96.91/95.30 YES 96.91/95.30 96.91/95.30 DP problem for innermost termination. 96.91/95.30 P = 96.91/95.30 f22#(x1, x2, x3, x4, x5, x6, x7) -> f21#(x1, x2, x3, x4, x5, x6, x7) 96.91/95.30 f21#(I0, I1, I2, I3, I4, I5, I6) -> f1#(2, 0, I2, I3, rnd5, rnd6, I6) [rnd6 = rnd6 /\ rnd5 = rnd5] 96.91/95.30 f2#(I7, I8, I9, I10, I11, I12, I13) -> f3#(I7, I8, 0, I10, I11, I12, I13) [1 + I8 <= I7] 96.91/95.30 f2#(I14, I15, I16, I17, I18, I19, I20) -> f14#(I14, 0, I16, I17, I18, I19, I20) [I14 <= I15] 96.91/95.30 f4#(I21, I22, I23, I24, I25, I26, I27) -> f3#(I21, I22, 1 + I23, I24, I25, I26, I27) [1 + I23 <= I21] 96.91/95.30 f4#(I28, I29, I30, I31, I32, I33, I34) -> f1#(I28, 1 + I29, I30, I31, I32, I33, I34) [I28 <= I30] 96.91/95.30 f19#(I35, I36, I37, I38, I39, I40, I41) -> f17#(I35, I36, I37, I38, I39, I40, I41) 96.91/95.30 f15#(I42, I43, I44, I45, I46, I47, I48) -> f18#(I42, I43, 0, I45, I46, I47, I48) [1 + I43 <= I42] 96.91/95.30 f15#(I49, I50, I51, I52, I53, I54, I55) -> f16#(I49, I50, I51, I52, I53, I54, I55) [I49 <= I50] 96.91/95.30 f20#(I56, I57, I58, I59, I60, I61, I62) -> f19#(I56, I57, I58, 0, I60, I61, I62) [1 + I58 <= I56] 96.91/95.30 f20#(I63, I64, I65, I66, I67, I68, I69) -> f14#(I63, 1 + I64, I65, I66, I67, I68, I69) [I63 <= I65] 96.91/95.30 f18#(I70, I71, I72, I73, I74, I75, I76) -> f20#(I70, I71, I72, I73, I74, I75, I76) 96.91/95.30 f17#(I77, I78, I79, I80, I81, I82, I83) -> f19#(I77, I78, I79, 1 + I80, I81, I82, I83) [1 + I80 <= I77] 96.91/95.30 f17#(I84, I85, I86, I87, I88, I89, I90) -> f18#(I84, I85, 1 + I86, I87, I88, I89, I90) [I84 <= I87] 96.91/95.30 f16#(I91, I92, I93, I94, I95, I96, I97) -> f13#(I91, I92, I93, I94, I95, I96, I97) 96.91/95.30 f16#(I98, I99, I100, I101, I102, I103, I104) -> f5#(I98, I99, I100, I101, I102, I103, I104) 96.91/95.30 f16#(I105, I106, I107, I108, I109, I110, I111) -> f5#(I105, I106, I107, I108, I109, I110, I111) 96.91/95.30 f14#(I112, I113, I114, I115, I116, I117, I118) -> f15#(I112, I113, I114, I115, I116, I117, I118) 96.91/95.30 f13#(I119, I120, I121, I122, I123, I124, I125) -> f12#(I119, I120, I121, I122, I123, I124, I125) 96.91/95.30 f13#(I126, I127, I128, I129, I130, I131, I132) -> f7#(I126, I127, I128, I129, I130, I131, I132) 96.91/95.30 f13#(I133, I134, I135, I136, I137, I138, I139) -> f7#(I133, I134, I135, I136, I137, I138, I139) 96.91/95.30 f12#(I140, I141, I142, I143, I144, I145, I146) -> f11#(I140, I141, I142, I143, I144, I145, I146) 96.91/95.30 f12#(I147, I148, I149, I150, I151, I152, I153) -> f8#(I147, I148, I149, I150, I151, I152, I153) 96.91/95.30 f12#(I154, I155, I156, I157, I158, I159, I160) -> f8#(I154, I155, I156, I157, I158, I159, I160) 96.91/95.30 f11#(I161, I162, I163, I164, I165, I166, I167) -> f9#(I161, I162, I163, I164, I165, I166, I167) 96.91/95.30 f11#(I168, I169, I170, I171, I172, I173, I174) -> f6#(I168, I169, I170, I171, I172, I173, 0) 96.91/95.30 f11#(I175, I176, I177, I178, I179, I180, I181) -> f9#(I175, I176, I177, I178, I179, I180, I181) 96.91/95.30 f9#(I189, I190, I191, I192, I193, I194, I195) -> f6#(I189, I190, I191, I192, I193, I194, 1) 96.91/95.30 f8#(I196, I197, I198, I199, I200, I201, I202) -> f6#(I196, I197, I198, I199, I200, I201, 1) 96.91/95.30 f7#(I203, I204, I205, I206, I207, I208, I209) -> f6#(I203, I204, I205, I206, I207, I208, 1) 96.91/95.30 f5#(I210, I211, I212, I213, I214, I215, I216) -> f6#(I210, I211, I212, I213, I214, I215, 1) 96.91/95.30 f3#(I217, I218, I219, I220, I221, I222, I223) -> f4#(I217, I218, I219, I220, I221, I222, I223) 96.91/95.30 f1#(I224, I225, I226, I227, I228, I229, I230) -> f2#(I224, I225, I226, I227, I228, I229, I230) 96.91/95.30 R = 96.91/95.30 f22(x1, x2, x3, x4, x5, x6, x7) -> f21(x1, x2, x3, x4, x5, x6, x7) 96.91/95.30 f21(I0, I1, I2, I3, I4, I5, I6) -> f1(2, 0, I2, I3, rnd5, rnd6, I6) [rnd6 = rnd6 /\ rnd5 = rnd5] 96.91/95.30 f2(I7, I8, I9, I10, I11, I12, I13) -> f3(I7, I8, 0, I10, I11, I12, I13) [1 + I8 <= I7] 96.91/95.30 f2(I14, I15, I16, I17, I18, I19, I20) -> f14(I14, 0, I16, I17, I18, I19, I20) [I14 <= I15] 96.91/95.30 f4(I21, I22, I23, I24, I25, I26, I27) -> f3(I21, I22, 1 + I23, I24, I25, I26, I27) [1 + I23 <= I21] 96.91/95.30 f4(I28, I29, I30, I31, I32, I33, I34) -> f1(I28, 1 + I29, I30, I31, I32, I33, I34) [I28 <= I30] 96.91/95.30 f19(I35, I36, I37, I38, I39, I40, I41) -> f17(I35, I36, I37, I38, I39, I40, I41) 96.91/95.30 f15(I42, I43, I44, I45, I46, I47, I48) -> f18(I42, I43, 0, I45, I46, I47, I48) [1 + I43 <= I42] 96.91/95.30 f15(I49, I50, I51, I52, I53, I54, I55) -> f16(I49, I50, I51, I52, I53, I54, I55) [I49 <= I50] 96.91/95.30 f20(I56, I57, I58, I59, I60, I61, I62) -> f19(I56, I57, I58, 0, I60, I61, I62) [1 + I58 <= I56] 96.91/95.30 f20(I63, I64, I65, I66, I67, I68, I69) -> f14(I63, 1 + I64, I65, I66, I67, I68, I69) [I63 <= I65] 96.91/95.30 f18(I70, I71, I72, I73, I74, I75, I76) -> f20(I70, I71, I72, I73, I74, I75, I76) 96.91/95.30 f17(I77, I78, I79, I80, I81, I82, I83) -> f19(I77, I78, I79, 1 + I80, I81, I82, I83) [1 + I80 <= I77] 96.91/95.30 f17(I84, I85, I86, I87, I88, I89, I90) -> f18(I84, I85, 1 + I86, I87, I88, I89, I90) [I84 <= I87] 96.91/95.30 f16(I91, I92, I93, I94, I95, I96, I97) -> f13(I91, I92, I93, I94, I95, I96, I97) 96.91/95.30 f16(I98, I99, I100, I101, I102, I103, I104) -> f5(I98, I99, I100, I101, I102, I103, I104) 96.91/95.30 f16(I105, I106, I107, I108, I109, I110, I111) -> f5(I105, I106, I107, I108, I109, I110, I111) 96.91/95.30 f14(I112, I113, I114, I115, I116, I117, I118) -> f15(I112, I113, I114, I115, I116, I117, I118) 96.91/95.30 f13(I119, I120, I121, I122, I123, I124, I125) -> f12(I119, I120, I121, I122, I123, I124, I125) 96.91/95.30 f13(I126, I127, I128, I129, I130, I131, I132) -> f7(I126, I127, I128, I129, I130, I131, I132) 96.91/95.30 f13(I133, I134, I135, I136, I137, I138, I139) -> f7(I133, I134, I135, I136, I137, I138, I139) 96.91/95.30 f12(I140, I141, I142, I143, I144, I145, I146) -> f11(I140, I141, I142, I143, I144, I145, I146) 96.91/95.30 f12(I147, I148, I149, I150, I151, I152, I153) -> f8(I147, I148, I149, I150, I151, I152, I153) 96.91/95.30 f12(I154, I155, I156, I157, I158, I159, I160) -> f8(I154, I155, I156, I157, I158, I159, I160) 96.91/95.30 f11(I161, I162, I163, I164, I165, I166, I167) -> f9(I161, I162, I163, I164, I165, I166, I167) 96.91/95.30 f11(I168, I169, I170, I171, I172, I173, I174) -> f6(I168, I169, I170, I171, I172, I173, 0) 96.91/95.30 f11(I175, I176, I177, I178, I179, I180, I181) -> f9(I175, I176, I177, I178, I179, I180, I181) 96.91/95.30 f6(I182, I183, I184, I185, I186, I187, I188) -> f10(I182, I183, I184, I185, I186, I187, I188) 96.91/95.30 f9(I189, I190, I191, I192, I193, I194, I195) -> f6(I189, I190, I191, I192, I193, I194, 1) 96.91/95.30 f8(I196, I197, I198, I199, I200, I201, I202) -> f6(I196, I197, I198, I199, I200, I201, 1) 96.91/95.30 f7(I203, I204, I205, I206, I207, I208, I209) -> f6(I203, I204, I205, I206, I207, I208, 1) 96.91/95.30 f5(I210, I211, I212, I213, I214, I215, I216) -> f6(I210, I211, I212, I213, I214, I215, 1) 96.91/95.30 f3(I217, I218, I219, I220, I221, I222, I223) -> f4(I217, I218, I219, I220, I221, I222, I223) 96.91/95.30 f1(I224, I225, I226, I227, I228, I229, I230) -> f2(I224, I225, I226, I227, I228, I229, I230) 96.91/95.30 96.91/95.30 The dependency graph for this problem is: 96.91/95.30 0 -> 1 96.91/95.30 1 -> 32 96.91/95.30 2 -> 31 96.91/95.30 3 -> 17 96.91/95.30 4 -> 31 96.91/95.30 5 -> 32 96.91/95.30 6 -> 12, 13 96.91/95.30 7 -> 11 96.91/95.30 8 -> 14, 