18.13/18.17 MAYBE 18.13/18.17 18.13/18.17 DP problem for innermost termination. 18.13/18.17 P = 18.13/18.17 f13#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> f12#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 18.13/18.17 f12#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10) -> f1#(I0, rnd2, I2, I3, I4, I5, I6, rnd8, I8, I9, 1) [y1 = 1 /\ rnd2 = rnd2 /\ rnd8 = rnd2] 18.13/18.17 f3#(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f6#(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) [I20 <= 0] 18.13/18.17 f3#(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f2#(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) [1 <= I31] 18.13/18.17 f2#(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f10#(I33, I34, I35, rnd4, I37, I38, I39, I40, rnd9, I42, 0) [rnd9 = rnd4 /\ rnd4 = rnd4 /\ 1 <= I43] 18.13/18.17 f2#(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f10#(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) [I54 <= 0] 18.13/18.17 f11#(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f7#(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) 18.13/18.17 f7#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f11#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) 18.13/18.17 f10#(I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f9#(I77, I78, I79, I80, I81, I82, rnd7, I84, I85, I86, I87) [rnd7 = rnd7 /\ I87 <= 0] 18.13/18.17 f10#(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f8#(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98) [1 <= I98] 18.13/18.17 f9#(I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f8#(I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, 1) [I99 <= I105 - I107] 18.13/18.17 f9#(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) -> f8#(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) [1 + I116 - I118 <= I110] 18.13/18.17 f8#(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f6#(I121, I122, I123, I124, rnd5, I126, I127, I128, I129, I130, I131) [rnd5 = rnd5] 18.13/18.17 f6#(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f7#(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) 18.13/18.17 f1#(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164) -> f3#(I154, I155, rnd3, I157, I158, 1, I160, 0, I162, rnd10, I164) [rnd10 = rnd3 /\ rnd3 = rnd3 /\ 1 <= I161] 18.13/18.17 f1#(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f2#(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175) [I172 <= 0] 18.13/18.17 R = 18.13/18.17 f13(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> f12(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 18.13/18.17 f12(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10) -> f1(I0, rnd2, I2, I3, I4, I5, I6, rnd8, I8, I9, 1) [y1 = 1 /\ rnd2 = rnd2 /\ rnd8 = rnd2] 18.13/18.17 f3(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f6(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) [I20 <= 0] 18.13/18.17 f3(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f2(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) [1 <= I31] 18.13/18.17 f2(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f10(I33, I34, I35, rnd4, I37, I38, I39, I40, rnd9, I42, 0) [rnd9 = rnd4 /\ rnd4 = rnd4 /\ 1 <= I43] 18.13/18.17 f2(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f10(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) [I54 <= 0] 18.13/18.17 f11(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f7(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) 18.13/18.17 f7(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f11(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) 18.13/18.17 f10(I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f9(I77, I78, I79, I80, I81, I82, rnd7, I84, I85, I86, I87) [rnd7 = rnd7 /\ I87 <= 0] 18.13/18.17 f10(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f8(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98) [1 <= I98] 18.13/18.17 f9(I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f8(I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, 1) [I99 <= I105 - I107] 18.13/18.17 f9(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) -> f8(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) [1 + I116 - I118 <= I110] 18.13/18.17 f8(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f6(I121, I122, I123, I124, rnd5, I126, I127, I128, I129, I130, I131) [rnd5 = rnd5] 18.13/18.17 f6(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f7(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) 18.13/18.17 f4(I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) -> f5(I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) 18.13/18.17 f1(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164) -> f3(I154, I155, rnd3, I157, I158, 1, I160, 0, I162, rnd10, I164) [rnd10 = rnd3 /\ rnd3 = rnd3 /\ 1 <= I161] 18.13/18.17 f1(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f2(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175) [I172 <= 0] 18.13/18.17 18.13/18.17 The dependency graph for this problem is: 18.13/18.17 0 -> 1 18.13/18.17 1 -> 14, 15 18.13/18.17 2 -> 13 18.13/18.17 3 -> 4, 5 18.13/18.17 4 -> 8 18.13/18.17 5 -> 8 18.13/18.17 6 -> 7 18.13/18.17 7 -> 6 18.13/18.17 8 -> 10, 11 18.13/18.17 9 -> 12 18.13/18.17 10 -> 12 18.13/18.17 11 -> 12 18.13/18.17 12 -> 13 18.13/18.17 13 -> 7 18.13/18.17 14 -> 2, 3 18.13/18.17 15 -> 4, 5 18.13/18.17 Where: 