/export/starexec/sandbox2/solver/bin/starexec_run_Transition /export/starexec/sandbox2/benchmark/theBenchmark.smt2 /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES DP problem for innermost termination. P = init#(x1, x2, x3, x4) -> f3#(rnd1, rnd2, rnd3, rnd4) f7#(I0, I1, I2, I3) -> f7#(I0 - 1, I1 + 1, I4, I5) [0 <= I1 - 1 /\ 0 <= I0 - 1] f3#(I6, I7, I8, I9) -> f7#(I10, 1, I11, I12) [0 <= I6 - 1 /\ -1 <= I10 - 1 /\ -1 <= I7 - 1] f6#(I13, I14, I15, I16) -> f5#(I17, 0, I16, I18) [-1 <= I17 - 1 /\ -1 <= I14 - 1 /\ -1 <= I13 - 1 /\ 1 <= I15 - 1 /\ I17 <= I13] f6#(I19, I20, I21, I22) -> f5#(I23, 0, I22, I24) [-1 <= I23 - 1 /\ -1 <= I20 - 1 /\ -1 <= I19 - 1 /\ I21 <= 1 /\ I23 <= I19] f6#(I25, I26, I27, I28) -> f6#(I29, I30, I27 - 1, I28) [-1 <= I30 - 1 /\ -1 <= I29 - 1 /\ 0 <= I26 - 1 /\ -1 <= I25 - 1 /\ I30 + 1 <= I26 /\ 1 <= I27 - 1 /\ I29 <= I25] f6#(I31, I32, I33, I34) -> f5#(I35, I36, I34, I37) [I36 + 2 <= I32 /\ -1 <= I35 - 1 /\ 0 <= I32 - 1 /\ -1 <= I31 - 1 /\ I33 <= 1 /\ I35 <= I31] f5#(I38, I39, I40, I41) -> f6#(I42, I43, I44, I40 + 1) [-1 <= I43 - 1 /\ -1 <= I42 - 1 /\ 0 <= I38 - 1 /\ I43 + 1 <= I38 /\ I42 + 1 <= I38 /\ 0 <= I39 - 1 /\ 0 <= I40 - 1 /\ -1 <= I44 - 1] f4#(I45, I46, I47, I48) -> f4#(I49, I50, I47 - 1, I48) [-1 <= I50 - 1 /\ -1 <= I49 - 1 /\ 0 <= I46 - 1 /\ -1 <= I45 - 1 /\ I50 + 1 <= I46 /\ 1 <= I47 - 1 /\ I49 <= I45] f4#(I51, I52, I53, I54) -> f5#(I55, I56, I54, I57) [I56 + 2 <= I52 /\ -1 <= I55 - 1 /\ 0 <= I52 - 1 /\ -1 <= I51 - 1 /\ I53 <= 1 /\ I55 <= I51] f2#(I58, I59, I60, I61) -> f4#(I62, I63, I64, I65) [0 <= y1 - 1 /\ -1 <= I64 - 1 /\ I62 <= I58 /\ I63 <= I58 /\ -1 <= I58 - 1 /\ -1 <= I62 - 1 /\ -1 <= I63 - 1 /\ y1 + 1 = I65] f3#(I66, I67, I68, I69) -> f2#(I70, I71, I72, I73) [-1 <= I70 - 1 /\ 0 <= I66 - 1] f1#(I74, I75, I76, I77) -> f2#(I78, I79, I80, I81) [-1 <= I78 - 1 /\ -1 <= I74 - 1 /\ I78 <= I74] R = init(x1, x2, x3, x4) -> f3(rnd1, rnd2, rnd3, rnd4) f7(I0, I1, I2, I3) -> f7(I0 - 1, I1 + 1, I4, I5) [0 <= I1 - 1 /\ 0 <= I0 - 1] f3(I6, I7, I8, I9) -> f7(I10, 1, I11, I12) [0 <= I6 - 1 /\ -1 <= I10 - 1 /\ -1 <= I7 - 1] f6(I13, I14, I15, I16) -> f5(I17, 