/export/starexec/sandbox/solver/bin/starexec_run_Transition /export/starexec/sandbox/benchmark/theBenchmark.smt2 /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- MAYBE DP problem for innermost termination. P = f15#(x1, x2, x3, x4, x5) -> f1#(x1, x2, x3, x4, x5) f14#(I0, I1, I2, I3, I4) -> f3#(I0, I1, I2, 1 + I3, I4) f13#(I5, I6, I7, I8, I9) -> f14#(I5, I6, I7, I8, I9) [1 <= I6] f13#(I10, I11, I12, I13, I14) -> f14#(I10, I11, I12, I13, I14) [1 + I11 <= 0] f4#(I15, I16, I17, I18, I19) -> f13#(I15, rnd2, I17, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19] f12#(I20, I21, I22, I23, I24) -> f4#(I20, I21, I22, I23, I24) f4#(I25, I26, I27, I28, I29) -> f12#(I25, I30, I27, I28, I29) [0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29] f8#(I31, I32, I33, I34, I35) -> f2#(I31, I32, 1 + I33, I34, I35) [-1 * I34 + I35 <= 0] f11#(I36, I37, I38, I39, I40) -> f3#(I36, I37, I38, 1 + I39, I40) f10#(I41, I42, I43, I44, I45) -> f11#(I41, I42, I43, I44, I45) [1 <= I42] f10#(I46, I47, I48, I49, I50) -> f11#(I46, I47, I48, I49, I50) [1 + I47 <= 0] f8#(I51, I52, I53, I54, I55) -> f10#(I51, I56, I53, I54, I55) [I56 = I56 /\ 0 <= -1 - I54 + I55] f8#(I57, I58, I59, I60, I61) -> f4#(I57, I62, I59, I60, I61) [0 <= I62 /\ I62 <= 0 /\ I62 = I62 /\ 0 <= -1 - I60 + I61] f2#(I68, I69, I70, I71, I72) -> f8#(I68, I69, I70, I71, I72) [0 <= -1 - I70 + I71] f3#(I73, I74, I75, I76, I77) -> f2#(I73, I74, 1 + I75, I76, I77) [-1 * I76 + I77 <= 0] f7#(I78, I79, I80, I81, I82) -> f3#(I78, I79, I80, I81, I82) f6#(I83, I84, I85, I86, I87) -> f7#(I83, I84, I85, 1 + I86, I87) f5#(I88, I89, I90, I91, I92) -> f6#(I88, I89, I90, I91, I92) [1 <= I89] f5#(I93, I94, I95, I96, I97) -> f6#(I93, I94, I95, I96, I97) [1 + I94 <= 0] f3#(I98, I99, I100, I101, I102) -> f5#(I98, I103, I100, I101, I102) [I103 = I103 /\ 0 <= -1 - I101 + I102] f3#(I104, I105, I106, I107, I108) -> f4#(I104, I109, I106, I107, I108) [0 <= I109 /\ I109 <= 0 /\ I109 = I109 /\ 0 <= -1 - I107 + I108] f1#(I110, I111, I112, I113, I114) -> f2#(I110, I111, I112, I113, I114) R = f15(x1, x2, x3, x4, x5) -> f1(x1, x2, x3, x4, x5) f14(I0, I1, I2, I3, I4) -> f3(I0, I1, I2, 1 + I3, I4) f13(I5, I6, I7, I8, I9) -> f14(I5, I6, I7, I8, I9) [1 <= I6] f13(I10, I11, I12, I13, I14) -> f14(I10, I11, I12, I13, I14) [1 + I11 <= 0] f4(I15, I16, I17, I18, I19) -> f13(I15, rnd2, I17, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19] f12(I20, I21, I22, I23, I24) -> f4(I20, I21, I22, I23, I24) f4(I25, I26, I27, I28, I29) -> f12(I25, I30, I27, I28, I29) [0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29] f8(I31, I32, I33, I34, I35) -> f2(I31, I32, 1 + I33, I34, I35) [-1 * I34 + I35 <= 0] f11(I36, I37, I38, I39, I40) -> f3(I36, I37, I38, 1 + I39, I40) f10(I41, I42, I43, I44, I45) -> f11(I41, I42, I43, I44, I45) [1 <= I42] f10(I46, I47, I48, I49, I50) -> f11(I46, I47, I48, I49, I50) [1 + I47 <= 0] f8(I51, I52, I53, I54, I55) -> f10(I51, I56, I53, I54, I55) [I56 = I56 /\ 0 <= -1 - I54 + I55] f8(I57, I58, I59, I60, I61) -> f4(I57, I62, I59, I60, I61) [0 <= I62 /\ I62 <= 0 /\ I62 = I62 /\ 0 <= -1 - I60 + I61] f2(I63, I64, I65, I66, I67) -> f9(rnd1, I64, I65, I66, I67) [rnd1 = rnd1 /\ -1 * I65 + I66 <= 0] f2(I68, I69, I70, I71, I72) -> f8(I68, I69, I70, I71, I72) [0 <= -1 - I70 + I71] f3(I73, I74, I75, I76, I77) -> f2(I73, I74, 1 + I75, I76, I77) [-1 * I76 + I77 <= 0] f7(I78, I79, I80, I81, I82) -> f3(I78, I79, I80, I81, I82) f6(I83, I84, I85, I86, I87) -> f7(I83, I84, I85, 1 + I86, I87) f5(I88, I89, I90, I91, I92) -> f6(I88, I89, I90, I91, I92) [1 <= I89] f5(I93, I94, I95, I96, I97) -> f6(I93, I94, I95, I96, I97) [1 + I94 <= 0] f3(I98, I99, I100, I101, I102) -> f5(I98, I103, I100, I101, I102) [I103 = I103 /\ 0 <= -1 - I101 + I102] f3(I104, I105, I106, I107, I108) -> f4(I104, I109, I106, I107, I108) [0 <= I109 /\ I109 <= 0 /\ I109 = I109 /\ 0 <= -1 - I107 + I108] f1(I110, I111, I112, I113, I114) -> f2(I110, I111, I112, I113, I114) The dependency graph for this problem is: 0 -> 21 1 -> 14, 19, 20 2 -> 1 3 -> 1 4 -> 2, 3 5 -> 4, 6 6 -> 5 7 -> 13 8 -> 14, 19, 20 9 -> 8 10 -> 8 11 -> 9, 10 12 -> 4, 6 13 -> 7, 11, 12 14 -> 13 15 -> 14, 19, 20 16 -> 15 17 -> 16 18 -> 16 19 -> 17, 18 20 -> 4, 6 21 -> 13 Where: 0) f15#(x1, x2, x3, x4, x5) -> f1#(x1, x2, x3, x4, x5) 1) f14#(I0, I1, I2, I3, I4) -> f3#(I0, I1, I2, 1 + I3, I4) 2) f13#(I5, I6, I7, I8, I9) -> f14#(I5, I6, I7, I8, I9) [1 <= I6] 3) f13#(I10, I11, I12, I13, I14) -> f14#(I10, I11, I12, I13, I14) [1 + I11 <= 0] 4) f4#(I15, I16, I17, I18, I19) -> f13#(I15, rnd2, I17, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19] 5) f12#(I20, I21, I22, I23, I24) -> f4#(I20, I21, I22, I23, I24) 6) f4#(I25, I26, I27, I28, I29) -> f12#(I25, I30, I27, I28, I29) [0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29] 7) f8#(I31, I32, I33, I34, I35) -> f2#(I31, I32, 1 + I33, I34, I35) [-1 * I34 + I35 <= 0] 8) f11#(I36, I37, I38, I39, I40) -> f3#(I36, I37, I38, 1 + I39, I40) 9) f10#(I41, I42, I43, I44, I45) -> f11#(I41, I42, I43, I44, I45) [1 <= I42] 10) f10#(I46, I47, I48, I49, I50) -> f11#(I46, I47, I48, I49, I50) [1 + I47 <= 0] 11) f8#(I51, I52, I53, I54, I55) -> f10#(I51, I56, I53, I54, I55) [I56 = I56 /\ 0 <= -1 - I54 + I55] 12) f8#(I57, I58, I59, I60, I61) -> f4#(I57, I62, I59, I60, I61) [0 <= I62 /\ I62 <= 0 /\ I62 = I62 /\ 0 <= -1 - I60 + I61] 13) f2#(I68, I69, I70, I71, I72) -> f8#(I68, I69, I70, I71, I72) [0 <= -1 - I70 + I71] 14) f3#(I73, I74, I75, I76, I77) -> f2#(I73, I74, 1 + I75, I76, I77) [-1 * I76 + I77 <= 0] 15) f7#(I78, I79, I80, I81, I82) -> f3#(I78, I79, I80, I81, I82) 16) f6#(I83, I84, I85, I86, I87) -> f7#(I83, I84, I85, 1 + I86, I87) 17) f5#(I88, I89, I90, I91, I92) -> f6#(I88, I89, I90, I91, I92) [1 <= I89] 18) f5#(I93, I94, I95, I96, I97) -> f6#(I93, I94, I95, I96, I97) [1 + I94 <= 0] 19) f3#(I98, I99, I100, I101, I102) -> f5#(I98, I103, I100, I101, I102) [I103 = I103 /\ 0 <= -1 - I101 + I102] 20) f3#(I104, I105, I106, I107, I108) -> f4#(I104, I109, I106, I107, I108) [0 <= I109 /\ I109 <= 0 /\ I109 = I109 /\ 0 <= -1 - I107 + I108] 21) f1#(I110, I111, I112, I113, I114) -> f2#(I110, I111, I112, I113, I114) We have the following SCCs. { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 } DP problem for innermost termination. P = f14#(I0, I1, I2, I3, I4) -> f3#(I0, I1, I2, 1 + I3, I4) f13#(I5, I6, I7, I8, I9) -> f14#(I5, I6, I7, I8, I9) [1 <= I6] f13#(I10, I11, I12, I13, I14) -> f14#(I10, I11, I12, I13, I14) [1 + I11 <= 0] f4#(I15, I16, I17, I18, I19) -> f13#(I15, rnd2, I17, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19] f12#(I20, I21, I22, I23, I24) -> f4#(I20, I21, I22, I23, I24) f4#(I25, I26, I27, I28, I29) -> f12#(I25, I30, I27, I28, I29) [0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29] f8#(I31, I32, I33, I34, I35) -> f2#(I31, I32, 1 + I33, I34, I35) [-1 * I34 + I35 <= 0] f11#(I36, I37, I38, I39, I40) -> f3#(I36, I37, I38, 1 + I39, I40) f10#(I41, I42, I43, I44, I45) -> f11#(I41, I42, I43, I44, I45) [1 <= I42] f10#(I46, I47, I48, I49, I50) -> f11#(I46, I47, I48, I49, I50) [1 + I47 <= 0] f8#(I51, I52, I53, I54, I55) -> f10#(I51, I56, I53, I54, I55) [I56 = I56 /\ 0 <= -1 - I54 + I55] f8#(I57, I58, I59, I60, I61) -> f4#(I57, I62, I59, I60, I61) [0 <= I62 /\ I62 <= 0 /\ I62 = I62 /\ 0 <= -1 - I60 + I61] f2#(I68, I69, I70, I71, I72) -> f8#(I68, I69, I70, I71, I72) [0 <= -1 - I70 + I71] f3#(I73, I74, I75, I76, I77) -> f2#(I73, I74, 1 + I75, I76, I77) [-1 * I76 + I77 <= 0] f7#(I78, I79, I80, I81, I82) -> f3#(I78, I79, I80, I81, I82) f6#(I83, I84, I85, I86, I87) -> f7#(I83, I84, I85, 1 + I86, I87) f5#(I88, I89, I90, I91, I92) -> f6#(I88, I89, I90, I91, I92) [1 <= I89] f5#(I93, I94, I95, I96, I97) -> f6#(I93, I94, I95, I96, I97) [1 + I94 <= 0] f3#(I98, I99, I100, I101, I102) -> f5#(I98, I103, I100, I101, I102) [I103 = I103 /\ 0 <= -1 - I101 + I102] f3#(I104, I105, I106, I107, I108) -> f4#(I104, I109, I106, I107, I108) [0 <= I109 /\ I109 <= 0 /\ I109 = I109 /\ 0 <= -1 - I107 + I108] R = f15(x1, x2, x3, x4, x5) -> f1(x1, x2, x3, x4, x5) f14(I0, I1, I2, I3, I4) -> f3(I0, I1, I2, 1 + I3, I4) f13(I5, I6, I7, I8, I9) -> f14(I5, I6, I7, I8, I9) [1 <= I6] f13(I10, I11, I12, I13, I14) -> f14(I10, I11, I12, I13, I14) [1 + I11 <= 