14.75/14.58 MAYBE 14.75/14.58 14.75/14.58 DP problem for innermost termination. 14.75/14.58 P = 14.75/14.58 f9#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f8#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 14.75/14.58 f8#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f3#(I0, 0, 1, 0, I4, rnd6, I6, rnd8, I8, 0) [rnd6 = rnd6 /\ rnd8 = rnd8] 14.75/14.58 f3#(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f7#(rnd1, I11, 1, I13, I14, I15, I16, I17, I18, 0) [rnd1 = rnd1 /\ 1 + I17 <= I15] 14.75/14.58 f3#(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f2#(I20, I21, I22, I23, I24, I25, I26, I27, I28, 0) [I25 <= I27] 14.75/14.58 f5#(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39) -> f3#(I30, I31, I32, I33, I34, I35, I36, 1 + I37, I38, I39) 14.75/14.58 f5#(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) -> f3#(I40, I41, I42, I43, I44, I45, I46, -1 + I47, I48, I49) 14.75/14.58 f7#(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f4#(I50, 1, I52, I53, I54, I55, rnd7, I57, I58, I59) [rnd7 = rnd7 /\ 1 <= I50] 14.75/14.58 f7#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f2#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) [I60 <= 0] 14.75/14.58 f6#(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) -> f2#(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) 14.75/14.58 f2#(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f6#(I80, I81, I82, 1, I84, I85, I86, I87, 0, I89) 14.75/14.58 f4#(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f1#(I90, 0, I92, I93, 0, I95, I100, I97, I98, I99) [I100 = I100 /\ 2 <= I96] 14.75/14.58 f4#(I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f5#(I101, 0, I103, I104, I105, I106, I107, I108, I109, 1) [I107 <= 1] 14.75/14.58 f1#(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) -> f3#(I111, I112, I113, I114, I115, I116, I117, I118, 1 + I119, I120) [2 <= I117] 14.75/14.58 f1#(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) -> f2#(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) [I127 <= 1] 14.75/14.58 R = 14.75/14.58 f9(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f8(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 14.75/14.58 f8(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f3(I0, 0, 1, 0, I4, rnd6, I6, rnd8, I8, 0) [rnd6 = rnd6 /\ rnd8 = rnd8] 14.75/14.58 f3(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f7(rnd1, I11, 1, I13, I14, I15, I16, I17, I18, 0) [rnd1 = rnd1 /\ 1 + I17 <= I15] 14.75/14.58 f3(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, 0) [I25 <= I27] 14.75/14.58 f5(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39) -> f3(I30, I31, I32, I33, I34, I35, I36, 1 + I37, I38, I39) 14.75/14.58 f5(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) -> f3(I40, I41, I42, I43, I44, I45, I46, -1 + I47, I48, I49) 14.75/14.58 f7(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f4(I50, 1, I52, I53, I54, I55, rnd7, I57, I58, I59) [rnd7 = rnd7 /\ 1 <= I50] 14.75/14.58 f7(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f2(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) [I60 <= 0] 14.75/14.58 f6(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) -> f2(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) 14.75/14.58 f2(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f6(I80, I81, I82, 1, I84, I85, I86, I87, 0, I89) 14.75/14.58 f4(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f1(I90, 0, I92, I93, 0, I95, I100, I97, I98, I99) [I100 = I100 /\ 2 <= I96] 14.75/14.58 f4(I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f5(I101, 0, I103, I104, I105, I106, I107, I108, I109, 1) [I107 <= 1] 14.75/14.58 f1(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) -> f3(I111, I112, I113, I114, I115, I116, I117, I118, 1 + I119, I120) [2 <= I117] 14.75/14.58 f1(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) -> f2(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) [I127 <= 1] 14.75/14.58 14.75/14.58 The dependency graph for this problem is: 14.75/14.58 0 -> 1 14.75/14.58 1 -> 2, 3 14.75/14.58 2 -> 6, 7 14.75/14.58 3 -> 9 14.75/14.58 4 -> 2, 3 14.75/14.58 5 -> 2, 3 14.75/14.58 6 -> 10, 11 14.75/14.58 7 -> 9 14.75/14.58 8 -> 9 14.75/14.58 9 -> 8 14.75/14.58 10 -> 12, 13 14.75/14.58 11 -> 4, 5 14.75/14.58 12 -> 2, 3 14.75/14.58 13 -> 9 14.75/14.58 Where: 14.75/14.58 