8, I9, I10, I11, I12, I13, I14, I15) -> f5(I8, I9, I10, I11, I12, I13, I14, I15) [0 <= I9] 31.62/31.47 f2(I16, I17, I18, I19, I20, I21, I22, I23) -> f11(I16, I17, I18, I20, I20, I21, I22, I23) [1 + I17 <= 0] 31.62/31.47 f12(I24, I25, I26, I27, I28, I29, I30, I31) -> f17(I24, I25, I26, I27, I28, I29, I30, I31) 31.62/31.47 f12(I32, I33, I34, I35, I36, I37, I38, I39) -> f14(I32, I33, I34, I35, rnd5, I37, I35, rnd8) [rnd8 = rnd8 /\ rnd5 = I35] 31.62/31.47 f17(I40, I41, I42, I43, I44, I45, I46, I47) -> f16(I40, I41, I42, I43, I44, I45, I46, I47) 31.62/31.47 f17(I48, I49, I50, I51, I52, I53, I54, I55) -> f15(I48, I49, I50, I51, I52, I53, I54, I55) 31.62/31.47 f17(I56, I57, I58, I59, I60, I61, I62, I63) -> f16(I56, I57, I58, I59, I60, I61, I62, I63) 31.62/31.47 f7(I64, I65, I66, I67, I68, I69, I70, I71) -> f10(I64, I65, I66, I67, I68, I69, I70, I71) 31.62/31.47 f16(I72, I73, I74, I75, I76, I77, I78, I79) -> f15(I72, I73, I74, 1 + I75, I76, I77, I78, I79) 31.62/31.47 f15(I80, I81, I82, I83, I84, I85, I86, I87) -> f11(I80, I81, I82, I83, I84, I85, I86, I87) 31.62/31.47 f14(I88, I89, I90, I91, I92, I93, I94, I95) -> f13(I88, I89, I90, I91, I92, I93, I94, I95) 31.62/31.47 f14(I96, I97, I98, I99, I100, I101, I102, I103) -> f4(I96, I97, I98, I99, I100, I101, I102, I103) 31.62/31.47 f14(I104, I105, I106, I107, I108, I109, I110, I111) -> f13(I104, I105, I106, I107, I108, I109, I110, I111) 31.62/31.47 f13(I112, I113, I114, I115, I116, I117, I118, I119) -> f7(I112, I113, I116, I115, I116, I117, I118, I119) 31.62/31.47 f11(I120, I121, I122, I123, I124, I125, I126, I127) -> f12(I120, I121, I122, I123, I124, I125, I126, I127) 31.62/31.47 f10(I128, I129, I130, I131, I132, I133, I134, I135) -> f9(I128, I129, I130, I131, I132, I133, I134, I135) 31.62/31.47 f10(I136, I137, I138, I139, I140, I141, I142, I143) -> f4(I136, I137, I138, I139, I144, I138, I142, I143) [I144 = I138] 31.62/31.47 f9(I145, I146, I147, I148, I149, I150, I151, I152) -> f8(I145, I146, I147, I148, I149, I150, I151, I152) 31.62/31.47 f9(I153, I154, I155, I156, I157, I158, I159, I160) -> f6(I153, I154, I155, I156, I157, I158, I159, I160) 31.62/31.47 f9(I161, I162, I163, I164, I165, I166, I167, I168) -> f8(I161, I162, I163, I164, I165, I166, I167, I168) 31.62/31.47 f8(I169, I170, I171, I172, I173, I174, I175, I176) -> f6(I169, I170, 1 + I171, I172, I173, I174, I175, I176) 31.62/31.47 f6(I177, I178, I179, I180, I181, I182, I183, I184) -> f7(I177, I178, I179, I180, I181, I182, I183, I184) 31.62/31.47 f3(I185, I186, I187, I188, I189, I190, I191, I192) -> f1(I185, I186, I187, I188, I189, I190, I191, I192) 31.62/31.47 f4(I193, I194, I195, I196, I197, I198, I199, I200) -> f5(I193, I194, I195, I196, I197, I198, I199, I200) 31.62/31.47 