15, 16 96.91/95.30 9 -> 6 96.91/95.30 10 -> 17 96.91/95.30 11 -> 9, 10 96.91/95.30 12 -> 6 96.91/95.30 13 -> 11 96.91/95.30 14 -> 18, 19, 20 96.91/95.30 15 -> 30 96.91/95.30 16 -> 30 96.91/95.30 17 -> 7, 8 96.91/95.30 18 -> 21, 22, 23 96.91/95.30 19 -> 29 96.91/95.30 20 -> 29 96.91/95.30 21 -> 24, 25, 26 96.91/95.30 22 -> 28 96.91/95.30 23 -> 28 96.91/95.30 24 -> 27 96.91/95.30 25 -> 96.91/95.30 26 -> 27 96.91/95.30 27 -> 96.91/95.30 28 -> 96.91/95.30 29 -> 96.91/95.30 30 -> 96.91/95.30 31 -> 4, 5 96.91/95.30 32 -> 2, 3 96.91/95.30 Where: 96.91/95.30 0) f22#(x1, x2, x3, x4, x5, x6, x7) -> f21#(x1, x2, x3, x4, x5, x6, x7) 96.91/95.30 1) f21#(I0, I1, I2, I3, I4, I5, I6) -> f1#(2, 0, I2, I3, rnd5, rnd6, I6) [rnd6 = rnd6 /\ rnd5 = rnd5] 96.91/95.30 2) f2#(I7, I8, I9, I10, I11, I12, I13) -> f3#(I7, I8, 0, I10, I11, I12, I13) [1 + I8 <= I7] 96.91/95.30 3) f2#(I14, I15, I16, I17, I18, I19, I20) -> f14#(I14, 0, I16, I17, I18, I19, I20) [I14 <= I15] 96.91/95.30 4) f4#(I21, I22, I23, I24, I25, I26, I27) -> f3#(I21, I22, 1 + I23, I24, I25, I26, I27) [1 + I23 <= I21] 96.91/95.30 5) f4#(I28, I29, I30, I31, I32, I33, I34) -> f1#(I28, 1 + I29, I30, I31, I32, I33, I34) [I28 <= I30] 96.91/95.30 6) f19#(I35, I36, I37, I38, I39, I40, I41) -> f17#(I35, I36, I37, I38, I39, I40, I41) 96.91/95.30 7) f15#(I42, I43, I44, I45, I46, I47, I48) -> f18#(I42, I43, 0, I45, I46, I47, I48) [1 + I43 <= I42] 96.91/95.30 8) f15#(I49, I50, I51, I52, I53, I54, I55) -> f16#(I49, I50, I51, I52, I53, I54, I55) [I49 <= I50] 96.91/95.30 9) f20#(I56, I57, I58, I59, I60, I61, I62) -> f19#(I56, I57, I58, 0, I60, I61, I62) [1 + I58 <= I56] 96.91/95.30 10) f20#(I63, I64, I65, I66, I67, I68, I69) -> f14#(I63, 1 + I64, I65, I66, I67, I68, I69) [I63 <= I65] 96.91/95.30 11) f18#(I70, I71, I72, I73, I74, I75, I76) -> f20#(I70, I71, I72, I73, I74, I75, I76) 96.91/95.30 12) f17#(I77, I78, I79, I80, I81, I82, I83) -> f19#(I77, I78, I79, 1 + I80, I81, I82, I83) [1 + I80 <= I77] 96.91/95.30 13) f17#(I84, I85, I86, I87, I88, I89, I90) -> f18#(I84, I85, 1 + I86, I87, I88, I89, I90) [I84 <= I87] 96.91/95.30 14) f16#(I91, I92, I93, I94, I95, I96, I97) -> f13#(I91, I92, I93, I94, I95, I96, I97) 96.91/95.30 15) f16#(I98, I99, I100, I101, I102, I103, I104) -> f5#(I98, I99, I100, I101, I102, I103, I104) 96.91/95.30 16) f16#(I105, I106, I107, I108, I109, I110, I111) -> f5#(I105, I106, I107, I108, I109, I110, I111) 96.91/95.30 17) f14#(I112, I113, I114, I115, I116, I117, I118) -> f15#(I112, I113, I114, I115, I116, I117, I118) 96.91/95.30 18) f13#(I119, I120, I121, I122, I123, I124, I125) -> f12#(I119, I120, I121, I122, I123, I124, I125) 96.91/95.30 19) f13#(I126, I127, I128, I129, I130, I131, I132) -> f7#(I126, I127, I128, I129, I130, I131, I132) 96.91/95.30 20) f13#(I133, I134, I135, I136, I137, I138, I139) -> f7#(I133, I134, I135, I136, I137, I138, I139) 96.91/95.30 21) f12#(I140, I141, I142, I143, I144, I145, I146) -> f11#(I140, I141, I142, I143, I144, I145, I146) 96.91/95.30 22) f12#(I147, I148, I149, I150, I151, I152, I153) -> f8#(I147, I148, I149, I150, I151, I152, I153) 96.91/95.30 23) f12#(I154, I155, I156, I157, I158, I159, I160) -> f8#(I154, I155, I156, I157, I158, I159, I160) 96.91/95.30 24) f11#(I161, I162, I163, I164, I165, I166, I167) -> f9#(I161, I162, I163, I164, I165, I166, I167) 96.91/95.30 25) f11#(I168, I169, I170, I171, I172, I173, I174) -> f6#(I168, I169, I170, I171, I172, I173, 0) 96.91/95.30 26) f11#(I175, I176, I177, I178, I179, I180, I181) -> f9#(I175, I176, I177, I178, I179, I180, I181) 96.91/95.30 27) f9#(I189, I190, I191, I192, I193, I194, I195) -> f6#(I189, I190, I191, I192, I193, I194, 1) 96.91/95.30 28) f8#(I196, I197, I198, I199, I200, I201, I202) -> f6#(I196, I197, I198, I199, I200, I201, 1) 96.91/95.30 29) f7#(I203, I204, I205, I206, I207, I208, I209) -> f6#(I203, I204, I205, I206, I207, I208, 1) 96.91/95.30 30) f5#(I210, I211, I212, I213, I214, I215, I216) -> f6#(I210, I211, I212, I213, I214, I215, 1) 96.91/95.30 31) f3#(I217, I218, I219, I220, I221, I222, I223) -> f4#(I217, I218, I219, I220, I221, I222, I223) 96.91/95.30 32) f1#(I224, I225, I226, I227, I228, I229, I230) -> f2#(I224, I225, I226, I227, I228, I229, I230) 96.91/95.30 96.91/95.30 We have the following SCCs. 96.91/95.30 { 2, 4, 5, 31, 32 } 96.91/95.30 { 6, 7, 9, 10, 11, 12, 13, 17 } 96.91/95.30 96.91/95.30 DP problem for innermost termination. 96.91/95.30 P = 96.91/95.30 f19#(I35, I36, I37, I38, I39, I40, I41) -> f17#(I35, I36, I37, I38, I39, I40, I41) 96.91/95.30 f15#(I42, I43, I44, I45, I46, I47, I48) -> f18#(I42, I43, 0, I45, I46, I47, I48) [1 + I43 <= I42] 96.91/95.30 f20#(I56, I57, I58, I59, I60, I61, I62) -> f19#(I56, I57, I58, 0, I60, I61, I62) [1 + I58 <= I56] 96.91/95.30 f20#(I63, I64, I65, I66, I67, I68, I69) -> f14#(I63, 1 + I64, I65, I66, I67, I68, I69) [I63 <= I65] 96.91/95.30 f18#(I70, I71, I72, I73, I74, I75, I76) -> f20#(I70, I71, I72, I73, I74, I75, I76) 96.91/95.30 f17#(I77, I78, I79, I80, I81, I82, I83) -> f19#(I77, I78, I79, 1 + I80, I81, I82, I83) [1 + I80 <= I77] 96.91/95.30 f17#(I84, I85, I86, I87, I88, I89, I90) -> f18#(I84, I85, 1 + I86, I87, I88, I89, I90) [I84 <= I87] 96.91/95.30 f14#(I112, I113, I114, I115, I116, I117, I118) -> f15#(I112, I113, I114, I115, I116, I117, I118) 96.91/95.30 R = 96.91/95.30 f22(x1, x2, x3, x4, x5, x6, x7) -> f21(x1, x2, x3, x4, x5, x6, x7) 96.91/95.30 f21(I0, I1, I2, I3, I4, I5, I6) -> f1(2, 0, I2, I3, rnd5, rnd6, I6) [rnd6 = rnd6 /\ rnd5 = rnd5] 96.91/95.30 f2(I7, I8, I9, I10, I11, I12, I13) -> f3(I7, I8, 0, I10, I11, I12, I13) [1 + I8 <= I7] 96.91/95.30 f2(I14, I15, I16, I17, I18, I19, I20) -> f14(I14, 0, I16, I17, I18, I19, I20) [I14 <= I15] 96.91/95.30 f4(I21, I22, I23, I24, I25, I26, I27) -> f3(I21, I22, 1 + I23, I24, I25, I26, I27) [1 + I23 <= I21] 96.91/95.30 f4(I28, I29, I30, I31, I32, I33, I34) -> f1(I28, 1 + I29, I30, I31, I32, I33, I34) [I28 <= I30] 96.91/95.30 f19(I35, I36, I37, I38, I39, I40, I41) -> f17(I35, I36, I37, I38, I39, I40, I41) 96.91/95.30 f15(I42, I43, I44, I45, I46, I47, I48) -> f18(I42, I43, 0, I45, I46, I47, I48) [1 + I43 <= I42] 96.91/95.30 f15(I49, I50, I51, I52, I53, I54, I55) -> f16(I49, I50, I51, I52, I53, I54, I55) [I49 <= I50] 96.91/95.30 f20(I56, I57, I58, I59, I60, I61, I62) -> f19(I56, I57, I58, 0, I60, I61, I62) [1 + I58 <= I56] 96.91/95.30 f20(I63, I64, I65, I66, I67, I68, I69) -> f14(I63, 1 + I64, I65, I66, I67, I68, I69) [I63 <= I65] 96.91/95.30 f18(I70, I71, I72, I73, I74, I75, I76) -> f20(I70, I71, I72, I73, I74, I75, I76) 96.91/95.30 f17(I77, I78, I79, I80, I81, I82, I83) -> f19(I77, I78, I79, 1 + I80, I81, I82, I83) [1 + I80 <= I77] 96.91/95.30 f17(I84, I85, I86, I87, I88, I89, I90) -> f18(I84, I85, 1 + I86, I87, I88, I89, I90) [I84 <= I87] 96.91/95.30 f16(I91, I92, I93, I94, I95, I96, I97) -> f13(I91, I92, I93, I94, I95, I96, I97) 96.91/95.30 f16(I98, I99, I100, I101, I102, I103, I104) -> f5(I98, I99, I100, I101, I102, I103, I104) 96.91/95.30 f16(I105, I106, I107, I108, I109, I110, I111) -> f5(I105, I106, I107, I108, I109, I110, I111) 96.91/95.30 f14(I112, I113, I114, I115, I116, I117, I118) -> f15(I112, I113, I114, I115, I116, I117, I118) 96.91/95.30 f13(I119, I120, I121, I122, I123, I124, I125) -> f12(I119, I120, I121, I122, I123, I124, I125) 96.91/95.30 f13(I126, I127, I128, I129, I130, I131, I132) -> f7(I126, I127, I128, I129, I130, I131, I132) 96.91/95.30 f13(I133, I134, I135, I136, I137, I138, I139) -> f7(I133, I134, I135, I136, I137, I138, I139) 