0] f4(I15, I16, I17, I18, I19) -> f13(I15, rnd2, I17, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19] f12(I20, I21, I22, I23, I24) -> f4(I20, I21, I22, I23, I24) f4(I25, I26, I27, I28, I29) -> f12(I25, I30, I27, I28, I29) [0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29] f8(I31, I32, I33, I34, I35) -> f2(I31, I32, 1 + I33, I34, I35) [-1 * I34 + I35 <= 0] f11(I36, I37, I38, I39, I40) -> f3(I36, I37, I38, 1 + I39, I40) f10(I41, I42, I43, I44, I45) -> f11(I41, I42, I43, I44, I45) [1 <= I42] f10(I46, I47, I48, I49, I50) -> f11(I46, I47, I48, I49, I50) [1 + I47 <= 0] f8(I51, I52, I53, I54, I55) -> f10(I51, I56, I53, I54, I55) [I56 = I56 /\ 0 <= -1 - I54 + I55] f8(I57, I58, I59, I60, I61) -> f4(I57, I62, I59, I60, I61) [0 <= I62 /\ I62 <= 0 /\ I62 = I62 /\ 0 <= -1 - I60 + I61] f2(I63, I64, I65, I66, I67) -> f9(rnd1, I64, I65, I66, I67) [rnd1 = rnd1 /\ -1 * I65 + I66 <= 0] f2(I68, I69, I70, I71, I72) -> f8(I68, I69, I70, I71, I72) [0 <= -1 - I70 + I71] f3(I73, I74, I75, I76, I77) -> f2(I73, I74, 1 + I75, I76, I77) [-1 * I76 + I77 <= 0] f7(I78, I79, I80, I81, I82) -> f3(I78, I79, I80, I81, I82) f6(I83, I84, I85, I86, I87) -> f7(I83, I84, I85, 1 + I86, I87) f5(I88, I89, I90, I91, I92) -> f6(I88, I89, I90, I91, I92) [1 <= I89] f5(I93, I94, I95, I96, I97) -> f6(I93, I94, I95, I96, I97) [1 + I94 <= 0] f3(I98, I99, I100, I101, I102) -> f5(I98, I103, I100, I101, I102) [I103 = I103 /\ 0 <= -1 - I101 + I102] f3(I104, I105, I106, I107, I108) -> f4(I104, I109, I106, I107, I108) [0 <= I109 /\ I109 <= 0 /\ I109 = I109 /\ 0 <= -1 - I107 + I108] f1(I110, I111, I112, I113, I114) -> f2(I110, I111, I112, I113, I114) We use the extended value criterion with the projection function NU: NU[f5#(x0,x1,x2,x3,x4)] = 0 NU[f6#(x0,x1,x2,x3,x4)] = 0 NU[f7#(x0,x1,x2,x3,x4)] = 0 NU[f10#(x0,x1,x2,x3,x4)] = 0 NU[f11#(x0,x1,x2,x3,x4)] = 0 NU[f2#(x0,x1,x2,x3,x4)] = -x3 + x4 - 1 NU[f8#(x0,x1,x2,x3,x4)] = -x3 + x4 - 1 NU[f12#(x0,x1,x2,x3,x4)] = 0 NU[f4#(x0,x1,x2,x3,x4)] = 0 NU[f13#(x0,x1,x2,x3,x4)] = 0 NU[f3#(x0,x1,x2,x3,x4)] = 0 NU[f14#(x0,x1,x2,x3,x4)] = 0 This gives the following inequalities: ==> 0 >= 0 1 <= I6 ==> 0 >= 0 1 + I11 <= 0 ==> 0 >= 0 rnd2 = rnd2 /\ 0 <= -1 - I18 + I19 ==> 0 >= 0 ==> 0 >= 0 0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29 ==> 0 >= 0 -1 * I34 + I35 <= 0 ==> -I34 + I35 - 1 >= -I34 + I35 - 1 ==> 0 >= 0 1 <= I42 ==> 0 >= 0 1 + I47 <= 0 ==> 0 >= 0 I56 = I56 /\ 0 <= -1 - I54 + I55 ==> -I54 + I55 - 1 >= 0 0 <= I62 /\ I62 <= 0 /\ I62 = I62 /\ 0 <= -1 - I60 + I61 ==> -I60 + I61 - 1 >= 0 0 <= -1 - I70 + I71 ==> -I71 + I72 - 1 >= -I71 + I72 - 1 -1 * I76 + I77 <= 0 ==> 0 > -I76 + I77 - 1 with 0 >= 0 ==> 0 >= 0 ==> 0 >= 0 1 <= I89 ==> 0 >= 0 1 + I94 <= 0 ==> 0 >= 0 I103 = I103 /\ 0 <= -1 - I101 + I102 ==> 0 >= 0 0 <= I109 /\ I109 <= 0 /\ I109 = I109 /\ 0 <= -1 - I107 + I108 ==> 0 >= 0 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f14#(I0, I1, I2, I3, I4) -> f3#(I0, I1, I2, 1 + I3, I4) f13#(I5, I6, I7, I8, I9) -> f14#(I5, I6, I7, I8, I9) [1 <= I6] f13#(I10, I11, I12, I13, I14) -> f14#(I10, I11, I12, I13, I14) [1 + I11 <= 0] f4#(I15, I16, I17, I18, I19) -> f13#(I15, rnd2, I17, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19] f12#(I20, I21, I22, I23, I24) -> f4#(I20, I21, I22, I23, I24) f4#(I25, I26, I27, I28, I29) -> f12#(I25, I30, I27, I28, I29) [0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29] f8#(I31, I32, I33, I34, I35) -> f2#(I31, I32, 1 + I33, I34, I35) [-1 * I34 + I35 <= 0] f11#(I36, I37, I38, I39, I40) -> f3#(I36, I37, I38, 1 + I39, I40) f10#(I41, I42, I43, I44, I45) -> f11#(I41, I42, I43, I44, I45) [1 <= I42] f10#(I46, I47, I48, I49, I50) -> f11#(I46, I47, I48, I49, I50) [1 + I47 <= 0] f8#(I51, I52, I53, I54, I55) -> f10#(I51, I56, I53, I54, I55) [I56 = I56 /\ 0 <= -1 - I54 + I55] f8#(I57, I58, I59, I60, I61) -> f4#(I57, I62, I59, I60, I61) [0 <= I62 /\ I62 <= 0 /\ I62 = I62 /\ 0 <= -1 - I60 + I61] f2#(I68, I69, I70, I71, I72) -> f8#(I68, I69, I70, I71, I72) [0 <= -1 - I70 + I71] f7#(I78, I79, I80, I81, I82) -> f3#(I78, I79, I80, I81, I82) f6#(I83, I84, I85, I86, I87) -> f7#(I83, I84, I85, 1 + I86, I87) f5#(I88, I89, I90, I91, I92) -> f6#(I88, I89, I90, I91, I92) [1 <= I89] f5#(I93, I94, I95, I96, I97) -> f6#(I93, I94, I95, I96, I97) [1 + I94 <= 0] f3#(I98, I99, I100, I101, I102) -> f5#(I98, I103, I100, I101, I102) [I103 = I103 /\ 0 <= -1 - I101 + I102] f3#(I104, I105, I106, I107, I108) -> f4#(I104, I109, I106, I107, I108) [0 <= I109 /\ I109 <= 0 /\ I109 = I109 /\ 0 <= -1 - I107 + I108] R = f15(x1, x2, x3, x4, x5) -> f1(x1, x2, x3, x4, x5) f14(I0, I1, I2, I3, I4) -> f3(I0, I1, I2, 1 + I3, I4) f13(I5, I6, I7, I8, I9) -> f14(I5, I6, I7, I8, I9) [1 <= I6] f13(I10, I11, I12, I13, I14) -> f14(I10, I11, I12, I13, I14) [1 + I11 <= 0] f4(I15, I16, I17, I18, I19) -> f13(I15, rnd2, I17, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19] f12(I20, I21, I22, I23, I24) -> f4(I20, I21, I22, I23, I24) f4(I25, I26, I27, I28, I29) -> f12(I25, I30, I27, I28, I29) [0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29] f8(I31, I32, I33, I34, I35) -> f2(I31, I32, 1 + I33, I34, I35) [-1 * I34 + I35 <= 0] f11(I36, I37, I38, I39, I40) -> f3(I36, I37, I38, 1 + I39, I40) f10(I41, I42, I43, I44, I45) -> f11(I41, I42, I43, I44, I45) [1 <= I42] f10(I46, I47, I48, I49, I50) -> f11(I46, I47, I48, I49, I50) [1 + I47 <= 0] f8(I51, I52, I53, I54, I55) -> f10(I51, I56, I53, I54, I55) [I56 = I56 /\ 0 <= -1 - I54 + I55] f8(I57, I58, I59, I60, I61) -> f4(I57, I62, I59, I60, I61) [0 <= I62 /\ I62 <= 0 /\ I62 = I62 /\ 0 <= -1 - I60 + I61] f2(I63, I64, I65, I66, I67) -> f9(rnd1, I64, I65, I66, I67) [rnd1 = rnd1 /\ -1 * I65 + I66 <= 0] f2(I68, I69, I70, I71, I72) -> f8(I68, I69, I70, I71, I72) [0 <= -1 - I70 + I71] f3(I73, I74, I75, I76, I77) -> f2(I73, I74, 1 + I75, I76, I77) [-1 * I76 + I77 <= 0] f7(I78, I79, I80, I81, I82) -> f3(I78, I79, I80, I81, I82) f6(I83, I84, I85, I86, I87) -> f7(I83, I84, I85, 1 + I86, I87) f5(I88, I89, I90, I91, I92) -> f6(I88, I89, I90, I91, I92) [1 <= I89] f5(I93, I94, I95, I96, I97) -> f6(I93, I94, I95, I96, I97) [1 + I94 <= 0] f3(I98, I99, I100, I101, I102) -> f5(I98, I103, I100, I101, I102) [I103 = I103 /\ 0 <= -1 - I101 + I102] f3(I104, I105, I106, I107, I108) -> f4(I104, I109, I106, I107, I108) [0 <= I109 /\ I109 <= 0 /\ I109 = I109 /\ 0 <= -1 - I107 + I108] f1(I110, I111, I112, I113, I114) -> f2(I110, I111, I112, I113, I114) The dependency graph for this problem is: 1 -> 19, 20 2 -> 1 3 -> 1 4 -> 2, 3 5 -> 4, 6 6 -> 5 7 -> 13 8 -> 19, 20 9 -> 8 10 -> 8 11 -> 9, 10 12 -> 4, 6 13 -> 7, 11, 12 15 -> 19, 20 16 -> 15 17 -> 16 18 -> 16 19 -> 17, 18 20 -> 4, 6 Where: 1) f14#(I0, I1, I2, I3, I4) -> f3#(I0, I1, I2, 1 + I3, I4) 2) f13#(I5, I6, I7, I8, I9) -> f14#(I5, I6, I7, I8, I9) [1 <= I6] 3) f13#(I10, I11, I12, I13, I14) -> f14#(I10, I11, I12, I13, I14) [1 + I11 <= 0] 4) f4#(I15, I16, I17, I18, I19) -> f13#(I15, rnd2, I17, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19] 5) f12#(I20, I21, I22, I23, I24) -> f4#(I20, I21, I22, I23, I24) 6) f4#(I25, I26, I27, I28, I29) -> f12#(I25, I30, I27, I28, I29) [0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29] 7) f8#(I31, I32, I33, I34, I35) -> f2#(I31, I32, 1 + I33, I34, I35) [-1 * I34 + I35 <= 0] 8) f11#(I36, I37, I38, I39, I40) -> f3#(I36, I37, I38, 1 + I39, I40) 9) f10#(I41, I42, I43, I44, I45) -> f11#(I41, I42, I43, I44, I45) [1 <= I42] 10) f10#(I46, I47, I48, I49, I50) -> f11#(I46, I47, I48, I49, I50) [1 + I47 <= 0] 11) f8#(I51, I52, I53, I54, I55) -> f10#(I51, I56, I53, I54, I55) [I56 = I56 /\ 0 <= -1 - I54 + I55] 12) f8#(I57, I58, I59, I60, I61) -> f4#(I57, I62, I59, I60, I61) [0 <= I62 /\ I62 <= 0 /\ I62 = I62 /\ 0 <= -1 - I60 + I61] 13) f2#(I68, I69, I70, I71, I72) -> f8#(I68, I69, I70, I71, I72) [0 <= -1 - I70 + I71] 15) f7#(I78, I79, I80, I81, I82) -> f3#(I78, I79, I80, I81, I82) 16) f6#(I83, I84, I85, I86, I87) -> f7#(I83, I84, I85, 1 + I86, I87) 17) f5#(I88, I89, I90, I91, I92) -> f6#(I88, I89, I90, I91, I92) [1 <= I89] 18) f5#(I93, I94, I95, I96, I97) -> f6#(I93, I94, I95, I96, I97) [1 + I94 <= 0] 19) f3#(I98, I99, I100, I101, I102) -> f5#(I98, I103, I100, I101, I102) [I103 = I103 /\ 0 <= -1 - I101 + I102] 20) f3#(I104, I105, I106, I107, I108) -> f4#(I104, I109, I106, I107, I108) [0 <= I109 /\ I109 <= 0 /\ I109 = I109 /\ 0 <= -1 - I107 + I108] We have the following SCCs. { 7, 13 } { 1, 2, 3, 4, 5, 6, 