f1(I201, I202, I203, I204, I205, I206, I207, I208) -> f3(I201, 1 + I202, I203, I204, I205, I206, I207, I208) [1 + I202 <= I201] 31.62/31.47 f1(I209, I210, I211, I212, I213, I214, I215, I216) -> f2(I209, I210, I211, I212, -2 + I210, I214, I215, I216) [I209 <= I210] 31.62/31.47 31.62/31.47 The dependency graph for this problem is: 31.62/31.47 0 -> 1 31.62/31.47 1 -> 23 31.62/31.47 2 -> 15 31.62/31.47 3 -> 5, 6, 7 31.62/31.47 4 -> 11, 12, 13 31.62/31.47 5 -> 9 31.62/31.47 6 -> 10 31.62/31.47 7 -> 9 31.62/31.47 8 -> 16, 17 31.62/31.47 9 -> 10 31.62/31.47 10 -> 15 31.62/31.47 11 -> 14 31.62/31.47 12 -> 31.62/31.47 13 -> 14 31.62/31.47 14 -> 8 31.62/31.47 15 -> 3, 4 31.62/31.47 16 -> 18, 19, 20 31.62/31.47 17 -> 31.62/31.47 18 -> 21 31.62/31.47 19 -> 22 31.62/31.47 20 -> 21 31.62/31.47 21 -> 22 31.62/31.47 22 -> 8 31.62/31.47 23 -> 24, 25 31.62/31.47 24 -> 23 31.62/31.47 25 -> 2 31.62/31.47 Where: 31.62/31.47 0) f19#(x1, x2, x3, x4, x5, x6, x7, x8) -> f18#(x1, x2, x3, x4, x5, x6, x7, x8) 31.62/31.47 1) f18#(I0, I1, I2, I3, I4, I5, I6, I7) -> f3#(I0, 0, I2, I3, I4, I5, I6, I7) 31.62/31.47 2) f2#(I16, I17, I18, I19, I20, I21, I22, I23) -> f11#(I16, I17, I18, I20, I20, I21, I22, I23) [1 + I17 <= 0] 31.62/31.47 3) f12#(I24, I25, I26, I27, I28, I29, I30, I31) -> f17#(I24, I25, I26, I27, I28, I29, I30, I31) 31.62/31.47 4) f12#(I32, I33, I34, I35, I36, I37, I38, I39) -> f14#(I32, I33, I34, I35, rnd5, I37, I35, rnd8) [rnd8 = rnd8 /\ rnd5 = I35] 31.62/31.47 5) f17#(I40, I41, I42, I43, I44, I45, I46, I47) -> f16#(I40, I41, I42, I43, I44, I45, I46, I47) 31.62/31.47 6) f17#(I48, I49, I50, I51, I52, I53, I54, I55) -> f15#(I48, I49, I50, I51, I52, I53, I54, I55) 31.62/31.47 7) f17#(I56, I57, I58, I59, I60, I61, I62, I63) -> f16#(I56, I57, I58, I59, I60, I61, I62, I63) 31.62/31.47 8) f7#(I64, I65, I66, I67, I68, I69, I70, I71) -> f10#(I64, I65, I66, I67, I68, I69, I70, I71) 31.62/31.47 9) f16#(I72, I73, I74, I75, I76, I77, I78, I79) -> f15#(I72, I73, I74, 1 + I75, I76, I77, I78, I79) 31.62/31.47 10) f15#(I80, I81, I82, I83, I84, I85, I86, I87) -> f11#(I80, I81, I82, I83, I84, I85, I86, I87) 31.62/31.47 11) f14#(I88, I89, I90, I91, I92, I93, I94, I95) -> f13#(I88, I89, I90, I91, I92, I93, I94, I95) 31.62/31.47 12) f14#(I96, I97, I98, I99, I100, I101, I102, I103) -> f4#(I96, I97, I98, I99, I100, I101, I102, I103) 31.62/31.47 13) f14#(I104, I105, I106, I107, I108, I109, I110, I111) -> f13#(I104, I105, I106, I107, I108, I109, I110, I111) 31.62/31.47 14) f13#(I112, I113, I114, I115, I116, I117, I118, I119) -> f7#(I112, I113, I116, I115, I116, I117, I118, I119) 31.62/31.47 15) f11#(I120, I121, I122, I123, I124, I125, I126, I127) -> f12#(I120, I121, I122, I123, I124, I125, I126, I127) 31.62/31.47 16) f10#(I128, I129, I130, I131, I132, I133, I134, I135) -> f9#(I128, I129, I130, I131, I132, I133, I134, I135) 