0) f9#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f8#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 14.75/14.58 1) f8#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f3#(I0, 0, 1, 0, I4, rnd6, I6, rnd8, I8, 0) [rnd6 = rnd6 /\ rnd8 = rnd8] 14.75/14.58 2) f3#(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f7#(rnd1, I11, 1, I13, I14, I15, I16, I17, I18, 0) [rnd1 = rnd1 /\ 1 + I17 <= I15] 14.75/14.58 3) f3#(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f2#(I20, I21, I22, I23, I24, I25, I26, I27, I28, 0) [I25 <= I27] 14.75/14.58 4) f5#(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39) -> f3#(I30, I31, I32, I33, I34, I35, I36, 1 + I37, I38, I39) 14.75/14.58 5) f5#(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) -> f3#(I40, I41, I42, I43, I44, I45, I46, -1 + I47, I48, I49) 14.75/14.58 6) f7#(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f4#(I50, 1, I52, I53, I54, I55, rnd7, I57, I58, I59) [rnd7 = rnd7 /\ 1 <= I50] 14.75/14.58 7) f7#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f2#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) [I60 <= 0] 14.75/14.58 8) f6#(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) -> f2#(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) 14.75/14.58 9) f2#(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f6#(I80, I81, I82, 1, I84, I85, I86, I87, 0, I89) 14.75/14.58 10) f4#(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f1#(I90, 0, I92, I93, 0, I95, I100, I97, I98, I99) [I100 = I100 /\ 2 <= I96] 14.75/14.58 11) f4#(I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f5#(I101, 0, I103, I104, I105, I106, I107, I108, I109, 1) [I107 <= 1] 14.75/14.58 12) f1#(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) -> f3#(I111, I112, I113, I114, I115, I116, I117, I118, 1 + I119, I120) [2 <= I117] 14.75/14.58 13) f1#(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) -> f2#(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) [I127 <= 1] 14.75/14.58 14.75/14.58 We have the following SCCs. 14.75/14.58 { 2, 4, 5, 6, 10, 11, 12 } 14.75/14.58 { 8, 9 } 14.75/14.58 14.75/14.58 DP problem for innermost termination. 14.75/14.58 P = 14.75/14.58 f6#(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) -> f2#(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) 14.75/14.58 f2#(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f6#(I80, I81, I82, 1, I84, I85, I86, I87, 0, I89) 14.75/14.58 R = 14.75/14.58 f9(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f8(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 14.75/14.58 f8(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f3(I0, 0, 1, 0, I4, rnd6, I6, rnd8, I8, 0) [rnd6 = rnd6 /\ rnd8 = rnd8] 14.75/14.58 f3(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f7(rnd1, I11, 1, I13, I14, I15, I16, I17, I18, 0) [rnd1 = rnd1 /\ 1 + I17 <= I15] 14.75/14.58 f3(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f2(I20, I21, I22, I23, I24, I25, I26, I27, I28, 0) [I25 <= I27] 14.75/14.58 f5(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39) -> f3(I30, I31, I32, I33, I34, I35, I36, 1 + I37, I38, I39) 14.75/14.58 f5(I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) -> f3(I40, I41, I42, I43, I44, I45, I46, -1 + I47, I48, I49) 14.75/14.58 f7(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f4(I50, 1, I52, I53, I54, I55, rnd7, I57, I58, I59) [rnd7 = rnd7 /\ 1 <= I50] 14.75/14.58 f7(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) -> f2(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69) [I60 <= 0] 14.75/14.58 f6(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) -> f2(I70, I71, I72, I73, I74, I75, I76, I77, I78, I79) 14.75/14.58 f2(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f6(I80, I81, I82, 1, I84, I85, I86, I87, 0, I89) 14.75/14.58 f4(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f1(I90, 0, I92, I93, 0, I95, I100, I97, I98, I99) [I100 = I100 /\ 2 <= I96] 14.75/14.58 f4(I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f5(I101, 0, I103, I104, I105, I106, I107, I108, I109, 1) [I107 <= 1] 14.75/14.58 f1(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120) -> f3(I111, I112, I113, I114, I115, I116, I117, I118, 1 + I119, I120) [2 <= I117] 14.75/14.58 f1(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) -> f2(I121, I122, I123, I124, I125, I126, I127, I128, I129, I130) [I127 <= 1] 14.75/14.58 14.75/17.56 EOF