/export/starexec/sandbox2/solver/bin/starexec_run_Transition /export/starexec/sandbox2/benchmark/theBenchmark.smt2 /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- MAYBE DP problem for innermost termination. P = init#(x1, x2, x3, x4, x5, x6) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6) f5#(I0, I1, I2, I3, I4, I5) -> f5#(I6, I7, I2 - 1, I3 + 1, I8, I9) [0 <= I2 - 1 /\ 0 <= y1 - 1 /\ -1 <= I3 - 1 /\ I6 - 2 <= I0 /\ I6 - 2 <= I1 /\ I7 - 2 <= I0 /\ I7 - 2 <= I1 /\ 2 <= I0 - 1 /\ 2 <= I1 - 1 /\ 4 <= I6 - 1 /\ 4 <= I7 - 1] f5#(I10, I11, I12, I13, I14, I15) -> f5#(I16, I17, I12 - 1, I13 + 1, I18, I19) [4 <= I17 - 1 /\ 4 <= I16 - 1 /\ 2 <= I11 - 1 /\ 2 <= I10 - 1 /\ I17 - 2 <= I11 /\ I17 - 2 <= I10 /\ I16 - 2 <= I11 /\ I16 - 2 <= I10 /\ 0 <= I12 - 1 /\ -1 <= I13 - 1] f5#(I20, I21, I22, I23, I24, I25) -> f5#(I26, I27, I22 - 1, I23 + 1, I28, I29) [2 <= I27 - 1 /\ 2 <= I26 - 1 /\ 1 <= I21 - 1 /\ 2 <= I20 - 1 /\ 0 <= I22 - 1 /\ -1 <= I23 - 1] f5#(I30, I31, I32, I33, I34, I35) -> f5#(I36, I37, I32 - 1, I33 + 1, I38, I39) [0 <= I32 - 1 /\ 0 <= I40 - 1 /\ -1 <= I33 - 1 /\ 2 <= I30 - 1 /\ 1 <= I31 - 1 /\ 2 <= I36 - 1 /\ 2 <= I37 - 1] f5#(I41, I42, I43, I44, I45, I46) -> f5#(I47, I48, I43 - 1, I44 + 1, I49, I50) [0 <= I43 - 1 /\ 0 <= I51 - 1 /\ -1 <= I44 - 1 /\ I47 <= I41 /\ I48 + 2 <= I42 /\ 2 <= I41 - 1 /\ 2 <= I42 - 1 /\ 2 <= I47 - 1 /\ 0 <= I48 - 1] f5#(I52, I53, I54, I55, I56, I57) -> f5#(I58, I59, I54 - 1, I55 + 1, I60, I61) [0 <= I59 - 1 /\ 2 <= I58 - 1 /\ 2 <= I53 - 1 /\ 2 <= I52 - 1 /\ I59 + 2 <= I53 /\ I58 <= I52 /\ 0 <= I54 - 1 /\ -1 <= I55 - 1] f2#(I62, I63, I64, I65, I66, I67) -> f5#(I68, I69, I70, I65 + 1, I71, I72) [0 <= I70 - 1 /\ 0 <= I73 - 1 /\ 0 <= I64 - 1 /\ -1 <= I65 - 1 /\ I68 - 2 <= I62 /\ I68 - 3 <= I63 /\ I69 - 2 <= I62 /\ I69 - 3 <= I63 /\ 0 <= I62 - 1 /\ -1 <= I63 - 1 /\ 2 <= I68 - 1 /\ 2 <= I69 - 1] f4#(I74, I75, I76, I77, I78, I79) -> f2#(I80, I81, I76 - 1, I78, I82, I83) [I79 + 2 <= I77 /\ 4 <= I81 - 1 /\ 0 <= I80 - 1 /\ 2 <= I77 - 1 /\ 0 <= I74 - 1 /\ I80 + 2 <= I77 /\ I80 <= I74] f2#(I84, I85, I86, I87, I88, I89) -> f2#(I90, I91, I86 - 1, I92, I93, I94) [0 <= I86 - 1 /\ 0 <= I95 - 1 /\ I90 <= I84 /\ I90 - 1 <= I85 /\ 0 <= I84 - 1 /\ -1 <= I85 - 1 /\ 0 <= I90 - 1 /\ 4 <= I91 - 1] f3#(I96, I97, I98, I99, I100, I101) -> f3#(I102, I103, I104, I105, I106, I107) [2 <= I102 - 1 /\ 2 <= I96 - 1 /\ I102 - 2 <= I96] f3#(I108, I109, I110, I111, I112, I113) -> f3#(I114, I115, I116, I117, I118, I119) [-1 <= I114 - 1 /\ 1 <= I108 - 1 /\ I114 + 2 <= I108] f2#(I120, I121, I122, I123, I124, I125) -> f3#(I126, I127, I128, I129, I130, I131) [0 = I122 /\ -1 <= I126 - 1 /\ -1 <= I121 - 1 /\ 0 <= I120 - 1 /\ I126 <= I121] f2#(I132, I133, I134, I135, I136, I137) -> f2#(I138, I139, I134 - 1, I140, I141, I142) [0 <= I134 - 1 /\ 0 <= I143 - 1 /\ I138 <= I132 /\ I138 - 1 <= I133 /\ I139 - 2 <= I133 /\ 0 <= I132 - 1 /\ -1 <= I133 - 1 /\ 0 <= I138 - 1 /\ 1 <= I139 - 1] f1#(I144, I145, I146, I147, I148, I149) -> f2#(I150, I151, I152, 1, I153, I154) [-1 <= I151 - 1 /\ 0 <= I150 - 1 /\ 0 <= I144 - 1 /\ I151 + 1 <= I144 /\ I150 <= I144 /\ -1 <= I152 - 1 /\ -1 <= I145 - 1] R = init(x1, x2, x3, x4, x5, x6) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6) f5(I0, I1, I2, I3, I4, I5) -> f5(I6, I7, I2 - 1, I3 + 1, I8, I9) [0 <= I2 - 1 /\ 0 <= y1 - 1 /\ -1 <= I3 - 1 /\ I6 - 2 <= I0 /\ I6 - 2 <= I1 /\ I7 - 2 <= I0 /\ I7 - 2 <= I1 /\ 2 <= I0 - 1 /\ 2 <= I1 - 1 /\ 4 <= I6 - 1 /\ 4 <= I7 - 1] f5(I10, I11, I12, I13, I14, I15) -> f5(I16, I17, I12 - 1, I13 + 1, I18, I19) [4 <= I17 - 1 /\ 4 <= I16 - 1 /\ 2 <= I11 - 1 /\ 2 <= I10 - 1 /\ I17 - 2 <= I11 /\ I17 - 2 <= I10 /\ I16 - 2 <= I11 /\ I16 - 2 <= I10 /\ 0 <= I12 - 1 /\ -1 <= I13 - 1] f5(I20, I21, I22, I23, I24, I25) -> f5(I26, I27, I22 - 1, I23 + 1, I28, I29) [2 <= I27 - 1 /\ 2 <= I26 - 1 /\ 1 <= I21 - 1 /\ 2 <= I20 - 1 /\ 0 <= I22 - 1 /\ -1 <= I23 - 1] f5(I30, I31, I32, I33, I34, I35) -> f5(I36, I37, I32 - 1, I33 + 1, I38, I39) [0 <= I32 - 1 /\ 0 <= I40 - 1 /\ -1 <= I33 - 1 /\ 2 <= I30 - 1 /\ 1 <= I31 - 1 /\ 2 <= I36 - 1 /\ 2 <= I37 - 1] f5(I41, I42, I43, I44, I45, I46) -> f5(I47, I48, I43 - 1, I44 + 1, I49, I50) [0 <= I43 - 1 /\ 0 <= I51 - 1 /\ -1 <= I44 - 1 /\ I47 <= I41 /\ I48 + 2 <= I42 /\ 2 <= I41 - 1 /\ 2 <= I42 - 1 /\ 2 <= I47 - 1 /\ 0 <= I48 - 1] f5(I52, I53, I54, I55, I56, I57) -> f5(I58, I59, I54 - 1, I55 + 1, I60, I61) [0 <= I59 - 1 /\ 2 <= I58 - 1 /\ 2 <= I53 - 1 /\ 2 <= I52 - 1 /\ I59 + 2 <= I53 /\ I58 <= I52 /\ 0 <= I54 - 1 /\ -1 <= I55 - 1] f2(I62, I63, I64, I65, I66, I67) -> f5(I68, I69, I70, I65 + 1, I71, I72) [0 <= I70 - 1 /\ 0 <= I73 - 1 /\ 0 <= I64 - 1 /\ -1 <= I65 - 1 /\ I68 - 2 <= I62 /\ I68 - 3 <= I63 /\ I69 - 2 <= I62 /\ I69 - 3 <= I63 /\ 0 <= I62 - 1 /\ -1 <= I63 - 1 /\ 2 <= I68 - 1 /\ 2 <= I69 - 1] f4(I74, I75, I76, I77, I78, I79) -> f2(I80, I81, I76 - 1, I78, I82, I83) [I79 + 2 <= I77 /\ 4 <= I81 - 1 /\ 0 <= I80 - 1 /\ 2 <= I77 - 1 /\ 0 <= I74 - 1 /\ I80 + 2 <= I77 /\ I80 <= I74] f2(I84, I85, I86, I87, I88, I89) -> f2(I90, I91, I86 - 1, I92, I93, I94) [0 <= I86 - 1 /\ 0 <= I95 - 1 /\ I90 <= I84 /\ I90 - 1 <= I85 /\ 0 <= I84 - 1 /\ -1 <= I85 - 1 /\ 0 <= I90 - 1 /\ 4 <= I91 - 1] f3(I96, I97, I98, I99, I100, I101) -> f3(I102, I103, I104, I105, I106, I107) [2 <= I102 - 1 /\ 2 <= I96 - 1 /\ I102 - 2 <= I96] f3(I108, I109, I110, I111, I112, I113) -> f3(I114, I115, I116, I117, I118, I119) [-1 <= I114 - 1 /\ 1 <= I108 - 1 /\ I114 + 2 <= I108] f2(I120, I121, I122, I123, I124, I125) -> f3(I126, I127, I128, I129, I130, I131) [0 = I122 /\ -1 <= I126 - 1 /\ -1 <= I121 - 1 /\ 0 <= I120 - 1 /\ I126 <= I121] f2(I132, I133, I134, I135, I136, I137) -> f2(I138, I139, I134 - 1, I140, I141, I142) [0 <= I134 - 1 /\ 0 <= I143 - 1 /\ I138 <= I132 /\ I138 - 1 <= I133 /\ I139 - 2 <= I133 /\ 0 <= I132 - 1 /\ -1 <= I133 - 1 /\ 0 <= I138 - 1 /\ 1 <= I139 - 1] f1(I144, I145, I146, I147, I148, I149) -> f2(I150, I151, I152, 1, I153, I154) [-1 <= I151 - 1 /\ 0 <= I150 - 1 /\ 0 <= I144 - 1 /\ I151 + 1 <= I144 /\ I150 <= I144 /\ -1 <= I152 - 1 /\ -1 <= I145 - 1] The dependency graph for this problem is: 0 -> 14 1 -> 1, 2, 3, 4, 5, 6 2 -> 1, 2, 3, 4, 5, 6 3 -> 1, 2, 3, 4, 5, 6 4 -> 1, 2, 3, 4, 5, 6 5 -> 1, 2, 3, 4, 5, 6 6 -> 1, 2, 3, 4, 5, 6 7 -> 1, 2, 3, 4, 5, 6 8 -> 7, 9, 12, 13 9 -> 7, 9, 12, 13 10 -> 10, 11 11 -> 10, 11 12 -> 10, 11 13 -> 7, 9, 12, 13 14 -> 7, 9, 12, 13 Where: 0) init#(x1, x2, x3, x4, x5, x6) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6) 1) f5#(I0, I1, I2, I3, I4, I5) -> f5#(I6, I7, I2 - 1, I3 + 1, I8, I9) [0 <= I2 - 1 /\ 0 <= y1 - 1 /\ -1 <= I3 - 1 /\ I6 - 2 <= I0 /\ I6 - 2 <= I1 /\ I7 - 2 <= I0 /\ I7 - 2 <= I1 /\ 2 <= I0 - 1 /\ 2 <= I1 - 1 /\ 4 <= I6 - 1 /\ 4 <= I7 - 1] 2) f5#(I10, I11, I12, I13, I14, I15) -> f5#(I16, I17, I12 - 1, I13 + 1, I18, I19) [4 <= I17 - 1 /\ 4 <= I16 - 1 /\ 2 <= I11 - 1 /\ 2 <= I10 - 1 /\ I17 - 2 <= I11 /\ I17 - 2 <= I10 /\ I16 - 2 <= I11 /\ I16 - 2 <= I10 /\ 0 <= I12 - 1 /\ -1 <= I13 - 1] 3) f5#(I20, I21, I22, I23, I24, I25) -> f5#(I26, I27, I22 - 1, I23 + 1, I28, I29) [2 <= I27 - 1 /\ 2 <= I26 - 1 /\ 1 <= I21 - 1 /\ 2 <= I20 - 1 /\ 0 <= I22 - 1 /\ -1 <= I23 - 1] 4) f5#(I30, I31, I32, I33, I34, I35) -> f5#(I36, I37, I32 - 1, I33 + 1, I38, I39) [0 <= I32 - 1 /\ 0 <= I40 - 1 /\ -1 <= I33 - 1 /\ 2 <= I30 - 1 /\ 1 <= I31 - 1 /\ 2 <= I36 - 1 /\ 2 <= I37 - 1] 5) f5#(I41, I42, I43, I44, I45, I46) -> f5#(I47, I48, I43 - 1, I44 + 1, I49, I50) [0 <= I43 - 1 /\ 0 <= I51 - 1 /\ -1 <= I44 - 1 /\ I47 <= I41 /\ I48 + 2 <= I42 /\ 2 <= I41 - 1 /\ 2 <= I42 - 1 /\ 2 <= I47 - 1 /\ 0 <= I48 - 1] 6) f5#(I52, I53, I54, I55, I56, I57) -> f5#(I58, I59, I54 - 1, I55 + 1, I60, I61) [0 <= I59 - 1 /\ 2 <= I58 - 1 /\ 2 <= I53 - 1 /\ 2 <= I52 - 1 /\ I59 + 2 <= I53 /\ I58 <= I52 /\ 0 <= I54 - 1 /\ -1 <= I55 - 1] 7) f2#(I62, I63, I64, I65, I66, I67) -> f5#(I68, I69, I70, I65 + 1, I71, I72) [0 <= I70 - 1 /\ 0 <= I73 - 1 /\ 0 <= I64 - 1 /\ -1 <= I65 - 1 /\ I68 - 2 <= I62 /\ I68 - 3 <= I63 /\ I69 - 2 <= I62 /\ I69 - 3 <= I63 /\ 0 <= I62 - 1 /\ -1 <= I63 - 1 /\ 2 <= I68 - 1 /\ 2 <= I69 - 1] 8) f4#(I74, I75, I76, I77, I78, I79) -> f2#(I80, I81, I76 - 1, I78, I82, I83) [I79 + 2 <= I77 /\ 4 <= I81 - 1 /\ 0 <= I80 - 1 /\ 2 <= I77 - 1 /\ 0 <= I74 - 1 /\ I80 + 2 <= I77 /\ I80 <= I74] 9) f2#(I84, I85, I86, I87, I88, I89) -> f2#(I90, I91, I86 - 1, I92, I93, I94) [0 <= I86 - 1 /\ 0 <= I95 - 1 /\ I90 <= I84 /\ I90 - 1 <= I85 /\ 0 <= I84 - 1 /\ -1 <= I85 - 1 /\ 0 <= I90 - 1 /\ 4 <= I91 - 1] 10) f3#(I96, I97, I98, I99, I100, I101) -> f3#(I102, I103, I104, I105, I106, I107) [2 <= I102 - 1 /\ 2 <= I96 - 1 /\ I102 - 2 <= I96] 11) f3#(I108, I109, I110, I111, I112, I113) -> f3#(I114, I115, I116, I117, I118, I119) [-1 <= I114 - 1 /\ 1 <= I108 - 1 /\ I114 + 2 <= I108] 12) f2#(I120, I121, I122, I123, I124, I125) -> f3#(I126, I127, I128, I129, I130, I131) [0 = I122 /\ -1 <= I126 - 1 /\ -1 <= I121 - 1 /\ 0 <= I120 - 1 /\ I126 <= I121] 13) f2#(I132, I133, I134, I135, I136, I137) -> f2#(I138, I139, I134 - 1, I140, I141, I142) [0 <= I134 - 1 /\ 0 <= I143 - 1 /\ I138 <= I132 /\ I138 - 1 <= I133 /\ I139 - 2 <= I133 /\ 0 <= I132 - 1 /\ -1 <= I133 - 1 /\ 0 <= I138 - 1 /\ 1 <= I139 - 1] 14) f1#(I144, I145, I146, I147, I148, I149) -> f2#(I150, I151, I152, 1, I153, I154) [-1 <= I151 - 1 /\ 0 <= I150 - 1 /\ 0 <= I144 - 1 /\ I151 + 1 <= I144 /\ I150 <= I144 /\ -1 <= I152 - 1 /\ -1 <= I145 - 1] We have the following SCCs. { 9, 13 } { 10, 11 } { 1, 2, 3, 4, 5, 6 } DP problem for innermost termination. P = f5#(I0, I1, I2, I3, I4, I5) -> f5#(I6, I7, I2 - 1, I3 + 1, I8, I9) [0 <= I2 - 1 /\ 0 <= y1 - 1 /\ -1 <= I3 - 1 /\ I6 - 2 <= I0 /\ I6 - 2 <= I1 /\ I7 - 2 <= I0 /\ I7 - 2 <= I1 /\ 2 <= I0 - 1 /\ 2 <= I1 - 1 /\ 4 <= I6 - 1 /\ 4 <= I7 - 1] f5#(I10, I11, I12, I13, I14, I15) -> f5#(I16, I17, I12 - 1, I13 + 1, I18, I19) [4 <= I17 - 1 /\ 4 <= I16 - 1 /\ 2 <= I11 - 1 /\ 2 <= I10 - 1 /\ I17 - 2 <= I11 /\ I17 - 2 <= I10 /\ I16 - 2 <= I11 /\ I16 - 2 <= I10 /\ 0 <= I12 - 1 /\ -1 <= I13 - 1] f5#(I20, I21, I22, I23, I24, I25) -> f5#(I26, I27, I22 - 1, I23 + 1, I28, I29) [2 <= I27 - 1 /\ 2 <= I26 - 1 /\ 1 <= I21 - 1 /\ 2 <= I20 - 1 /\ 0 <= I22 - 1 /\ -1 <= I23 - 1] f5#(I30, I31, I32, I33, I34, I35) -> f5#(I36, I37, I32 - 1, I33 + 1, I38, I39) [0 <= I32 - 1 /\ 0 <= I40 - 1 /\ -1 <= I33 - 1 /\ 2 <= I30 - 1 /\ 1 <= I31 - 1 /\ 2 <= I36 - 1 /\ 2 <= I37 - 1] f5#(I41, I42, I43, I44, I45, I46) -> f5#(I47, I48, I43 - 1, I44 + 1, I49, I50) [0 <= I43 - 1 /\ 0 <= I51 - 1 /\ -1 <= I44 - 1 /\ I47 <= I41 /\ I48 + 2 <= I42 /\ 2 <= I41 - 1 /\ 2 <= I42 - 1 /\ 2 <= I47 - 1 /\ 0 <= I48 - 1] f5#(I52, I53, I54, I55, I56, I57) -> f5#(I58, I59, I54 - 1, I55 + 1, I60, I61) [0 <= I59 - 1 /\ 2 <= I58 - 1 /\ 2 <= I53 - 1 /\ 2 <= I52 - 1 /\ I59 + 2 <= I53 /\ I58 <= I52 /\ 0 <= I54 - 1 /\ -1 <= I55 - 1] R = init(x1, x2, x3, x4, x5, x6) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6) f5(I0, I1, I2, I3, I4, I5) -> f5(I6, I7, I2 - 1, I3 + 1, I8, I9) [0 <= I2 - 1 /\ 0 <= y1 - 1 /\ -1 <= I3 - 1 /\ I6 - 2 <= I0 /\ I6 - 2 <= I1 /\ I7 - 2 <= I0 /\ I7 - 2 <= I1 /\ 2 <= I0 - 1 /\ 2 <= I1 - 1 /\ 4 <= I6 - 1 /\ 4 <= I7 - 1] f5(I10, I11, I12, I13, I14, I15) -> f5(I16, I17, I12 - 1, I13 + 1, I18, I19) [4 <= I17 - 1 /\ 4 <= I16 - 1 /\ 2 <= I11 - 1 /\ 2 <= I10 - 1 /\ I17 - 2 <= I11 /\ I17 - 2 <= I10 /\ I16 - 2 <= I11 /\ I16 - 2 <= I10 /\ 0 <= I12 - 1 /\ -1 <= I13 - 1] f5(I20, I21, I22, I23, I24, I25) -> f5(I26, I27, I22 - 1, I23 + 1, I28, I29) [2 <= I27 - 1 /\ 2 <= I26 - 1 /\ 1 <= I21 - 1 /\ 2 <= I20 - 1 /\ 0 <= I22 - 1 /\ -1 <= I23 - 1] f5(I30, I31, I32, I33, I34, I35) -> f5(I36, I37, I32 - 1, I33 + 1, I38, I39) [0 <= I32 - 1 /\ 0 <= I40 - 1 /\ -1 <= I33 - 1 /\ 2 <= I30 - 1 /\ 1 <= I31 - 1 /\ 2 <= I36 - 1 /\ 2 <= I37 - 1] f5(I41, I42, I43, I44, I45, I46) -> f5(I47, I48, I43 - 1, I44 + 1, I49, I50) [0 <= I43 - 1 /\ 0 <= I51 - 1 /\ -1 <= I44 - 1 /\ I47 <= I41 /\ I48 + 2 <= I42 /\ 2 <= I41 - 1 /\ 2 <= I42 - 1 /\ 2 <= I47 - 1 /\ 0 <= I48 - 1] f5(I52, I53, I54, I55, I56, I57) -> f5(I58, I59, I54 - 1, I55 + 1, I60, I61) [0 <= I59 - 1 /\ 2 <= I58 - 1 /\ 2 <= I53 - 1 /\ 2 <= I52 - 1 /\ I59 + 2 <= I53 /\ I58 <= I52 /\ 0 <= I54 - 1 /\ -1 <= I55 - 1] f2(I62, I63, I64, I65, I66, I67) -> f5(I68, I69, I70, I65 + 1, I71, I72) [0 <= I70 - 1 /\ 0 <= I73 - 1 /\ 0 <= I64 - 1 /\ -1 <= I65 - 1 /\ I68 - 2 <= I62 /\ I68 - 3 <= I63 /\ I69 - 2 <= I62 /\ I69 - 3 <= I63 /\ 0 <= I62 - 1 /\ -1 <= I63 - 1 /\ 2 <= I68 - 1 /\ 2 <= I69 - 1] f4(I74, I75, I76, I77, I78, I79) -> f2(I80, I81, I76 - 1, I78, I82, I83) [I79 + 2 <= I77 /\ 4 <= I81 - 1 /\ 0 <= I80 - 1 /\ 2 <= I77 - 1 /\ 0 <= I74 - 1 /\ I80 + 2 <= I77 /\ I80 <= I74] f2(I84, I85, I86, I87, I88, I89) -> f2(I90, I91, I86 - 1, I92, I93, I94) [0 <= I86 - 1 /\ 0 <= I95 - 1 /\ I90 <= I84 /\ I90 - 1 <= I85 /\ 0 <= I84 - 1 /\ -1 <= I85 - 1 /\ 0 <= I90 - 1 /\ 4 <= I91 - 1] f3(I96, I97, I98, I99, I100, I101) -> f3(I102, I103, I104, I105, I106, I107) [2 <= I102 - 1 /\ 2 <= I96 - 1 /\ I102 - 2 <= I96] f3(I108, I109, I110, I111, I112, I113) -> f3(I114, I115, I116, I117, I118, I119) [-1 <= I114 - 1 /\ 1 <= I108 - 1 /\ I114 + 2 <= I108] f2(I120, I121, I122, I123, I124, I125) -> f3(I126, I127, I128, I129, I130, I131) [0 = I122 /\ -1 <= I126 - 1 /\ -1 <= I121 - 1 /\ 0 <= I120 - 1 /\ I126 <= I121] f2(I132, I133, I134, I135, I136, I137) -> f2(I138, I139, I134 - 1, I140, I141, I142) [0 <= I134 - 1 /\ 0 <= I143 - 1 /\ I138 <= I132 /\ I138 - 1 <= I133 /\ I139 - 2 <= I133 /\ 0 <= I132 - 1 /\ -1 <= I133 - 1 /\ 0 <= I138 - 1 /\ 1 <= I139 - 1] f1(I144, I145, I146, I147, I148, I149) -> f2(I150, I151, I152, 