31.62/31.47 17) f10#(I136, I137, I138, I139, I140, I141, I142, I143) -> f4#(I136, I137, I138, I139, I144, I138, I142, I143) [I144 = I138] 31.62/31.47 18) f9#(I145, I146, I147, I148, I149, I150, I151, I152) -> f8#(I145, I146, I147, I148, I149, I150, I151, I152) 31.62/31.47 19) f9#(I153, I154, I155, I156, I157, I158, I159, I160) -> f6#(I153, I154, I155, I156, I157, I158, I159, I160) 31.62/31.47 20) f9#(I161, I162, I163, I164, I165, I166, I167, I168) -> f8#(I161, I162, I163, I164, I165, I166, I167, I168) 31.62/31.47 21) f8#(I169, I170, I171, I172, I173, I174, I175, I176) -> f6#(I169, I170, 1 + I171, I172, I173, I174, I175, I176) 31.62/31.47 22) f6#(I177, I178, I179, I180, I181, I182, I183, I184) -> f7#(I177, I178, I179, I180, I181, I182, I183, I184) 31.62/31.47 23) f3#(I185, I186, I187, I188, I189, I190, I191, I192) -> f1#(I185, I186, I187, I188, I189, I190, I191, I192) 31.62/31.47 24) f1#(I201, I202, I203, I204, I205, I206, I207, I208) -> f3#(I201, 1 + I202, I203, I204, I205, I206, I207, I208) [1 + I202 <= I201] 31.62/31.47 25) f1#(I209, I210, I211, I212, I213, I214, I215, I216) -> f2#(I209, I210, I211, I212, -2 + I210, I214, I215, I216) [I209 <= I210] 31.62/31.47 31.62/31.47 We have the following SCCs. 31.62/31.47 { 23, 24 } 31.62/31.47 { 3, 5, 6, 7, 9, 10, 15 } 31.62/31.47 { 8, 16, 18, 19, 20, 21, 22 } 31.62/31.47 31.62/31.47 DP problem for innermost termination. 31.62/31.47 P = 31.62/31.47 f7#(I64, I65, I66, I67, I68, I69, I70, I71) -> f10#(I64, I65, I66, I67, I68, I69, I70, I71) 31.62/31.47 f10#(I128, I129, I130, I131, I132, I133, I134, I135) -> f9#(I128, I129, I130, I131, I132, I133, I134, I135) 31.62/31.47 f9#(I145, I146, I147, I148, I149, I150, I151, I152) -> f8#(I145, I146, I147, I148, I149, I150, I151, I152) 31.62/31.47 f9#(I153, I154, I155, I156, I157, I158, I159, I160) -> f6#(I153, I154, I155, I156, I157, I158, I159, I160) 31.62/31.47 f9#(I161, I162, I163, I164, I165, I166, I167, I168) -> f8#(I161, I162, I163, I164, I165, I166, I167, I168) 31.62/31.47 f8#(I169, I170, I171, I172, I173, I174, I175, I176) -> f6#(I169, I170, 1 + I171, I172, I173, I174, I175, I176) 31.62/31.47 f6#(I177, I178, I179, I180, I181, I182, I183, I184) -> f7#(I177, I178, I179, I180, I181, I182, I183, I184) 31.62/31.47 R = 31.62/31.47 f19(x1, x2, x3, x4, x5, x6, x7, x8) -> f18(x1, x2, x3, x4, x5, x6, x7, x8) 31.62/31.47 f18(I0, I1, I2, I3, I4, I5, I6, I7) -> f3(I0, 0, I2, I3, I4, I5, I6, I7) 31.62/31.47 f2(I8, I9, I10, I11, I12, I13, I14, I15) -> f5(I8, I9, I10, I11, I12, I13, I14, I15) [0 <= I9] 31.62/31.47 f2(I16, I17, I18, I19, I20, I21, I22, I23) -> f11(I16, I17, I18, I20, I20, I21, I22, I23) [1 + I17 <= 0] 31.62/31.47 