/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 = init#(x1, x2, x3, x4) -> f3#(rnd1, rnd2, rnd3, rnd4) f4#(I0, I1, I2, I3) -> f4#(I4, I5, I6, I7) [I4 <= I0 /\ 0 <= y1 - 1 /\ 2 <= I0 - 1 /\ 0 <= I4 - 1] f4#(I8, I9, I10, I11) -> f4#(I12, I13, I14, I15) [I12 + 2 <= I8 /\ 0 <= I16 - 1 /\ 2 <= I8 - 1 /\ -1 <= I12 - 1] f4#(I17, I18, I19, I20) -> f4#(I21, I22, I23, I24) [I21 + 2 <= I17 /\ 0 <= I25 - 1 /\ 1 <= I17 - 1 /\ -1 <= I21 - 1] f6#(I26, I27, I28, I29) -> f6#(I26, I27, I28 - 1, I29) [0 <= I28 - 1] f6#(I30, I31, I32, I33) -> f5#(I31 + 1, I30, I33, I34) [0 = I32] f5#(I35, I36, I37, I38) -> f6#(I36, I35, I39, I37 + 1) [0 <= I37 - 1 /\ I35 <= I36 - 1 /\ -1 <= I39 - 1] f3#(I40, I41, I42, I43) -> f5#(0, I44, 1, I45) [0 <= I40 - 1 /\ -1 <= I44 - 1 /\ -1 <= I41 - 1] f2#(I46, I47, I48, I49) -> f4#(I50, I51, I52, I53) [0 <= y2 - 1 /\ 0 <= I54 - 1 /\ I50 <= I47 /\ 0 <= I46 - 1 /\ -1 <= I47 - 1 /\ -1 <= I50 - 1] f3#(I55, I56, I57, I58) -> f2#(I59, I60, I61, I62) [-1 <= I60 - 1 /\ 0 <= I59 - 1 /\ 0 <= I55 - 1 /\ I59 <= I55] f1#(I63, I64, I65, I66) -> f2#(I67, I68, I69, I70) [-1 <= I68 - 1 /\ 0 <= I67 - 1 /\ -1 <= I64 - 1 /\ 0 <= I63 - 1 /\ I68 <= I64 /\ I67 - 1 <= I64 /\ I67 <= I63] R = init(x1, x2, x3, x4) -> f3(rnd1, rnd2, rnd3, rnd4) f4(I0, I1, I2, I3) -> f4(I4, I5, I6, I7) [I4 <= I0 /\ 0 <= y1 - 1 /\ 2 <= I0 - 1 /\ 0 <= I4 - 1] f4(I8, I9, I10, I11) -> f4(I12, I13, I14, I15) [I12 + 2 <= I8 /\ 0 <= I16 - 1 /\ 2 <= I8 - 1 /\ -1 <= I12 - 1] f4(I17, I18, I19, I20) -> f4(I21, I22, I23, I24) [I21 + 2 <= I17 /\ 0 <= I25 - 1 /\ 1 <= I17 - 1 /\ -1 <= I21 - 1] f6(I26, I27, I28, I29) -> f6(I26, I27, I28 - 1, I29) [0 <= I28 - 1] f6(I30, I31, I32, I33) -> f5(I31 + 1, I30, I33, I34) [0 = I32] f5(I35, I36, I37, I38) -> f6(I36, I35, I39, I37 + 1) [0 <= I37 - 1 /\ I35 <= I36 - 1 /\ -1 <= I39 - 1] f3(I40, I41, I42, I43) -> f5(0, I44, 1, I45) [0 <= I40 - 1 /\ -1 <= I44 - 1 /\ -1 <= I41 - 1] f2(I46, I47, I48, I49) -> f4(I50, I51, I52, I53) [0 <= y2 - 1 /\ 0 <= I54 - 1 /\ I50 <= I47 /\ 0 <= I46 - 1 /\ -1 <= I47 - 1 /\ -1 <= I50 - 1] f3(I55, I56, I57, I58) -> f2(I59, I60, I61, I62) [-1 <= I60 - 1 /\ 0 <= I59 - 1 /\ 0 <= I55 - 1 /\ I59 <= I55] f1(I63, I64, I65, I66) -> f2(I67, I68, I69, I70) [-1 <= I68 - 1 /\ 0 <= I67 - 1 /\ -1 <= I64 - 1 /\ 0 <= I63 - 1 /\ I68 <= I64 /\ I67 - 1 <= I64 /\ I67 <= I63] The dependency graph for this problem is: 0 -> 7, 9 1 -> 1, 2, 3 2 -> 1, 2, 3 3 -> 1, 2, 3 4 -> 4, 5 5 -> 6 6 -> 4, 5 7 -> 6 8 -> 1, 2, 3 9 -> 8 10 -> 8 Where: 0) init#(x1, x2, x3, x4) -> f3#(rnd1, rnd2, rnd3, rnd4) 1) f4#(I0, I1, I2, I3) -> f4#(I4, I5, I6, I7) [I4 <= I0 /\ 0 <= y1 - 1 /\ 2 <= I0 - 1 /\ 0 <= I4 - 1] 2) f4#(I8, I9, I10, I11) -> f4#(I12, I13, I14, I15) [I12 + 2 <= I8 /\ 0 <= I16 - 1 /\ 2 <= I8 - 1 /\ -1 <= I12 - 1] 3) f4#(I17, I18, I19, I20) -> f4#(I21, I22, I23, I24) [I21 + 2 <= I17 /\ 0 <= I25 - 1 /\ 1 <= I17 - 1 /\ -1 <= I21 - 1] 4) f6#(I26, I27, I28, I29) -> f6#(I26, I27, I28 - 1, I29) [0 <= I28 - 1] 5) f6#(I30, I31, I32, I33) -> f5#(I31 + 1, I30, I33, I34) [0 = I32] 6) f5#(I35, I36, I37, I38) -> f6#(I36, I35, I39, I37 + 1) [0 <= I37 - 1 /\ I35 <= I36 - 1 /\ -1 <= I39 - 1] 7) f3#(I40, I41, I42, I43) -> f5#(0, I44, 1, I45) [0 <= I40 - 1 /\ -1 <= I44 - 1 /\ -1 <= I41 - 1] 8) f2#(I46, I47, I48, I49) -> f4#(I50, I51, I52, I53) [0 <= y2 - 1 /\ 0 <= I54 - 1 /\ I50 <= I47 /\ 0 <= I46 - 1 /\ -1 <= I47 - 1 /\ -1 <= I50 - 1] 9) f3#(I55, I56, I57, I58) -> f2#(I59, I60, I61, I62) [-1 <= I60 - 1 /\ 0 <= I59 - 1 /\ 0 <= I55 - 1 /\ I59 <= I55] 10) f1#(I63, I64, I65, I66) -> f2#(I67, I68, I69, I70) [-1 <= I68 - 1 /\ 0 <= I67 - 1 /\ -1 <= I64 - 1 /\ 0 <= I63 - 1 /\ I68 <= I64 /\ I67 - 1 <= I64 /\ I67 <= I63] We have the following SCCs. { 4, 5, 6 } { 1, 2, 3 } DP problem for innermost termination. P = f4#(I0, I1, I2, I3) -> f4#(I4, I5, I6, I7) [I4 <= I0 /\ 0 <= y1 - 1 /\ 2 <= I0 - 1 /\ 0 <= I4 - 1] f4#(I8, I9, I10, I11) -> f4#(I12, I13, I14, I15) [I12 + 2 <= I8 /\ 0 <= I16 - 1 /\ 2 <= I8 - 1 /\ -1 <= I12 - 1] f4#(I17, I18, I19, I20) -> f4#(I21, I22, I23, I24) [I21 + 2 <= I17 /\ 0 <= I25 - 1 /\ 1 <= I17 - 1 /\ -1 <= I21 - 1] R = init(x1, x2, x3, x4) -> f3(rnd1, rnd2, rnd3, rnd4) f4(I0, I1, I2, I3) -> f4(I4, I5, I6, I7) [I4 <= I0 /\ 0 <= y1 - 1 /\ 2 <= I0 - 1 /\ 0 <= I4 - 1] f4(I8, I9, I10, I11) -> f4(I12, I13, I14, I15) [I12 + 2 <= I8 /\ 0 <= I16 - 1 /\ 2 <= I8 - 1 /\ -1 <= I12 - 1] f4(I17, I18, I19, I20) -> f4(I21, I22, I23, I24) [I21 + 2 <= I17 /\ 0 <= I25 - 1 /\ 1 <= I17 - 1 /\ -1 <= I21 - 1] f6(I26, I27, I28, I29) -> f6(I26, I27, I28 - 1, I29) [0 <= I28 - 1] f6(I30, I31, I32, I33) -> f5(I31 + 1, I30, I33, I34) [0 = I32] f5(I35, I36, I37, I38) -> f6(I36, I35, I39, I37 + 1) [0 <= I37 - 1 /\ I35 <= I36 - 1 /\ -1 <= I39 - 1] f3(I40, I41, I42, I43) -> f5(0, I44, 1, I45) [0 <= I40 - 1 /\ -1 <= I44 - 1 /\ -1 <= I41 - 1] f2(I46, I47, I48, I49) -> f4(I50, I51, I52, I53) [0 <= y2 - 1 /\ 0 <= I54 - 1 /\ I50 <= I47 /\ 0 <= I46 - 1 /\ -1 <= I47 - 1 /\ -1 <= I50 - 1] f3(I55, I56, I57, I58) -> f2(I59, I60, I61, I62) [-1 <= I60 - 1 /\ 0 <= I59 - 1 /\ 0 <= I55 - 1 /\ I59 <= I55] f1(I63, I64, I65, I66) -> f2(I67, I68, I69, I70) [-1 <= I68 - 1 /\ 0 <= I67 - 1 /\ -1 <= I64 - 1 /\ 0 <= I63 - 1 /\ I68 <= I64 /\ I67 - 1 <= I64 /\ I67 <= I63] We use the basic value criterion with the projection function NU: NU[f4#(z1,z2,z3,z4)] = z1 This gives the following inequalities: I4 <= I0 /\ 0 <= y1 - 1 /\ 2 <= I0 - 1 /\ 0 <= I4 - 1 ==> I0 (>! \union =) I4 I12 + 2 <= I8 /\ 0 <= I16 - 1 /\ 2 <= I8 - 1 /\ -1 <= I12 - 1 ==> I8 >! I12 I21 + 2 <= I17 /\ 0 <= I25 - 1 /\ 1 <= I17 - 1 /\ -1 <= I21 - 1 ==> I17 >! I21 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f4#(I0, I1, I2, I3) -> f4#(I4, I5, I6, I7) [I4 <= I0 /\ 0 <= y1 - 1 /\ 2 <= I0 - 1 /\ 0 <= I4 - 1] R = init(x1, x2, x3, x4) -> f3(rnd1, rnd2, rnd3, rnd4) f4(I0, I1, I2, I3) -> f4(I4, I5, I6, I7) [I4 <= I0 /\ 0 <= y1 - 1 /\ 2 <= I0 - 1 /\ 0 <= I4 - 1] f4(I8, I9, I10, I11) -> f4(I12, I13, I14, I15) [I12 + 2 <= I8 /\ 0 <= I16 - 1 /\ 2 <= I8 - 1 /\ -1 <= I12 - 1] f4(I17, I18, I19, I20) -> f4(I21, I22, I23, I24) [I21 + 2 <= I17 /\ 0 <= I25 - 1 /\ 1 <= I17 - 1 /\ -1 <= I21 - 1] f6(I26, I27, I28, I29) -> f6(I26, I27, I28 - 1, I29) [0 <= I28 - 1] f6(I30, I31, I32, I33) -> f5(I31 + 1, I30, I33, I34) [0 = I32] f5(I35, I36, I37, I38) -> f6(I36, I35, I39, I37 + 1) [0 <= I37 - 1 /\ I35 <= I36 - 1 /\ -1 <= I39 - 1] f3(I40, I41, I42, I43) -> f5(0, I44, 1, I45) [0 <= I40 - 1 /\ -1 <= I44 - 1 /\ -1 <= I41 - 1] f2(I46, I47, I48, I49) -> f4(I50, I51, I52, I53) [0 <= y2 - 1 /\ 0 <= I54 - 1 /\ I50 <= I47 /\ 0 <= I46 - 1 /\ -1 <= I47 - 1 /\ -1 <= I50 - 1] f3(I55, I56, I57, I58) -> f2(I59, I60, I61, I62) [-1 <= I60 - 1 /\ 0 <= I59 - 1 /\ 0 <= I55 - 1 /\ I59 <= I55] f1(I63, I64, I65, I66) -> f2(I67, I68, I69, I70) [-1 <= I68 - 1 /\ 0 <= I67 - 1 /\ -1 <= I64 - 1 /\ 0 <= I63 - 1 /\ I68 <= I64 /\ I67 - 1 <= I64 /\ I67 <= I63]