245.64/242.20 YES 245.64/242.20 245.64/242.20 DP problem for innermost termination. 245.64/242.20 P = 245.64/242.20 f9#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) -> f8#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) 245.64/242.20 f8#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f1#(3, 1, I2, I3, I4, I5, I6, 0, I8, I9, I10, I11, 3, I13, I14, I4, I16, I17, I18, I19, I20, I21) 245.64/242.20 f2#(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f1#(I22, rnd2, I24, I25, I26, I27, I28, 1 + I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) [rnd2 = rnd2 /\ 1 + I29 <= I34] 245.64/242.20 f2#(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f6#(I44, I45, 1, I47, I48, I49, I50, I51, 0, I53, I44, I55, I56, I49, I58, I59, I45, I61, I62, I45, I64, I65) [I56 <= I51] 245.64/242.20 f5#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f3#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) 245.64/242.20 f7#(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f6#(I88, I89, rnd3, I91, I92, I93, I94, I95, 1 + I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) [rnd3 = rnd3 /\ 1 + I96 <= I98] 245.64/242.20 f7#(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f5#(I110, I111, I112, 1, I114, I115, I116, I117, I118, 0, I120, I110, I122, I123, I116, I125, I126, I112, I128, I129, I112, I131) [I120 <= I118] 245.64/242.20 f6#(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) -> f7#(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) 245.64/242.20 f3#(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f5#(I154, I155, I156, rnd4, I158, I159, I160, I161, I162, 1 + I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175) [rnd4 = rnd4 /\ 1 + I163 <= I165] 245.64/242.20 f1#(I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) -> f2#(I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) 245.64/242.20 R = 245.64/242.20 f9(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) -> f8(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) 245.64/242.20 f8(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f1(3, 1, I2, I3, I4, I5, I6, 0, I8, I9, I10, I11, 3, I13, I14, I4, I16, I17, I18, I19, I20, I21) 245.64/242.20 f2(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f1(I22, rnd2, I24, I25, I26, I27, I28, 1 + I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) [rnd2 = rnd2 /\ 1 + I29 <= I34] 245.64/242.20 f2(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f6(I44, I45, 1, I47, I48, I49, I50, I51, 0, I53, I44, I55, I56, I49, I58, I59, I45, I61, I62, I45, I64, I65) [I56 <= I51] 245.64/242.20 f5(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f3(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) 245.64/242.20 f7(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f6(I88, I89, rnd3, I91, I92, I93, I94, I95, 1 + I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) [rnd3 = rnd3 /\ 1 + I96 <= I98] 245.64/242.20 f7(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f5(I110, I111, I112, 1, I114, I115, I116, I117, I118, 0, I120, I110, I122, I123, I116, I125, I126, I112, I128, I129, I112, I131) [I120 <= I118] 245.64/242.20 f6(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) -> f7(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) 245.64/242.20 f3(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f5(I154, I155, I156, rnd4, I158, I159, I160, I161, I162, 1 + I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175) [rnd4 = rnd4 /\ 1 + I163 <= I165] 245.64/242.20 f3(I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197) -> f4(I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I179, I195, I196, I179) [I187 <= I185] 245.64/242.20 f1(I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) -> f2(I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) 245.64/242.20 245.64/242.20 The dependency graph for this problem is: 245.64/242.20 0 -> 1 245.64/242.20 1 -> 9 245.64/242.20 2 -> 9 245.64/242.20 3 -> 7 245.64/242.20 4 -> 8 245.64/242.20 5 -> 7 245.64/242.20 6 -> 4 245.64/242.20 7 -> 5, 6 245.64/242.20 8 -> 4 245.64/242.20 9 -> 2, 3 245.64/242.20 Where: 245.64/242.20 0) f9#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) -> f8#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) 245.64/242.20 1) f8#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f1#(3, 1, I2, I3, I4, I5, I6, 0, I8, I9, I10, I11, 3, I13, I14, I4, I16, I17, I18, I19, I20, I21) 245.64/242.20 2) f2#(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f1#(I22, rnd2, I24, I25, I26, I27, I28, 1 + I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) [rnd2 = rnd2 /\ 1 + I29 <= I34] 245.64/242.20 3) f2#(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f6#(I44, I45, 1, I47, I48, I49, I50, I51, 0, I53, I44, I55, I56, I49, I58, I59, I45, I61, I62, I45, I64, I65) [I56 <= I51] 245.64/242.20 4) f5#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f3#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) 245.64/242.20 5) f7#(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f6#(I88, I89, rnd3, I91, I92, I93, I94, I95, 1 + I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) [rnd3 = rnd3 /\ 1 + I96 <= I98] 245.64/242.20 6) f7#(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f5#(I110, I111, I112, 1, I114, I115, I116, I117, I118, 0, I120, I110, I122, I123, I116, I125, I126, I112, I128, I129, I112, I131) [I120 <= I118] 245.64/242.20 7) f6#(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) -> f7#(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) 245.64/242.20 8) f3#(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f5#(I154, I155, I156, rnd4, I158, I159, I160, I161, I162, 1 + I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175) [rnd4 = rnd4 /\ 1 + I163 <= I165] 245.64/242.20 9) f1#(I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) -> f2#(I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) 245.64/242.20 245.64/242.20 We have the following SCCs. 245.64/242.20 { 2, 9 } 245.64/242.20 { 5, 7 } 245.64/242.20 { 4, 8 } 245.64/242.20 245.64/242.20 DP problem for innermost termination. 245.64/242.20 P = 245.64/242.20 f5#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f3#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) 245.64/242.20 f3#(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f5#(I154, I155, I156, rnd4, I158, I159, I160, I161, I162, 1 + I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175) [rnd4 = rnd4 /\ 1 + I163 <= I165] 245.64/242.20 R = 245.64/242.20 f9(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) -> f8(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) 245.64/242.20 f8(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f1(3, 1, I2, I3, I4, I5, I6, 0, I8, I9, I10, I11, 3, I13, I14, I4, I16, I17, I18, I19, I20, I21) 245.64/242.20 f2(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f1(I22, rnd2, I24, I25, I26, I27, I28, 1 + I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) [rnd2 = rnd2 /\ 1 + I29 <= I34] 245.64/242.20 f2(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f6(I44, I45, 1, I47, I48, I49, I50, I51, 0, I53, I44, I55, I56, I49, I58, I59, I45, I61, I62, I45, I64, I65) [I56 <= I51] 245.64/242.20 f5(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f3(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) 245.64/242.20 f7(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f6(I88, I89, rnd3, I91, I92, I93, I94, I95, 1 + I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) [rnd3 = rnd3 /\ 1 + I96 <= I98] 245.64/242.20 f7(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f5(I110, I111, I112, 1, I114, I115, I116, I117, I118, 0, I120, I110, I122, I123, I116, I125, I126, I112, I128, I129, I112, I131) [I120 <= I118] 245.64/242.20 f6(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) -> f7(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) 245.64/242.20 f3(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f5(I154, I155, I156, rnd4, I158, I159, I160, I161, I162, 1 + I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175) [rnd4 = rnd4 /\ 1 + I163 <= I165] 245.64/242.20 f3(I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197) -> f4(I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I179, I195, I196, I179) [I187 <= I185] 245.64/242.20 f1(I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) -> f2(I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) 245.64/242.20 245.64/242.20 We use the reverse value criterion with the projection function NU: 245.64/242.20 NU[f3#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14,z15,z16,z17,z18,z19,z20,z21,z22)] = z12 + -1 * (1 + z10) 245.64/242.20 NU[f5#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14,z15,z16,z17,z18,z19,z20,z21,z22)] = z12 + -1 * (1 + z10) 245.64/242.20 245.64/242.20 This gives the following inequalities: 245.64/242.20 ==> I77 + -1 * (1 + I75) >= I77 + -1 * (1 + I75) 245.64/242.20 rnd4 = rnd4 /\ 1 + I163 <= I165 ==> I165 + -1 * (1 + I163) > I165 + -1 * (1 + (1 + I163)) with I165 + -1 * (1 + I163) >= 0 245.64/242.20 245.64/242.20 We remove all the strictly oriented dependency pairs. 