MAYBE Initial complexity problem: 1: T: (1, 1) f0(a, b, c) -> f5(0, 0, c) (?, 1) f5(a, b, c) -> f5(a + 1, b + 2, d + e) (?, 1) f5(a, b, c) -> f16(a, b, c) start location: f0 leaf cost: 0 Repeatedly removing leaves of the complexity graph in problem 1 produces the following problem: 2: T: (1, 1) f0(a, b, c) -> f5(0, 0, c) (?, 1) f5(a, b, c) -> f5(a + 1, b + 2, d + e) start location: f0 leaf cost: 1 Applied AI with 'oct' on problem 2 to obtain the following invariants: For symbol f5: X_2 >= 0 /\ X_1 + X_2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 >= 0 This yielded the following problem: 3: T: (?, 1) f5(a, b, c) -> f5(a + 1, b + 2, d + e) [ b >= 0 /\ a + b >= 0 /\ -a + b >= 0 /\ a >= 0 ] (1, 1) f0(a, b, c) -> f5(0, 0, c) start location: f0 leaf cost: 1 By chaining the transition f0(a, b, c) -> f5(0, 0, c) with all transitions in problem 3, the following new transition is obtained: f0(a, b, c) -> f5(1, 2, d + e) [ 0 >= 0 ] We thus obtain the following problem: 4: T: (1, 2) f0(a, b, c) -> f5(1, 2, d + e) [ 0 >= 0 ] (?, 1) f5(a, b, c) -> f5(a + 1, b + 2, d + e) [ b >= 0 /\ a + b >= 0 /\ -a + b >= 0 /\ a >= 0 ] start location: f0 leaf cost: 1 By chaining the transition f0(a, b, c) -> f5(1, 2, d + e) [ 0 >= 0 ] with all transitions in problem 4, the following new transition is obtained: f0(a, b, c) -> f5(2, 4, d' + e') [ 0 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 1 >= 0 ] We thus obtain the following problem: 5: T: (1, 3) f0(a, b, c) -> f5(2, 4, d' + e') [ 0 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 1 >= 0 ] (?, 1) f5(a, b, c) -> f5(a + 1, b + 2, d + e) [ b >= 0 /\ a + b >= 0 /\ -a + b >= 0 /\ a >= 0 ] start location: f0 leaf cost: 1 By chaining the transition f0(a, b, c) -> f5(2, 4, d' + e') [ 0 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 1 >= 0 ] with all transitions in problem 5, the following new transition is obtained: f0(a, b, c) -> f5(3, 6, d + e) [ 0 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 1 >= 0 /\ 4 >= 0 /\ 6 >= 0 ] We thus obtain the following problem: 6: T: (1, 4) f0(a, b, c) -> f5(3, 6, d + e) [ 0 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 1 >= 0 /\ 4 >= 0 /\ 6 >= 0 ] (?, 1) f5(a, b, c) -> f5(a + 1, b + 2, d + e) [ b >= 0 /\ a + b >= 0 /\ -a + b >= 0 /\ a >= 0 ] start location: f0 leaf cost: 1 By chaining the transition f0(a, b, c) -> f5(3, 6, d + e) [ 0 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 1 >= 0 /\ 4 >= 0 /\ 6 >= 0 ] with all transitions in problem 6, the following new transition is obtained: f0(a, b, c) -> f5(4, 8, d' + e') [ 0 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 1 >= 0 /\ 4 >= 0 /\ 6 >= 0 /\ 9 >= 0 ] We thus obtain the following problem: 7: T: (1, 5) f0(a, b, c) -> f5(4, 8, d' + e') [ 0 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 1 >= 0 /\ 4 >= 0 /\ 6 >= 0 /\ 9 >= 0 ] (?, 1) f5(a, b, c) -> f5(a + 1, b + 2, d + e) [ b >= 0 /\ a + b >= 0 /\ -a + b >= 0 /\ a >= 0 ] start location: f0 leaf cost: 1 By chaining the transition f0(a, b, c) -> f5(4, 8, d' + e') [ 0 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 1 >= 0 /\ 4 >= 0 /\ 6 >= 0 /\ 9 >= 0 ] with all transitions in problem 7, the following new transition is obtained: f0(a, b, c) -> f5(5, 10, d + e) [ 0 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 1 >= 0 /\ 4 >= 0 /\ 6 >= 0 /\ 9 >= 0 /\ 8 >= 0 /\ 12 >= 0 ] We thus obtain the following problem: 8: T: (1, 6) f0(a, b, c) -> f5(5, 10, d + e) [ 0 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 1 >= 0 /\ 4 >= 0 /\ 6 >= 0 /\ 9 >= 0 /\ 8 >= 0 /\ 12 >= 0 ] (?, 1) f5(a, b, c) -> f5(a + 1, b + 2, d + e) [ b >= 0 /\ a + b >= 0 /\ -a + b >= 0 /\ a >= 0 ] start location: f0 leaf cost: 1 By chaining the transition f0(a, b, c) -> f5(5, 10, d + e) [ 0 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 1 >= 0 /\ 4 >= 0 /\ 6 >= 0 /\ 9 >= 0 /\ 8 >= 0 /\ 12 >= 0 ] with all transitions in problem 8, the following new transition is obtained: f0(a, b, c) -> f5(6, 12, d' + e') [ 0 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 1 >= 0 /\ 4 >= 0 /\ 6 >= 0 /\ 9 >= 0 /\ 8 >= 0 /\ 12 >= 0 /\ 10 >= 0 /\ 15 >= 0 /\ 5 >= 0 ] We thus obtain the following problem: 9: T: (1, 7) f0(a, b, c) -> f5(6, 12, d' + e') [ 0 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 1 >= 0 /\ 4 >= 0 /\ 6 >= 0 /\ 9 >= 0 /\ 8 >= 0 /\ 12 >= 0 /\ 10 >= 0 /\ 15 >= 0 /\ 5 >= 0 ] (?, 1) f5(a, b, c) -> f5(a + 1, b + 2, d + e) [ b >= 0 /\ a + b >= 0 /\ -a + b >= 0 /\ a >= 0 ] start location: f0 leaf cost: 1 By chaining the transition f0(a, b, c) -> f5(6, 12, d' + e') [ 0 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 1 >= 0 /\ 4 >= 0 /\ 6 >= 0 /\ 9 >= 0 /\ 8 >= 0 /\ 12 >= 0 /\ 10 >= 0 /\ 15 >= 0 /\ 5 >= 0 ] with all transitions in problem 9, the following new transition is obtained: f0(a, b, c) -> f5(7, 14, d + e) [ 0 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 1 >= 0 /\ 4 >= 0 /\ 6 >= 