15, 16, 17, 18, 19, 20 } DP problem for innermost termination. P = f14#(I0, I1, I2, I3, I4) -> f3#(I0, I1, I2, 1 + I3, I4) f13#(I5, I6, I7, I8, I9) -> f14#(I5, I6, I7, I8, I9) [1 <= I6] f13#(I10, I11, I12, I13, I14) -> f14#(I10, I11, I12, I13, I14) [1 + I11 <= 0] f4#(I15, I16, I17, I18, I19) -> f13#(I15, rnd2, I17, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19] f12#(I20, I21, I22, I23, I24) -> f4#(I20, I21, I22, I23, I24) f4#(I25, I26, I27, I28, I29) -> f12#(I25, I30, I27, I28, I29) [0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29] f7#(I78, I79, I80, I81, I82) -> f3#(I78, I79, I80, I81, I82) f6#(I83, I84, I85, I86, I87) -> f7#(I83, I84, I85, 1 + I86, I87) f5#(I88, I89, I90, I91, I92) -> f6#(I88, I89, I90, I91, I92) [1 <= I89] f5#(I93, I94, I95, I96, I97) -> f6#(I93, I94, I95, I96, I97) [1 + I94 <= 0] f3#(I98, I99, I100, I101, I102) -> f5#(I98, I103, I100, I101, I102) [I103 = I103 /\ 0 <= -1 - I101 + I102] f3#(I104, I105, I106, I107, I108) -> f4#(I104, I109, I106, I107, I108) [0 <= I109 /\ I109 <= 0 /\ I109 = I109 /\ 0 <= -1 - I107 + I108] R = f15(x1, x2, x3, x4, x5) -> f1(x1, x2, x3, x4, x5) f14(I0, I1, I2, I3, I4) -> f3(I0, I1, I2, 1 + I3, I4) f13(I5, I6, I7, I8, I9) -> f14(I5, I6, I7, I8, I9) [1 <= I6] f13(I10, I11, I12, I13, I14) -> f14(I10, I11, I12, I13, I14) [1 + I11 <= 0] f4(I15, I16, I17, I18, I19) -> f13(I15, rnd2, I17, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19] f12(I20, I21, I22, I23, I24) -> f4(I20, I21, I22, I23, I24) f4(I25, I26, I27, I28, I29) -> f12(I25, I30, I27, I28, I29) [0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29] f8(I31, I32, I33, I34, I35) -> f2(I31, I32, 1 + I33, I34, I35) [-1 * I34 + I35 <= 0] f11(I36, I37, I38, I39, I40) -> f3(I36, I37, I38, 1 + I39, I40) f10(I41, I42, I43, I44, I45) -> f11(I41, I42, I43, I44, I45) [1 <= I42] f10(I46, I47, I48, I49, I50) -> f11(I46, I47, I48, I49, I50) [1 + I47 <= 0] f8(I51, I52, I53, I54, I55) -> f10(I51, I56, I53, I54, I55) [I56 = I56 /\ 0 <= -1 - I54 + I55] f8(I57, I58, I59, I60, I61) -> f4(I57, I62, I59, I60, I61) [0 <= I62 /\ I62 <= 0 /\ I62 = I62 /\ 0 <= -1 - I60 + I61] f2(I63, I64, I65, I66, I67) -> f9(rnd1, I64, I65, I66, I67) [rnd1 = rnd1 /\ -1 * I65 + I66 <= 0] f2(I68, I69, I70, I71, I72) -> f8(I68, I69, I70, I71, I72) [0 <= -1 - I70 + I71] f3(I73, I74, I75, I76, I77) -> f2(I73, I74, 1 + I75, I76, I77) [-1 * I76 + I77 <= 0] f7(I78, I79, I80, I81, I82) -> f3(I78, I79, I80, I81, I82) f6(I83, I84, I85, I86, I87) -> f7(I83, I84, I85, 1 + I86, I87) f5(I88, I89, I90, I91, I92) -> f6(I88, I89, I90, I91, I92) [1 <= I89] f5(I93, I94, I95, I96, I97) -> f6(I93, I94, I95, I96, I97) [1 + I94 <= 0] f3(I98, I99, I100, I101, I102) -> f5(I98, I103, I100, I101, I102) [I103 = I103 /\ 0 <= -1 - I101 + I102] f3(I104, I105, I106, I107, I108) -> f4(I104, I109, I106, I107, I108) [0 <= I109 /\ I109 <= 0 /\ I109 = I109 /\ 0 <= -1 - I107 + I108] f1(I110, I111, I112, I113, I114) -> f2(I110, I111, I112, I113, I114) We use the extended value criterion with the projection function NU: NU[f5#(x0,x1,x2,x3,x4)] = -x3 + x4 - 2 NU[f6#(x0,x1,x2,x3,x4)] = -x3 + x4 - 2 NU[f7#(x0,x1,x2,x3,x4)] = -x3 + x4 - 1 NU[f12#(x0,x1,x2,x3,x4)] = -x3 + x4 - 2 NU[f4#(x0,x1,x2,x3,x4)] = -x3 + x4 - 2 NU[f13#(x0,x1,x2,x3,x4)] = -x3 + x4 - 2 NU[f3#(x0,x1,x2,x3,x4)] = -x3 + x4 - 1 NU[f14#(x0,x1,x2,x3,x4)] = -x3 + x4 - 2 This gives the following inequalities: ==> -I3 + I4 - 2 >= -(1 + I3) + I4 - 1 1 <= I6 ==> -I8 + I9 - 2 >= -I8 + I9 - 2 1 + I11 <= 0 ==> -I13 + I14 - 2 >= -I13 + I14 - 2 rnd2 = rnd2 /\ 0 <= -1 - I18 + I19 ==> -I18 + I19 - 2 >= -I18 + I19 - 2 ==> -I23 + I24 - 2 >= -I23 + I24 - 2 0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29 ==> -I28 + I29 - 2 >= -I28 + I29 - 2 ==> -I81 + I82 - 1 >= -I81 + I82 - 1 ==> -I86 + I87 - 2 >= -(1 + I86) + I87 - 1 1 <= I89 ==> -I91 + I92 - 2 >= -I91 + I92 - 2 1 + I94 <= 0 ==> -I96 + I97 - 2 >= -I96 + I97 - 2 I103 = I103 /\ 0 <= -1 - I101 + I102 ==> -I101 + I102 - 1 > -I101 + I102 - 2 with -I101 + I102 - 1 >= 0 0 <= I109 /\ I109 <= 0 /\ I109 = I109 /\ 0 <= -1 - I107 + I108 ==> -I107 + I108 - 1 >= -I107 + I108 - 2 