9.12/9.15 MAYBE 9.12/9.15 9.12/9.15 DP problem for innermost termination. 9.12/9.15 P = 9.12/9.15 f7#(x1, x2, x3, x4, x5) -> f6#(x1, x2, x3, x4, x5) 9.12/9.15 f4#(I5, I6, I7, I8, I9) -> f1#(I5, I6, 1, 1 + I8, I9) [0 <= I7 /\ I7 <= 0 /\ 0 <= -1 - I8 + I9] 9.12/9.15 f6#(I10, I11, I12, I13, I14) -> f4#(I10, I11, 0, I13, I14) 9.12/9.15 f3#(I21, I22, I23, I24, I25) -> f4#(I21, I22, 0, I24, 1 + I25) 9.12/9.15 f2#(I26, I27, I28, I29, I30) -> f3#(I26, I27, I28, I29, I30) [I27 = I27] 9.12/9.15 f1#(I31, I32, I33, I34, I35) -> f2#(I31, I32, I33, I34, I35) [0 <= -1 - I34 + I35] 9.12/9.15 R = 9.12/9.15 f7(x1, x2, x3, x4, x5) -> f6(x1, x2, x3, x4, x5) 9.12/9.15 f4(I0, I1, I2, I3, I4) -> f5(rnd1, I1, I2, I3, I4) [rnd1 = rnd1 /\ -1 * I3 + I4 <= 0] 9.12/9.15 f4(I5, I6, I7, I8, I9) -> f1(I5, I6, 1, 1 + I8, I9) [0 <= I7 /\ I7 <= 0 /\ 0 <= -1 - I8 + I9] 9.12/9.15 f6(I10, I11, I12, I13, I14) -> f4(I10, I11, 0, I13, I14) 9.12/9.15 f1(I15, I16, I17, I18, I19) -> f5(I20, I16, I17, I18, I19) [I20 = I20 /\ -1 * I18 + I19 <= 0] 9.12/9.15 f3(I21, I22, I23, I24, I25) -> f4(I21, I22, 0, I24, 1 + I25) 9.12/9.15 f2(I26, I27, I28, I29, I30) -> f3(I26, I27, I28, I29, I30) [I27 = I27] 9.12/9.15 f1(I31, I32, I33, I34, I35) -> f2(I31, I32, I33, I34, I35) [0 <= -1 - I34 + I35] 9.12/9.15 9.12/9.15 The dependency graph for this problem is: 9.12/9.15 0 -> 2 9.12/9.15 1 -> 5 9.12/9.15 2 -> 1 9.12/9.15 3 -> 1 9.12/9.15 4 -> 3 9.12/9.15 5 -> 4 9.12/9.15 Where: 9.12/9.15 0) f7#(x1, x2, x3, x4, x5) -> f6#(x1, x2, x3, x4, x5) 9.12/9.15 1) f4#(I5, I6, I7, I8, I9) -> f1#(I5, I6, 1, 1 + I8, I9) [0 <= I7 /\ I7 <= 0 /\ 0 <= -1 - I8 + I9] 9.12/9.15 2) f6#(I10, I11, I12, I13, I14) -> f4#(I10, I11, 0, I13, I14) 9.12/9.15 3) f3#(I21, I22, I23, I24, I25) -> f4#(I21, I22, 0, I24, 1 + I25) 9.12/9.15 4) f2#(I26, I27, I28, I29, I30) -> f3#(I26, I27, I28, I29, I30) [I27 = I27] 9.12/9.15 5) f1#(I31, I32, I33, I34, I35) -> f2#(I31, I32, I33, I34, I35) [0 <= -1 - I34 + I35] 9.12/9.15 9.12/9.15 We have the following SCCs. 9.12/9.15 { 1, 3, 4, 5 } 9.12/9.15 9.12/9.15 DP problem for innermost termination. 9.12/9.15 P = 9.12/9.15 f4#(I5, I6, I7, I8, I9) -> f1#(I5, I6, 1, 1 + I8, I9) [0 <= I7 /\ I7 <= 0 /\ 0 <= -1 - I8 + I9] 9.12/9.15 f3#(I21, I22, I23, I24, I25) -> f4#(I21, I22, 0, I24, 1 + I25) 9.12/9.15 f2#(I26, I27, I28, I29, I30) -> f3#(I26, I27, I28, I29, I30) [I27 = I27] 9.12/9.15 f1#(I31, I32, I33, I34, I35) -> f2#(I31, I32, I33, I34, I35) [0 <= -1 - I34 + I35] 9.12/9.15 R = 9.12/9.15 f7(x1, x2, x3, x4, x5) -> f6(x1, x2, x3, x4, x5) 9.12/9.15 f4(I0, I1, I2, I3, I4) -> f5(rnd1, I1, I2, I3, I4) [rnd1 = rnd1 /\ -1 * I3 + I4 <= 0] 9.12/9.15 f4(I5, I6, I7, I8, I9) -> f1(I5, I6, 1, 1 + I8, I9) [0 <= I7 /\ I7 <= 0 /\ 0 <= -1 - I8 + I9] 9.12/9.15 f6(I10, I11, I12, I13, I14) -> f4(I10, I11, 0, I13, I14) 9.12/9.15 f1(I15, I16, I17, I18, I19) -> f5(I20, I16, I17, I18, I19) [I20 = I20 /\ -1 * I18 + I19 <= 0] 9.12/9.15 f3(I21, I22, I23, I24, I25) -> f4(I21, I22, 0, I24, 1 + I25) 9.12/9.15 f2(I26, I27, I28, I29, I30) -> f3(I26, I27, I28, I29, I30) [I27 = I27] 9.12/9.15 f1(I31, I32, I33, I34, I35) -> f2(I31, I32, I33, I34, I35) [0 <= -1 - I34 + I35] 9.12/9.15 9.16/12.12 EOF