1.12/1.16 MAYBE 1.12/1.16 1.12/1.16 DP problem for innermost termination. 1.12/1.16 P = 1.12/1.16 init#(x1, x2, x3, x4, x5, x6, x7) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7) 1.12/1.16 f2#(I0, I1, I2, I3, I4, I5, I6) -> f2#(I7, I8, I9, I10, I4, I5 + 1, I4) [-1 <= I4 - 1 /\ 0 <= I3 - 1 /\ -1 <= I5 - 1 /\ I5 <= I4 - 1 /\ -1 <= y1 - 1 /\ -1 <= I1 - 1 /\ 0 <= I1 + 1 + y1 /\ I7 <= I0 /\ 0 <= I0 - 1 /\ 0 <= I7 - 1 /\ I1 = I2 /\ I4 = I6 /\ I1 + 1 + y1 = I8 /\ I1 + 1 + y1 = I9 /\ 10 - (I1 + 1 + y1) = I10] 1.12/1.16 f2#(I11, I12, I13, I14, I15, I16, I17) -> f2#(I18, I12 + 1, I12 + 1, 10 - (I12 + 1), I15, I16, I15) [I15 = I17 /\ I12 = I13 /\ 0 <= I18 - 1 /\ 0 <= I11 - 1 /\ I18 <= I11 /\ -1 <= I15 - 1 /\ I15 <= I16 /\ -1 <= I12 - 1 /\ 0 <= I14 - 1] 1.12/1.16 f1#(I19, I20, I21, I22, I23, I24, I25) -> f2#(I26, I27, I28, I29, I20, 3, I20) [-1 <= I27 - 1 /\ 2 <= I20 - 1 /\ -1 <= I30 - 1 /\ -1 <= I28 - 1 /\ I26 <= I19 /\ 0 <= I19 - 1 /\ 0 <= I26 - 1 /\ I30 - I28 = I29] 1.12/1.16 f1#(I31, I32, I33, I34, I35, I36, I37) -> f2#(I38, I39, 0, I40, 2, 2, 2) [2 = I32 /\ 0 <= I38 - 1 /\ 0 <= I31 - 1 /\ I38 <= I31 /\ -1 <= I40 - 1 /\ -1 <= I39 - 1] 1.12/1.16 f1#(I41, I42, I43, I44, I45, I46, I47) -> f2#(I48, I49, 0, 0, 1, 1, 1) [1 = I42 /\ 0 <= I48 - 1 /\ 0 <= I41 - 1 /\ -1 <= I49 - 1 /\ I48 <= I41] 1.12/1.16 f1#(I50, I51, I52, I53, I54, I55, I56) -> f2#(I57, 0, 0, 0, 0, 0, 0) [0 = I51 /\ 0 <= I57 - 1 /\ 0 <= I50 - 1 /\ I57 <= I50] 1.12/1.16 R = 1.12/1.16 init(x1, x2, x3, x4, x5, x6, x7) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7) 1.12/1.16 f2(I0, I1, I2, I3, I4, I5, I6) -> f2(I7, I8, I9, I10, I4, I5 + 1, I4) [-1 <= I4 - 1 /\ 0 <= I3 - 1 /\ -1 <= I5 - 1 /\ I5 <= I4 - 1 /\ -1 <= y1 - 1 /\ -1 <= I1 - 1 /\ 0 <= I1 + 1 + y1 /\ I7 <= I0 /\ 0 <= I0 - 1 /\ 0 <= I7 - 1 /\ I1 = I2 /\ I4 = I6 /\ I1 + 1 + y1 = I8 /\ I1 + 1 + y1 = I9 /\ 10 - (I1 + 1 + y1) = I10] 1.12/1.16 f2(I11, I12, I13, I14, I15, I16, I17) -> f2(I18, I12 + 1, I12 + 1, 10 - (I12 + 1), I15, I16, I15) [I15 = I17 /\ I12 = I13 /\ 0 <= I18 - 1 /\ 0 <= I11 - 1 /\ I18 <= I11 /\ -1 <= I15 - 1 /\ I15 <= I16 /\ -1 <= I12 - 1 /\ 0 <= I14 - 1] 1.12/1.16 f1(I19, I20, I21, I22, I23, I24, I25) -> f2(I26, I27, I28, I29, I20, 3, I20) [-1 <= I27 - 1 /\ 2 <= I20 - 1 /\ -1 <= I30 - 1 /\ -1 <= I28 - 1 /\ I26 <= I19 /\ 0 <= I19 - 1 /\ 0 <= I26 - 1 /\ I30 - I28 = I29] 1.12/1.16 f1(I31, I32, I33, I34, I35, I36, I37) -> f2(I38, I39, 0, I40, 2, 2, 2) [2 = I32 /\ 0 <= I38 - 1 /\ 0 <= I31 - 1 /\ I38 <= I31 /\ -1 <= I40 - 1 /\ -1 <= I39 - 1] 1.12/1.16 f1(I41, I42, I43, I44, I45, I46, I47) -> f2(I48, I49, 0, 0, 1, 1, 1) [1 = I42 /\ 0 <= I48 - 1 /\ 0 <= I41 - 1 /\ -1 <= I49 - 1 /\ I48 <= I41] 1.12/1.16 f1(I50, I51, I52, I53, I54, I55, I56) -> f2(I57, 0, 0, 0, 0, 0, 0) [0 = I51 /\ 0 <= I57 - 1 /\ 0 <= I50 - 1 /\ I57 <= I50] 1.12/1.16 1.12/1.16 The dependency graph for this problem is: 1.12/1.16 0 -> 3, 4, 5, 6 1.12/1.16 1 -> 1, 2 1.12/1.16 2 -> 2 1.12/1.16 3 -> 1, 2 1.12/1.16 4 -> 2 1.12/1.16 5 -> 1.12/1.16 6 -> 1.12/1.16 Where: 1.12/1.16 0) init#(x1, x2, x3, x4, x5, x6, x7) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7) 1.12/1.16 1) f2#(I0, I1, I2, I3, I4, I5, I6) -> f2#(I7, I8, I9, I10, I4, I5 + 1, I4) [-1 <= I4 - 1 /\ 0 <= I3 - 1 /\ -1 <= I5 - 1 /\ I5 <= I4 - 1 /\ -1 <= y1 - 1 /\ -1 <= I1 - 1 /\ 0 <= I1 + 1 + y1 /\ I7 <= I0 /\ 0 <= I0 - 1 /\ 0 <= I7 - 1 /\ I1 = I2 /\ I4 = I6 /\ I1 + 1 + y1 = I8 /\ I1 + 1 + y1 = I9 /\ 10 - (I1 + 1 + y1) = I10] 1.12/1.16 2) f2#(I11, I12, I13, I14, I15, I16, I17) -> f2#(I18, I12 + 1, I12 + 1, 10 - (I12 + 1), I15, I16, I15) [I15 = I17 /\ I12 = I13 /\ 0 <= I18 - 1 /\ 0 <= I11 - 1 /\ I18 <= I11 /\ -1 <= I15 - 1 /\ I15 <= I16 /\ -1 <= I12 - 1 /\ 0 <= I14 - 1] 1.12/1.16 3) f1#(I19, I20, I21, I22, I23, I24, I25) -> f2#(I26, I27, I28, I29, I20, 3, I20) [-1 <= I27 - 1 /\ 2 <= I20 - 1 /\ -1 <= I30 - 1 /\ -1 <= I28 - 1 /\ I26 <= I19 /\ 0 <= I19 - 1 /\ 0 <= I26 - 1 /\ I30 - I28 = I29] 1.12/1.16 4) f1#(I31, I32, I33, I34, I35, I36, I37) -> f2#(I38, I39, 0, I40, 2, 2, 2) [2 = I32 /\ 0 <= I38 - 1 /\ 0 <= I31 - 1 /\ I38 <= I31 /\ -1 <= I40 - 1 /\ -1 <= I39 - 1] 1.12/1.16 