96.91/95.30 f12(I140, I141, I142, I143, I144, I145, I146) -> f11(I140, I141, I142, I143, I144, I145, I146) 96.91/95.30 f12(I147, I148, I149, I150, I151, I152, I153) -> f8(I147, I148, I149, I150, I151, I152, I153) 96.91/95.30 f12(I154, I155, I156, I157, I158, I159, I160) -> f8(I154, I155, I156, I157, I158, I159, I160) 96.91/95.30 f11(I161, I162, I163, I164, I165, I166, I167) -> f9(I161, I162, I163, I164, I165, I166, I167) 96.91/95.30 f11(I168, I169, I170, I171, I172, I173, I174) -> f6(I168, I169, I170, I171, I172, I173, 0) 96.91/95.30 f11(I175, I176, I177, I178, I179, I180, I181) -> f9(I175, I176, I177, I178, I179, I180, I181) 96.91/95.30 f6(I182, I183, I184, I185, I186, I187, I188) -> f10(I182, I183, I184, I185, I186, I187, I188) 96.91/95.30 f9(I189, I190, I191, I192, I193, I194, I195) -> f6(I189, I190, I191, I192, I193, I194, 1) 96.91/95.30 f8(I196, I197, I198, I199, I200, I201, I202) -> f6(I196, I197, I198, I199, I200, I201, 1) 96.91/95.30 f7(I203, I204, I205, I206, I207, I208, I209) -> f6(I203, I204, I205, I206, I207, I208, 1) 96.91/95.30 f5(I210, I211, I212, I213, I214, I215, I216) -> f6(I210, I211, I212, I213, I214, I215, 1) 96.91/95.30 f3(I217, I218, I219, I220, I221, I222, I223) -> f4(I217, I218, I219, I220, I221, I222, I223) 96.91/95.30 f1(I224, I225, I226, I227, I228, I229, I230) -> f2(I224, I225, I226, I227, I228, I229, I230) 96.91/95.30 96.91/95.30 We use the extended value criterion with the projection function NU: 96.91/95.30 NU[f14#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x1 - 1 96.91/95.30 NU[f20#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x1 - 2 96.91/95.30 NU[f18#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x1 - 2 96.91/95.30 NU[f15#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x1 - 1 96.91/95.30 NU[f17#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x1 - 2 96.91/95.30 NU[f19#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x1 - 2 96.91/95.30 96.91/95.30 This gives the following inequalities: 96.91/95.30 ==> I35 - I36 - 2 >= I35 - I36 - 2 96.91/95.30 1 + I43 <= I42 ==> I42 - I43 - 1 > I42 - I43 - 2 with I42 - I43 - 1 >= 0 96.91/95.30 1 + I58 <= I56 ==> I56 - I57 - 2 >= I56 - I57 - 2 96.91/95.30 I63 <= I65 ==> I63 - I64 - 2 >= I63 - (1 + I64) - 1 96.91/95.30 ==> I70 - I71 - 2 >= I70 - I71 - 2 96.91/95.30 1 + I80 <= I77 ==> I77 - I78 - 2 >= I77 - I78 - 2 96.91/95.30 I84 <= I87 ==> I84 - I85 - 2 >= I84 - I85 - 2 96.91/95.30 ==> I112 - I113 - 1 >= I112 - I113 - 1 96.91/95.30 96.91/95.30 We remove all the strictly oriented dependency pairs. 96.91/95.30 96.91/95.30 DP problem for innermost termination. 96.91/95.30 P = 96.91/95.30 f19#(I35, I36, I37, I38, I39, I40, I41) -> f17#(I35, I36, I37, I38, I39, I40, I41) 96.91/95.30 f20#(I56, I57, I58, I59, I60, I61, I62) -> f19#(I56, I57, I58, 0, I60, I61, I62) [1 + I58 <= I56] 96.91/95.30 f20#(I63, I64, I65, I66, I67, I68, I69) -> f14#(I63, 1 + I64, I65, I66, I67, I68, I69) [I63 <= I65] 96.91/95.30 f18#(I70, I71, I72, I73, I74, I75, I76) -> f20#(I70, I71, I72, I73, I74, I75, I76) 96.91/95.30 f17#(I77, I78, I79, I80, I81, I82, I83) -> f19#(I77, I78, I79, 1 + I80, I81, I82, I83) [1 + I80 <= I77] 96.91/95.30 f17#(I84, I85, I86, I87, I88, I89, I90) -> f18#(I84, I85, 1 + I86, I87, I88, I89, I90) [I84 <= I87] 96.91/95.30 f14#(I112, I113, I114, I115, I116, I117, I118) -> f15#(I112, I113, I114, I115, I116, I117, I118) 96.91/95.30 R = 96.91/95.30 f22(x1, x2, x3, x4, x5, x6, x7) -> f21(x1, x2, x3, x4, x5, x6, x7) 96.91/95.30 f21(I0, I1, I2, I3, I4, I5, I6) -> f1(2, 0, I2, I3, rnd5, rnd6, I6) [rnd6 = rnd6 /\ rnd5 = rnd5] 96.91/95.30 f2(I7, I8, I9, I10, I11, I12, I13) -> f3(I7, I8, 0, I10, I11, I12, I13) [1 + I8 <= I7] 96.91/95.30 f2(I14, I15, I16, I17, I18, I19, I20) -> f14(I14, 0, I16, I17, I18, I19, I20) [I14 <= I15] 96.91/95.30 f4(I21, I22, I23, I24, I25, I26, I27) -> f3(I21, I22, 1 + I23, I24, I25, I26, I27) [1 + I23 <= I21] 96.91/95.30 f4(I28, I29, I30, I31, I32, I33, I34) -> f1(I28, 1 + I29, I30, I31, I32, I33, I34) [I28 <= I30] 96.91/95.30 f19(I35, I36, I37, I38, I39, I40, I41) -> f17(I35, I36, I37, I38, I39, I40, I41) 96.91/95.30 f15(I42, I43, I44, I45, I46, I47, I48) -> f18(I42, I43, 0, I45, I46, I47, I48) [1 + I43 <= I42] 96.91/95.30 f15(I49, I50, I51, I52, I53, I54, I55) -> f16(I49, I50, I51, I52, I53, I54, I55) [I49 <= I50] 96.91/95.30 f20(I56, I57, I58, I59, I60, I61, I62) -> f19(I56, I57, I58, 0, I60, I61, I62) [1 + I58 <= I56] 96.91/95.30 f20(I63, I64, I65, I66, I67, I68, I69) -> f14(I63, 1 + I64, I65, I66, I67, I68, I69) [I63 <= I65] 96.91/95.30 f18(I70, I71, I72, I73, I74, I75, I76) -> f20(I70, I71, I72, I73, I74, I75, I76) 96.91/95.30 f17(I77, I78, I79, I80, I81, I82, I83) -> f19(I77, I78, I79, 1 + I80, I81, I82, I83) [1 + I80 <= I77] 96.91/95.30 f17(I84, I85, I86, I87, I88, I89, I90) -> f18(I84, I85, 1 + I86, I87, I88, I89, I90) [I84 <= I87] 96.91/95.30 f16(I91, I92, I93, I94, I95, I96, I97) -> f13(I91, I92, I93, I94, I95, I96, I97) 96.91/95.30 f16(I98, I99, I100, I101, I102, I103, I104) -> f5(I98, I99, I100, I101, I102, I103, I104) 96.91/95.30 f16(I105, I106, I107, I108, I109, I110, I111) -> f5(I105, I106, I107, I108, I109, I110, I111) 96.91/95.30 f14(I112, I113, I114, I115, I116, I117, I118) -> f15(I112, I113, I114, I115, I116, I117, I118) 96.91/95.30 f13(I119, I120, I121, I122, I123, I124, I125) -> f12(I119, I120, I121, I122, I123, I124, I125) 96.91/95.30 f13(I126, I127, I128, I129, I130, I131, I132) -> f7(I126, I127, I128, I129, I130, I131, I132) 96.91/95.30 f13(I133, I134, I135, I136, I137, I138, I139) -> f7(I133, I134, I135, I136, I137, I138, I139) 96.91/95.30 f12(I140, I141, I142, I143, I144, I145, I146) -> f11(I140, I141, I142, I143, I144, I145, I146) 96.91/95.30 f12(I147, I148, I149, I150, I151, I152, I153) -> f8(I147, I148, I149, I150, I151, I152, I153) 96.91/95.30 f12(I154, I155, I156, I157, I158, I159, I160) -> f8(I154, I155, I156, I157, I158, I159, I160) 96.91/95.30 f11(I161, I162, I163, I164, I165, I166, I167) -> f9(I161, I162, I163, I164, I165, I166, I167) 96.91/95.30 f11(I168, I169, I170, I171, I172, I173, I174) -> f6(I168, I169, I170, I171, I172, I173, 0) 96.91/95.30 f11(I175, I176, I177, I178, I179, I180, I181) -> f9(I175, I176, I177, I178, I179, I180, I181) 96.91/95.30 f6(I182, I183, I184, I185, I186, I187, I188) -> f10(I182, I183, I184, I185, I186, I187, I188) 96.91/95.30 f9(I189, I190, I191, I192, I193, I194, I195) -> f6(I189, I190, I191, I192, I193, I194, 1) 96.91/95.30 f8(I196, I197, I198, I199, I200, I201, I202) -> f6(I196, I197, I198, I199, I200, I201, 1) 96.91/95.30 f7(I203, I204, I205, I206, I207, I208, I209) -> f6(I203, I204, I205, I206, I207, I208, 1) 96.91/95.30 f5(I210, I211, I212, I213, I214, I215, I216) -> f6(I210, I211, I212, I213, I214, I215, 1) 96.91/95.30 f3(I217, I218, I219, I220, I221, I222, I223) -> f4(I217, I218, I219, I220, I221, I222, I223) 96.91/95.30 f1(I224, I225, I226, I227, I228, I229, I230) -> f2(I224, I225, I226, I227, I228, I229, I230) 96.91/95.30 96.91/95.30 The dependency graph for this problem is: 96.91/95.30 6 -> 12, 13 96.91/95.30 9 -> 6 96.91/95.30 10 -> 17 96.91/95.30 11 -> 9, 10 96.91/95.30 12 -> 6 96.91/95.30 13 -> 11 96.91/95.30 17 -> 96.91/95.30 Where: 96.91/95.30 6) f19#(I35, I36, I37, I38, I39, I40, I41) -> f17#(I35, I36, I37, I38, I39, I40, I41) 96.91/95.30 9) f20#(I56, I57, I58, I59, I60, I61, I62) -> f19#(I56, I57, I58, 0, I60, I61, I62) [1 + I58 <= I56] 96.91/95.30 10) f20#(I63, I64, I65, I66, I67, I68, I69) -> f14#(I63, 1 + I64, I65, I66, I67, I68, I69) [I63 <= I65] 96.91/95.30 11) f18#(I70, I71, I72, I73, I74, I75, I76) -> f20#(I70, I71, I72, I73, I74, I75, I76) 96.91/95.30 12) f17#(I77, I78, I79, I80, I81, I82, I83) -> f19#(I77, I78, I79, 1 + I80, I81, I82, I83) [1 + I80 <= I77] 96.91/95.30 13) f17#(I84, I85, I86, I87, I88, I89, I90) -> f18#(I84, I85, 1 + I86, I87, I88, I89, I90) [I84 <= I87] 96.91/95.30 17) f14#(I112, I113, I114, I115, I116, I117, I118) -> f15#(I112, I113, I114, I115, I116, I117, I118) 96.91/95.30 96.91/95.30 We have the following SCCs. 96.91/95.30 { 6, 9, 11, 12, 13 } 96.91/95.30 96.91/95.30 DP problem for innermost termination. 