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f14#(I0, I1, I2, I3, I4) -> f3#(I0, I1, I2, 1 + I3, I4) f13#(I5, I6, I7, I8, I9) -> f14#(I5, I6, I7, I8, I9) [1 <= I6] f13#(I10, I11, I12, I13, I14) -> f14#(I10, I11, I12, I13, I14) [1 + I11 <= 0] f4#(I15, I16, I17, I18, I19) -> f13#(I15, rnd2, I17, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19] f12#(I20, I21, I22, I23, I24) -> f4#(I20, I21, I22, I23, I24) f4#(I25, I26, I27, I28, I29) -> f12#(I25, I30, I27, I28, I29) [0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29] f7#(I78, I79, I80, I81, I82) -> f3#(I78, I79, I80, I81, I82) f6#(I83, I84, I85, I86, I87) -> f7#(I83, I84, I85, 1 + I86, I87) f5#(I88, I89, I90, I91, I92) -> f6#(I88, I89, I90, I91, I92) [1 <= I89] f5#(I93, I94, I95, I96, I97) -> f6#(I93, I94, I95, I96, I97) [1 + I94 <= 0] f3#(I104, I105, I106, I107, I108) -> f4#(I104, I109, I106, I107, I108) [0 <= I109 /\ I109 <= 0 /\ I109 = I109 /\ 0 <= -1 - I107 + I108] R = f15(x1, x2, x3, x4, x5) -> f1(x1, x2, x3, x4, x5) f14(I0, I1, I2, I3, I4) -> f3(I0, I1, I2, 1 + I3, I4) f13(I5, I6, I7, I8, I9) -> f14(I5, I6, I7, I8, I9) [1 <= I6] f13(I10, I11, I12, I13, I14) -> f14(I10, I11, I12, I13, I14) [1 + I11 <= 0] f4(I15, I16, I17, I18, I19) -> f13(I15, rnd2, I17, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19] f12(I20, I21, I22, I23, I24) -> f4(I20, I21, I22, I23, I24) f4(I25, I26, I27, I28, I29) -> f12(I25, I30, I27, I28, I29) [0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29] f8(I31, I32, I33, I34, I35) -> f2(I31, I32, 1 + I33, I34, I35) [-1 * I34 + I35 <= 0] f11(I36, I37, I38, I39, I40) -> f3(I36, I37, I38, 1 + I39, I40) f10(I41, I42, I43, I44, I45) -> f11(I41, I42, I43, I44, I45) [1 <= I42] f10(I46, I47, I48, I49, I50) -> f11(I46, I47, I48, I49, I50) [1 + I47 <= 0] f8(I51, I52, I53, I54, I55) -> f10(I51, I56, I53, I54, I55) [I56 = I56 /\ 0 <= -1 - I54 + I55] f8(I57, I58, I59, I60, I61) -> f4(I57, I62, I59, I60, I61) [0 <= I62 /\ I62 <= 0 /\ I62 = I62 /\ 0 <= -1 - I60 + I61] f2(I63, I64, I65, I66, I67) -> f9(rnd1, I64, I65, I66, I67) [rnd1 = rnd1 /\ -1 * I65 + I66 <= 0] f2(I68, I69, I70, I71, I72) -> f8(I68, I69, I70, I71, I72) [0 <= -1 - I70 + I71] f3(I73, I74, I75, I76, I77) -> f2(I73, I74, 1 + I75, I76, I77) [-1 * I76 + I77 <= 0] f7(I78, I79, I80, I81, I82) -> f3(I78, I79, I80, I81, I82) f6(I83, I84, I85, I86, I87) -> f7(I83, I84, I85, 1 + I86, I87) f5(I88, I89, I90, I91, I92) -> f6(I88, I89, I90, I91, I92) [1 <= I89] f5(I93, I94, I95, I96, I97) -> f6(I93, I94, I95, I96, I97) [1 + I94 <= 0] f3(I98, I99, I100, I101, I102) -> f5(I98, I103, I100, I101, I102) [I103 = I103 /\ 0 <= -1 - I101 + I102] f3(I104, I105, I106, I107, I108) -> f4(I104, I109, I106, I107, I108) [0 <= I109 /\ I109 <= 0 /\ I109 = I109 /\ 0 <= -1 - I107 + I108] f1(I110, I111, I112, I113, I114) -> f2(I110, I111, I112, I113, I114) The dependency graph for this problem is: 1 -> 20 2 -> 1 3 -> 1 4 -> 2, 3 5 -> 4, 6 6 -> 5 15 -> 20 16 -> 15 17 -> 16 18 -> 16 20 -> 4, 6 Where: 1) f14#(I0, I1, I2, I3, I4) -> f3#(I0, I1, I2, 1 + I3, I4) 2) f13#(I5, I6, I7, I8, I9) -> f14#(I5, I6, I7, I8, I9) [1 <= I6] 3) f13#(I10, I11, I12, I13, I14) -> f14#(I10, I11, I12, I13, I14) [1 + I11 <= 0] 4) f4#(I15, I16, I17, I18, I19) -> f13#(I15, rnd2, I17, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19] 5) f12#(I20, I21, I22, I23, I24) -> f4#(I20, I21, I22, I23, I24) 6) f4#(I25, I26, I27, I28, I29) -> f12#(I25, I30, I27, I28, I29) [0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29] 15) f7#(I78, I79, I80, I81, I82) -> f3#(I78, I79, I80, I81, I82) 16) f6#(I83, I84, I85, I86, I87) -> f7#(I83, I84, I85, 1 + I86, I87) 17) f5#(I88, I89, I90, I91, I92) -> f6#(I88, I89, I90, I91, I92) [1 <= I89] 18) f5#(I93, I94, I95, I96, I97) -> f6#(I93, I94, I95, I96, I97) [1 + I94 <= 0] 20) f3#(I104, I105, I106, I107, I108) -> f4#(I104, I109, I106, I107, I108) [0 <= I109 /\ I109 <= 0 /\ I109 = I109 /\ 0 <= -1 - I107 + I108] We have the following SCCs. { 1, 2, 3, 4, 5, 6, 20 } DP problem for innermost termination. P = f14#(I0, I1, I2, I3, I4) -> f3#(I0, I1, I2, 1 + I3, I4) f13#(I5, I6, I7, I8, I9) -> f14#(I5, I6, I7, I8, I9) [1 <= I6] f13#(I10, I11, I12, I13, I14) -> f14#(I10, I11, I12, I13, I14) [1 + I11 <= 0] f4#(I15, I16, I17, I18, I19) -> f13#(I15, rnd2, I17, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19] f12#(I20, I21, I22, I23, I24) -> f4#(I20, I21, I22, I23, I24) f4#(I25, I26, I27, I28, I29) -> f12#(I25, I30, I27, I28, I29) [0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29] f3#(I104, I105, I106, I107, I108) -> f4#(I104, I109, I106, I107, I108) [0 <= I109 /\ I109 <= 0 /\ I109 = I109 /\ 0 <= -1 - I107 + I108] R = f15(x1, x2, x3, x4, x5) -> f1(x1, x2, x3, x4, x5) f14(I0, I1, I2, I3, I4) -> f3(I0, I1, I2, 1 + I3, I4) f13(I5, I6, I7, I8, I9) -> f14(I5, I6, I7, I8, I9) [1 <= I6] f13(I10, I11, I12, I13, I14) -> f14(I10, I11, I12, I13, I14) [1 + I11 <= 0] f4(I15, I16, I17, I18, I19) -> f13(I15, rnd2, I17, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19] f12(I20, I21, I22, I23, I24) -> f4(I20, I21, I22, I23, I24) f4(I25, I26, I27, I28, I29) -> f12(I25, I30, I27, I28, I29) [0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29] f8(I31, I32, I33, I34, I35) -> f2(I31, I32, 1 + I33, I34, I35) [-1 * I34 + I35 <= 0] f11(I36, I37, I38, I39, I40) -> f3(I36, I37, I38, 1 + I39, I40) f10(I41, I42, I43, I44, I45) -> f11(I41, I42, I43, I44, I45) [1 <= I42] f10(I46, I47, I48, I49, I50) -> f11(I46, I47, I48, I49, I50) [1 + I47 <= 0] f8(I51, I52, I53, I54, I55) -> f10(I51, I56, I53, I54, I55) [I56 = I56 /\ 0 <= -1 - I54 + I55] f8(I57, I58, I59, I60, I61) -> f4(I57, I62, I59, I60, I61) [0 <= I62 /\ I62 <= 0 /\ I62 = I62 /\ 0 <= -1 - I60 + I61] f2(I63, I64, I65, I66, I67) -> f9(rnd1, I64, I65, I66, I67) [rnd1 = rnd1 /\ -1 * I65 + I66 <= 0] f2(I68, I69, I70, I71, I72) -> f8(I68, I69, I70, I71, I72) [0 <= -1 - I70 + I71] f3(I73, I74, I75, I76, I77) -> f2(I73, I74, 1 + I75, I76, I77) [-1 * I76 + I77 <= 0] f7(I78, I79, I80, I81, I82) -> f3(I78, I79, I80, I81, I82) f6(I83, I84, I85, I86, I87) -> f7(I83, I84, I85, 1 + I86, I87) f5(I88, I89, I90, I91, I92) -> f6(I88, I89, I90, I91, I92) [1 <= I89] f5(I93, I94, I95, I96, I97) -> f6(I93, I94, I95, I96, I97) [1 + I94 <= 0] f3(I98, I99, I100, I101, I102) -> f5(I98, I103, I100, I101, I102) [I103 = I103 /\ 0 <= -1 - I101 + I102] f3(I104, I105, I106, I107, I108) -> f4(I104, I109, I106, I107, I108) [0 <= I109 /\ I109 <= 0 /\ I109 = I109 /\ 0 <= -1 - I107 + I108] f1(I110, I111, I112, I113, I114) -> f2(I110, I111, I112, I113, I114) We use the extended value criterion with the projection function NU: NU[f12#(x0,x1,x2,x3,x4)] = -x3 + x4 - 1 NU[f4#(x0,x1,x2,x3,x4)] = -x3 + x4 - 1 NU[f13#(x0,x1,x2,x3,x4)] = -x3 + x4 - 1 NU[f3#(x0,x1,x2,x3,x4)] = -x3 + x4 NU[f14#(x0,x1,x2,x3,x4)] = -x3 + x4 - 1 This gives the following inequalities: ==> -I3 + I4 - 1 >= -(1 + I3) + I4 1 <= I6 ==> -I8 + I9 - 1 >= -I8 + I9 - 1 1 + I11 <= 0 ==> -I13 + I14 - 1 >= -I13 + I14 - 1 rnd2 = rnd2 /\ 0 <= -1 - I18 + I19 ==> -I18 + I19 - 1 >= -I18 + I19 - 1 ==> -I23 + I24 - 1 >= -I23 + I24 - 1 0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29 ==> -I28 + I29 - 1 >= -I28 + I29 - 1 0 <= I109 /\ I109 <= 0 /\ I109 = I109 /\ 0 <= -1 - I107 + I108 ==> -I107 + I108 > -I107 + I108 - 1 with -I107 + I108 >= 0 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f14#(I0, I1, I2, I3, I4) -> f3#(I0, I1, I2, 1 + I3, I4) f13#(I5, I6, I7, I8, I9) -> f14#(I5, I6, I7, I8, I9) [1 <= I6] f13#(I10, I11, I12, I13, I14) -> f14#(I10, I11, I12, I13, I14) [1 + I11 <= 0] f4#(I15, I16, I17, I18, I19) -> f13#(I15, rnd2, I17, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19] f12#(I20, I21, I22, I23, I24) -> f4#(I20, I21, I22, I23, I24) f4#(I25, I26, I27, I28, I29) -> f12#(I25, I30, I27, I28, I29) [0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29] R = f15(x1, x2, x3, x4, x5) -> f1(x1, x2, x3, x4, x5) f14(I0, I1, I2, I3, I4) -> f3(I0, I1, I2, 1 + I3, I4) f13(I5, I6, I7, I8, I9) -> f14(I5, I6, I7, I8, I9) [1 <= I6] f13(I10, I11, I12, I13, I14) -> f14(I10, I11, I12, I13, I14) [1 + I11 <= 0] f4(I15, I16, I17, I18, I19) -> f13(I15, rnd2, I17, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19] f12(I20, I21, I22, I23, I24) -> f4(I20, I21, I22, I23, I24) f4(I25, I26, I27, I28, I29) -> f12(I25, I30, I27, I28, I29) [0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29] f8(I31, I32, I33, I34, I35) -> f2(I31, I32, 