18.13/18.17 0) f13#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> f12#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 18.13/18.17 1) f12#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10) -> f1#(I0, rnd2, I2, I3, I4, I5, I6, rnd8, I8, I9, 1) [y1 = 1 /\ rnd2 = rnd2 /\ rnd8 = rnd2] 18.13/18.17 2) f3#(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f6#(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) [I20 <= 0] 18.13/18.17 3) f3#(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f2#(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) [1 <= I31] 18.13/18.17 4) f2#(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f10#(I33, I34, I35, rnd4, I37, I38, I39, I40, rnd9, I42, 0) [rnd9 = rnd4 /\ rnd4 = rnd4 /\ 1 <= I43] 18.13/18.17 5) f2#(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f10#(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) [I54 <= 0] 18.13/18.17 6) f11#(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f7#(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) 18.13/18.17 7) f7#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f11#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) 18.13/18.17 8) f10#(I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f9#(I77, I78, I79, I80, I81, I82, rnd7, I84, I85, I86, I87) [rnd7 = rnd7 /\ I87 <= 0] 18.13/18.17 9) f10#(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f8#(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98) [1 <= I98] 18.13/18.17 10) f9#(I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f8#(I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, 1) [I99 <= I105 - I107] 18.13/18.17 11) f9#(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) -> f8#(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) [1 + I116 - I118 <= I110] 18.13/18.17 12) f8#(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f6#(I121, I122, I123, I124, rnd5, I126, I127, I128, I129, I130, I131) [rnd5 = rnd5] 18.13/18.17 13) f6#(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f7#(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) 18.13/18.17 14) f1#(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164) -> f3#(I154, I155, rnd3, I157, I158, 1, I160, 0, I162, rnd10, I164) [rnd10 = rnd3 /\ rnd3 = rnd3 /\ 1 <= I161] 18.13/18.17 15) f1#(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f2#(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175) [I172 <= 0] 18.13/18.17 18.13/18.17 We have the following SCCs. 18.13/18.17 { 6, 7 } 18.13/18.17 18.13/18.17 DP problem for innermost termination. 18.13/18.17 P = 18.13/18.17 f11#(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f7#(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) 18.13/18.17 f7#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f11#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) 18.13/18.17 R = 18.13/18.17 f13(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> f12(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 18.13/18.17 f12(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10) -> f1(I0, rnd2, I2, I3, I4, I5, I6, rnd8, I8, I9, 1) [y1 = 1 /\ rnd2 = rnd2 /\ rnd8 = rnd2] 18.13/18.17 f3(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f6(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) [I20 <= 0] 18.13/18.17 f3(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f2(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) [1 <= I31] 18.13/18.17 f2(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f10(I33, I34, I35, rnd4, I37, I38, I39, I40, rnd9, I42, 0) [rnd9 = rnd4 /\ rnd4 = rnd4 /\ 1 <= I43] 18.13/18.17 f2(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f10(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) [I54 <= 0] 18.13/18.17 f11(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f7(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) 18.13/18.17 f7(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f11(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) 18.13/18.17 f10(I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87) -> f9(I77, I78, I79, I80, I81, I82, rnd7, I84, I85, I86, I87) [rnd7 = rnd7 /\ I87 <= 0] 18.13/18.17 f10(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f8(I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98) [1 <= I98] 18.13/18.17 f9(I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109) -> f8(I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, 1) [I99 <= I105 - I107] 18.13/18.17 f9(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) -> f8(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) [1 + I116 - I118 <= I110] 18.13/18.17 f8(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f6(I121, I122, I123, I124, rnd5, I126, I127, I128, I129, I130, I131) [rnd5 = rnd5] 18.13/18.17 f6(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f7(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142) 18.13/18.17 f4(I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) -> f5(I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153) 18.13/18.17 f1(I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164) -> f3(I154, I155, rnd3, I157, I158, 1, I160, 0, I162, rnd10, I164) [rnd10 = rnd3 /\ rnd3 = rnd3 /\ 1 <= I161] 18.13/18.17 f1(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175) -> f2(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175) [I172 <= 0] 18.13/18.17 18.13/21.14 EOF