1, I153, I154) [-1 <= I151 - 1 /\ 0 <= I150 - 1 /\ 0 <= I144 - 1 /\ I151 + 1 <= I144 /\ I150 <= I144 /\ -1 <= I152 - 1 /\ -1 <= I145 - 1] We use the basic value criterion with the projection function NU: NU[f5#(z1,z2,z3,z4,z5,z6)] = z3 This gives the following inequalities: 0 <= I2 - 1 /\ 0 <= y1 - 1 /\ -1 <= I3 - 1 /\ I6 - 2 <= I0 /\ I6 - 2 <= I1 /\ I7 - 2 <= I0 /\ I7 - 2 <= I1 /\ 2 <= I0 - 1 /\ 2 <= I1 - 1 /\ 4 <= I6 - 1 /\ 4 <= I7 - 1 ==> I2 >! I2 - 1 4 <= I17 - 1 /\ 4 <= I16 - 1 /\ 2 <= I11 - 1 /\ 2 <= I10 - 1 /\ I17 - 2 <= I11 /\ I17 - 2 <= I10 /\ I16 - 2 <= I11 /\ I16 - 2 <= I10 /\ 0 <= I12 - 1 /\ -1 <= I13 - 1 ==> I12 >! I12 - 1 2 <= I27 - 1 /\ 2 <= I26 - 1 /\ 1 <= I21 - 1 /\ 2 <= I20 - 1 /\ 0 <= I22 - 1 /\ -1 <= I23 - 1 ==> I22 >! I22 - 1 0 <= I32 - 1 /\ 0 <= I40 - 1 /\ -1 <= I33 - 1 /\ 2 <= I30 - 1 /\ 1 <= I31 - 1 /\ 2 <= I36 - 1 /\ 2 <= I37 - 1 ==> I32 >! I32 - 1 0 <= I43 - 1 /\ 0 <= I51 - 1 /\ -1 <= I44 - 1 /\ I47 <= I41 /\ I48 + 2 <= I42 /\ 2 <= I41 - 1 /\ 2 <= I42 - 1 /\ 2 <= I47 - 1 /\ 0 <= I48 - 1 ==> I43 >! I43 - 1 0 <= I59 - 1 /\ 2 <= I58 - 1 /\ 2 <= I53 - 1 /\ 2 <= I52 - 1 /\ I59 + 2 <= I53 /\ I58 <= I52 /\ 0 <= I54 - 1 /\ -1 <= I55 - 1 ==> I54 >! I54 - 1 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. DP problem for innermost termination. P = f3#(I96, I97, I98, I99, I100, I101) -> f3#(I102, I103, I104, I105, I106, I107) [2 <= I102 - 1 /\ 2 <= I96 - 1 /\ I102 - 2 <= I96] f3#(I108, I109, I110, I111, I112, I113) -> f3#(I114, I115, I116, I117, I118, I119) [-1 <= I114 - 1 /\ 1 <= I108 - 1 /\ I114 + 2 <= I108] R = init(x1, x2, x3, x4, x5, x6) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6) f5(I0, I1, I2, I3, I4, I5) -> f5(I6, I7, I2 - 1, I3 + 1, I8, I9) [0 <= I2 - 1 /\ 0 <= y1 - 1 /\ -1 <= I3 - 1 /\ I6 - 2 <= I0 /\ I6 - 2 <= I1 /\ I7 - 2 <= I0 /\ I7 - 2 <= I1 /\ 2 <= I0 - 1 /\ 2 <= I1 - 1 /\ 4 <= I6 - 1 /\ 4 <= I7 - 1] f5(I10, I11, I12, I13, I14, I15) -> f5(I16, I17, I12 - 1, I13 + 1, I18, I19) [4 <= I17 - 1 /\ 4 <= I16 - 1 /\ 2 <= I11 - 1 /\ 2 <= I10 - 1 /\ I17 - 2 <= I11 /\ I17 - 2 <= I10 /\ I16 - 2 <= I11 /\ I16 - 2 <= I10 /\ 0 <= I12 - 1 /\ -1 <= I13 - 1] f5(I20, I21, I22, I23, I24, I25) -> f5(I26, I27, I22 - 1, I23 + 1, I28, I29) [2 <= I27 - 1 /\ 2 <= I26 - 1 /\ 1 <= I21 - 1 /\ 2 <= I20 - 1 /\ 0 <= I22 - 1 /\ -1 <= I23 - 1] f5(I30, I31, I32, I33, I34, I35) -> f5(I36, I37, I32 - 1, I33 + 1, I38, I39) [0 <= I32 - 1 /\ 0 <= I40 - 1 /\ -1 <= I33 - 1 /\ 2 <= I30 - 1 /\ 1 <= I31 - 1 /\ 2 <= I36 - 1 /\ 2 <= I37 - 1] f5(I41, I42, I43, I44, I45, I46) -> f5(I47, I48, I43 - 1, I44 + 1, I49, I50) [0 <= I43 - 1 /\ 0 <= I51 - 1 /\ -1 <= I44 - 1 /\ I47 <= I41 /\ I48 + 2 <= I42 /\ 2 <= I41 - 1 /\ 2 <= I42 - 1 /\ 2 <= I47 - 1 /\ 0 <= I48 - 1] f5(I52, I53, I54, I55, I56, I57) -> f5(I58, I59, I54 - 1, I55 + 1, I60, I61) [0 <= I59 - 1 /\ 2 <= I58 - 1 /\ 2 <= I53 - 1 /\ 2 <= I52 - 1 /\ I59 + 2 <= I53 /\ I58 <= I52 /\ 0 <= I54 - 1 /\ -1 <= I55 - 1] f2(I62, I63, I64, I65, I66, I67) -> f5(I68, I69, I70, I65 + 1, I71, I72) [0 <= I70 - 1 /\ 0 <= I73 - 1 /\ 0 <= I64 - 1 /\ -1 <= I65 - 1 /\ I68 - 2 <= I62 /\ I68 - 3 <= I63 /\ I69 - 2 <= I62 /\ I69 - 3 <= I63 /\ 0 <= I62 - 1 /\ -1 <= I63 - 1 /\ 2 <= I68 - 1 /\ 2 <= I69 - 1] f4(I74, I75, I76, I77, I78, I79) -> f2(I80, I81, I76 - 1, I78, I82, I83) [I79 + 2 <= I77 /\ 4 <= I81 - 1 /\ 0 <= I80 - 1 /\ 2 <= I77 - 1 /\ 0 <= I74 - 1 /\ I80 + 2 <= I77 /\ I80 <= I74] f2(I84, I85, I86, I87, I88, I89) -> f2(I90, I91, I86 - 1, I92, I93, I94) [0 <= I86 - 1 /\ 0 <= I95 - 1 /\ I90 <= I84 /\ I90 - 1 <= I85 /\ 0 <= I84 - 1 /\ -1 <= I85 - 1 /\ 0 <= I90 - 1 /\ 4 <= I91 - 1] f3(I96, I97, I98, I99, I100, I101) -> f3(I102, I103, I104, I105, I106, I107) [2 <= I102 - 1 /\ 2 <= I96 - 1 /\ I102 - 2 <= I96] f3(I108, I109, I110, I111, I112, I113) -> f3(I114, I115, I116, I117, I118, I119) [-1 <= I114 - 1 /\ 1 <= I108 - 1 /\ I114 + 2 <= I108] f2(I120, I121, I122, I123, I124, I125) -> f3(I126, I127, I128, I129, I130, I131) [0 = I122 /\ -1 <= I126 - 1 /\ -1 <= I121 - 1 /\ 0 <= I120 - 1 /\ I126 <= I121] f2(I132, I133, I134, I135, I136, I137) -> f2(I138, I139, I134 - 1, I140, I141, I142) [0 <= I134 - 1 /\ 0 <= I143 - 1 /\ I138 <= I132 /\ I138 - 1 <= I133 /\ I139 - 2 <= I133 /\ 0 <= I132 - 1 /\ -1 <= I133 - 1 /\ 0 <= I138 - 1 /\ 1 <= I139 - 1] f1(I144, I145, I146, I147, I148, I149) -> f2(I150, I151, I152, 1, I153, I154) [-1 <= I151 - 1 /\ 0 <= I150 - 1 /\ 0 <= I144 - 1 /\ I151 + 1 <= I144 /\ I150 <= I144 /\ -1 <= I152 - 1 /\ -1 <= I145 - 1]