96.91/95.30 P = 96.91/95.30 f19#(I35, I36, I37, I38, I39, I40, I41) -> f17#(I35, I36, I37, I38, I39, I40, I41) 96.91/95.30 f20#(I56, I57, I58, I59, I60, I61, I62) -> f19#(I56, I57, I58, 0, I60, I61, I62) [1 + I58 <= I56] 96.91/95.30 f18#(I70, I71, I72, I73, I74, I75, I76) -> f20#(I70, I71, I72, I73, I74, I75, I76) 96.91/95.30 f17#(I77, I78, I79, I80, I81, I82, I83) -> f19#(I77, I78, I79, 1 + I80, I81, I82, I83) [1 + I80 <= I77] 96.91/95.30 f17#(I84, I85, I86, I87, I88, I89, I90) -> f18#(I84, I85, 1 + I86, I87, I88, I89, I90) [I84 <= I87] 96.91/95.30 R = 96.91/95.30 f22(x1, x2, x3, x4, x5, x6, x7) -> f21(x1, x2, x3, x4, x5, x6, x7) 96.91/95.30 f21(I0, I1, I2, I3, I4, I5, I6) -> f1(2, 0, I2, I3, rnd5, rnd6, I6) [rnd6 = rnd6 /\ rnd5 = rnd5] 96.91/95.30 f2(I7, I8, I9, I10, I11, I12, I13) -> f3(I7, I8, 0, I10, I11, I12, I13) [1 + I8 <= I7] 96.91/95.30 f2(I14, I15, I16, I17, I18, I19, I20) -> f14(I14, 0, I16, I17, I18, I19, I20) [I14 <= I15] 96.91/95.30 f4(I21, I22, I23, I24, I25, I26, I27) -> f3(I21, I22, 1 + I23, I24, I25, I26, I27) [1 + I23 <= I21] 96.91/95.30 f4(I28, I29, I30, I31, I32, I33, I34) -> f1(I28, 1 + I29, I30, I31, I32, I33, I34) [I28 <= I30] 96.91/95.30 f19(I35, I36, I37, I38, I39, I40, I41) -> f17(I35, I36, I37, I38, I39, I40, I41) 96.91/95.30 f15(I42, I43, I44, I45, I46, I47, I48) -> f18(I42, I43, 0, I45, I46, I47, I48) [1 + I43 <= I42] 96.91/95.30 f15(I49, I50, I51, I52, I53, I54, I55) -> f16(I49, I50, I51, I52, I53, I54, I55) [I49 <= I50] 96.91/95.30 f20(I56, I57, I58, I59, I60, I61, I62) -> f19(I56, I57, I58, 0, I60, I61, I62) [1 + I58 <= I56] 96.91/95.30 f20(I63, I64, I65, I66, I67, I68, I69) -> f14(I63, 1 + I64, I65, I66, I67, I68, I69) [I63 <= I65] 96.91/95.30 f18(I70, I71, I72, I73, I74, I75, I76) -> f20(I70, I71, I72, I73, I74, I75, I76) 96.91/95.30 f17(I77, I78, I79, I80, I81, I82, I83) -> f19(I77, I78, I79, 1 + I80, I81, I82, I83) [1 + I80 <= I77] 96.91/95.30 f17(I84, I85, I86, I87, I88, I89, I90) -> f18(I84, I85, 1 + I86, I87, I88, I89, I90) [I84 <= I87] 96.91/95.30 f16(I91, I92, I93, I94, I95, I96, I97) -> f13(I91, I92, I93, I94, I95, I96, I97) 96.91/95.30 f16(I98, I99, I100, I101, I102, I103, I104) -> f5(I98, I99, I100, I101, I102, I103, I104) 96.91/95.30 f16(I105, I106, I107, I108, I109, I110, I111) -> f5(I105, I106, I107, I108, I109, I110, I111) 96.91/95.30 f14(I112, I113, I114, I115, I116, I117, I118) -> f15(I112, I113, I114, I115, I116, I117, I118) 96.91/95.30 f13(I119, I120, I121, I122, I123, I124, I125) -> f12(I119, I120, I121, I122, I123, I124, I125) 96.91/95.30 f13(I126, I127, I128, I129, I130, I131, I132) -> f7(I126, I127, I128, I129, I130, I131, I132) 96.91/95.30 f13(I133, I134, I135, I136, I137, I138, I139) -> f7(I133, I134, I135, I136, I137, I138, I139) 96.91/95.30 f12(I140, I141, I142, I143, I144, I145, I146) -> f11(I140, I141, I142, I143, I144, I145, I146) 96.91/95.30 f12(I147, I148, I149, I150, I151, I152, I153) -> f8(I147, I148, I149, I150, I151, I152, I153) 96.91/95.30 f12(I154, I155, I156, I157, I158, I159, I160) -> f8(I154, I155, I156, I157, I158, I159, I160) 96.91/95.30 f11(I161, I162, I163, I164, I165, I166, I167) -> f9(I161, I162, I163, I164, I165, I166, I167) 96.91/95.30 f11(I168, I169, I170, I171, I172, I173, I174) -> f6(I168, I169, I170, I171, I172, I173, 0) 96.91/95.30 f11(I175, I176, I177, I178, I179, I180, I181) -> f9(I175, I176, I177, I178, I179, I180, I181) 96.91/95.30 f6(I182, I183, I184, I185, I186, I187, I188) -> f10(I182, I183, I184, I185, I186, I187, I188) 96.91/95.30 f9(I189, I190, I191, I192, I193, I194, I195) -> f6(I189, I190, I191, I192, I193, I194, 1) 96.91/95.30 f8(I196, I197, I198, I199, I200, I201, I202) -> f6(I196, I197, I198, I199, I200, I201, 1) 96.91/95.30 f7(I203, I204, I205, I206, I207, I208, I209) -> f6(I203, I204, I205, I206, I207, I208, 1) 96.91/95.30 f5(I210, I211, I212, I213, I214, I215, I216) -> f6(I210, I211, I212, I213, I214, I215, 1) 96.91/95.30 f3(I217, I218, I219, I220, I221, I222, I223) -> f4(I217, I218, I219, I220, I221, I222, I223) 96.91/95.30 f1(I224, I225, I226, I227, I228, I229, I230) -> f2(I224, I225, I226, I227, I228, I229, I230) 96.91/95.30 96.91/95.30 We use the extended value criterion with the projection function NU: 96.91/95.30 NU[f18#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x2 - 1 96.91/95.30 NU[f20#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x2 - 1 96.91/95.30 NU[f17#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x2 - 2 96.91/95.30 NU[f19#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x2 - 2 96.91/95.30 96.91/95.30 This gives the following inequalities: 96.91/95.30 ==> I35 - I37 - 2 >= I35 - I37 - 2 96.91/95.30 1 + I58 <= I56 ==> I56 - I58 - 1 > I56 - I58 - 2 with I56 - I58 - 1 >= 0 96.91/95.30 ==> I70 - I72 - 1 >= I70 - I72 - 1 96.91/95.30 1 + I80 <= I77 ==> I77 - I79 - 2 >= I77 - I79 - 2 96.91/95.30 I84 <= I87 ==> I84 - I86 - 2 >= I84 - (1 + I86) - 1 96.91/95.30 96.91/95.30 We remove all the strictly oriented dependency pairs. 96.91/95.30 96.91/95.30 DP problem for innermost termination. 96.91/95.30 P = 96.91/95.30 f19#(I35, I36, I37, I38, I39, I40, I41) -> f17#(I35, I36, I37, I38, I39, I40, I41) 96.91/95.30 f18#(I70, I71, I72, I73, I74, I75, I76) -> f20#(I70, I71, I72, I73, I74, I75, I76) 96.91/95.30 f17#(I77, I78, I79, I80, I81, I82, I83) -> f19#(I77, I78, I79, 1 + I80, I81, I82, I83) [1 + I80 <= I77] 96.91/95.30 f17#(I84, I85, I86, I87, I88, I89, I90) -> f18#(I84, I85, 1 + I86, I87, I88, I89, I90) [I84 <= I87] 96.91/95.30 R = 96.91/95.30 f22(x1, x2, x3, x4, x5, x6, x7) -> f21(x1, x2, x3, x4, x5, x6, x7) 96.91/95.30 f21(I0, I1, I2, I3, I4, I5, I6) -> f1(2, 0, I2, I3, rnd5, rnd6, I6) [rnd6 = rnd6 /\ rnd5 = rnd5] 96.91/95.30 f2(I7, I8, I9, I10, I11, I12, I13) -> f3(I7, I8, 0, I10, I11, I12, I13) [1 + I8 <= I7] 96.91/95.30 f2(I14, I15, I16, I17, I18, I19, I20) -> f14(I14, 0, I16, I17, I18, I19, I20) [I14 <= I15] 96.91/95.30 f4(I21, I22, I23, I24, I25, I26, I27) -> f3(I21, I22, 1 + I23, I24, I25, I26, I27) [1 + I23 <= I21] 96.91/95.30 f4(I28, I29, I30, I31, I32, I33, I34) -> f1(I28, 1 + I29, I30, I31, I32, I33, I34) [I28 <= I30] 96.91/95.30 f19(I35, I36, I37, I38, I39, I40, I41) -> f17(I35, I36, I37, I38, I39, I40, I41) 96.91/95.30 f15(I42, I43, I44, I45, I46, I47, I48) -> f18(I42, I43, 0, I45, I46, I47, I48) [1 + I43 <= I42] 96.91/95.30 f15(I49, I50, I51, I52, I53, I54, I55) -> f16(I49, I50, I51, I52, I53, I54, I55) [I49 <= I50] 96.91/95.30 f20(I56, I57, I58, I59, I60, I61, I62) -> f19(I56, I57, I58, 0, I60, I61, I62) [1 + I58 <= I56] 96.91/95.30 f20(I63, I64, I65, I66, I67, I68, I69) -> f14(I63, 1 + I64, I65, I66, I67, I68, I69) [I63 <= I65] 96.91/95.30 f18(I70, I71, I72, I73, I74, I75, I76) -> f20(I70, I71, I72, I73, I74, I75, I76) 