0, I16, I18) [-1 <= I17 - 1 /\ -1 <= I14 - 1 /\ -1 <= I13 - 1 /\ 1 <= I15 - 1 /\ I17 <= I13] f6(I19, I20, I21, I22) -> f5(I23, 0, I22, I24) [-1 <= I23 - 1 /\ -1 <= I20 - 1 /\ -1 <= I19 - 1 /\ I21 <= 1 /\ I23 <= I19] f6(I25, I26, I27, I28) -> f6(I29, I30, I27 - 1, I28) [-1 <= I30 - 1 /\ -1 <= I29 - 1 /\ 0 <= I26 - 1 /\ -1 <= I25 - 1 /\ I30 + 1 <= I26 /\ 1 <= I27 - 1 /\ I29 <= I25] f6(I31, I32, I33, I34) -> f5(I35, I36, I34, I37) [I36 + 2 <= I32 /\ -1 <= I35 - 1 /\ 0 <= I32 - 1 /\ -1 <= I31 - 1 /\ I33 <= 1 /\ I35 <= I31] f5(I38, I39, I40, I41) -> f6(I42, I43, I44, I40 + 1) [-1 <= I43 - 1 /\ -1 <= I42 - 1 /\ 0 <= I38 - 1 /\ I43 + 1 <= I38 /\ I42 + 1 <= I38 /\ 0 <= I39 - 1 /\ 0 <= I40 - 1 /\ -1 <= I44 - 1] f4(I45, I46, I47, I48) -> f4(I49, I50, I47 - 1, I48) [-1 <= I50 - 1 /\ -1 <= I49 - 1 /\ 0 <= I46 - 1 /\ -1 <= I45 - 1 /\ I50 + 1 <= I46 /\ 1 <= I47 - 1 /\ I49 <= I45] f4(I51, I52, I53, I54) -> f5(I55, I56, I54, I57) [I56 + 2 <= I52 /\ -1 <= I55 - 1 /\ 0 <= I52 - 1 /\ -1 <= I51 - 1 /\ I53 <= 1 /\ I55 <= I51] f2(I58, I59, I60, I61) -> f4(I62, I63, I64, I65) [0 <= y1 - 1 /\ -1 <= I64 - 1 /\ I62 <= I58 /\ I63 <= I58 /\ -1 <= I58 - 1 /\ -1 <= I62 - 1 /\ -1 <= I63 - 1 /\ y1 + 1 = I65] f3(I66, I67, I68, I69) -> f2(I70, I71, I72, I73) [-1 <= I70 - 1 /\ 0 <= I66 - 1] f1(I74, I75, I76, I77) -> f2(I78, I79, I80, I81) [-1 <= I78 - 1 /\ -1 <= I74 - 1 /\ I78 <= I74] The dependency graph for this problem is: 0 -> 2, 11 1 -> 1 2 -> 1 3 -> 4 -> 5 -> 3, 4, 5, 6 6 -> 7 7 -> 3, 4, 5, 6 8 -> 8, 9 9 -> 7 10 -> 8, 9 11 -> 10 12 -> 10 Where: 0) init#(x1, x2, x3, x4) -> f3#(rnd1, rnd2, rnd3, rnd4) 1) f7#(I0, I1, I2, I3) -> f7#(I0 - 1, I1 + 1, I4, I5) [0 <= I1 - 1 /\ 0 <= I0 - 1] 2) f3#(I6, I7, I8, I9) -> f7#(I10, 1, I11, I12) [0 <= I6 - 1 /\ -1 <= I10 - 1 /\ -1 <= I7 - 1] 3) f6#(I13, I14, I15, I16) -> f5#(I17, 0, I16, I18) [-1 <= I17 - 1 /\ -1 <= I14 - 1 /\ -1 <= I13 - 1 /\ 1 <= I15 - 1 /\ I17 <= I13] 4) f6#(I19, I20, I21, I22) -> f5#(I23, 0, I22, I24) [-1 <= I23 - 1 /\ -1 <= I20 - 1 /\ -1 <= I19 - 1 /\ I21 <= 1 /\ I23 <= I19] 5) f6#(I25, I26, I27, I28) -> f6#(I29, I30, I27 - 