MAYBE Initial complexity problem: 1: T: (1, 1) f0(a, b, c, d, e, f, g, h, i, j, k) -> f5(a, b, c, d, e, f, g, h, i, j, k) (1, 1) f0(a, b, c, d, e, f, g, h, i, j, k) -> f12(m, b, c, d, e, f, g, h, i, j, k) [ 15 >= l ] (?, 1) f12(a, b, c, d, e, f, g, h, i, j, k) -> f20(a, m, m, d, e, f, g, h, i, j, k) [ 0 >= a + 1 ] (?, 1) f12(a, b, c, d, e, f, g, h, i, j, k) -> f20(a, m, m, d, e, f, g, h, i, j, k) [ a >= 1 ] (1, 1) f0(a, b, c, d, e, f, g, h, i, j, k) -> f5(a, b, c, 1, 1, f, g, h, i, j, k) [ 15 >= m ] (?, 1) f20(a, b, c, d, e, f, g, h, i, j, k) -> f12(a - 1, b, c, d, e, 0, 0, h, i, j, k) (?, 1) f12(a, b, c, d, e, f, g, h, i, j, k) -> f5(0, b, c, 0, 0, f, g, m, m, 0, 0) [ a = 0 ] start location: f0 leaf cost: 0 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [a]. We thus obtain the following problem: 2: T: (?, 1) f12(a) -> f5(0) [ a = 0 ] (?, 1) f20(a) -> f12(a - 1) (1, 1) f0(a) -> f5(a) [ 15 >= m ] (?, 1) f12(a) -> f20(a) [ a >= 1 ] (?, 1) f12(a) -> f20(a) [ 0 >= a + 1 ] (1, 1) f0(a) -> f12(m) [ 15 >= l ] (1, 1) f0(a) -> f5(a) start location: f0 leaf cost: 0 Repeatedly removing leaves of the complexity graph in problem 2 produces the following problem: 3: T: (?, 1) f20(a) -> f12(a - 1) (?, 1) f12(a) -> f20(a) [ a >= 1 ] (?, 1) f12(a) -> f20(a) [ 0 >= a + 1 ] (1, 1) f0(a) -> f12(m) [ 15 >= l ] start location: f0 leaf cost: 3 By chaining the transition f12(a) -> f20(a) [ a >= 1 ] with all transitions in problem 3, the following new transition is obtained: f12(a) -> f12(a - 1) [ a >= 1 ] We thus obtain the following problem: 4: T: (?, 2) f12(a) -> f12(a - 1) [ a >= 1 ] (?, 1) f20(a) -> f12(a - 1) (?, 1) f12(a) -> f20(a) [ 0 >= a + 1 ] (1, 1) f0(a) -> f12(m) [ 15 >= l ] start location: f0 leaf cost: 3 By chaining the transition f12(a) -> f20(a) [ 0 >= a + 1 ] with all transitions in problem 4, the following new transition is obtained: f12(a) -> f12(a - 1) [ 0 >= a + 1 ] We thus obtain the following problem: 5: T: (?, 2) f12(a) -> f12(a - 1) [ 0 >= a + 1 ] (?, 2) f12(a) -> f12(a - 1) [ a >= 1 ] (?, 1) f20(a) -> f12(a - 1) (1, 1) f0(a) -> f12(m) [ 15 >= l ] start location: f0 leaf cost: 3 Testing for reachability in the complexity graph removes the following transition from problem 5: f20(a) -> f12(a - 1) We thus obtain the following problem: 6: T: (?, 