0 /\ 9 >= 0 /\ 8 >= 0 /\ 12 >= 0 /\ 10 >= 0 /\ 15 >= 0 /\ 5 >= 0 /\ 18 >= 0 ] We thus obtain the following problem: 10: T: (1, 8) f0(a, b, c) -> f5(7, 14, d + e) [ 0 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 1 >= 0 /\ 4 >= 0 /\ 6 >= 0 /\ 9 >= 0 /\ 8 >= 0 /\ 12 >= 0 /\ 10 >= 0 /\ 15 >= 0 /\ 5 >= 0 /\ 18 >= 0 ] (?, 1) f5(a, b, c) -> f5(a + 1, b + 2, d + e) [ b >= 0 /\ a + b >= 0 /\ -a + b >= 0 /\ a >= 0 ] start location: f0 leaf cost: 1 By chaining the transition f0(a, b, c) -> f5(7, 14, d + e) [ 0 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 1 >= 0 /\ 4 >= 0 /\ 6 >= 0 /\ 9 >= 0 /\ 8 >= 0 /\ 12 >= 0 /\ 10 >= 0 /\ 15 >= 0 /\ 5 >= 0 /\ 18 >= 0 ] with all transitions in problem 10, the following new transition is obtained: f0(a, b, c) -> f5(8, 16, d' + e') [ 0 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 1 >= 0 /\ 4 >= 0 /\ 6 >= 0 /\ 9 >= 0 /\ 8 >= 0 /\ 12 >= 0 /\ 10 >= 0 /\ 15 >= 0 /\ 5 >= 0 /\ 18 >= 0 /\ 14 >= 0 /\ 21 >= 0 /\ 7 >= 0 ] We thus obtain the following problem: 11: T: (1, 9) f0(a, b, c) -> f5(8, 16, d' + e') [ 0 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 1 >= 0 /\ 4 >= 0 /\ 6 >= 0 /\ 9 >= 0 /\ 8 >= 0 /\ 12 >= 0 /\ 10 >= 0 /\ 15 >= 0 /\ 5 >= 0 /\ 18 >= 0 /\ 14 >= 0 /\ 21 >= 0 /\ 7 >= 0 ] (?, 1) f5(a, b, c) -> f5(a + 1, b + 2, d + e) [ b >= 0 /\ a + b >= 0 /\ -a + b >= 0 /\ a >= 0 ] start location: f0 leaf cost: 1 By chaining the transition f0(a, b, c) -> f5(8, 16, d' + e') [ 0 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 1 >= 0 /\ 4 >= 0 /\ 6 >= 0 /\ 9 >= 0 /\ 8 >= 0 /\ 12 >= 0 /\ 10 >= 0 /\ 15 >= 0 /\ 5 >= 0 /\ 18 >= 0 /\ 14 >= 0 /\ 21 >= 0 /\ 7 >= 0 ] with all transitions in problem 11, the following new transition is obtained: f0(a, b, c) -> f5(9, 18, d + e) [ 0 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 1 >= 0 /\ 4 >= 0 /\ 6 >= 0 /\ 9 >= 0 /\ 8 >= 0 /\ 12 >= 0 /\ 10 >= 0 /\ 15 >= 0 /\ 5 >= 0 /\ 18 >= 0 /\ 14 >= 0 /\ 21 >= 0 /\ 7 >= 0 /\ 16 >= 0 /\ 24 >= 0 ] We thus obtain the following problem: 12: T: (1, 10) f0(a, b, c) -> f5(9, 18, d + e) [ 0 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 1 >= 0 /\ 4 >= 0 /\ 6 >= 0 /\ 9 >= 0 /\ 8 >= 0 /\ 12 >= 0 /\ 10 >= 0 /\ 15 >= 0 /\ 5 >= 0 /\ 18 >= 0 /\ 14 >= 0 /\ 21 >= 0 /\ 7 >= 0 /\ 16 >= 0 /\ 24 >= 0 ] (?, 1) f5(a, b, c) -> f5(a + 1, b + 2, d + e) [ b >= 0 /\ a + b >= 0 /\ -a + b >= 0 /\ a >= 0 ] start location: f0 leaf cost: 1 By chaining the transition f0(a, b, c) -> f5(9, 18, d + e) [ 0 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 1 >= 0 /\ 4 >= 0 /\ 6 >= 0 /\ 9 >= 0 /\ 8 >= 0 /\ 12 >= 0 /\ 10 >= 0 /\ 15 >= 0 /\ 5 >= 0 /\ 18 >= 0 /\ 14 >= 0 /\ 21 >= 0 /\ 7 >= 0 /\ 16 >= 0 /\ 24 >= 0 ] with all transitions in problem 12, the following new transition is obtained: f0(a, b, c) -> f5(10, 20, d' + e') [ 0 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 1 >= 0 /\ 4 >= 0 /\ 6 >= 0 /\ 9 >= 0 /\ 8 >= 0 /\ 12 >= 0 /\ 10 >= 0 /\ 15 >= 0 /\ 5 >= 0 /\ 18 >= 0 /\ 14 >= 0 /\ 21 >= 0 /\ 7 >= 0 /\ 16 >= 0 /\ 24 >= 0 /\ 27 >= 0 ] We thus obtain the following problem: 13: T: (1, 11) f0(a, b, c) -> f5(10, 20, d' + e') [ 0 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 1 >= 0 /\ 4 >= 0 /\ 6 >= 0 /\ 9 >= 0 /\ 8 >= 0 /\ 12 >= 0 /\ 10 >= 0 /\ 15 >= 0 /\ 5 >= 0 /\ 18 >= 0 /\ 14 >= 0 /\ 21 >= 0 /\ 7 >= 0 /\ 16 >= 0 /\ 24 >= 0 /\ 27 >= 0 ] (?, 1) f5(a, b, c) -> f5(a + 1, b + 2, d + e) [ b >= 0 /\ a + b >= 0 /\ -a + b >= 0 /\ a >= 0 ] start location: f0 leaf cost: 1 By chaining the transition f0(a, b, c) -> f5(10, 20, d' + e') [ 0 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 1 >= 0 /\ 4 >= 0 /\ 6 >= 0 /\ 9 >= 0 /\ 8 >= 0 /\ 12 >= 0 /\ 10 >= 0 /\ 15 >= 0 /\ 5 >= 0 /\ 18 >= 0 /\ 14 >= 0 /\ 21 >= 0 /\ 7 >= 0 /\ 16 >= 0 /\ 24 >= 0 /\ 27 >= 0 ] with all transitions in problem 13, the following new transition is obtained: f0(a, b, c) -> f5(11, 22, d + e) [ 0 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 1 >= 0 /\ 4 >= 0 /\ 6 >= 0 /\ 9 >= 0 /\ 8 >= 0 /\ 12 >= 0 /\ 10 >= 0 /\ 15 >= 0 /\ 5 >= 0 /\ 18 >= 0 /\ 14 >= 0 /\ 21 >= 0 /\ 7 >= 0 /\ 16 >= 0 /\ 24 >= 0 /\ 27 >= 0 /\ 20 >= 0 /\ 30 >= 0 ] We thus obtain the following problem: 14: T: (1, 12) f0(a, b, c) -> f5(11, 22, d + e) [ 0 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 1 >= 0 /\ 4 >= 0 /\ 6 >= 0 /\ 9 >= 0 /\ 8 >= 0 /\ 12 >= 0 /\ 10 >= 0 /\ 15 >= 0 /\ 5 >= 0 /\ 18 >= 0 /\ 14 >= 0 /\ 21 >= 0 /\ 7 >= 0 /\ 16 >= 0 /\ 24 >= 0 /\ 27 >= 0 /\ 20 >= 0 /\ 30 >= 0 ] (?, 1) f5(a, b, c) -> f5(a + 1, b + 2, d + e) [ b >= 0 /\ a + b >= 0 /\ -a + b >= 0 /\ a >= 0 ] start location: f0 leaf cost: 1 By chaining the transition f0(a, b, c) -> f5(11, 22, d + e) [ 0 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 1 >= 0 /\ 4 >= 0 /\ 6 >= 0 /\ 9 >= 0 /\ 8 >= 0 /\ 12 >= 0 /\ 10 >= 0 /\ 15 >= 0 /\ 5 >= 0 /\ 18 >= 0 /\ 14 >= 0 /\ 21 >= 0 /\ 7 >= 0 /\ 16 >= 0 /\ 24 >= 0 /\ 27 >= 0 /\ 20 >= 0 /\ 30 >= 0 ] with all transitions in