1, I28) [-1 <= I30 - 1 /\ -1 <= I29 - 1 /\ 0 <= I26 - 1 /\ -1 <= I25 - 1 /\ I30 + 1 <= I26 /\ 1 <= I27 - 1 /\ I29 <= I25] 6) f6#(I31, I32, I33, I34) -> f5#(I35, I36, I34, I37) [I36 + 2 <= I32 /\ -1 <= I35 - 1 /\ 0 <= I32 - 1 /\ -1 <= I31 - 1 /\ I33 <= 1 /\ I35 <= I31] 7) f5#(I38, I39, I40, I41) -> f6#(I42, I43, I44, I40 + 1) [-1 <= I43 - 1 /\ -1 <= I42 - 1 /\ 0 <= I38 - 1 /\ I43 + 1 <= I38 /\ I42 + 1 <= I38 /\ 0 <= I39 - 1 /\ 0 <= I40 - 1 /\ -1 <= I44 - 1] 8) f4#(I45, I46, I47, I48) -> f4#(I49, I50, I47 - 1, I48) [-1 <= I50 - 1 /\ -1 <= I49 - 1 /\ 0 <= I46 - 1 /\ -1 <= I45 - 1 /\ I50 + 1 <= I46 /\ 1 <= I47 - 1 /\ I49 <= I45] 9) f4#(I51, I52, I53, I54) -> f5#(I55, I56, I54, I57) [I56 + 2 <= I52 /\ -1 <= I55 - 1 /\ 0 <= I52 - 1 /\ -1 <= I51 - 1 /\ I53 <= 1 /\ I55 <= I51] 10) f2#(I58, I59, I60, I61) -> f4#(I62, I63, I64, I65) [0 <= y1 - 1 /\ -1 <= I64 - 1 /\ I62 <= I58 /\ I63 <= I58 /\ -1 <= I58 - 1 /\ -1 <= I62 - 1 /\ -1 <= I63 - 1 /\ y1 + 1 = I65] 11) f3#(I66, I67, I68, I69) -> f2#(I70, I71, I72, I73) [-1 <= I70 - 1 /\ 0 <= I66 - 1] 12) f1#(I74, I75, I76, I77) -> f2#(I78, I79, I80, I81) [-1 <= I78 - 1 /\ -1 <= I74 - 1 /\ I78 <= I74] We have the following SCCs. { 1 } { 8 } { 5, 6, 7 } DP problem for innermost termination. P = f6#(I25, I26, I27, I28) -> f6#(I29, I30, I27 - 1, I28) [-1 <= I30 - 1 /\ -1 <= I29 - 1 /\ 0 <= I26 - 1 /\ -1 <= I25 - 1 /\ I30 + 1 <= I26 /\ 1 <= I27 - 1 /\ I29 <= I25] f6#(I31, I32, I33, I34) -> f5#(I35, I36, I34, I37) [I36 + 2 <= I32 /\ -1 <= I35 - 1 /\ 0 <= I32 - 1 /\ -1 <= I31 - 1 /\ I33 <= 1 /\ I35 <= I31] f5#(I38, I39, I40, I41) -> f6#(I42, I43, I44, I40 + 1) [-1 <= I43 - 1 /\ -1 <= I42 - 1 /\ 0 <= I38 - 1 /\ I43 + 1 <= I38 /\ I42 + 1 <= I38 /\ 0 <= I39 - 1 /\ 0 <= I40 - 1 /\ -1 <= I44 - 1] R = init(x1, x2, x3, x4) -> f3(rnd1, rnd2, rnd3, rnd4) f7(I0, I1, I2, I3) -> f7(I0 - 1, I1 + 1, I4, I5) [0 <= I1 - 1 /\ 0 <= I0 - 1] f3(I6, I7, I8, I9) -> f7(I10, 1, I11, I12) [0 <= I6 - 1 /\ -1 <= I10 - 1 /\ -1 <= I7 - 1] f6(I13, I14, I15, I16) -> f5(I17, 0, I16, I18) [-1 <= I17 - 1 /\ -1 <= I14 - 1 /\ -1 <= I13 - 1 /\ 1 <= I15 - 1 /\ I17 <= I13] f6(I19, I20, I21, I22) -> f5(I23, 