2) f12(a) -> f12(a - 1) [ 0 >= a + 1 ] (?, 2) f12(a) -> f12(a - 1) [ a >= 1 ] (1, 1) f0(a) -> f12(m) [ 15 >= l ] start location: f0 leaf cost: 3 By chaining the transition f0(a) -> f12(m) [ 15 >= l ] with all transitions in problem 6, the following new transitions are obtained: f0(a) -> f12(m - 1) [ 15 >= l /\ 0 >= m + 1 ] f0(a) -> f12(m - 1) [ 15 >= l /\ m >= 1 ] We thus obtain the following problem: 7: T: (1, 3) f0(a) -> f12(m - 1) [ 15 >= l /\ 0 >= m + 1 ] (1, 3) f0(a) -> f12(m - 1) [ 15 >= l /\ m >= 1 ] (?, 2) f12(a) -> f12(a - 1) [ 0 >= a + 1 ] (?, 2) f12(a) -> f12(a - 1) [ a >= 1 ] start location: f0 leaf cost: 3 By chaining the transition f0(a) -> f12(m - 1) [ 15 >= l /\ 0 >= m + 1 ] with all transitions in problem 7, the following new transition is obtained: f0(a) -> f12(m - 2) [ 15 >= l /\ 0 >= m + 1 /\ 0 >= m ] We thus obtain the following problem: 8: T: (1, 5) f0(a) -> f12(m - 2) [ 15 >= l /\ 0 >= m + 1 /\ 0 >= m ] (1, 3) f0(a) -> f12(m - 1) [ 15 >= l /\ m >= 1 ] (?, 2) f12(a) -> f12(a - 1) [ 0 >= a + 1 ] (?, 2) f12(a) -> f12(a - 1) [ a >= 1 ] start location: f0 leaf cost: 3 By chaining the transition f0(a) -> f12(m - 2) [ 15 >= l /\ 0 >= m + 1 /\ 0 >= m ] with all transitions in problem 8, the following new transition is obtained: f0(a) -> f12(m - 3) [ 15 >= l /\ 0 >= m + 1 /\ 0 >= m /\ 0 >= m - 1 ] We thus obtain the following problem: 9: T: (1, 7) f0(a) -> f12(m - 3) [ 15 >= l /\ 0 >= m + 1 /\ 0 >= m /\ 0 >= m - 1 ] (1, 3) f0(a) -> f12(m - 1) [ 15 >= l /\ m >= 1 ] (?, 2) f12(a) -> f12(a - 1) [ 0 >= a + 1 ] (?, 2) f12(a) -> f12(a - 1) [ a >= 1 ] start location: f0 leaf cost: 3 By chaining the transition f0(a) -> f12(m - 3) [ 15 >= l /\ 0 >= m + 1 /\ 0 >= m /\ 0 >= m - 1 ] with all transitions in problem 9, the following new transition is obtained: f0(a) -> f12(m - 4) [ 15 >= l /\ 0 >= m + 1 /\ 0 >= m /\ 0 >= m - 1 /\ 0 >= m - 2 ] We thus obtain the following problem: 10: T: (1, 9) f0(a) -> f12(m - 4) [ 15 >= l /\ 0 >= m + 1 /\ 0 >= m /\ 0 >= m - 1 /\ 0 >= m - 2 ] (1, 3) f0(a) -> f12(m - 1) [ 15 >= l /\ m >= 1 ] (?, 2) f12(a) -> f12(a - 1) [ 0 >= a + 1 ] (?, 2) f12(a) -> f12(a - 1) [ a >= 1 ] start location: f0 leaf cost: 3 By chaining the transition f0(a) -> f12(m - 4) [ 15 >= l /\ 0 >= m + 1 /\ 0 >= m /\ 0 >= m - 1 /\ 0 >= m - 2 ] with all