96.91/95.30 f17(I77, I78, I79, I80, I81, I82, I83) -> f19(I77, I78, I79, 1 + I80, I81, I82, I83) [1 + I80 <= I77] 96.91/95.30 f17(I84, I85, I86, I87, I88, I89, I90) -> f18(I84, I85, 1 + I86, I87, I88, I89, I90) [I84 <= I87] 96.91/95.30 f16(I91, I92, I93, I94, I95, I96, I97) -> f13(I91, I92, I93, I94, I95, I96, I97) 96.91/95.30 f16(I98, I99, I100, I101, I102, I103, I104) -> f5(I98, I99, I100, I101, I102, I103, I104) 96.91/95.30 f16(I105, I106, I107, I108, I109, I110, I111) -> f5(I105, I106, I107, I108, I109, I110, I111) 96.91/95.30 f14(I112, I113, I114, I115, I116, I117, I118) -> f15(I112, I113, I114, I115, I116, I117, I118) 96.91/95.30 f13(I119, I120, I121, I122, I123, I124, I125) -> f12(I119, I120, I121, I122, I123, I124, I125) 96.91/95.30 f13(I126, I127, I128, I129, I130, I131, I132) -> f7(I126, I127, I128, I129, I130, I131, I132) 96.91/95.30 f13(I133, I134, I135, I136, I137, I138, I139) -> f7(I133, I134, I135, I136, I137, I138, I139) 96.91/95.30 f12(I140, I141, I142, I143, I144, I145, I146) -> f11(I140, I141, I142, I143, I144, I145, I146) 96.91/95.30 f12(I147, I148, I149, I150, I151, I152, I153) -> f8(I147, I148, I149, I150, I151, I152, I153) 96.91/95.30 f12(I154, I155, I156, I157, I158, I159, I160) -> f8(I154, I155, I156, I157, I158, I159, I160) 96.91/95.30 f11(I161, I162, I163, I164, I165, I166, I167) -> f9(I161, I162, I163, I164, I165, I166, I167) 96.91/95.30 f11(I168, I169, I170, I171, I172, I173, I174) -> f6(I168, I169, I170, I171, I172, I173, 0) 96.91/95.30 f11(I175, I176, I177, I178, I179, I180, I181) -> f9(I175, I176, I177, I178, I179, I180, I181) 96.91/95.30 f6(I182, I183, I184, I185, I186, I187, I188) -> f10(I182, I183, I184, I185, I186, I187, I188) 96.91/95.30 f9(I189, I190, I191, I192, I193, I194, I195) -> f6(I189, I190, I191, I192, I193, I194, 1) 96.91/95.30 f8(I196, I197, I198, I199, I200, I201, I202) -> f6(I196, I197, I198, I199, I200, I201, 1) 96.91/95.30 f7(I203, I204, I205, I206, I207, I208, I209) -> f6(I203, I204, I205, I206, I207, I208, 1) 96.91/95.30 f5(I210, I211, I212, I213, I214, I215, I216) -> f6(I210, I211, I212, I213, I214, I215, 1) 96.91/95.30 f3(I217, I218, I219, I220, I221, I222, I223) -> f4(I217, I218, I219, I220, I221, I222, I223) 96.91/95.30 f1(I224, I225, I226, I227, I228, I229, I230) -> f2(I224, I225, I226, I227, I228, I229, I230) 96.91/95.30 96.91/95.30 The dependency graph for this problem is: 96.91/95.30 6 -> 12, 13 96.91/95.30 11 -> 96.91/95.30 12 -> 6 96.91/95.30 13 -> 11 96.91/95.30 Where: 96.91/95.30 6) f19#(I35, I36, I37, I38, I39, I40, I41) -> f17#(I35, I36, I37, I38, I39, I40, I41) 96.91/95.30 11) f18#(I70, I71, I72, I73, I74, I75, I76) -> f20#(I70, I71, I72, I73, I74, I75, I76) 96.91/95.30 12) f17#(I77, I78, I79, I80, I81, I82, I83) -> f19#(I77, I78, I79, 1 + I80, I81, I82, I83) [1 + I80 <= I77] 96.91/95.30 13) f17#(I84, I85, I86, I87, I88, I89, I90) -> f18#(I84, I85, 1 + I86, I87, I88, I89, I90) [I84 <= I87] 96.91/95.30 96.91/95.30 We have the following SCCs. 96.91/95.30 { 6, 12 } 96.91/95.30 96.91/95.30 DP problem for innermost termination. 96.91/95.30 P = 96.91/95.30 f19#(I35, I36, I37, I38, I39, I40, I41) -> f17#(I35, I36, I37, I38, I39, I40, I41) 96.91/95.30 f17#(I77, I78, I79, I80, I81, I82, I83) -> f19#(I77, I78, I79, 1 + I80, I81, I82, I83) [1 + I80 <= I77] 96.91/95.30 R = 96.91/95.30 f22(x1, x2, x3, x4, x5, x6, x7) -> f21(x1, x2, x3, x4, x5, x6, x7) 96.91/95.30 f21(I0, I1, I2, I3, I4, I5, I6) -> f1(2, 0, I2, I3, rnd5, rnd6, I6) [rnd6 = rnd6 /\ rnd5 = rnd5] 96.91/95.30 f2(I7, I8, I9, I10, I11, I12, I13) -> f3(I7, I8, 0, I10, I11, I12, I13) [1 + I8 <= I7] 96.91/95.30 f2(I14, I15, I16, I17, I18, I19, I20) -> f14(I14, 0, I16, I17, I18, I19, I20) [I14 <= I15] 96.91/95.30 f4(I21, I22, I23, I24, I25, I26, I27) -> f3(I21, I22, 1 + I23, I24, I25, I26, I27) [1 + I23 <= I21] 96.91/95.30 f4(I28, I29, I30, I31, I32, I33, I34) -> f1(I28, 1 + I29, I30, I31, I32, I33, I34) [I28 <= I30] 96.91/95.30 f19(I35, I36, I37, I38, I39, I40, I41) -> f17(I35, I36, I37, I38, I39, I40, I41) 96.91/95.30 f15(I42, I43, I44, I45, I46, I47, I48) -> f18(I42, I43, 0, I45, I46, I47, I48) [1 + I43 <= I42] 96.91/95.30 f15(I49, I50, I51, I52, I53, I54, I55) -> f16(I49, I50, I51, I52, I53, I54, I55) [I49 <= I50] 96.91/95.30 f20(I56, I57, I58, I59, I60, I61, I62) -> f19(I56, I57, I58, 0, I60, I61, I62) [1 + I58 <= I56] 96.91/95.30 f20(I63, I64, I65, I66, I67, I68, I69) -> f14(I63, 1 + I64, I65, I66, I67, I68, I69) [I63 <= I65] 96.91/95.30 f18(I70, I71, I72, I73, I74, I75, I76) -> f20(I70, I71, I72, I73, I74, I75, I76) 96.91/95.30 f17(I77, I78, I79, I80, I81, I82, I83) -> f19(I77, I78, I79, 1 + I80, I81, I82, I83) [1 + I80 <= I77] 96.91/95.30 f17(I84, I85, I86, I87, I88, I89, I90) -> f18(I84, I85, 1 + I86, I87, I88, I89, I90) [I84 <= I87] 96.91/95.30 f16(I91, I92, I93, I94, I95, I96, I97) -> f13(I91, I92, I93, I94, I95, I96, I97) 96.91/95.30 f16(I98, I99, I100, I101, I102, I103, I104) -> f5(I98, I99, I100, I101, I102, I103, I104) 96.91/95.30 f16(I105, I106, I107, I108, I109, I110, I111) -> f5(I105, I106, I107, I108, I109, I110, I111) 96.91/95.30 f14(I112, I113, I114, I115, I116, I117, I118) -> f15(I112, I113, I114, I115, I116, I117, I118) 96.91/95.30 f13(I119, I120, I121, I122, I123, I124, I125) -> f12(I119, I120, I121, I122, I123, I124, I125) 96.91/95.30 f13(I126, I127, I128, I129, I130, I131, I132) -> f7(I126, I127, I128, I129, I130, I131, I132) 96.91/95.30 f13(I133, I134, I135, I136, I137, I138, I139) -> f7(I133, I134, I135, I136, I137, I138, I139) 96.91/95.30 f12(I140, I141, I142, I143, I144, I145, I146) -> f11(I140, I141, I142, I143, I144, I145, I146) 96.91/95.30 f12(I147, I148, I149, I150, I151, I152, I153) -> f8(I147, I148, I149, I150, I151, I152, I153) 96.91/95.30 f12(I154, I155, I156, I157, I158, I159, I160) -> f8(I154, I155, I156, I157, I158, I159, I160) 96.91/95.30 f11(I161, I162, I163, I164, I165, I166, I167) -> f9(I161, I162, I163, I164, I165, I166, I167) 96.91/95.30 f11(I168, I169, I170, I171, I172, I173, I174) -> f6(I168, I169, I170, I171, I172, I173, 0) 96.91/95.30 f11(I175, I176, I177, I178, I179, I180, I181) -> f9(I175, I176, I177, I178, I179, I180, I181) 96.91/95.30 f6(I182, I183, I184, I185, I186, I187, I188) -> f10(I182, I183, I184, I185, I186, I187, I188) 96.91/95.30 f9(I189, I190, I191, I192, I193, I194, I195) -> f6(I189, I190, I191, I192, I193, I194, 1) 96.91/95.30 f8(I196, I197, I198, I199, I200, I201, I202) -> f6(I196, I197, I198, I199, I200, I201, 1) 96.91/95.30 f7(I203, I204, I205, I206, I207, I208, I209) -> f6(I203, I204, I205, I206, I207, I208, 1) 96.91/95.30 f5(I210, I211, I212, I213, I214, I215, I216) -> f6(I210, I211, I212, I213, I214, I215, 1) 96.91/95.30 f3(I217, I218, I219, I220, I221, I222, I223) -> f4(I217, I218, I219, I220, I221, I222, I223) 96.91/95.30 f1(I224, I225, I226, I227, I228, I229, I230) -> f2(I224, I225, I226, I227, I228, I229, I230) 96.91/95.30 96.91/95.30 We use the reverse value criterion with the projection function NU: 96.91/95.30 NU[f17#(z1,z2,z3,z4,z5,z6,z7)] = z1 + -1 * (1 + z4) 96.91/95.30 NU[f19#(z1,z2,z3,z4,z5,z6,z7)] = z1 + -1 * (1 + z4) 96.91/95.30 96.91/95.30 This gives the following inequalities: 96.91/95.30 ==> I35 + -1 * (1 + I38) >= I35 + -1 * (1 + I38) 96.91/95.30 1 + I80 <= I77 ==> I77 + -1 * (1 + I80) > I77 + -1 * (1 + (1 + I80)) with I77 + -1 * (1 + I80) >= 0 96.91/95.30 96.91/95.30 We remove all the strictly oriented dependency pairs. 