0, I22, I24) [-1 <= I23 - 1 /\ -1 <= I20 - 1 /\ -1 <= I19 - 1 /\ I21 <= 1 /\ I23 <= I19] f6(I25, I26, I27, I28) -> f6(I29, I30, I27 - 1, I28) [-1 <= I30 - 1 /\ -1 <= I29 - 1 /\ 0 <= I26 - 1 /\ -1 <= I25 - 1 /\ I30 + 1 <= I26 /\ 1 <= I27 - 1 /\ I29 <= I25] f6(I31, I32, I33, I34) -> f5(I35, I36, I34, I37) [I36 + 2 <= I32 /\ -1 <= I35 - 1 /\ 0 <= I32 - 1 /\ -1 <= I31 - 1 /\ I33 <= 1 /\ I35 <= I31] f5(I38, I39, I40, I41) -> f6(I42, I43, I44, I40 + 1) [-1 <= I43 - 1 /\ -1 <= I42 - 1 /\ 0 <= I38 - 1 /\ I43 + 1 <= I38 /\ I42 + 1 <= I38 /\ 0 <= I39 - 1 /\ 0 <= I40 - 1 /\ -1 <= I44 - 1] f4(I45, I46, I47, I48) -> f4(I49, I50, I47 - 1, I48) [-1 <= I50 - 1 /\ -1 <= I49 - 1 /\ 0 <= I46 - 1 /\ -1 <= I45 - 1 /\ I50 + 1 <= I46 /\ 1 <= I47 - 1 /\ I49 <= I45] f4(I51, I52, I53, I54) -> f5(I55, I56, I54, I57) [I56 + 2 <= I52 /\ -1 <= I55 - 1 /\ 0 <= I52 - 1 /\ -1 <= I51 - 1 /\ I53 <= 1 /\ I55 <= I51] f2(I58, I59, I60, I61) -> f4(I62, I63, I64, I65) [0 <= y1 - 1 /\ -1 <= I64 - 1 /\ I62 <= I58 /\ I63 <= I58 /\ -1 <= I58 - 1 /\ -1 <= I62 - 1 /\ -1 <= I63 - 1 /\ y1 + 1 = I65] f3(I66, I67, I68, I69) -> f2(I70, I71, I72, I73) [-1 <= I70 - 1 /\ 0 <= I66 - 1] f1(I74, I75, I76, I77) -> f2(I78, I79, I80, I81) [-1 <= I78 - 1 /\ -1 <= I74 - 1 /\ I78 <= I74] We use the basic value criterion with the projection function NU: NU[f5#(z1,z2,z3,z4)] = z1 NU[f6#(z1,z2,z3,z4)] = z1 This gives the following inequalities: -1 <= I30 - 1 /\ -1 <= I29 - 1 /\ 0 <= I26 - 1 /\ -1 <= I25 - 1 /\ I30 + 1 <= I26 /\ 1 <= I27 - 1 /\ I29 <= I25 ==> I25 (>! \union =) I29 I36 + 2 <= I32 /\ -1 <= I35 - 1 /\ 0 <= I32 - 1 /\ -1 <= I31 - 1 /\ I33 <= 1 /\ I35 <= I31 ==> I31 (>! \union =) I35 -1 <= I43 - 1 /\ -1 <= I42 - 1 /\ 0 <= I38 - 1 /\ I43 + 1 <= I38 /\ I42 + 1 <= I38 /\ 0 <= I39 - 1 /\ 0 <= I40 - 1 /\ -1 <= I44 - 1 ==> I38 >! I42 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f6#(I25, I26, I27, I28) -> f6#(I29, I30, I27 - 1, I28) [-1 <= I30 - 1 /\ -1 <= I29 - 1 /\ 0 <= I26 - 1 /\ -1 <= I25 - 1 /\ I30 + 1 <= I26 /\ 1 <= I27 - 1 /\ I29 <= I25] f6#(I31, I32, I33, I34) -> f5#(I35, I36, I34, I37) [I36 + 2 <= I32 /\ -1 <= I35 - 1 /\ 0 <= I32 - 1 /\ -1 <= I31 - 1 /\ I33 <= 1 /\ I35 <= I31] R = init(x1, x2, x3, x4) -> f3(rnd1, rnd2, rnd3, rnd4) f7(I0, I1, I2, I3) -> f7(I0 - 1, I1 + 1, I4, I5) [0 <= I1 - 1 /\ 0 <= I0 - 1] f3(I6, I7, I8, I9) -> f7(I10, 1, I11, I12) [0 <= I6 - 1 /\ -1 <= I10 - 1 /\ -1 <= I7 - 1] f6(I13, I14, I15, I16) -> f5(I17, 0, I16, I18) [-1 <= I17 - 1 /\ -1 <= I14 - 1 /\ -1 <= I13 - 1 /\ 1 <= I15 - 1 /\ I17 <= I13] f6(I19, I20, I21, I22) -> f5(I23, 0, I22, I24) [-1 <= I23 - 1 /\ -1 <= I20 - 1 /\ -1 <= I19 - 1 /\ I21 <= 1 /\ I23 <= I19] f6(I25, I26, I27, I28) -> f6(I29, I30, I27 - 1, I28) [-1 <= I30 - 1 /\ -1 <= I29 - 1 /\ 0 <= I26 - 1 /\ -1 <= I25 - 1 /\ I30 + 1 <= I26 /\ 1 <= I27 - 1 /\ I29 <= I25] f6(I31, I32, I33, I34) -> f5(I35, I36, I34, I37) [I36 + 2 <= I32 /\ -1 <= I35 - 1 /\ 0 <= I32 - 1 /\ -1 <= I31 - 1 /\ I33 <= 1 /\ I35 <= I31] f5(I38, I39, I40, I41) -> f6(I42, I43, I44, I40 + 1) [-1 <= I43 - 1 /\ -1 <= I42 - 1 /\ 0 <= I38 - 1 /\ I43 + 1 <= I38 /\ I42 + 1 <= I38 /\ 0 <= I39 - 1 /\ 0 <= I40 - 1 /\ -1 <= I44 - 1] f4(I45, I46, I47, I48) -> f4(I49, I50, I47 - 1, I48) [-1 <= I50 - 1 /\ -1 <= I49 - 1 /\ 0 <= I46 - 1 /\ -1 <= I45 - 1 /\ I50 + 1 <= I46 /\ 1 <= I47 - 1 /\ I49 <= I45] f4(I51, I52, I53, I54) -> f5(I55, I56, I54, I57) [I56 + 2 <= I52 /\ -1 <= I55 - 1 /\ 0 <= I52 - 1 /\ -1 <= I51 - 1 /\ I53 <= 1 /\ I55 <= I51] f2(I58, I59, I60, I61) -> f4(I62, I63, I64, I65) [0 <= y1 - 1 /\ -1 <= I64 - 1 /\ I62 <= I58 /\ I63 <= I58 /\ -1 <= I58 - 1 /\ -1 <= I62 - 1 /\ -1 <= I63 - 1 /\ y1 + 1 = I65] f3(I66, I67, I68, I69) -> f2(I70, I71, I72, I73) [-1 <= I70 - 1 /\ 0 <= I66 - 1] f1(I74, I75, I76, I77) -> f2(I78, I79, I80, I81) [-1 <= I78 - 1 /\ -1 <= I74 - 1 /\ I78 <= I74] The dependency graph for this problem is: 5 -> 5, 6 6 -> Where: 5) f6#(I25, I26, I27, I28) -> f6#(I29, I30, I27 - 1, I28) [-1 <= I30 - 1 /\ -1 <= I29 - 1 /\ 0 <= I26 - 1 /\ -1 <= I25 - 1 /\ I30 + 1 <= I26 /\ 1 <= I27 - 1 /\ I29 <= I25] 6) f6#(I31, I32, I33, I34) -> f5#(I35, I36, I34, I37) [I36 + 2 <= I32 /\ -1 <= I35 - 1 /\ 0 <= I32 - 1 /\ -1 <= I31 - 1 /\ I33 <= 1 /\ I35 <= I31] We have the