problem 14, the following new transition is obtained: f0(a, b, c) -> f5(12, 24, d' + e') [ 0 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 1 >= 0 /\ 4 >= 0 /\ 6 >= 0 /\ 9 >= 0 /\ 8 >= 0 /\ 12 >= 0 /\ 10 >= 0 /\ 15 >= 0 /\ 5 >= 0 /\ 18 >= 0 /\ 14 >= 0 /\ 21 >= 0 /\ 7 >= 0 /\ 16 >= 0 /\ 24 >= 0 /\ 27 >= 0 /\ 20 >= 0 /\ 30 >= 0 /\ 22 >= 0 /\ 33 >= 0 /\ 11 >= 0 ] We thus obtain the following problem: 15: T: (1, 13) f0(a, b, c) -> f5(12, 24, d' + e') [ 0 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 1 >= 0 /\ 4 >= 0 /\ 6 >= 0 /\ 9 >= 0 /\ 8 >= 0 /\ 12 >= 0 /\ 10 >= 0 /\ 15 >= 0 /\ 5 >= 0 /\ 18 >= 0 /\ 14 >= 0 /\ 21 >= 0 /\ 7 >= 0 /\ 16 >= 0 /\ 24 >= 0 /\ 27 >= 0 /\ 20 >= 0 /\ 30 >= 0 /\ 22 >= 0 /\ 33 >= 0 /\ 11 >= 0 ] (?, 1) f5(a, b, c) -> f5(a + 1, b + 2, d + e) [ b >= 0 /\ a + b >= 0 /\ -a + b >= 0 /\ a >= 0 ] start location: f0 leaf cost: 1 By chaining the transition f0(a, b, c) -> f5(12, 24, d' + e') [ 0 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 1 >= 0 /\ 4 >= 0 /\ 6 >= 0 /\ 9 >= 0 /\ 8 >= 0 /\ 12 >= 0 /\ 10 >= 0 /\ 15 >= 0 /\ 5 >= 0 /\ 18 >= 0 /\ 14 >= 0 /\ 21 >= 0 /\ 7 >= 0 /\ 16 >= 0 /\ 24 >= 0 /\ 27 >= 0 /\ 20 >= 0 /\ 30 >= 0 /\ 22 >= 0 /\ 33 >= 0 /\ 11 >= 0 ] with all transitions in problem 15, the following new transition is obtained: f0(a, b, c) -> f5(13, 26, d + e) [ 0 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 1 >= 0 /\ 4 >= 0 /\ 6 >= 0 /\ 9 >= 0 /\ 8 >= 0 /\ 12 >= 0 /\ 10 >= 0 /\ 15 >= 0 /\ 5 >= 0 /\ 18 >= 0 /\ 14 >= 0 /\ 21 >= 0 /\ 7 >= 0 /\ 16 >= 0 /\ 24 >= 0 /\ 27 >= 0 /\ 20 >= 0 /\ 30 >= 0 /\ 22 >= 0 /\ 33 >= 0 /\ 11 >= 0 /\ 36 >= 0 ] We thus obtain the following problem: 16: T: (1, 14) f0(a, b, c) -> f5(13, 26, d + e) [ 0 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 1 >= 0 /\ 4 >= 0 /\ 6 >= 0 /\ 9 >= 0 /\ 8 >= 0 /\ 12 >= 0 /\ 10 >= 0 /\ 15 >= 0 /\ 5 >= 0 /\ 18 >= 0 /\ 14 >= 0 /\ 21 >= 0 /\ 7 >= 0 /\ 16 >= 0 /\ 24 >= 0 /\ 27 >= 0 /\ 20 >= 0 /\ 30 >= 0 /\ 22 >= 0 /\ 33 >= 0 /\ 11 >= 0 /\ 36 >= 0 ] (?, 1) f5(a, b, c) -> f5(a + 1, b + 2, d + e) [ b >= 0 /\ a + b >= 0 /\ -a + b >= 0 /\ a >= 0 ] start location: f0 leaf cost: 1 By chaining the transition f0(a, b, c) -> f5(13, 26, d + e) [ 0 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 1 >= 0 /\ 4 >= 0 /\ 6 >= 0 /\ 9 >= 0 /\ 8 >= 0 /\ 12 >= 0 /\ 10 >= 0 /\ 15 >= 0 /\ 5 >= 0 /\ 18 >= 0 /\ 14 >= 0 /\ 21 >= 0 /\ 7 >= 0 /\ 16 >= 0 /\ 24 >= 0 /\ 27 >= 0 /\ 20 >= 0 /\ 30 >= 0 /\ 22 >= 0 /\ 33 >= 0 /\ 11 >= 0 /\ 36 >= 0 ] with all transitions in problem 16, the following new transition is obtained: f0(a, b, c) -> f5(14, 28, d' + e') [ 0 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 1 >= 0 /\ 4 >= 0 /\ 6 >= 0 /\ 9 >= 0 /\ 8 >= 0 /\ 12 >= 0 /\ 10 >= 0 /\ 15 >= 0 /\ 5 >= 0 /\ 18 >= 0 /\ 14 >= 0 /\ 21 >= 0 /\ 7 >= 0 /\ 16 >= 0 /\ 24 >= 0 /\ 27 >= 0 /\ 20 >= 0 /\ 30 >= 0 /\ 22 >= 0 /\ 33 >= 0 /\ 11 >= 0 /\ 36 >= 0 /\ 26 >= 0 /\ 39 >= 0 /\ 13 >= 0 ] We thus obtain the following problem: 17: T: (1, 15) f0(a, b, c) -> f5(14, 28, d' + e') [ 0 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 1 >= 0 /\ 4 >= 0 /\ 6 >= 0 /\ 9 >= 0 /\ 8 >= 0 /\ 12 >= 0 /\ 10 >= 0 /\ 15 >= 0 /\ 5 >= 0 /\ 18 >= 0 /\ 14 >= 0 /\ 21 >= 0 /\ 7 >= 0 /\ 16 >= 0 /\ 24 >= 0 /\ 27 >= 0 /\ 20 >= 0 /\ 30 >= 0 /\ 22 >= 0 /\ 33 >= 0 /\ 11 >= 0 /\ 36 >= 0 /\ 26 >= 0 /\ 39 >= 0 /\ 13 >= 0 ] (?, 1) f5(a, b, c) -> f5(a + 1, b + 2, d + e) [ b >= 0 /\ a + b >= 0 /\ -a + b >= 0 /\ a >= 0 ] start location: f0 leaf cost: 1 By chaining the transition f0(a, b, c) -> f5(14, 28, d' + e') [ 0 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 1 >= 0 /\ 4 >= 0 /\ 6 >= 0 /\ 9 >= 0 /\ 8 >= 0 /\ 12 >= 0 /\ 10 >= 0 /\ 15 >= 0 /\ 5 >= 0 /\ 18 >= 0 /\ 14 >= 0 /\ 21 >= 0 /\ 7 >= 0 /\ 16 >= 0 /\ 24 >= 0 /\ 27 >= 0 /\ 20 >= 0 /\ 30 >= 0 /\ 22 >= 0 /\ 33 >= 0 /\ 11 >= 0 /\ 36 >= 0 /\ 26 >= 0 /\ 39 >= 0 /\ 13 >= 0 ] with all transitions in problem 17, the following new transition is obtained: f0(a, b, c) -> f5(15, 30, d + e) [ 0 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 1 >= 0 /\ 4 >= 0 /\ 6 >= 0 /\ 9 >= 0 /\ 8 >= 0 /\ 12 >= 0 /\ 10 >= 0 /\ 15 >= 0 /\ 5 >= 0 /\ 18 >= 0 /\ 14 >= 0 /\ 21 >= 0 /\ 7 >= 0 /\ 16 >= 0 /\ 24 >= 0 /\ 27 >= 0 /\ 20 >= 0 /\ 30 >= 0 /\ 22 >= 0 /\ 33 >= 0 /\ 11 >= 0 /\ 36 >= 0 /\ 26 >= 0 /\ 39 >= 0 /\ 13 >= 0 /\ 28 >= 0 /\ 42 >= 0 ] We thus obtain the following problem: 18: T: (1, 16) f0(a, b, c) -> f5(15, 30, d + e) [ 0 >= 0 /\ 2 >= 0 /\ 3 >= 0 /\ 1 >= 0 /\ 4 >= 0 /\ 6 >= 0 /\ 9 >= 0 /\ 8 >= 0 /\ 12 >= 0 /\ 10 >= 0 /\ 15 >= 0 /\ 5 >= 0 /\ 18 >= 0 /\ 14 >= 0 /\ 21 >= 0 /\ 7 >= 0 /\ 16 >= 0 /\ 24 >= 0 /\ 27 >= 0 /\ 20 >= 0 /\ 30 >= 0 /\ 22 >= 0 /\ 33 >= 0 /\ 11 >= 0 /\ 36 >= 0 /\ 26 >= 0 /\ 39 >= 0 /\ 13 >= 0 /\ 28 >= 0 /\ 42 >= 0 ] (?, 1) f5(a, b, c) -> f5(a + 1, b + 2, d + e) [ b >= 0 /\ a + b >= 0 /\ -a + b >= 0 /\ a >= 0 ] start location: f0 leaf cost: 1 Complexity upper bound ? Time: 0.724 sec (SMT: 0.666 sec)