96.91/95.30 96.91/95.30 DP problem for innermost termination. 96.91/95.30 P = 96.91/95.30 f19#(I35, I36, I37, I38, I39, I40, I41) -> f17#(I35, I36, I37, I38, I39, I40, I41) 96.91/95.30 R = 96.91/95.30 f22(x1, x2, x3, x4, x5, x6, x7) -> f21(x1, x2, x3, x4, x5, x6, x7) 96.91/95.30 f21(I0, I1, I2, I3, I4, I5, I6) -> f1(2, 0, I2, I3, rnd5, rnd6, I6) [rnd6 = rnd6 /\ rnd5 = rnd5] 96.91/95.30 f2(I7, I8, I9, I10, I11, I12, I13) -> f3(I7, I8, 0, I10, I11, I12, I13) [1 + I8 <= I7] 96.91/95.30 f2(I14, I15, I16, I17, I18, I19, I20) -> f14(I14, 0, I16, I17, I18, I19, I20) [I14 <= I15] 96.91/95.30 f4(I21, I22, I23, I24, I25, I26, I27) -> f3(I21, I22, 1 + I23, I24, I25, I26, I27) [1 + I23 <= I21] 96.91/95.30 f4(I28, I29, I30, I31, I32, I33, I34) -> f1(I28, 1 + I29, I30, I31, I32, I33, I34) [I28 <= I30] 96.91/95.30 f19(I35, I36, I37, I38, I39, I40, I41) -> f17(I35, I36, I37, I38, I39, I40, I41) 96.91/95.30 f15(I42, I43, I44, I45, I46, I47, I48) -> f18(I42, I43, 0, I45, I46, I47, I48) [1 + I43 <= I42] 96.91/95.30 f15(I49, I50, I51, I52, I53, I54, I55) -> f16(I49, I50, I51, I52, I53, I54, I55) [I49 <= I50] 96.91/95.30 f20(I56, I57, I58, I59, I60, I61, I62) -> f19(I56, I57, I58, 0, I60, I61, I62) [1 + I58 <= I56] 96.91/95.30 f20(I63, I64, I65, I66, I67, I68, I69) -> f14(I63, 1 + I64, I65, I66, I67, I68, I69) [I63 <= I65] 96.91/95.30 f18(I70, I71, I72, I73, I74, I75, I76) -> f20(I70, I71, I72, I73, I74, I75, I76) 96.91/95.30 f17(I77, I78, I79, I80, I81, I82, I83) -> f19(I77, I78, I79, 1 + I80, I81, I82, I83) [1 + I80 <= I77] 96.91/95.30 f17(I84, I85, I86, I87, I88, I89, I90) -> f18(I84, I85, 1 + I86, I87, I88, I89, I90) [I84 <= I87] 96.91/95.30 f16(I91, I92, I93, I94, I95, I96, I97) -> f13(I91, I92, I93, I94, I95, I96, I97) 96.91/95.30 f16(I98, I99, I100, I101, I102, I103, I104) -> f5(I98, I99, I100, I101, I102, I103, I104) 96.91/95.30 f16(I105, I106, I107, I108, I109, I110, I111) -> f5(I105, I106, I107, I108, I109, I110, I111) 96.91/95.30 f14(I112, I113, I114, I115, I116, I117, I118) -> f15(I112, I113, I114, I115, I116, I117, I118) 96.91/95.30 f13(I119, I120, I121, I122, I123, I124, I125) -> f12(I119, I120, I121, I122, I123, I124, I125) 96.91/95.30 f13(I126, I127, I128, I129, I130, I131, I132) -> f7(I126, I127, I128, I129, I130, I131, I132) 96.91/95.30 f13(I133, I134, I135, I136, I137, I138, I139) -> f7(I133, I134, I135, I136, I137, I138, I139) 96.91/95.30 f12(I140, I141, I142, I143, I144, I145, I146) -> f11(I140, I141, I142, I143, I144, I145, I146) 96.91/95.30 f12(I147, I148, I149, I150, I151, I152, I153) -> f8(I147, I148, I149, I150, I151, I152, I153) 96.91/95.30 f12(I154, I155, I156, I157, I158, I159, I160) -> f8(I154, I155, I156, I157, I158, I159, I160) 96.91/95.30 f11(I161, I162, I163, I164, I165, I166, I167) -> f9(I161, I162, I163, I164, I165, I166, I167) 96.91/95.30 f11(I168, I169, I170, I171, I172, I173, I174) -> f6(I168, I169, I170, I171, I172, I173, 0) 96.91/95.30 f11(I175, I176, I177, I178, I179, I180, I181) -> f9(I175, I176, I177, I178, I179, I180, I181) 96.91/95.30 f6(I182, I183, I184, I185, I186, I187, I188) -> f10(I182, I183, I184, I185, I186, I187, I188) 96.91/95.30 f9(I189, I190, I191, I192, I193, I194, I195) -> f6(I189, I190, I191, I192, I193, I194, 1) 96.91/95.30 f8(I196, I197, I198, I199, I200, I201, I202) -> f6(I196, I197, I198, I199, I200, I201, 1) 96.91/95.30 f7(I203, I204, I205, I206, I207, I208, I209) -> f6(I203, I204, I205, I206, I207, I208, 1) 96.91/95.30 f5(I210, I211, I212, I213, I214, I215, I216) -> f6(I210, I211, I212, I213, I214, I215, 1) 96.91/95.30 f3(I217, I218, I219, I220, I221, I222, I223) -> f4(I217, I218, I219, I220, I221, I222, I223) 96.91/95.30 f1(I224, I225, I226, I227, I228, I229, I230) -> f2(I224, I225, I226, I227, I228, I229, I230) 96.91/95.30 96.91/95.30 The dependency graph for this problem is: 96.91/95.30 6 -> 96.91/95.30 Where: 96.91/95.30 6) f19#(I35, I36, I37, I38, I39, I40, I41) -> f17#(I35, I36, I37, I38, I39, I40, I41) 96.91/95.30 96.91/95.30 We have the following SCCs. 96.91/95.30 96.91/95.30 96.91/95.30 DP problem for innermost termination. 96.91/95.30 P = 96.91/95.30 f2#(I7, I8, I9, I10, I11, I12, I13) -> f3#(I7, I8, 0, I10, I11, I12, I13) [1 + I8 <= I7] 96.91/95.30 f4#(I21, I22, I23, I24, I25, I26, I27) -> f3#(I21, I22, 1 + I23, I24, I25, I26, I27) [1 + I23 <= I21] 96.91/95.30 f4#(I28, I29, I30, I31, I32, I33, I34) -> f1#(I28, 1 + I29, I30, I31, I32, I33, I34) [I28 <= I30] 96.91/95.30 f3#(I217, I218, I219, I220, I221, I222, I223) -> f4#(I217, I218, I219, I220, I221, I222, I223) 96.91/95.30 f1#(I224, I225, I226, I227, I228, I229, I230) -> f2#(I224, I225, I226, I227, I228, I229, I230) 96.91/95.30 R = 96.91/95.30 f22(x1, x2, x3, x4, x5, x6, x7) -> f21(x1, x2, x3, x4, x5, x6, x7) 96.91/95.30 f21(I0, I1, I2, I3, I4, I5, I6) -> f1(2, 0, I2, I3, rnd5, rnd6, I6) [rnd6 = rnd6 /\ rnd5 = rnd5] 96.91/95.30 f2(I7, I8, I9, I10, I11, I12, I13) -> f3(I7, I8, 0, I10, I11, I12, I13) [1 + I8 <= I7] 96.91/95.30 f2(I14, I15, I16, I17, I18, I19, I20) -> f14(I14, 0, I16, I17, I18, I19, I20) [I14 <= I15] 96.91/95.30 f4(I21, I22, I23, I24, I25, I26, I27) -> f3(I21, I22, 1 + I23, I24, I25, I26, I27) [1 + I23 <= I21] 96.91/95.30 f4(I28, I29, I30, I31, I32, I33, I34) -> f1(I28, 1 + I29, I30, I31, I32, I33, I34) [I28 <= I30] 96.91/95.30 f19(I35, I36, I37, I38, I39, I40, I41) -> f17(I35, I36, I37, I38, I39, I40, I41) 96.91/95.30 f15(I42, I43, I44, I45, I46, I47, I48) -> f18(I42, I43, 0, I45, I46, I47, I48) [1 + I43 <= I42] 96.91/95.30 f15(I49, I50, I51, I52, I53, I54, I55) -> f16(I49, I50, I51, I52, I53, I54, I55) [I49 <= I50] 96.91/95.30 f20(I56, I57, I58, I59, I60, I61, I62) -> f19(I56, I57, I58, 0, I60, I61, I62) [1 + I58 <= I56] 96.91/95.30 f20(I63, I64, I65, I66, I67, I68, I69) -> f14(I63, 1 + I64, I65, I66, I67, I68, I69) [I63 <= I65] 96.91/95.30 f18(I70, I71, I72, I73, I74, I75, I76) -> f20(I70, I71, I72, I73, I74, I75, I76) 96.91/95.30 f17(I77, I78, I79, I80, I81, I82, I83) -> f19(I77, I78, I79, 1 + I80, I81, I82, I83) [1 + I80 <= I77] 96.91/95.30 f17(I84, I85, I86, I87, I88, I89, I90) -> f18(I84, I85, 1 + I86, I87, I88, I89, I90) [I84 <= I87] 96.91/95.30 f16(I91, I92, I93, I94, I95, I96, I97) -> f13(I91, I92, I93, I94, I95, I96, I97) 96.91/95.30 f16(I98, I99, I100, I101, I102, I103, I104) -> f5(I98, I99, I100, I101, I102, I103, I104) 96.91/95.30 f16(I105, I106, I107, I108, I109, I110, I111) -> f5(I105, I106, I107, I108, I109, I110, I111) 96.91/95.30 f14(I112, I113, I114, I115, I116, I117, I118) -> f15(I112, I113, I114, I115, I116, I117, I118) 96.91/95.30 f13(I119, I120, I121, I122, I123, I124, I125) -> f12(I119, I120, I121, I122, I123, I124, I125) 96.91/95.30 f13(I126, I127, I128, I129, I130, I131, I132) -> f7(I126, I127, I128, I129, I130, I131, I132) 96.91/95.30 f13(I133, I134, I135, I136, I137, I138, I139) -> f7(I133, I134, I135, I136, I137, I138, I139) 96.91/95.30 f12(I140, I141, I142, I143, I144, I145, I146) -> f11(I140, I141, I142, I143, I144, I145, I146) 96.91/95.30 f12(I147, I148, I149, I150, I151, I152, I153) -> f8(I147, I148, I149, I150, I151, I152, I153) 96.91/95.30 f12(I154, I155, I156, I157, I158, I159, I160) -> f8(I154, I155, I156, I157, I158, I159, I160) 96.91/95.30 f11(I161, I162, I163, I164, I165, I166, I167) -> f9(I161, I162, I163, I164, I165, I166, I167) 96.91/95.30 f11(I168, I169, I170, I171, I172, I173, I174) -> f6(I168, I169, I170, I171, I172, I173, 0) 96.91/95.30 f11(I175, I176, I177, I178, I179, I180, I181) -> f9(I175, I176, I177, I178, I179, I180, I181) 