16.08/15.91 YES 16.08/15.91 16.08/15.91 DP problem for innermost termination. 16.08/15.91 P = 16.08/15.91 f5#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f4#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 16.08/15.91 f4#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f3#(1, 0, I2, I2, I4, 2, I2, I7, I8, I9) 16.08/15.91 f3#(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1#(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) 16.08/15.91 f1#(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f3#(I20 + I21, rnd2, I22, I23, I24, 1 + I25, I26, I27, I20, I29) [rnd2 = I20 /\ I25 <= I26] 16.08/15.91 R = 16.08/15.91 f5(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f4(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 16.08/15.91 f4(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f3(1, 0, I2, I2, I4, 2, I2, I7, I8, I9) 16.08/15.91 f3(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) 16.08/15.91 f1(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f3(I20 + I21, rnd2, I22, I23, I24, 1 + I25, I26, I27, I20, I29) [rnd2 = I20 /\ I25 <= I26] 16.08/15.91 f1(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39) -> f2(I30, I31, I32, I33, I30, I35, I36, I30, I38, I30) [1 + I36 <= I35] 16.08/15.91 16.08/15.91 The dependency graph for this problem is: 16.08/15.91 0 -> 1 16.08/15.91 1 -> 2 16.08/15.91 2 -> 3 16.08/15.91 3 -> 2 16.08/15.91 Where: 16.08/15.91 0) f5#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f4#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 16.08/15.91 1) f4#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f3#(1, 0, I2, I2, I4, 2, I2, I7, I8, I9) 16.08/15.91 2) f3#(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1#(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) 16.08/15.91 3) f1#(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f3#(I20 + I21, rnd2, I22, I23, I24, 1 + I25, I26, I27, I20, I29) [rnd2 = I20 /\ I25 <= I26] 16.08/15.91 16.08/15.91 We have the following SCCs. 16.08/15.91 { 2, 3 } 16.08/15.91 16.08/15.91 DP problem for innermost termination. 16.08/15.91 P = 16.08/15.91 f3#(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1#(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) 16.08/15.91 f1#(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f3#(I20 + I21, rnd2, I22, I23, I24, 1 + I25, I26, I27, I20, I29) [rnd2 = I20 /\ I25 <= I26] 16.08/15.91 R = 16.08/15.91 f5(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f4(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 16.08/15.91 f4(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f3(1, 0, I2, I2, I4, 2, I2, I7, I8, I9) 16.08/15.91 f3(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) 16.08/15.91 f1(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f3(I20 + I21, rnd2, I22, I23, I24, 1 + I25, I26, I27, I20, I29) [rnd2 = I20 /\ I25 <= I26] 16.08/15.91 f1(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39) -> f2(I30, I31, I32, I33, I30, I35, I36, I30, I38, I30) [1 + I36 <= I35] 16.08/15.91 16.08/15.91 We use the reverse value criterion with the projection function NU: 16.08/15.91 NU[f1#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10)] = z7 + -1 * z6 16.08/15.91 NU[f3#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10)] = z7 + -1 * z6 16.08/15.91 16.08/15.91 This gives the following inequalities: 16.08/15.91 ==> I16 + -1 * I15 >= I16 + -1 * I15 16.08/15.91 rnd2 = I20 /\ I25 <= I26 ==> I26 + -1 * I25 > I26 + -1 * (1 + I25) with I26 + -1 * I25 >= 0 16.08/15.91 16.08/15.91 We remove all the strictly oriented dependency pairs. 16.08/15.91 16.08/15.91 DP problem for innermost termination. 16.08/15.91 P = 16.08/15.91 f3#(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1#(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) 16.08/15.91 R = 16.08/15.91 f5(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f4(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) 16.08/15.91 f4(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9) -> f3(1, 0, I2, I2, I4, 2, I2, I7, I8, I9) 16.08/15.91 f3(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) 16.08/15.91 f1(I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f3(I20 + I21, rnd2, I22, I23, I24, 1 + I25, I26, I27, I20, I29) [rnd2 = I20 /\ I25 <= I26] 16.08/15.91 f1(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39) -> f2(I30, I31, I32, I33, I30, I35, I36, I30, I38, I30) [1 + I36 <= I35] 16.08/15.91 16.08/15.91 The dependency graph for this problem is: 16.08/15.91 2 -> 16.08/15.91 Where: 16.08/15.91 2) f3#(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f1#(I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) 16.08/15.91 16.08/15.91 We have the following SCCs. 16.08/15.91 16.08/18.88 EOF