f12(I24, I25, I26, I27, I28, I29, I30, I31) -> f17(I24, I25, I26, I27, I28, I29, I30, I31) 31.62/31.47 f12(I32, I33, I34, I35, I36, I37, I38, I39) -> f14(I32, I33, I34, I35, rnd5, I37, I35, rnd8) [rnd8 = rnd8 /\ rnd5 = I35] 31.62/31.47 f17(I40, I41, I42, I43, I44, I45, I46, I47) -> f16(I40, I41, I42, I43, I44, I45, I46, I47) 31.62/31.47 f17(I48, I49, I50, I51, I52, I53, I54, I55) -> f15(I48, I49, I50, I51, I52, I53, I54, I55) 31.62/31.47 f17(I56, I57, I58, I59, I60, I61, I62, I63) -> f16(I56, I57, I58, I59, I60, I61, I62, I63) 31.62/31.47 f7(I64, I65, I66, I67, I68, I69, I70, I71) -> f10(I64, I65, I66, I67, I68, I69, I70, I71) 31.62/31.47 f16(I72, I73, I74, I75, I76, I77, I78, I79) -> f15(I72, I73, I74, 1 + I75, I76, I77, I78, I79) 31.62/31.47 f15(I80, I81, I82, I83, I84, I85, I86, I87) -> f11(I80, I81, I82, I83, I84, I85, I86, I87) 31.62/31.47 f14(I88, I89, I90, I91, I92, I93, I94, I95) -> f13(I88, I89, I90, I91, I92, I93, I94, I95) 31.62/31.47 f14(I96, I97, I98, I99, I100, I101, I102, I103) -> f4(I96, I97, I98, I99, I100, I101, I102, I103) 31.62/31.47 f14(I104, I105, I106, I107, I108, I109, I110, I111) -> f13(I104, I105, I106, I107, I108, I109, I110, I111) 31.62/31.47 f13(I112, I113, I114, I115, I116, I117, I118, I119) -> f7(I112, I113, I116, I115, I116, I117, I118, I119) 31.62/31.47 f11(I120, I121, I122, I123, I124, I125, I126, I127) -> f12(I120, I121, I122, I123, I124, I125, I126, I127) 31.62/31.47 f10(I128, I129, I130, I131, I132, I133, I134, I135) -> f9(I128, I129, I130, I131, I132, I133, I134, I135) 31.62/31.47 f10(I136, I137, I138, I139, I140, I141, I142, I143) -> f4(I136, I137, I138, I139, I144, I138, I142, I143) [I144 = I138] 31.62/31.47 f9(I145, I146, I147, I148, I149, I150, I151, I152) -> f8(I145, I146, I147, I148, I149, I150, I151, I152) 31.62/31.47 f9(I153, I154, I155, I156, I157, I158, I159, I160) -> f6(I153, I154, I155, I156, I157, I158, I159, I160) 31.62/31.47 f9(I161, I162, I163, I164, I165, I166, I167, I168) -> f8(I161, I162, I163, I164, I165, I166, I167, I168) 31.62/31.47 f8(I169, I170, I171, I172, I173, I174, I175, I176) -> f6(I169, I170, 1 + I171, I172, I173, I174, I175, I176) 31.62/31.47 f6(I177, I178, I179, I180, I181, I182, I183, I184) -> f7(I177, I178, I179, I180, I181, I182, I183, I184) 31.62/31.47 f3(I185, I186, I187, I188, I189, I190, I191, I192) -> f1(I185, I186, I187, I188, I189, I190, I191, I192) 31.62/31.47 f4(I193, I194, I195, I196, I197, I198, I199, I200) -> f5(I193, I194, I195, I196, I197, I198, I199, I200) 31.62/31.47 f1(I201, I202, I203, I204, I205, I206, I207, I208) -> f3(I201, 1 + I202, I203, I204, I205, I206, I207, I208) [1 + I202 <= I201] 31.62/31.47 f1(I209, I210, I211, I212, I213, I214, I215, I216) -> f2(I209, I210, I211, I212, -2 + I210, I214, I215, I216) [I209 <= I210] 31.62/31.47 31.62/34.45 EOF