96.91/95.30 f6(I182, I183, I184, I185, I186, I187, I188) -> f10(I182, I183, I184, I185, I186, I187, I188) 96.91/95.30 f9(I189, I190, I191, I192, I193, I194, I195) -> f6(I189, I190, I191, I192, I193, I194, 1) 96.91/95.30 f8(I196, I197, I198, I199, I200, I201, I202) -> f6(I196, I197, I198, I199, I200, I201, 1) 96.91/95.30 f7(I203, I204, I205, I206, I207, I208, I209) -> f6(I203, I204, I205, I206, I207, I208, 1) 96.91/95.30 f5(I210, I211, I212, I213, I214, I215, I216) -> f6(I210, I211, I212, I213, I214, I215, 1) 96.91/95.30 f3(I217, I218, I219, I220, I221, I222, I223) -> f4(I217, I218, I219, I220, I221, I222, I223) 96.91/95.30 f1(I224, I225, I226, I227, I228, I229, I230) -> f2(I224, I225, I226, I227, I228, I229, I230) 96.91/95.30 96.91/95.30 We use the extended value criterion with the projection function NU: 96.91/95.30 NU[f1#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x1 - 1 96.91/95.30 NU[f4#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x1 - 2 96.91/95.30 NU[f3#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x1 - 2 96.91/95.30 NU[f2#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x1 - 1 96.91/95.30 96.91/95.30 This gives the following inequalities: 96.91/95.30 1 + I8 <= I7 ==> I7 - I8 - 1 > I7 - I8 - 2 with I7 - I8 - 1 >= 0 96.91/95.30 1 + I23 <= I21 ==> I21 - I22 - 2 >= I21 - I22 - 2 96.91/95.30 I28 <= I30 ==> I28 - I29 - 2 >= I28 - (1 + I29) - 1 96.91/95.30 ==> I217 - I218 - 2 >= I217 - I218 - 2 96.91/95.30 ==> I224 - I225 - 1 >= I224 - I225 - 1 96.91/95.30 96.91/95.30 We remove all the strictly oriented dependency pairs. 96.91/95.30 96.91/95.30 DP problem for innermost termination. 96.91/95.30 P = 96.91/95.30 f4#(I21, I22, I23, I24, I25, I26, I27) -> f3#(I21, I22, 1 + I23, I24, I25, I26, I27) [1 + I23 <= I21] 96.91/95.30 f4#(I28, I29, I30, I31, I32, I33, I34) -> f1#(I28, 1 + I29, I30, I31, I32, I33, I34) [I28 <= I30] 96.91/95.30 f3#(I217, I218, I219, I220, I221, I222, I223) -> f4#(I217, I218, I219, I220, I221, I222, I223) 96.91/95.30 f1#(I224, I225, I226, I227, I228, I229, I230) -> f2#(I224, I225, I226, I227, I228, I229, I230) 96.91/95.30 R = 96.91/95.30 f22(x1, x2, x3, x4, x5, x6, x7) -> f21(x1, x2, x3, x4, x5, x6, x7) 96.91/95.30 f21(I0, I1, I2, I3, I4, I5, I6) -> f1(2, 0, I2, I3, rnd5, rnd6, I6) [rnd6 = rnd6 /\ rnd5 = rnd5] 96.91/95.30 f2(I7, I8, I9, I10, I11, I12, I13) -> f3(I7, I8, 0, I10, I11, I12, I13) [1 + I8 <= I7] 96.91/95.30 f2(I14, I15, I16, I17, I18, I19, I20) -> f14(I14, 0, I16, I17, I18, I19, I20) [I14 <= I15] 96.91/95.30 f4(I21, I22, I23, I24, I25, I26, I27) -> f3(I21, I22, 1 + I23, I24, I25, I26, I27) [1 + I23 <= I21] 96.91/95.30 f4(I28, I29, I30, I31, I32, I33, I34) -> f1(I28, 1 + I29, I30, I31, I32, I33, I34) [I28 <= I30] 96.91/95.30 f19(I35, I36, I37, I38, I39, I40, I41) -> f17(I35, I36, I37, I38, I39, I40, I41) 96.91/95.30 f15(I42, I43, I44, I45, I46, I47, I48) -> f18(I42, I43, 0, I45, I46, I47, I48) [1 + I43 <= I42] 96.91/95.30 f15(I49, I50, I51, I52, I53, I54, I55) -> f16(I49, I50, I51, I52, I53, I54, I55) [I49 <= I50] 96.91/95.30 f20(I56, I57, I58, I59, I60, I61, I62) -> f19(I56, I57, I58, 0, I60, I61, I62) [1 + I58 <= I56] 96.91/95.30 f20(I63, I64, I65, I66, I67, I68, I69) -> f14(I63, 1 + I64, I65, I66, I67, I68, I69) [I63 <= I65] 96.91/95.30 f18(I70, I71, I72, I73, I74, I75, I76) -> f20(I70, I71, I72, I73, I74, I75, I76) 96.91/95.30 f17(I77, I78, I79, I80, I81, I82, I83) -> f19(I77, I78, I79, 1 + I80, I81, I82, I83) [1 + I80 <= I77] 96.91/95.30 f17(I84, I85, I86, I87, I88, I89, I90) -> f18(I84, I85, 1 + I86, I87, I88, I89, I90) [I84 <= I87] 96.91/95.30 f16(I91, I92, I93, I94, I95, I96, I97) -> f13(I91, I92, I93, I94, I95, I96, I97) 96.91/95.30 f16(I98, I99, I100, I101, I102, I103, I104) -> f5(I98, I99, I100, I101, I102, I103, I104) 96.91/95.30 f16(I105, I106, I107, I108, I109, I110, I111) -> f5(I105, I106, I107, I108, I109, I110, I111) 96.91/95.30 f14(I112, I113, I114, I115, I116, I117, I118) -> f15(I112, I113, I114, I115, I116, I117, I118) 96.91/95.30 f13(I119, I120, I121, I122, I123, I124, I125) -> f12(I119, I120, I121, I122, I123, I124, I125) 96.91/95.30 f13(I126, I127, I128, I129, I130, I131, I132) -> f7(I126, I127, I128, I129, I130, I131, I132) 96.91/95.30 f13(I133, I134, I135, I136, I137, I138, I139) -> f7(I133, I134, I135, I136, I137, I138, I139) 96.91/95.30 f12(I140, I141, I142, I143, I144, I145, I146) -> f11(I140, I141, I142, I143, I144, I145, I146) 96.91/95.30 f12(I147, I148, I149, I150, I151, I152, I153) -> f8(I147, I148, I149, I150, I151, I152, I153) 96.91/95.30 f12(I154, I155, I156, I157, I158, I159, I160) -> f8(I154, I155, I156, I157, I158, I159, I160) 96.91/95.30 f11(I161, I162, I163, I164, I165, I166, I167) -> f9(I161, I162, I163, I164, I165, I166, I167) 96.91/95.30 f11(I168, I169, I170, I171, I172, I173, I174) -> f6(I168, I169, I170, I171, I172, I173, 0) 96.91/95.30 f11(I175, I176, I177, I178, I179, I180, I181) -> f9(I175, I176, I177, I178, I179, I180, I181) 96.91/95.30 f6(I182, I183, I184, I185, I186, I187, I188) -> f10(I182, I183, I184, I185, I186, I187, I188) 96.91/95.30 f9(I189, I190, I191, I192, I193, I194, I195) -> f6(I189, I190, I191, I192, I193, I194, 1) 96.91/95.30 f8(I196, I197, I198, I199, I200, I201, I202) -> f6(I196, I197, I198, I199, I200, I201, 1) 96.91/95.30 f7(I203, I204, I205, I206, I207, I208, I209) -> f6(I203, I204, I205, I206, I207, I208, 1) 96.91/95.30 f5(I210, I211, I212, I213, I214, I215, I216) -> f6(I210, I211, I212, I213, I214, I215, 1) 96.91/95.30 f3(I217, I218, I219, I220, I221, I222, I223) -> f4(I217, I218, I219, I220, I221, I222, I223) 96.91/95.30 f1(I224, I225, I226, I227, I228, I229, I230) -> f2(I224, I225, I226, I227, I228, I229, I230) 96.91/95.30 96.91/95.30 The dependency graph for this problem is: 96.91/95.30 4 -> 31 96.91/95.30 5 -> 32 96.91/95.30 31 -> 4, 5 96.91/95.30 32 -> 96.91/95.30 Where: 96.91/95.30 4) f4#(I21, I22, I23, I24, I25, I26, I27) -> f3#(I21, I22, 1 + I23, I24, I25, I26, I27) [1 + I23 <= I21] 96.91/95.30 5) f4#(I28, I29, I30, I31, I32, I33, I34) -> f1#(I28, 1 + I29, I30, I31, I32, I33, I34) [I28 <= I30] 96.91/95.30 31) f3#(I217, I218, I219, I220, I221, I222, I223) -> f4#(I217, I218, I219, I220, I221, I222, I223) 96.91/95.30 32) f1#(I224, I225, I226, I227, I228, I229, I230) -> f2#(I224, I225, I226, I227, I228, I229, I230) 96.91/95.30 96.91/95.30 We have the following SCCs. 96.91/95.30 { 4, 31 } 96.91/95.30 96.91/95.30 DP problem for innermost termination. 