transitions in problem 10, the following new transition is obtained: f0(a) -> f12(m - 5) [ 15 >= l /\ 0 >= m + 1 /\ 0 >= m /\ 0 >= m - 1 /\ 0 >= m - 2 /\ 0 >= m - 3 ] We thus obtain the following problem: 11: T: (1, 11) f0(a) -> f12(m - 5) [ 15 >= l /\ 0 >= m + 1 /\ 0 >= m /\ 0 >= m - 1 /\ 0 >= m - 2 /\ 0 >= m - 3 ] (1, 3) f0(a) -> f12(m - 1) [ 15 >= l /\ m >= 1 ] (?, 2) f12(a) -> f12(a - 1) [ 0 >= a + 1 ] (?, 2) f12(a) -> f12(a - 1) [ a >= 1 ] start location: f0 leaf cost: 3 By chaining the transition f0(a) -> f12(m - 5) [ 15 >= l /\ 0 >= m + 1 /\ 0 >= m /\ 0 >= m - 1 /\ 0 >= m - 2 /\ 0 >= m - 3 ] with all transitions in problem 11, the following new transition is obtained: f0(a) -> f12(m - 6) [ 15 >= l /\ 0 >= m + 1 /\ 0 >= m /\ 0 >= m - 1 /\ 0 >= m - 2 /\ 0 >= m - 3 /\ 0 >= m - 4 ] We thus obtain the following problem: 12: T: (1, 13) f0(a) -> f12(m - 6) [ 15 >= l /\ 0 >= m + 1 /\ 0 >= m /\ 0 >= m - 1 /\ 0 >= m - 2 /\ 0 >= m - 3 /\ 0 >= m - 4 ] (1, 3) f0(a) -> f12(m - 1) [ 15 >= l /\ m >= 1 ] (?, 2) f12(a) -> f12(a - 1) [ 0 >= a + 1 ] (?, 2) f12(a) -> f12(a - 1) [ a >= 1 ] start location: f0 leaf cost: 3 By chaining the transition f0(a) -> f12(m - 6) [ 15 >= l /\ 0 >= m + 1 /\ 0 >= m /\ 0 >= m - 1 /\ 0 >= m - 2 /\ 0 >= m - 3 /\ 0 >= m - 4 ] with all transitions in problem 12, the following new transition is obtained: f0(a) -> f12(m - 7) [ 15 >= l /\ 0 >= m + 1 /\ 0 >= m /\ 0 >= m - 1 /\ 0 >= m - 2 /\ 0 >= m - 3 /\ 0 >= m - 4 /\ 0 >= m - 5 ] We thus obtain the following problem: 13: T: (1, 15) f0(a) -> f12(m - 7) [ 15 >= l /\ 0 >= m + 1 /\ 0 >= m /\ 0 >= m - 1 /\ 0 >= m - 2 /\ 0 >= m - 3 /\ 0 >= m - 4 /\ 0 >= m - 5 ] (1, 3) f0(a) -> f12(m - 1) [ 15 >= l /\ m >= 1 ] (?, 2) f12(a) -> f12(a - 1) [ 0 >= a + 1 ] (?, 2) f12(a) -> f12(a - 1) [ a >= 1 ] start location: f0 leaf cost: 3 By chaining the transition f0(a) -> f12(m - 7) [ 15 >= l /\ 0 >= m + 1 /\ 0 >= m /\ 0 >= m - 1 /\ 0 >= m - 2 /\ 0 >= m - 3 /\ 0 >= m - 4 /\ 0 >= m - 5 ] with all transitions in problem 13, the following new transition is obtained: f0(a) -> f12(m - 8) [ 15 >= l /\ 0 >= m + 1 /\ 0 >= m /\ 0 >= m - 1 /\ 0 >= m - 2 /\ 0 >= m - 3 /\ 0 >= m - 4 /\ 0 >= m - 5 /\ 0 >= m - 6 ] We thus obtain the following problem: 14: T: (1, 17) f0(a) -> f12(m - 8) [ 15 >= l /\ 0 >= m + 1 /\ 0 >= m /\ 0 >= m - 1 /\ 0 >= m - 2 /\ 0 >= m - 3 /\ 0 >= m - 4 /\ 0 >= m - 5 /\ 0 >= m - 6 ] (1, 3) f0(a) -> f12(m - 1) [ 15 >= l /\ m >= 1 ] (?, 2) f12(a) -> f12(a - 1) [ 0 >= a + 1 ] (?, 2) f12(a) -> f12(a - 1) [ a >= 1 ] start location: f0 leaf cost: 3 By chaining the transition f0(a) -> f12(m - 8) [ 15 >= l /\ 0 >= m + 1 /\ 0 >= m /\ 0 >= m - 1 /\ 0 >= m - 2 /\ 0 >= m - 3 /\ 0 >= m - 4 /\ 0 >= m - 5 /\ 0 >= m - 6 ] with all transitions in problem 14, the following new transition is obtained: f0(a) -> f12(m - 9) [ 15 >= l /\ 0 >= m + 1 /\ 0 >= m /\ 0 >= m - 1 /\ 0 >= m - 2 /\ 0 >= m - 3 /\ 0 >= m - 4 /\ 0 >= m - 5 /\ 0 >= m - 6 /\ 0 >= m - 7 ] We thus obtain the following problem: 15: T: (1, 19) f0(a) -> f12(m - 9) [ 15 >= l /\ 0 >= m + 1 /\ 0 >= m /\ 0 >= m - 1 /\ 0 >= m - 2 /\ 0 >= m - 3 /\ 0 >= m - 4 /\ 0 >= m - 5 /\ 0 >= m - 6 /\ 0 >= m - 7 ] (1, 3) f0(a) -> f12(m - 1) [ 15 >= l /\ m >= 1 ] (?, 2) f12(a) -> f12(a - 1) [ 0 >= a + 1 ] (?, 2) f12(a) -> f12(a - 1) [ a >= 1 ] start location: f0 leaf cost: 3 By chaining the transition f0(a) -> f12(m - 9) [ 15 >= l /\ 0 >= m + 1 /\ 0 >= m /\ 0 >= m - 1 /\ 0 >= m - 2 /\ 0 >= m - 3 /\ 0 >= m - 4 /\ 0 >= m - 5 /\ 0 >= m - 6 /\ 0 >= m - 7 ] with all transitions in problem 15, the following new transition is obtained: f0(a) -> f12(m - 10) [ 15 >= l /\ 0 >= m + 1 /\ 0 >= m /\ 0 >= m - 1 /\ 0 >= m - 2 /\ 0 >= m - 3 /\ 0 >= m - 4 /\ 0 >= m - 5 /\ 0 >= m - 6 /\ 0 >= m - 7 /\ 0 >= m - 8 ] We thus obtain the following problem: 16: T: (1, 21) f0(a) -> f12(m - 10) [ 15 >= l /\ 0 >= m + 1 /\ 0 >= m /\ 0 >= m - 1 /\ 0 >= m - 2 /\ 0 >= m - 3 /\ 0 >= m - 4 /\ 0 >= m - 5 /\ 0 >= m - 6 /\ 0 >= m - 7 /\ 0 >= m - 8 ] (1, 3) f0(a) -> f12(m - 1) [ 15 >= l /\ m >= 1 ] (?, 2) f12(a) -> f12(a - 1) [ 0 >= a + 1 ] (?, 2) f12(a) -> f12(a - 1) [ a >= 1 ] start location: f0 leaf cost: 3 By chaining the transition f0(a) -> f12(m - 10) [ 15 >= l /\ 0 >= m + 1 /\ 0 >= m /\ 0 >= m - 1 /\ 0 >= m - 2 /\ 0 >= m - 3 /\ 0 >= m - 4 /\ 0 >= m - 5 /\ 0 >= m - 6 /\ 0 >= m - 7 /\ 0 >= m - 8 ] with all transitions in problem 16, the following new transition is obtained: f0(a) -> f12(m - 11) [ 15 >= l /\ 0 >= m + 1 /\ 0 >= m /\ 0 >= m - 1 /\ 0 >= m - 2 /\ 0 >= m - 3 /\ 0 >= m - 4 /\ 0 >= m - 5 /\ 0 >= m - 6 /\ 0 >= m - 7 /\ 0 >= m - 8 /\ 0 >= m - 9 ] We thus