MAYBE Initial complexity problem: 1: T: (1, 1) f10(a, b, c, d, e, f) -> f4(4, 0, 0, d, e, f) (?, 1) f4(a, b, c, d, e, f) -> f9(a, b, c, c, c, f) (?, 1) f7(a, b, c, d, e, f) -> f4(a, b + 1, g, h, e, g) (?, 1) f4(a, b, c, d, e, f) -> f4(a, b + 1, g, h, e, g) (?, 1) f6(a, b, c, d, e, f) -> f4(a, b + 1, g, h, e, g) start location: f10 leaf cost: 0 Repeatedly removing leaves of the complexity graph in problem 1 produces the following problem: 2: T: (1, 1) f10(a, b, c, d, e, f) -> f4(4, 0, 0, d, e, f) (?, 1) f7(a, b, c, d, e, f) -> f4(a, b + 1, g, h, e, g) (?, 1) f4(a, b, c, d, e, f) -> f4(a, b + 1, g, h, e, g) (?, 1) f6(a, b, c, d, e, f) -> f4(a, b + 1, g, h, e, g) start location: f10 leaf cost: 1 Testing for reachability in the complexity graph removes the following transitions from problem 2: f7(a, b, c, d, e, f) -> f4(a, b + 1, g, h, e, g) f6(a, b, c, d, e, f) -> f4(a, b + 1, g, h, e, g) We thus obtain the following problem: 3: T: (?, 1) f4(a, b, c, d, e, f) -> f4(a, b + 1, g, h, e, g) (1, 1) f10(a, b, c, d, e, f) -> f4(4, 0, 0, d, e, f) start location: f10 leaf cost: 1 Applied AI with 'oct' on problem 3 to obtain the following invariants: For symbol f4: X_2 >= 0 /\ X_1 + X_2 - 4 >= 0 /\ -X_1 + X_2 + 4 >= 0 /\ -X_1 + 4 >= 0 /\ X_1 - 4 >= 0 This yielded the following problem: 4: T: (1, 1) f10(a, b, c, d, e, f) -> f4(4, 0, 0, d, e, f) (?, 1) f4(a, b, c, d, e, f) -> f4(a, b + 1, g, h, e, g) [ b >= 0 /\ a + b - 4 >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ a - 4 >= 0 ] start location: f10 leaf cost: 1 By chaining the transition f10(a, b, c, d, e, f) -> f4(4, 0, 0, d, e, f) with all transitions in problem 4, the following new transition is obtained: f10(a, b, c, d, e, f) -> f4(4, 1, g, h, e, g) [ 0 >= 0 ] We thus obtain the following problem: 5: T: (1, 2) f10(a, b, c, d, e, f) -> f4(4, 1, g, h, e, g) [ 0 >= 0 ] (?, 1) f4(a, b, c, d, e, f) -> f4(a, b + 1, g, h, e, g) [ b >= 0 /\ a + b - 4 >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ a - 4 >= 0 ] start location: f10 leaf cost: 1 By chaining the transition f10(a, b, c, d, e, f) -> f4(4, 1, g, h, e, g) [ 0 >= 0 ] with all transitions in problem 5, the following new transition is obtained: f10(a, b, c, d, e, f) -> f4(4, 2, g', h', e, g') [ 0 >= 0 /\ 1 >= 0 ] We thus obtain the following problem: 6: T: (1, 3) f10(a, b, c, d, e, f) -> f4(4, 2, g', h', e, g') [ 0 >= 0 /\ 1 >= 0 ] (?, 1) f4(a, b, c, d, e, f) -> f4(a, b + 1, g, h, e, g) [ b >= 0 /\ a + b - 4 >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ a - 4 >= 0 ] start location: f10 leaf cost: 1 By chaining the transition f10(a, b, c, d, e, f) -> f4(4, 2, g', h', e, g') [ 0 >= 0 /\ 1 >= 0 ] with all transitions in problem 6, the following new transition is obtained: f10(a, b, c, d, e, f) -> f4(4, 3, g, h, e, g) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 ] We thus obtain the following problem: 7: T: (1, 4) f10(a, b, c, d, e, f) -> f4(4, 3, g, h, e, g) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 ] (?, 1) f4(a, b, c, d, e, f) -> f4(a, b + 1, g, h, e, g) [ b >= 0 /\ a + b - 4 >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ a - 4 >= 0 ] start location: f10 leaf cost: 1 By chaining the transition f10(a, b, c, d, e, f) -> f4(4, 3, g, h, e, g) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 ] with all transitions in problem 7, the following new transition is obtained: f10(a, b, c, d, e, f) -> f4(4, 4, g', h', e, g') [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 ] We thus obtain the following problem: 8: T: (1, 5) f10(a, b, c, d, e, f) -> f4(4, 4, g', h', e, g') [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 ] (?, 1) f4(a, b, c, d, e, f) -> f4(a, b + 1, g, h, e, g) [ b >= 0 /\ a + b - 4 >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ a - 4 >= 0 ] start location: f10 leaf cost: 1 By chaining the transition f10(a, b, c, d, e, f) -> f4(4, 4, g', h', e, g') [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 ] with