5) f1#(I41, I42, I43, I44, I45, I46, I47) -> f2#(I48, I49, 0, 0, 1, 1, 1) [1 = I42 /\ 0 <= I48 - 1 /\ 0 <= I41 - 1 /\ -1 <= I49 - 1 /\ I48 <= I41] 1.12/1.16 6) f1#(I50, I51, I52, I53, I54, I55, I56) -> f2#(I57, 0, 0, 0, 0, 0, 0) [0 = I51 /\ 0 <= I57 - 1 /\ 0 <= I50 - 1 /\ I57 <= I50] 1.12/1.16 1.12/1.16 We have the following SCCs. 1.12/1.16 { 1 } 1.12/1.16 { 2 } 1.12/1.16 1.12/1.16 DP problem for innermost termination. 1.12/1.16 P = 1.12/1.16 f2#(I11, I12, I13, I14, I15, I16, I17) -> f2#(I18, I12 + 1, I12 + 1, 10 - (I12 + 1), I15, I16, I15) [I15 = I17 /\ I12 = I13 /\ 0 <= I18 - 1 /\ 0 <= I11 - 1 /\ I18 <= I11 /\ -1 <= I15 - 1 /\ I15 <= I16 /\ -1 <= I12 - 1 /\ 0 <= I14 - 1] 1.12/1.16 R = 1.12/1.16 init(x1, x2, x3, x4, x5, x6, x7) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7) 1.12/1.16 f2(I0, I1, I2, I3, I4, I5, I6) -> f2(I7, I8, I9, I10, I4, I5 + 1, I4) [-1 <= I4 - 1 /\ 0 <= I3 - 1 /\ -1 <= I5 - 1 /\ I5 <= I4 - 1 /\ -1 <= y1 - 1 /\ -1 <= I1 - 1 /\ 0 <= I1 + 1 + y1 /\ I7 <= I0 /\ 0 <= I0 - 1 /\ 0 <= I7 - 1 /\ I1 = I2 /\ I4 = I6 /\ I1 + 1 + y1 = I8 /\ I1 + 1 + y1 = I9 /\ 10 - (I1 + 1 + y1) = I10] 1.12/1.16 f2(I11, I12, I13, I14, I15, I16, I17) -> f2(I18, I12 + 1, I12 + 1, 10 - (I12 + 1), I15, I16, I15) [I15 = I17 /\ I12 = I13 /\ 0 <= I18 - 1 /\ 0 <= I11 - 1 /\ I18 <= I11 /\ -1 <= I15 - 1 /\ I15 <= I16 /\ -1 <= I12 - 1 /\ 0 <= I14 - 1] 1.12/1.16 f1(I19, I20, I21, I22, I23, I24, I25) -> f2(I26, I27, I28, I29, I20, 3, I20) [-1 <= I27 - 1 /\ 2 <= I20 - 1 /\ -1 <= I30 - 1 /\ -1 <= I28 - 1 /\ I26 <= I19 /\ 0 <= I19 - 1 /\ 0 <= I26 - 1 /\ I30 - I28 = I29] 1.12/1.16 f1(I31, I32, I33, I34, I35, I36, I37) -> f2(I38, I39, 0, I40, 2, 2, 2) [2 = I32 /\ 0 <= I38 - 1 /\ 0 <= I31 - 1 /\ I38 <= I31 /\ -1 <= I40 - 1 /\ -1 <= I39 - 1] 1.12/1.16 f1(I41, I42, I43, I44, I45, I46, I47) -> f2(I48, I49, 0, 0, 1, 1, 1) [1 = I42 /\ 0 <= I48 - 1 /\ 0 <= I41 - 1 /\ -1 <= I49 - 1 /\ I48 <= I41] 1.12/1.16 f1(I50, I51, I52, I53, I54, I55, I56) -> f2(I57, 0, 0, 0, 0, 0, 0) [0 = I51 /\ 0 <= I57 - 1 /\ 0 <= I50 - 1 /\ I57 <= I50] 1.12/1.16 1.12/4.14 EOF