obtain the following problem: 17: T: (1, 23) f0(a) -> f12(m - 11) [ 15 >= l /\ 0 >= m + 1 /\ 0 >= m /\ 0 >= m - 1 /\ 0 >= m - 2 /\ 0 >= m - 3 /\ 0 >= m - 4 /\ 0 >= m - 5 /\ 0 >= m - 6 /\ 0 >= m - 7 /\ 0 >= m - 8 /\ 0 >= m - 9 ] (1, 3) f0(a) -> f12(m - 1) [ 15 >= l /\ m >= 1 ] (?, 2) f12(a) -> f12(a - 1) [ 0 >= a + 1 ] (?, 2) f12(a) -> f12(a - 1) [ a >= 1 ] start location: f0 leaf cost: 3 By chaining the transition f0(a) -> f12(m - 11) [ 15 >= l /\ 0 >= m + 1 /\ 0 >= m /\ 0 >= m - 1 /\ 0 >= m - 2 /\ 0 >= m - 3 /\ 0 >= m - 4 /\ 0 >= m - 5 /\ 0 >= m - 6 /\ 0 >= m - 7 /\ 0 >= m - 8 /\ 0 >= m - 9 ] with all transitions in problem 17, the following new transition is obtained: f0(a) -> f12(m - 12) [ 15 >= l /\ 0 >= m + 1 /\ 0 >= m /\ 0 >= m - 1 /\ 0 >= m - 2 /\ 0 >= m - 3 /\ 0 >= m - 4 /\ 0 >= m - 5 /\ 0 >= m - 6 /\ 0 >= m - 7 /\ 0 >= m - 8 /\ 0 >= m - 9 /\ 0 >= m - 10 ] We thus obtain the following problem: 18: T: (1, 25) f0(a) -> f12(m - 12) [ 15 >= l /\ 0 >= m + 1 /\ 0 >= m /\ 0 >= m - 1 /\ 0 >= m - 2 /\ 0 >= m - 3 /\ 0 >= m - 4 /\ 0 >= m - 5 /\ 0 >= m - 6 /\ 0 >= m - 7 /\ 0 >= m - 8 /\ 0 >= m - 9 /\ 0 >= m - 10 ] (1, 3) f0(a) -> f12(m - 1) [ 15 >= l /\ m >= 1 ] (?, 2) f12(a) -> f12(a - 1) [ 0 >= a + 1 ] (?, 2) f12(a) -> f12(a - 1) [ a >= 1 ] start location: f0 leaf cost: 3 By chaining the transition f0(a) -> f12(m - 12) [ 15 >= l /\ 0 >= m + 1 /\ 0 >= m /\ 0 >= m - 1 /\ 0 >= m - 2 /\ 0 >= m - 3 /\ 0 >= m - 4 /\ 0 >= m - 5 /\ 0 >= m - 6 /\ 0 >= m - 7 /\ 0 >= m - 8 /\ 0 >= m - 9 /\ 0 >= m - 10 ] with all transitions in problem 18, the following new transition is obtained: f0(a) -> f12(m - 13) [ 15 >= l /\ 0 >= m + 1 /\ 0 >= m /\ 0 >= m - 1 /\ 0 >= m - 2 /\ 0 >= m - 3 /\ 0 >= m - 4 /\ 0 >= m - 5 /\ 0 >= m - 6 /\ 0 >= m - 7 /\ 0 >= m - 8 /\ 0 >= m - 9 /\ 0 >= m - 10 /\ 0 >= m - 11 ] We thus obtain the following problem: 19: T: (1, 27) f0(a) -> f12(m - 13) [ 15 >= l /\ 0 >= m + 1 /\ 0 >= m /\ 0 >= m - 1 /\ 0 >= m - 2 /\ 0 >= m - 3 /\ 0 >= m - 4 /\ 0 >= m - 5 /\ 0 >= m - 6 /\ 0 >= m - 7 /\ 0 >= m - 8 /\ 0 >= m - 9 /\ 0 >= m - 10 /\ 0 >= m - 11 ] (1, 3) f0(a) -> f12(m - 1) [ 15 >= l /\ m >= 1 ] (?, 2) f12(a) -> f12(a - 1) [ 0 >= a + 1 ] (?, 2) f12(a) -> f12(a - 1) [ a >= 1 ] start location: f0 leaf cost: 3 Complexity upper bound ? Time: 0.805 sec (SMT: 0.746 sec)