following SCCs. { 5 } DP problem for innermost termination. P = f6#(I25, I26, I27, I28) -> f6#(I29, I30, I27 - 1, I28) [-1 <= I30 - 1 /\ -1 <= I29 - 1 /\ 0 <= I26 - 1 /\ -1 <= I25 - 1 /\ I30 + 1 <= I26 /\ 1 <= I27 - 1 /\ I29 <= I25] R = init(x1, x2, x3, x4) -> f3(rnd1, rnd2, rnd3, rnd4) f7(I0, I1, I2, I3) -> f7(I0 - 1, I1 + 1, I4, I5) [0 <= I1 - 1 /\ 0 <= I0 - 1] f3(I6, I7, I8, I9) -> f7(I10, 1, I11, I12) [0 <= I6 - 1 /\ -1 <= I10 - 1 /\ -1 <= I7 - 1] f6(I13, I14, I15, I16) -> f5(I17, 0, I16, I18) [-1 <= I17 - 1 /\ -1 <= I14 - 1 /\ -1 <= I13 - 1 /\ 1 <= I15 - 1 /\ I17 <= I13] f6(I19, I20, I21, I22) -> f5(I23, 0, I22, I24) [-1 <= I23 - 1 /\ -1 <= I20 - 1 /\ -1 <= I19 - 1 /\ I21 <= 1 /\ I23 <= I19] f6(I25, I26, I27, I28) -> f6(I29, I30, I27 - 1, I28) [-1 <= I30 - 1 /\ -1 <= I29 - 1 /\ 0 <= I26 - 1 /\ -1 <= I25 - 1 /\ I30 + 1 <= I26 /\ 1 <= I27 - 1 /\ I29 <= I25] f6(I31, I32, I33, I34) -> f5(I35, I36, I34, I37) [I36 + 2 <= I32 /\ -1 <= I35 - 1 /\ 0 <= I32 - 1 /\ -1 <= I31 - 1 /\ I33 <= 1 /\ I35 <= I31] f5(I38, I39, I40, I41) -> f6(I42, I43, I44, I40 + 1) [-1 <= I43 - 1 /\ -1 <= I42 - 1 /\ 0 <= I38 - 1 /\ I43 + 1 <= I38 /\ I42 + 1 <= I38 /\ 0 <= I39 - 1 /\ 0 <= I40 - 1 /\ -1 <= I44 - 1] f4(I45, I46, I47, I48) -> f4(I49, I50, I47 - 1, I48) [-1 <= I50 - 1 /\ -1 <= I49 - 1 /\ 0 <= I46 - 1 /\ -1 <= I45 - 1 /\ I50 + 1 <= I46 /\ 1 <= I47 - 1 /\ I49 <= I45] f4(I51, I52, I53, I54) -> f5(I55, I56, I54, I57) [I56 + 2 <= I52 /\ -1 <= I55 - 1 /\ 0 <= I52 - 1 /\ -1 <= I51 - 1 /\ I53 <= 1 /\ I55 <= I51] f2(I58, I59, I60, I61) -> f4(I62, I63, I64, I65) [0 <= y1 - 1 /\ -1 <= I64 - 1 /\ I62 <= I58 /\ I63 <= I58 /\ -1 <= I58 - 1 /\ -1 <= I62 - 1 /\ -1 <= I63 - 1 /\ y1 + 1 = I65] f3(I66, I67, I68, I69) -> f2(I70, I71, I72, I73) [-1 <= I70 - 1 /\ 0 <= I66 - 1] f1(I74, I75, I76, I77) -> f2(I78, I79, I80, I81) [-1 <= I78 - 1 /\ -1 <= I74 - 1 /\ I78 <= I74] We use the basic value criterion with the projection function NU: NU[f6#(z1,z2,z3,z4)] = z3 This gives the following inequalities: -1 <= I30 - 1 /\ -1 <= I29 - 1 /\ 0 <= I26 - 1 /\ -1 <= I25 - 1 /\ I30 + 1 <= I26 /\ 1 <= I27 - 1 /\ I29 <= I25 ==> I27 >! I27 - 1 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. DP problem for innermost termination. P = f4#(I45, I46, I47, I48) -> f4#(I49, I50, I47 - 1, I48) [-1 <= I50 - 1 /\ -1 <= I49 - 1 /\ 0 <= I46 - 1 /\ -1 <= I45 - 1 /\ I50 + 1 <= I46 /\ 1 <= I47 - 1 /\ I49 <= I45] R = init(x1, x2, x3, x4) -> f3(rnd1, rnd2, rnd3, rnd4) f7(I0, I1, I2, I3) -> f7(I0 - 1, I1 + 1, I4, I5) [0 <= I1 - 1 /\ 0 <= I0 - 1] f3(I6, I7, I8, I9) -> f7(I10, 1, I11, I12) [0 <= I6 - 1 /\ -1 <= I10 - 1 /\ -1 <= I7 - 1] f6(I13, I14, I15, I16) -> f5(I17, 0, I16, I18) [-1 <= I17 - 1 /\ -1 <= I14 - 1 /\ -1 <= I13 - 1 /\ 1 <= I15 - 1 /\ I17 <= I13] f6(I19, I20, I21, I22) -> f5(I23, 0, I22, I24) [-1 <= I23 - 1 /\ -1 <= I20 - 1 /\ -1 <= I19 - 1 /\ I21 <= 1 /\ I23 <= I19] f6(I25, I26, I27, I28) -> f6(I29, I30, I27 - 1, I28) [-1 <= I30 - 1 /\ -1 <= I29 - 1 /\ 0 <= I26 - 1 /\ -1 <= I25 - 1 /\ I30 + 1 <= I26 /\ 1 <= I27 - 1 /\ I29 <= I25] f6(I31, I32, I33, I34) -> f5(I35, I36, I34, I37) [I36 + 2 <= I32 /\ -1 <= I35 - 1 /\ 0 <= I32 - 1 /\ -1 <= I31 - 1 /\ I33 <= 1 /\ I35 <= I31] f5(I38, I39, I40, I41) -> f6(I42, I43, I44, I40 + 1) [-1 <= I43 - 1 /\ -1 <= I42 - 1 /\ 0 <= I38 - 1 /\ I43 + 1 <= I38 /\ I42 + 1 <= I38 /\ 0 <= I39 - 1 /\ 0 <= I40 - 1 /\ -1 <= I44 - 1] f4(I45, I46, I47, I48) -> f4(I49, I50, I47 - 1, I48) [-1 <= I50 - 1 /\ -1 <= I49 - 1 /\ 0 <= I46 - 1 /\ -1 <= I45 - 1 /\ I50 + 1 <= I46 /\ 1 <= I47 - 1 /\ I49 <= I45] f4(I51, I52, I53, I54) -> f5(I55, I56, I54, I57) [I56 + 2 <= I52 /\ -1 <= I55 - 1 /\ 0 <= I52 - 1 /\ -1 <= I51 - 1 /\ I53 <= 1 /\ I55 <= I51] f2(I58, I59, I60, I61) -> f4(I62, I63, I64, I65) [0 <= y1 - 1 /\ -1 <= I64 - 1 /\ I62 <= I58 /\ I63 <= I58 /\ -1 <= I58 - 1 /\ -1 <= I62 - 1 /\ -1 <= I63 - 1 /\ y1 + 1 = I65] f3(I66, I67, I68, I69) -> f2(I70, I71, I72, I73) [-1 <= I70 - 1 /\ 0 <= I66 - 1] f1(I74, I75, I76, I77) -> f2(I78, I79, I80, I81) [-1 <= I78 - 1 /\ -1 <= I74 - 1 /\ I78 <= I74] We use the basic value criterion with the projection function NU: NU[f4#(z1,z2,z3,z4)] = z3 This gives the following inequalities: -1 <= I50 - 1 /\ -1 <= I49 - 1 /\ 0 <= I46 - 1 /\ -1 <= I45 - 