all transitions in problem 8, the following new transition is obtained: f10(a, b, c, d, e, f) -> f4(4, 5, g, h, e, g) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 ] We thus obtain the following problem: 9: T: (1, 6) f10(a, b, c, d, e, f) -> f4(4, 5, g, h, e, g) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 ] (?, 1) f4(a, b, c, d, e, f) -> f4(a, b + 1, g, h, e, g) [ b >= 0 /\ a + b - 4 >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ a - 4 >= 0 ] start location: f10 leaf cost: 1 By chaining the transition f10(a, b, c, d, e, f) -> f4(4, 5, g, h, e, g) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 ] with all transitions in problem 9, the following new transition is obtained: f10(a, b, c, d, e, f) -> f4(4, 6, g', h', e, g') [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 ] We thus obtain the following problem: 10: T: (1, 7) f10(a, b, c, d, e, f) -> f4(4, 6, g', h', e, g') [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 ] (?, 1) f4(a, b, c, d, e, f) -> f4(a, b + 1, g, h, e, g) [ b >= 0 /\ a + b - 4 >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ a - 4 >= 0 ] start location: f10 leaf cost: 1 By chaining the transition f10(a, b, c, d, e, f) -> f4(4, 6, g', h', e, g') [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 ] with all transitions in problem 10, the following new transition is obtained: f10(a, b, c, d, e, f) -> f4(4, 7, g, h, e, g) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 ] We thus obtain the following problem: 11: T: (1, 8) f10(a, b, c, d, e, f) -> f4(4, 7, g, h, e, g) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 ] (?, 1) f4(a, b, c, d, e, f) -> f4(a, b + 1, g, h, e, g) [ b >= 0 /\ a + b - 4 >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ a - 4 >= 0 ] start location: f10 leaf cost: 1 By chaining the transition f10(a, b, c, d, e, f) -> f4(4, 7, g, h, e, g) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 ] with all transitions in problem 11, the following new transition is obtained: f10(a, b, c, d, e, f) -> f4(4, 8, g', h', e, g') [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 ] We thus obtain the following problem: 12: T: (1, 9) f10(a, b, c, d, e, f) -> f4(4, 8, g', h', e, g') [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 ] (?, 1) f4(a, b, c, d, e, f) -> f4(a, b + 1, g, h, e, g) [ b >= 0 /\ a + b - 4 >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ a - 4 >= 0 ] start location: f10 leaf cost: 1 By chaining the transition f10(a, b, c, d, e, f) -> f4(4, 8, g', h', e, g') [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 ] with all transitions in problem 12, the following new transition is obtained: f10(a, b, c, d, e, f) -> f4(4, 9, g, h, e, g) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 /\ 8 >= 0 ] We thus obtain the following problem: 13: T: (1, 10) f10(a, b, c, d, e, f) -> f4(4, 9, g, h, e, g) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 /\ 8 >= 0 ] (?, 1) f4(a, b, c, d, e, f) -> f4(a, b + 1, g, h, e, g) [ b >= 0 /\ a + b - 4 >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ a - 4 >= 0 ] start location: f10 leaf cost: 1 By chaining the transition f10(a, b, c, d, e, f) -> f4(4, 9, g, h, e, g) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 /\ 8 >= 0 ] with all transitions in problem 13, the following new transition is obtained: f10(a, b, c, d, e, f) -> f4(4, 10, g', h', e, g') [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 /\ 8 >= 0 /\ 9 >= 0 ] We thus obtain the following problem: 14: T: (1, 11) f10(a, b, c, d, e, f) -> f4(4, 10, g', h', e, g') [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 /\ 8 >= 0 /\ 9 >= 0 ] (?, 1) f4(a, b, c, d, e, f) -> f4(a, b + 1, g, h, e, g) [ b >= 0 /\ a + b - 4 >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ a - 4 >= 0 ] start location: f10 leaf cost: 1 By chaining the transition f10(a, b, c, d, e, f) -> f4(4, 10, g', h', e, g') [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 /\ 8 >= 0 /\ 9 >= 0 ] with all transitions in problem 14, the following new transition is obtained: f10(a, b, c, d, e, f) -> f4(4, 11, g, h, e, g) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 /\ 8 >= 0 /\ 9 >= 0 /\ 10 >= 0 ] We thus obtain the following problem: 15: T: (1, 12) f10(a, b, c, d, e, f) -> f4(4, 11, g, h, e, g) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 /\ 8 >= 0 /\ 9 >= 0 /\ 10 >= 0 ] (?, 1) f4(a, b, c, d, e, f) -> f4(a, b + 1, g, h, e, g) [ b >= 0 /\ a + b - 4 >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ a - 4 >= 0 ] start location: f10 leaf cost: 1 By chaining the transition f10(a, b, c, d, e, f) -> f4(4, 11, g, h, e, g) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 /\ 8 >= 0 /\ 9 >= 0 /\ 10 >= 0 ] with all transitions in problem 15, the following new transition is obtained: f10(a, b, c, d, e, f) -> f4(4, 12, g', h', e, g') [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 /\ 8 >= 0 /\ 9 >= 0 /\ 10 >= 0 /\ 11 >= 0 ] We thus obtain the following problem: 16: T: (1, 13) f10(a, b, c, d, e, f) -> f4(4, 12, g', h', e, g') [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 /\ 8 >= 0 /\ 9 >= 0 /\ 10 >= 0 /\ 11 >= 0 ] (?, 1) f4(a, b, c, d, e, f) -> f4(a, b + 1, g, h, e, g) [ b >= 0 /\ a + b - 4 >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ a - 4 >= 0 ] start location: f10 leaf cost: 1 By chaining the transition f10(a, b, c, d, e, f) -> f4(4, 12, g', h', e, g') [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 /\ 8 >= 0 /\ 9 >= 0 /\ 10 >= 0 /\ 11 >= 0 ] with all transitions in problem 16, the following new transition is obtained: f10(a, b, c, d, e, f) -> f4(4, 13, g, h, e, g) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 /\ 8 >= 0 /\ 9 >= 0 /\ 10 >= 0 /\ 11 >= 0 /\ 12 >= 0 ] We thus obtain the following problem: 17: T: (1, 14) f10(a, b, c, d, e, f) -> f4(4, 13, g, h, e, g) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 /\ 8 >= 0 /\ 9 >= 0 /\ 10 >= 0 /\ 11 >= 0 /\ 12 >= 0 ] (?, 1) f4(a, b, c, d, e, f) -> f4(a, b + 1, g, h, e, g) [ b >= 0 /\ a + b - 4 >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ a - 4 >= 0 ] start location: f10 leaf cost: 1 By chaining the transition f10(a, b, c, d, e, f) -> f4(4, 13, g, h, e, g) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 /\ 8 >= 0 /\ 9 >= 0 /\ 10 >= 0 /\ 11 >= 0 /\ 12 >= 0 ] with all transitions in problem 17, the following new transition is obtained: f10(a, b, c, d, e, f) -> f4(4, 14, g', h', e, g') [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 /\ 8 >= 0 /\ 9 >= 0 /\ 10 >= 0 /\ 11 >= 0 /\ 12 >= 0 /\ 13 >= 0 ] We thus obtain the following problem: 18: T: (1, 15) f10(a, b, c, d, e, f) -> f4(4, 14, g', h', e, g') [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 /\ 8 >= 0 /\ 9 >= 0 /\ 10 >= 0 /\ 11 >= 0 /\ 12 >= 0 /\ 13 >= 0 ] (?, 1) f4(a, b, c, d, e, f) -> f4(a, b + 1, g, h, e, g) [ b >= 0 /\ a + b - 4 >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ a - 4 >= 0 ] start location: f10 leaf cost: 1 By chaining the transition f10(a, b, c, d, e, f) -> f4(4, 14, g', h', e, g') [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 /\ 8 >= 0 /\ 9 >= 0 /\ 10 >= 0 /\ 11 >= 0 /\ 12 >= 0 /\ 13 >= 0 ] with all transitions in problem 18, the following new transition is obtained: f10(a, b, c, d, e, f) -> f4(4, 15, g, h, e, g) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 /\ 8 >= 0 /\ 9 >= 0 /\ 10 >= 0 /\ 11 >= 0 /\ 12 >= 0 /\ 13 >= 0 /\ 14 >= 0 ] We thus obtain the following problem: 19: T: (1, 16) f10(a, b, c, d, e, f) -> f4(4, 15, g, h, e, g) [ 0 >= 0 /\ 1 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 4 >= 0 /\ 5 >= 0 /\ 6 >= 0 /\ 7 >= 0 /\ 8 >= 0 /\ 9 >= 0 /\ 10 >= 0 /\ 11 >= 0 /\ 12 >= 0 /\ 13 >= 0 /\ 14 >= 0 ] (?, 1) f4(a, b, c, d, e, f) -> f4(a, b + 1, g, h, e, g) [ b >= 0 /\ a + b - 4 >= 0 /\ -a + b + 4 >= 0 /\ -a + 4 >= 0 /\ a - 4 >= 0 ] start location: f10 leaf cost: 1 Complexity upper bound ? Time: 0.988 sec (SMT: 0.916 sec)