1 + I33, I34, I35) [-1 * I34 + I35 <= 0] f11(I36, I37, I38, I39, I40) -> f3(I36, I37, I38, 1 + I39, I40) f10(I41, I42, I43, I44, I45) -> f11(I41, I42, I43, I44, I45) [1 <= I42] f10(I46, I47, I48, I49, I50) -> f11(I46, I47, I48, I49, I50) [1 + I47 <= 0] f8(I51, I52, I53, I54, I55) -> f10(I51, I56, I53, I54, I55) [I56 = I56 /\ 0 <= -1 - I54 + I55] f8(I57, I58, I59, I60, I61) -> f4(I57, I62, I59, I60, I61) [0 <= I62 /\ I62 <= 0 /\ I62 = I62 /\ 0 <= -1 - I60 + I61] f2(I63, I64, I65, I66, I67) -> f9(rnd1, I64, I65, I66, I67) [rnd1 = rnd1 /\ -1 * I65 + I66 <= 0] f2(I68, I69, I70, I71, I72) -> f8(I68, I69, I70, I71, I72) [0 <= -1 - I70 + I71] f3(I73, I74, I75, I76, I77) -> f2(I73, I74, 1 + I75, I76, I77) [-1 * I76 + I77 <= 0] f7(I78, I79, I80, I81, I82) -> f3(I78, I79, I80, I81, I82) f6(I83, I84, I85, I86, I87) -> f7(I83, I84, I85, 1 + I86, I87) f5(I88, I89, I90, I91, I92) -> f6(I88, I89, I90, I91, I92) [1 <= I89] f5(I93, I94, I95, I96, I97) -> f6(I93, I94, I95, I96, I97) [1 + I94 <= 0] f3(I98, I99, I100, I101, I102) -> f5(I98, I103, I100, I101, I102) [I103 = I103 /\ 0 <= -1 - I101 + I102] f3(I104, I105, I106, I107, I108) -> f4(I104, I109, I106, I107, I108) [0 <= I109 /\ I109 <= 0 /\ I109 = I109 /\ 0 <= -1 - I107 + I108] f1(I110, I111, I112, I113, I114) -> f2(I110, I111, I112, I113, I114) The dependency graph for this problem is: 1 -> 2 -> 1 3 -> 1 4 -> 2, 3 5 -> 4, 6 6 -> 5 Where: 1) f14#(I0, I1, I2, I3, I4) -> f3#(I0, I1, I2, 1 + I3, I4) 2) f13#(I5, I6, I7, I8, I9) -> f14#(I5, I6, I7, I8, I9) [1 <= I6] 3) f13#(I10, I11, I12, I13, I14) -> f14#(I10, I11, I12, I13, I14) [1 + I11 <= 0] 4) f4#(I15, I16, I17, I18, I19) -> f13#(I15, rnd2, I17, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19] 5) f12#(I20, I21, I22, I23, I24) -> f4#(I20, I21, I22, I23, I24) 6) f4#(I25, I26, I27, I28, I29) -> f12#(I25, I30, I27, I28, I29) [0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29] We have the following SCCs. { 5, 6 } DP problem for innermost termination. P = f12#(I20, I21, I22, I23, I24) -> f4#(I20, I21, I22, I23, I24) f4#(I25, I26, I27, I28, I29) -> f12#(I25, I30, I27, I28, I29) [0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29] R = f15(x1, x2, x3, x4, x5) -> f1(x1, x2, x3, x4, x5) f14(I0, I1, I2, I3, I4) -> f3(I0, I1, I2, 1 + I3, I4) f13(I5, I6, I7, I8, I9) -> f14(I5, I6, I7, I8, I9) [1 <= I6] f13(I10, I11, I12, I13, I14) -> f14(I10, I11, I12, I13, I14) [1 + I11 <= 0] f4(I15, I16, I17, I18, I19) -> f13(I15, rnd2, I17, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19] f12(I20, I21, I22, I23, I24) -> f4(I20, I21, I22, I23, I24) f4(I25, I26, I27, I28, I29) -> f12(I25, I30, I27, I28, I29) [0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29] f8(I31, I32, I33, I34, I35) -> f2(I31, I32, 1 + I33, I34, I35) [-1 * I34 + I35 <= 0] f11(I36, I37, I38, I39, I40) -> f3(I36, I37, I38, 1 + I39, I40) f10(I41, I42, I43, I44, I45) -> f11(I41, I42, I43, I44, I45) [1 <= I42] f10(I46, I47, I48, I49, I50) -> f11(I46, I47, I48, I49, I50) [1 + I47 <= 0] f8(I51, I52, I53, I54, I55) -> f10(I51, I56, I53, I54, I55) [I56 = I56 /\ 0 <= -1 - I54 + I55] f8(I57, I58, I59, I60, I61) -> f4(I57, I62, I59, I60, I61) [0 <= I62 /\ I62 <= 0 /\ I62 = I62 /\ 0 <= -1 - I60 + I61] f2(I63, I64, I65, I66, I67) -> f9(rnd1, I64, I65, I66, I67) [rnd1 = rnd1 /\ -1 * I65 + I66 <= 0] f2(I68, I69, I70, I71, I72) -> f8(I68, I69, I70, I71, I72) [0 <= -1 - I70 + I71] f3(I73, I74, I75, I76, I77) -> f2(I73, I74, 1 + I75, I76, I77) [-1 * I76 + I77 <= 0] f7(I78, I79, I80, I81, I82) -> f3(I78, I79, I80, I81, I82) f6(I83, I84, I85, I86, I87) -> f7(I83, I84, I85, 1 + I86, I87) f5(I88, I89, I90, I91, I92) -> f6(I88, I89, I90, I91, I92) [1 <= I89] f5(I93, I94, I95, I96, I97) -> f6(I93, I94, I95, I96, I97) [1 + I94 <= 0] f3(I98, I99, I100, I101, I102) -> f5(I98, I103, I100, I101, I102) [I103 = I103 /\ 0 <= -1 - I101 + I102] f3(I104, I105, I106, I107, I108) -> f4(I104, I109, I106, I107, I108) [0 <= I109 /\ I109 <= 0 /\ I109 = I109 /\ 0 <= -1 - I107 + I108] f1(I110, I111, I112, I113, I114) -> f2(I110, I111, I112, I113, I114)