1 /\ I50 + 1 <= I46 /\ 1 <= I47 - 1 /\ I49 <= I45 ==> I47 >! I47 - 1 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. DP problem for innermost termination. P = f7#(I0, I1, I2, I3) -> f7#(I0 - 1, I1 + 1, I4, I5) [0 <= I1 - 1 /\ 0 <= I0 - 1] R = init(x1, x2, x3, x4) -> f3(rnd1, rnd2, rnd3, rnd4) f7(I0, I1, I2, I3) -> f7(I0 - 1, I1 + 1, I4, I5) [0 <= I1 - 1 /\ 0 <= I0 - 1] f3(I6, I7, I8, I9) -> f7(I10, 1, I11, I12) [0 <= I6 - 1 /\ -1 <= I10 - 1 /\ -1 <= I7 - 1] f6(I13, I14, I15, I16) -> f5(I17, 0, I16, I18) [-1 <= I17 - 1 /\ -1 <= I14 - 1 /\ -1 <= I13 - 1 /\ 1 <= I15 - 1 /\ I17 <= I13] f6(I19, I20, I21, I22) -> f5(I23, 0, I22, I24) [-1 <= I23 - 1 /\ -1 <= I20 - 1 /\ -1 <= I19 - 1 /\ I21 <= 1 /\ I23 <= I19] f6(I25, I26, I27, I28) -> f6(I29, I30, I27 - 1, I28) [-1 <= I30 - 1 /\ -1 <= I29 - 1 /\ 0 <= I26 - 1 /\ -1 <= I25 - 1 /\ I30 + 1 <= I26 /\ 1 <= I27 - 1 /\ I29 <= I25] f6(I31, I32, I33, I34) -> f5(I35, I36, I34, I37) [I36 + 2 <= I32 /\ -1 <= I35 - 1 /\ 0 <= I32 - 1 /\ -1 <= I31 - 1 /\ I33 <= 1 /\ I35 <= I31] f5(I38, I39, I40, I41) -> f6(I42, I43, I44, I40 + 1) [-1 <= I43 - 1 /\ -1 <= I42 - 1 /\ 0 <= I38 - 1 /\ I43 + 1 <= I38 /\ I42 + 1 <= I38 /\ 0 <= I39 - 1 /\ 0 <= I40 - 1 /\ -1 <= I44 - 1] f4(I45, I46, I47, I48) -> f4(I49, I50, I47 - 1, I48) [-1 <= I50 - 1 /\ -1 <= I49 - 1 /\ 0 <= I46 - 1 /\ -1 <= I45 - 1 /\ I50 + 1 <= I46 /\ 1 <= I47 - 1 /\ I49 <= I45] f4(I51, I52, I53, I54) -> f5(I55, I56, I54, I57) [I56 + 2 <= I52 /\ -1 <= I55 - 1 /\ 0 <= I52 - 1 /\ -1 <= I51 - 1 /\ I53 <= 1 /\ I55 <= I51] f2(I58, I59, I60, I61) -> f4(I62, I63, I64, I65) [0 <= y1 - 1 /\ -1 <= I64 - 1 /\ I62 <= I58 /\ I63 <= I58 /\ -1 <= I58 - 1 /\ -1 <= I62 - 1 /\ -1 <= I63 - 1 /\ y1 + 1 = I65] f3(I66, I67, I68, I69) -> f2(I70, I71, I72, I73) [-1 <= I70 - 1 /\ 0 <= I66 - 1] f1(I74, I75, I76, I77) -> f2(I78, I79, I80, I81) [-1 <= I78 - 1 /\ -1 <= I74 - 1 /\ I78 <= I74] We use the basic value criterion with the projection function NU: NU[f7#(z1,z2,z3,z4)] = z1 This gives the following inequalities: 0 <= I1 - 1 /\ 0 <= I0 - 1 ==> I0 >! I0 - 1 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed.