11.13/11.08 MAYBE 11.13/11.08 11.13/11.08 DP problem for innermost termination. 11.13/11.08 P = 11.13/11.08 f10#(x1, x2, x3, x4, x5) -> f1#(x1, x2, x3, x4, x5) 11.13/11.08 f9#(I5, I6, I7, I8, I9) -> f2#(I5, I6, I7, I8, I9) 11.13/11.08 f2#(I10, I11, I12, I13, I14) -> f9#(I10, I11, I12, I13, I15) [I16 = -1 + I14 /\ I16 <= I11 /\ I11 <= I16 /\ I15 = I15 /\ -1 * I15 <= 0] 11.13/11.08 f6#(I23, I24, I25, I26, I27) -> f7#(I23, I24, I25, I26, I27) [I26 = I26] 11.13/11.08 f2#(I28, I29, I30, I31, I32) -> f6#(I28, I29, I30, I31, -1 + I32) 11.13/11.08 f5#(I33, I34, I35, I36, I37) -> f2#(I33, I34, I35, I36, I37) 11.13/11.08 f4#(I38, I39, I40, I41, I42) -> f5#(I38, I39, I40, I41, I42) [-1 * I42 <= 0] 11.13/11.08 f3#(I43, I44, I45, I46, I47) -> f4#(I43, I44, I45, I46, I47) [I45 = I45] 11.13/11.08 f2#(I48, I49, I50, I51, I52) -> f3#(I48, I49, I50, I51, -1 + I52) 11.13/11.08 f1#(I53, I54, I55, I56, I57) -> f2#(I53, I54, I55, I56, I57) 11.13/11.08 R = 11.13/11.08 f10(x1, x2, x3, x4, x5) -> f1(x1, x2, x3, x4, x5) 11.13/11.08 f2(I0, I1, I2, I3, I4) -> f8(rnd1, I1, I2, I3, rnd5) [y1 = -1 + I4 /\ y1 <= I1 /\ I1 <= y1 /\ rnd5 = rnd5 /\ 0 <= -1 - rnd5 /\ rnd1 = rnd1] 11.13/11.08 f9(I5, I6, I7, I8, I9) -> f2(I5, I6, I7, I8, I9) 11.13/11.08 f2(I10, I11, I12, I13, I14) -> f9(I10, I11, I12, I13, I15) [I16 = -1 + I14 /\ I16 <= I11 /\ I11 <= I16 /\ I15 = I15 /\ -1 * I15 <= 0] 11.13/11.08 f7(I17, I18, I19, I20, I21) -> f8(I22, I18, I19, I20, I21) [I22 = I22 /\ 0 <= -1 - I21] 11.13/11.08 f6(I23, I24, I25, I26, I27) -> f7(I23, I24, I25, I26, I27) [I26 = I26] 11.13/11.08 f2(I28, I29, I30, I31, I32) -> f6(I28, I29, I30, I31, -1 + I32) 11.13/11.08 f5(I33, I34, I35, I36, I37) -> f2(I33, I34, I35, I36, I37) 11.13/11.08 f4(I38, I39, I40, I41, I42) -> f5(I38, I39, I40, I41, I42) [-1 * I42 <= 0] 11.13/11.08 f3(I43, I44, I45, I46, I47) -> f4(I43, I44, I45, I46, I47) [I45 = I45] 11.13/11.08 f2(I48, I49, I50, I51, I52) -> f3(I48, I49, I50, I51, -1 + I52) 11.13/11.08 f1(I53, I54, I55, I56, I57) -> f2(I53, I54, I55, I56, I57) 11.13/11.08 11.13/11.08 The dependency graph for this problem is: 11.13/11.08 0 -> 9 11.13/11.08 1 -> 2, 4, 8 11.13/11.08 2 -> 1 11.13/11.08 3 -> 11.13/11.08 4 -> 3 11.13/11.08 5 -> 2, 4, 8 11.13/11.08 6 -> 5 11.13/11.08 7 -> 6 11.13/11.08 8 -> 7 11.13/11.08 9 -> 2, 4, 8 11.13/11.08 Where: 11.13/11.08 0) f10#(x1, x2, x3, x4, x5) -> f1#(x1, x2, x3, x4, x5) 11.13/11.08 1) f9#(I5, I6, I7, I8, I9) -> f2#(I5, I6, I7, I8, I9) 11.13/11.08 2) f2#(I10, I11, I12, I13, I14) -> f9#(I10, I11, I12, I13, I15) [I16 = -1 + I14 /\ I16 <= I11 /\ I11 <= I16 /\ I15 = I15 /\ -1 * I15 <= 0] 11.13/11.08 3) f6#(I23, I24, I25, I26, I27) -> f7#(I23, I24, I25, I26, I27) [I26 = I26] 11.13/11.08 4) f2#(I28, I29, I30, I31, I32) -> f6#(I28, I29, I30, I31, -1 + I32) 11.13/11.08 5) f5#(I33, I34, I35, I36, I37) -> f2#(I33, I34, I35, I36, I37) 11.13/11.08 6) f4#(I38, I39, I40, I41, I42) -> f5#(I38, I39, I40, I41, I42) [-1 * I42 <= 0] 11.13/11.08 7) f3#(I43, I44, I45, I46, I47) -> f4#(I43, I44, I45, I46, I47) [I45 = I45] 11.13/11.08 8) f2#(I48, I49, I50, I51, I52) -> f3#(I48, I49, I50, I51, -1 + I52) 11.13/11.08 9) f1#(I53, I54, I55, I56, I57) -> f2#(I53, I54, I55, I56, I57) 11.13/11.08 11.13/11.08 We have the following SCCs. 11.13/11.08 { 1, 2, 5, 6, 7, 8 } 11.13/11.08 11.13/11.08 DP problem for innermost termination. 11.13/11.08 P = 11.13/11.08 f9#(I5, I6, I7, I8, I9) -> f2#(I5, I6, I7, I8, I9) 11.13/11.08 f2#(I10, I11, I12, I13, I14) -> f9#(I10, I11, I12, I13, I15) [I16 = -1 + I14 /\ I16 <= I11 /\ I11 <= I16 /\ I15 = I15 /\ -1 * I15 <= 0] 11.13/11.08 f5#(I33, I34, I35, I36, I37) -> f2#(I33, I34, I35, I36, I37) 11.13/11.08 f4#(I38, I39, I40, I41, I42) -> f5#(I38, I39, I40, I41, I42) [-1 * I42 <= 0] 11.13/11.08 f3#(I43, I44, I45, I46, I47) -> f4#(I43, I44, I45, I46, I47) [I45 = I45] 11.13/11.08 f2#(I48, I49, I50, I51, I52) -> f3#(I48, I49, I50, I51, -1 + I52) 11.13/11.08 R = 11.13/11.08 f10(x1, x2, x3, x4, x5) -> f1(x1, x2, x3, x4, x5) 11.13/11.08 f2(I0, I1, I2, I3, I4) -> f8(rnd1, I1, I2, I3, rnd5) [y1 = -1 + I4 /\ y1 <= I1 /\ I1 <= y1 /\ rnd5 = rnd5 /\ 0 <= -1 - rnd5 /\ rnd1 = rnd1] 11.13/11.08 f9(I5, I6, I7, I8, I9) -> f2(I5, I6, I7, I8, I9) 11.13/11.08 f2(I10, I11, I12, I13, I14) -> f9(I10, I11, I12, I13, I15) [I16 = -1 + I14 /\ I16 <= I11 /\ I11 <= I16 /\ I15 = I15 /\ -1 * I15 <= 0] 11.13/11.08 f7(I17, I18, I19, I20, I21) -> f8(I22, I18, I19, I20, I21) [I22 = I22 /\ 0 <= -1 - I21] 11.13/11.08 f6(I23, I24, I25, I26, I27) -> f7(I23, I24, I25, I26, I27) [I26 = I26] 11.13/11.08 f2(I28, I29, I30, I31, I32) -> f6(I28, I29, I30, I31, -1 + I32) 11.13/11.08 f5(I33, I34, I35, I36, I37) -> f2(I33, I34, I35, I36, I37) 11.13/11.08 f4(I38, I39, I40, I41, I42) -> f5(I38, I39, I40, I41, I42) [-1 * I42 <= 0] 11.13/11.08 f3(I43, I44, I45, I46, I47) -> f4(I43, I44, I45, I46, I47) [I45 = I45] 11.13/11.08 f2(I48, I49, I50, I51, I52) -> f3(I48, I49, I50, I51, -1 + I52) 11.13/11.08 f1(I53, I54, I55, I56, I57) -> f2(I53, I54, I55, I56, I57) 11.13/11.08 11.13/14.06 EOF