96.91/95.30 P = 96.91/95.30 f4#(I21, I22, I23, I24, I25, I26, I27) -> f3#(I21, I22, 1 + I23, I24, I25, I26, I27) [1 + I23 <= I21] 96.91/95.30 f3#(I217, I218, I219, I220, I221, I222, I223) -> f4#(I217, I218, I219, I220, I221, I222, I223) 96.91/95.30 R = 96.91/95.30 f22(x1, x2, x3, x4, x5, x6, x7) -> f21(x1, x2, x3, x4, x5, x6, x7) 96.91/95.30 f21(I0, I1, I2, I3, I4, I5, I6) -> f1(2, 0, I2, I3, rnd5, rnd6, I6) [rnd6 = rnd6 /\ rnd5 = rnd5] 96.91/95.30 f2(I7, I8, I9, I10, I11, I12, I13) -> f3(I7, I8, 0, I10, I11, I12, I13) [1 + I8 <= I7] 96.91/95.30 f2(I14, I15, I16, I17, I18, I19, I20) -> f14(I14, 0, I16, I17, I18, I19, I20) [I14 <= I15] 96.91/95.30 f4(I21, I22, I23, I24, I25, I26, I27) -> f3(I21, I22, 1 + I23, I24, I25, I26, I27) [1 + I23 <= I21] 96.91/95.30 f4(I28, I29, I30, I31, I32, I33, I34) -> f1(I28, 1 + I29, I30, I31, I32, I33, I34) [I28 <= I30] 96.91/95.30 f19(I35, I36, I37, I38, I39, I40, I41) -> f17(I35, I36, I37, I38, I39, I40, I41) 96.91/95.30 f15(I42, I43, I44, I45, I46, I47, I48) -> f18(I42, I43, 0, I45, I46, I47, I48) [1 + I43 <= I42] 96.91/95.30 f15(I49, I50, I51, I52, I53, I54, I55) -> f16(I49, I50, I51, I52, I53, I54, I55) [I49 <= I50] 96.91/95.30 f20(I56, I57, I58, I59, I60, I61, I62) -> f19(I56, I57, I58, 0, I60, I61, I62) [1 + I58 <= I56] 96.91/95.30 f20(I63, I64, I65, I66, I67, I68, I69) -> f14(I63, 1 + I64, I65, I66, I67, I68, I69) [I63 <= I65] 96.91/95.30 f18(I70, I71, I72, I73, I74, I75, I76) -> f20(I70, I71, I72, I73, I74, I75, I76) 96.91/95.30 f17(I77, I78, I79, I80, I81, I82, I83) -> f19(I77, I78, I79, 1 + I80, I81, I82, I83) [1 + I80 <= I77] 96.91/95.30 f17(I84, I85, I86, I87, I88, I89, I90) -> f18(I84, I85, 1 + I86, I87, I88, I89, I90) [I84 <= I87] 96.91/95.30 f16(I91, I92, I93, I94, I95, I96, I97) -> f13(I91, I92, I93, I94, I95, I96, I97) 96.91/95.30 f16(I98, I99, I100, I101, I102, I103, I104) -> f5(I98, I99, I100, I101, I102, I103, I104) 96.91/95.30 f16(I105, I106, I107, I108, I109, I110, I111) -> f5(I105, I106, I107, I108, I109, I110, I111) 96.91/95.30 f14(I112, I113, I114, I115, I116, I117, I118) -> f15(I112, I113, I114, I115, I116, I117, I118) 96.91/95.30 f13(I119, I120, I121, I122, I123, I124, I125) -> f12(I119, I120, I121, I122, I123, I124, I125) 96.91/95.30 f13(I126, I127, I128, I129, I130, I131, I132) -> f7(I126, I127, I128, I129, I130, I131, I132) 96.91/95.30 f13(I133, I134, I135, I136, I137, I138, I139) -> f7(I133, I134, I135, I136, I137, I138, I139) 96.91/95.30 f12(I140, I141, I142, I143, I144, I145, I146) -> f11(I140, I141, I142, I143, I144, I145, I146) 96.91/95.30 f12(I147, I148, I149, I150, I151, I152, I153) -> f8(I147, I148, I149, I150, I151, I152, I153) 96.91/95.30 f12(I154, I155, I156, I157, I158, I159, I160) -> f8(I154, I155, I156, I157, I158, I159, I160) 96.91/95.30 f11(I161, I162, I163, I164, I165, I166, I167) -> f9(I161, I162, I163, I164, I165, I166, I167) 96.91/95.30 f11(I168, I169, I170, I171, I172, I173, I174) -> f6(I168, I169, I170, I171, I172, I173, 0) 96.91/95.30 f11(I175, I176, I177, I178, I179, I180, I181) -> f9(I175, I176, I177, I178, I179, I180, I181) 96.91/95.30 f6(I182, I183, I184, I185, I186, I187, I188) -> f10(I182, I183, I184, I185, I186, I187, I188) 96.91/95.30 f9(I189, I190, I191, I192, I193, I194, I195) -> f6(I189, I190, I191, I192, I193, I194, 1) 96.91/95.30 f8(I196, I197, I198, I199, I200, I201, I202) -> f6(I196, I197, I198, I199, I200, I201, 1) 96.91/95.30 f7(I203, I204, I205, I206, I207, I208, I209) -> f6(I203, I204, I205, I206, I207, I208, 1) 96.91/95.30 f5(I210, I211, I212, I213, I214, I215, I216) -> f6(I210, I211, I212, I213, I214, I215, 1) 96.91/95.30 f3(I217, I218, I219, I220, I221, I222, I223) -> f4(I217, I218, I219, I220, I221, I222, I223) 96.91/95.30 f1(I224, I225, I226, I227, I228, I229, I230) -> f2(I224, I225, I226, I227, I228, I229, I230) 96.91/95.30 96.91/95.30 We use the reverse value criterion with the projection function NU: 96.91/95.30 NU[f3#(z1,z2,z3,z4,z5,z6,z7)] = z1 + -1 * (1 + z3) 96.91/95.30 NU[f4#(z1,z2,z3,z4,z5,z6,z7)] = z1 + -1 * (1 + z3) 96.91/95.30 96.91/95.30 This gives the following inequalities: 96.91/95.30 1 + I23 <= I21 ==> I21 + -1 * (1 + I23) > I21 + -1 * (1 + (1 + I23)) with I21 + -1 * (1 + I23) >= 0 96.91/95.30 ==> I217 + -1 * (1 + I219) >= I217 + -1 * (1 + I219) 96.91/95.30 96.91/95.30 We remove all the strictly oriented dependency pairs. 96.91/95.30 96.91/95.30 DP problem for innermost termination. 96.91/95.30 P = 96.91/95.30 f3#(I217, I218, I219, I220, I221, I222, I223) -> f4#(I217, I218, I219, I220, I221, I222, I223) 96.91/95.30 R = 96.91/95.30 f22(x1, x2, x3, x4, x5, x6, x7) -> f21(x1, x2, x3, x4, x5, x6, x7) 96.91/95.30 f21(I0, I1, I2, I3, I4, I5, I6) -> f1(2, 0, I2, I3, rnd5, rnd6, I6) [rnd6 = rnd6 /\ rnd5 = rnd5] 96.91/95.30 f2(I7, I8, I9, I10, I11, I12, I13) -> f3(I7, I8, 0, I10, I11, I12, I13) [1 + I8 <= I7] 96.91/95.30 f2(I14, I15, I16, I17, I18, I19, I20) -> f14(I14, 0, I16, I17, I18, I19, I20) [I14 <= I15] 96.91/95.30 f4(I21, I22, I23, I24, I25, I26, I27) -> f3(I21, I22, 1 + I23, I24, I25, I26, I27) [1 + I23 <= I21] 96.91/95.30 f4(I28, I29, I30, I31, I32, I33, I34) -> f1(I28, 1 + I29, I30, I31, I32, I33, I34) [I28 <= I30] 96.91/95.30 f19(I35, I36, I37, I38, I39, I40, I41) -> f17(I35, I36, I37, I38, I39, I40, I41) 96.91/95.30 f15(I42, I43, I44, I45, I46, I47, I48) -> f18(I42, I43, 0, I45, I46, I47, I48) [1 + I43 <= I42] 96.91/95.30 f15(I49, I50, I51, I52, I53, I54, I55) -> f16(I49, I50, I51, I52, I53, I54, I55) [I49 <= I50] 96.91/95.30 f20(I56, I57, I58, I59, I60, I61, I62) -> f19(I56, I57, I58, 0, I60, I61, I62) [1 + I58 <= I56] 96.91/95.30 f20(I63, I64, I65, I66, I67, I68, I69) -> f14(I63, 1 + I64, I65, I66, I67, I68, I69) [I63 <= I65] 96.91/95.30 f18(I70, I71, I72, I73, I74, I75, I76) -> f20(I70, I71, I72, I73, I74, I75, I76) 96.91/95.30 f17(I77, I78, I79, I80, I81, I82, I83) -> f19(I77, I78, I79, 1 + I80, I81, I82, I83) [1 + I80 <= I77] 96.91/95.30 f17(I84, I85, I86, I87, I88, I89, I90) -> f18(I84, I85, 1 + I86, I87, I88, I89, I90) [I84 <= I87] 96.91/95.30 f16(I91, I92, I93, I94, I95, I96, I97) -> f13(I91, I92, I93, I94, I95, I96, I97) 96.91/95.30 f16(I98, I99, I100, I101, I102, I103, I104) -> f5(I98, I99, I100, I101, I102, I103, I104) 96.91/95.30 f16(I105, I106, I107, I108, I109, I110, I111) -> f5(I105, I106, I107, I108, I109, I110, I111) 96.91/95.30 f14(I112, I113, I114, I115, I116, I117, I118) -> f15(I112, I113, I114, I115, I116, I117, I118) 96.91/95.30 f13(I119, I120, I121, I122, I123, I124, I125) -> f12(I119, I120, I121, I122, I123, I124, I125) 96.91/95.30 f13(I126, I127, I128, I129, I130, I131, I132) -> f7(I126, I127, I128, I129, I130, I131, I132) 96.91/95.30 f13(I133, I134, I135, I136, I137, I138, I139) -> f7(I133, I134, I135, I136, I137, I138, I139) 96.91/95.30 f12(I140, I141, I142, I143, I144, I145, I146) -> f11(I140, I141, I142, I143, I144, I145, I146) 96.91/95.30 f12(I147, I148, I149, I150, I151, I152, I153) -> f8(I147, I148, I149, I150, I151, I152, I153) 96.91/95.30 f12(I154, I155, I156, I157, I158, I159, I160) -> f8(I154, I155, I156, I157, I158, I159, I160) 96.91/95.30 f11(I161, I162, I163, I164, I165, I166, I167) -> f9(I161, I162, I163, I164, I165, I166, I167) 96.91/95.30 f11(I168, I169, I170, I171, I172, I173, I174) -> f6(I168, I169, I170, I171, I172, I173, 0) 96.91/95.30 f11(I175, I176, I177, I178, I179, I180, I181) -> f9(I175, I176, I177, I178, I179, I180, I181) 96.91/95.30 f6(I182, I183, I184, I185, I186, I187, I188) -> f10(I182, I183, I184, I185, I186, I187, I188) 96.91/95.30 f9(I189, I190, I191, I192, I193, I194, I195) -> f6(I189, I190, I191, I192, I193, I194, 1) 96.91/95.30 f8(I196, I197, I198, I199, I200, I201, I202) -> f6(I196, I197, I198, I199, I200, I201, 1) 96.91/95.30 f7(I203, I204, I205, I206, I207, I208, I209) -> f6(I203, I204, I205, I206, I207, I208, 1) 96.91/95.30 f5(I210, I211, I212, I213, I214, I215, I216) -> f6(I210, I211, I212, I213, I214, I215, 1) 96.91/95.30 f3(I217, I218, I219, I220, I221, I222, I223) -> f4(I217, I218, I219, I220, I221, I222, I223) 96.91/95.30 f1(I224, I225, I226, I227, I228, I229, I230) -> f2(I224, I225, I226, I227, I228, I229, I230) 96.91/95.30 96.91/95.30 The dependency graph for this problem is: 96.91/95.30 31 -> 96.91/95.30 Where: 96.91/95.30 31) f3#(I217, I218, I219, I220, I221, I222, I223) -> f4#(I217, I218, I219, I220, I221, I222, I223) 96.91/95.30 96.91/95.30 We have the following SCCs. 96.91/95.30 96.91/98.27 EOF