245.64/242.20 245.64/242.20 DP problem for innermost termination. 245.64/242.20 P = 245.64/242.20 f5#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f3#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) 245.64/242.20 R = 245.64/242.20 f9(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) -> f8(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) 245.64/242.20 f8(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f1(3, 1, I2, I3, I4, I5, I6, 0, I8, I9, I10, I11, 3, I13, I14, I4, I16, I17, I18, I19, I20, I21) 245.64/242.20 f2(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f1(I22, rnd2, I24, I25, I26, I27, I28, 1 + I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) [rnd2 = rnd2 /\ 1 + I29 <= I34] 245.64/242.20 f2(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f6(I44, I45, 1, I47, I48, I49, I50, I51, 0, I53, I44, I55, I56, I49, I58, I59, I45, I61, I62, I45, I64, I65) [I56 <= I51] 245.64/242.20 f5(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f3(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) 245.64/242.20 f7(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f6(I88, I89, rnd3, I91, I92, I93, I94, I95, 1 + I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) [rnd3 = rnd3 /\ 1 + I96 <= I98] 245.64/242.20 f7(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f5(I110, I111, I112, 1, I114, I115, I116, I117, I118, 0, I120, I110, I122, I123, I116, I125, I126, I112, I128, I129, I112, I131) [I120 <= I118] 245.64/242.20 f6(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) -> f7(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) 245.64/242.20 f3(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f5(I154, I155, I156, rnd4, I158, I159, I160, I161, I162, 1 + I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175) [rnd4 = rnd4 /\ 1 + I163 <= I165] 245.64/242.20 f3(I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197) -> f4(I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I179, I195, I196, I179) [I187 <= I185] 245.64/242.20 f1(I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) -> f2(I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) 245.64/242.20 245.64/242.20 The dependency graph for this problem is: 245.64/242.20 4 -> 245.64/242.20 Where: 245.64/242.20 4) f5#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f3#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) 245.64/242.20 245.64/242.20 We have the following SCCs. 245.64/242.20 245.64/242.20 245.64/242.20 DP problem for innermost termination. 245.64/242.20 P = 245.64/242.20 f7#(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f6#(I88, I89, rnd3, I91, I92, I93, I94, I95, 1 + I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) [rnd3 = rnd3 /\ 1 + I96 <= I98] 245.64/242.20 f6#(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) -> f7#(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) 245.64/242.20 R = 245.64/242.20 f9(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) -> f8(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) 245.64/242.20 f8(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f1(3, 1, I2, I3, I4, I5, I6, 0, I8, I9, I10, I11, 3, I13, I14, I4, I16, I17, I18, I19, I20, I21) 245.64/242.20 f2(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f1(I22, rnd2, I24, I25, I26, I27, I28, 1 + I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) [rnd2 = rnd2 /\ 1 + I29 <= I34] 245.64/242.20 f2(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f6(I44, I45, 1, I47, I48, I49, I50, I51, 0, I53, I44, I55, I56, I49, I58, I59, I45, I61, I62, I45, I64, I65) [I56 <= I51] 245.64/242.20 f5(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f3(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) 245.64/242.20 f7(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f6(I88, I89, rnd3, I91, I92, I93, I94, I95, 1 + I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) [rnd3 = rnd3 /\ 1 + I96 <= I98] 245.64/242.20 f7(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f5(I110, I111, I112, 1, I114, I115, I116, I117, I118, 0, I120, I110, I122, I123, I116, I125, I126, I112, I128, I129, I112, I131) [I120 <= I118] 245.64/242.20 f6(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) -> f7(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) 245.64/242.20 f3(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f5(I154, I155, I156, rnd4, I158, I159, I160, I161, I162, 1 + I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175) [rnd4 = rnd4 /\ 1 + I163 <= I165] 245.64/242.20 f3(I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197) -> f4(I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I179, I195, I196, I179) [I187 <= I185] 245.64/242.20 f1(I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) -> f2(I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) 245.64/242.20 245.64/242.20 We use the reverse value criterion with the projection function NU: 245.64/242.20 NU[f6#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14,z15,z16,z17,z18,z19,z20,z21,z22)] = z11 + -1 * (1 + z9) 245.64/242.20 NU[f7#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14,z15,z16,z17,z18,z19,z20,z21,z22)] = z11 + -1 * (1 + z9) 245.64/242.20 245.64/242.20 This gives the following inequalities: 245.64/242.20 rnd3 = rnd3 /\ 1 + I96 <= I98 ==> I98 + -1 * (1 + I96) > I98 + -1 * (1 + (1 + I96)) with I98 + -1 * (1 + I96) >= 0 245.64/242.20 ==> I142 + -1 * (1 + I140) >= I142 + -1 * (1 + I140) 245.64/242.20 245.64/242.20 We remove all the strictly oriented dependency pairs. 245.64/242.20 245.64/242.20 DP problem for innermost termination. 245.64/242.20 P = 245.64/242.20 f6#(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) -> f7#(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) 245.64/242.20 R = 245.64/242.20 f9(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) -> f8(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) 245.64/242.20 f8(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f1(3, 1, I2, I3, I4, I5, I6, 0, I8, I9, I10, I11, 3, I13, I14, I4, I16, I17, I18, I19, I20, I21) 245.64/242.20 f2(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f1(I22, rnd2, I24, I25, I26, I27, I28, 1 + I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) [rnd2 = rnd2 /\ 1 + I29 <= I34] 245.64/242.20 f2(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f6(I44, I45, 1, I47, I48, I49, I50, I51, 0, I53, I44, I55, I56, I49, I58, I59, I45, I61, I62, I45, I64, I65) [I56 <= I51] 245.64/242.20 f5(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f3(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) 245.64/242.20 f7(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f6(I88, I89, rnd3, I91, I92, I93, I94, I95, 1 + I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) [rnd3 = rnd3 /\ 1 + I96 <= I98] 245.64/242.20 f7(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f5(I110, I111, I112, 1, I114, I115, I116, I117, I118, 0, I120, I110, I122, I123, I116, I125, I126, I112, I128, I129, I112, I131) [I120 <= I118] 245.64/242.20 f6(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) -> f7(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) 245.64/242.20 f3(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f5(I154, I155, I156, rnd4, I158, I159, I160, I161, I162, 1 + I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175) [rnd4 = rnd4 /\ 1 + I163 <= I165] 245.64/242.20 f3(I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197) -> f4(I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I179, I195, I196, I179) [I187 <= I185] 245.64/242.20 f1(I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) -> f2(I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) 245.64/242.20 245.64/242.20 The dependency graph for this problem is: 245.64/242.20 7 -> 245.64/242.20 Where: 245.64/242.20 7) f6#(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) -> f7#(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) 245.64/242.20 245.64/242.20 We have the following SCCs. 245.64/242.20 245.64/242.20 245.64/242.20 DP problem for innermost termination. 245.64/242.20 P = 245.64/242.20 f2#(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f1#(I22, rnd2, I24, I25, I26, I27, I28, 1 + I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) [rnd2 = rnd2 /\ 1 + I29 <= I34] 245.64/242.20 f1#(I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) -> f2#(I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) 245.64/242.20 R = 245.64/242.20 f9(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) -> f8(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) 245.64/242.20 f8(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f1(3, 1, I2, I3, I4, I5, I6, 0, I8, I9, I10, I11, 3, I13, I14, I4, I16, I17, I18, I19, I20, I21) 245.64/242.20 f2(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f1(I22, rnd2, I24, I25, I26, I27, I28, 1 + I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) [rnd2 = rnd2 /\ 1 + I29 <= I34] 245.64/242.20 f2(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f6(I44, I45, 1, I47, I48, I49, I50, I51, 0, I53, I44, I55, I56, I49, I58, I59, I45, I61, I62, I45, I64, I65) [I56 <= I51] 245.64/242.20 f5(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f3(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) 245.64/242.20 f7(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f6(I88, I89, rnd3, I91, I92, I93, I94, I95, 1 + I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) [rnd3 = rnd3 /\ 1 + I96 <= I98] 245.64/242.20 f7(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f5(I110, I111, I112, 1, I114, I115, I116, I117, I118, 0, I120, I110, I122, I123, I116, I125, I126, I112, I128, I129, I112, I131) [I120 <= I118] 245.64/242.20 f6(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) -> f7(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) 245.64/242.20 f3(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f5(I154, I155, I156, rnd4, I158, I159, I160, I161, I162, 1 + I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175) [rnd4 = rnd4 /\ 1 + I163 <= I165] 245.64/242.20 f3(I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197) -> f4(I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I179, I195, I196, I179) [I187 <= I185] 245.64/242.20 f1(I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) -> f2(I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) 245.64/242.20 245.64/242.20 We use the reverse value criterion with the projection function NU: 245.64/242.20 NU[f1#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14,z15,z16,z17,z18,z19,z20,z21,z22)] = z13 + -1 * (1 + z8) 245.64/242.20 NU[f2#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14,z15,z16,z17,z18,z19,z20,z21,z22)] = z13 + -1 * (1 + z8) 245.64/242.20 245.64/242.20 This gives the following inequalities: 245.64/242.20 rnd2 = rnd2 /\ 1 + I29 <= I34 ==> I34 + -1 * (1 + I29) > I34 + -1 * (1 + (1 + I29)) with I34 + -1 * (1 + I29) >= 0 245.64/242.20 ==> I210 + -1 * (1 + I205) >= I210 + -1 * (1 + I205) 245.64/242.20 245.64/242.20 We remove all the strictly oriented dependency pairs. 245.64/242.20 245.64/242.20 DP problem for innermost termination. 245.64/242.20 P = 245.64/242.20 f1#(I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) -> f2#(I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) 245.64/242.20 R = 245.64/242.20 f9(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) -> f8(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) 245.64/242.20 f8(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f1(3, 1, I2, I3, I4, I5, I6, 0, I8, I9, I10, I11, 3, I13, I14, I4, I16, I17, I18, I19, I20, I21) 245.64/242.20 f2(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f1(I22, rnd2, I24, I25, I26, I27, I28, 1 + I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) [rnd2 = rnd2 /\ 1 + I29 <= I34] 245.64/242.20 f2(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f6(I44, I45, 1, I47, I48, I49, I50, I51, 0, I53, I44, I55, I56, I49, I58, I59, I45, I61, I62, I45, I64, I65) [I56 <= I51] 245.64/242.20 f5(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f3(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) 245.64/242.20 f7(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f6(I88, I89, rnd3, I91, I92, I93, I94, I95, 1 + I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) [rnd3 = rnd3 /\ 1 + I96 <= I98] 245.64/242.20 f7(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f5(I110, I111, I112, 1, I114, I115, I116, I117, I118, 0, I120, I110, I122, I123, I116, I125, I126, I112, I128, I129, I112, I131) [I120 <= I118] 245.64/242.20 f6(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) -> f7(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) 245.64/242.20 f3(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f5(I154, I155, I156, rnd4, I158, I159, I160, I161, I162, 1 + I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175) [rnd4 = rnd4 /\ 1 + I163 <= I165] 245.64/242.20 f3(I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197) -> f4(I176, I177, I178, I179, I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I179, I195, I196, I179) [I187 <= I185] 245.64/242.20 f1(I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) -> f2(I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) 245.64/242.20 245.64/242.20 The dependency graph for this problem is: 245.64/242.20 9 -> 245.64/242.20 Where: 245.64/242.20 9) f1#(I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) -> f2#(I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219) 245.64/242.20 245.64/242.20 We have the following SCCs. 245.64/242.20 245.64/245.14 EOF