MAYBE Initial complexity problem: 1: T: (?, 1) eval(a, b) -> eval(a - 1, a) [ a >= 1 /\ b >= 1 ] (?, 1) eval(a, b) -> eval(b - 2, a + 1) [ a >= 1 /\ b >= 1 ] (1, 1) start(a, b) -> eval(a, b) start location: start leaf cost: 0 By chaining the transition start(a, b) -> eval(a, b) with all transitions in problem 1, the following new transitions are obtained: start(a, b) -> eval(b - 2, a + 1) [ a >= 1 /\ b >= 1 ] start(a, b) -> eval(a - 1, a) [ a >= 1 /\ b >= 1 ] We thus obtain the following problem: 2: T: (1, 2) start(a, b) -> eval(b - 2, a + 1) [ a >= 1 /\ b >= 1 ] (1, 2) start(a, b) -> eval(a - 1, a) [ a >= 1 /\ b >= 1 ] (?, 1) eval(a, b) -> eval(a - 1, a) [ a >= 1 /\ b >= 1 ] (?, 1) eval(a, b) -> eval(b - 2, a + 1) [ a >= 1 /\ b >= 1 ] start location: start leaf cost: 0 By chaining the transition start(a, b) -> eval(b - 2, a + 1) [ a >= 1 /\ b >= 1 ] with all transitions in problem 2, the following new transitions are obtained: start(a, b) -> eval(a - 1, b - 1) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 ] start(a, b) -> eval(b - 3, b - 2) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 ] We thus obtain the following problem: 3: T: (1, 3) start(a, b) -> eval(a - 1, b - 1) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 ] (1, 3) start(a, b) -> eval(b - 3, b - 2) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 ] (1, 2) start(a, b) -> eval(a - 1, a) [ a >= 1 /\ b >= 1 ] (?, 1) eval(a, b) -> eval(a - 1, a) [ a >= 1 /\ b >= 1 ] (?, 1) eval(a, b) -> eval(b - 2, a + 1) [ a >= 1 /\ b >= 1 ] start location: start leaf cost: 0 By chaining the transition start(a, b) -> eval(a - 1, b - 1) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 ] with all transitions in problem 3, the following new transitions are obtained: start(a, b) -> eval(b - 3, a) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 ] start(a, b) -> eval(a - 2, a - 1) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 ] We thus obtain the following problem: 4: T: (1, 4) start(a, b) -> eval(b - 3, a) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 ] (1, 4) start(a, b) -> eval(a - 2, a - 1) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 ] (1, 3) start(a, b) -> eval(b - 3, b - 2) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 ] (1, 2) start(a, b) -> eval(a - 1, a) [ a >= 1 /\ b >= 1 ] (?, 1) eval(a, b) -> eval(a - 1, a) [ a >= 1 /\ b >= 1 ] (?, 1) eval(a, b) -> eval(b - 2, a + 1) [ a >= 1 /\ b >= 1 ] start location: start leaf cost: 0 By chaining the transition start(a, b) -> eval(b - 3, a) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 ] with all transitions in problem 4, the following new transitions are obtained: start(a, b) -> eval(a - 2, b - 2) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 ] start(a, b) -> eval(b - 4, b - 3) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 ] We thus obtain the following problem: 5: T: (1, 5) start(a, b) -> eval(a - 2, b - 2) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 ] (1, 5) start(a, b) -> eval(b - 4, b - 3) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 ] (1, 4) start(a, b) -> eval(a - 2, a - 1) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 ] (1, 3) start(a, b) -> eval(b - 3, b - 2) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 ] (1, 2) start(a, b) -> eval(a - 1, a) [ a >= 1 /\ b >= 1 ] (?, 1) eval(a, b) -> eval(a - 1, a) [ a >= 1 /\ b >= 1 ] (?, 1) eval(a, b) -> eval(b - 2, a + 1) [ a >= 1 /\ b >= 1 ] start location: start leaf cost: 0 By chaining the transition start(a, b) -> eval(a - 2, b - 2) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 ] with all transitions in problem 5, the following new transitions are obtained: start(a, b) -> eval(b - 4, a - 1) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 ] start(a, b) -> eval(a - 3, a - 2) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 ] We thus obtain the following problem: 6: T: (1, 6) start(a, b) -> eval(b - 4, a - 1) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 ] (1, 6) start(a, b) -> eval(a - 3, a - 2) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 ] (1, 5) start(a, b) -> eval(b - 4, b - 3) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 ] (1, 4) start(a, b) -> eval(a - 2, a - 1) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 ] (1, 3) start(a, b) -> eval(b - 3, b - 2) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 ] (1, 2) start(a, b) -> eval(a - 1, a) [ a >= 1 /\ b >= 1 ] (?, 1) eval(a, b) -> eval(a - 1, a) [ a >= 1 /\ b >= 1 ] (?, 1) eval(a, b) -> eval(b - 2, a + 1) [ a >= 1 /\ b >= 1 ] start location: start leaf cost: 0 By chaining the transition start(a, b) -> eval(b - 4, a - 1) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 ] with all transitions in problem 6, the following new transitions are obtained: start(a, b) -> eval(a - 3, b - 3) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 ] start(a, b) -> eval(b - 5, b - 4) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 ] We thus obtain the following problem: 7: T: (1, 7) start(a, b) -> eval(a - 3, b - 3) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 ] (1, 7) start(a, b) -> eval(b - 5, b - 4) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 ] (1, 6) start(a, b) -> eval(a - 3, a - 2) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 ] (1, 5) start(a, b) -> eval(b - 4, b - 3) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 ] (1, 4) start(a, b) -> eval(a - 2, a - 1) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 ] (1, 3) start(a, b) -> eval(b - 3, b - 2) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 ] (1, 2) start(a, b) -> eval(a - 1, a) [ a >= 1 /\ b >= 1 ] (?, 1) eval(a, b) -> eval(a - 1, a) [ a >= 1 /\ b >= 1 ] (?, 1) eval(a, b) -> eval(b - 2, a + 1) [ a >= 1 /\ b >= 1 ] start location: start leaf cost: 0 By chaining the transition start(a, b) -> eval(a - 3, b - 3) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 ] with all transitions in problem 7, the following new transitions are obtained: start(a, b) -> eval(b - 5, a - 2) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 ] start(a, b) -> eval(a - 4, a - 3) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 ] We thus obtain the following problem: 8: T: (1, 8) start(a, b) -> eval(b - 5, a - 2) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 ] (1, 8) start(a, b) -> eval(a - 4, a - 3) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 ] (1, 7) start(a, b) -> eval(b - 5, b - 4) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 ] (1, 6) start(a, b) -> eval(a - 3, a - 2) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 ] (1, 5) start(a, b) -> eval(b - 4, b - 3) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 ] (1, 4) start(a, b) -> eval(a - 2, a - 1) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 ] (1, 3) start(a, b) -> eval(b - 3, b - 2) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 ] (1, 2) start(a, b) -> eval(a - 1, a) [ a >= 1 /\ b >= 1 ] (?, 1) eval(a, b) -> eval(a - 1, a) [ a >= 1 /\ b >= 1 ] (?, 1) eval(a, b) -> eval(b - 2, a + 1) [ a >= 1 /\ b >= 1 ] start location: start leaf cost: 0 By chaining the transition start(a, b) -> eval(b - 5, a - 2) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 ] with all transitions in problem 8, the following new transitions are obtained: start(a, b) -> eval(a - 4, b - 4) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 ] start(a, b) -> eval(b - 6, b - 5) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 ] We thus obtain the following problem: 9: T: (1, 9) start(a, b) -> eval(a - 4, b - 4) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 ] (1, 9) start(a, b) -> eval(b - 6, b - 5) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 ] (1, 8) start(a, b) -> eval(a - 4, a - 3) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 ] (1, 7) start(a, b) -> eval(b - 5, b - 4) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 ] (1, 6) start(a, b) -> eval(a - 3, a - 2) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 ] (1, 5) start(a, b) -> eval(b - 4, b - 3) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 ] (1, 4) start(a, b) -> eval(a - 2, a - 1) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 ] (1, 3) start(a, b) -> eval(b - 3, b - 2) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 ] (1, 2) start(a, b) -> eval(a - 1, a) [ a >= 1 /\ b >= 1 ] (?, 1) eval(a, b) -> eval(a - 1, a) [ a >= 1 /\ b >= 1 ] (?, 1) eval(a, b) -> eval(b - 2, a + 1) [ a >= 1 /\ b >= 1 ] start location: start leaf cost: 0 By chaining the transition start(a, b) -> eval(a - 4, b - 4) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 ] with all transitions in problem 9, the following new transitions are obtained: start(a, b) -> eval(b - 6, a - 3) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 ] start(a, b) -> eval(a - 5, a - 4) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 ] We thus obtain the following problem: 10: T: (1, 10) start(a, b) -> eval(b - 6, a - 3) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 ] (1, 10) start(a, b) -> eval(a - 5, a - 4) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 ] (1, 9) start(a, b) -> eval(b - 6, b - 5) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 ] (1, 8) start(a, b) -> eval(a - 4, a - 3) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 ] (1, 7) start(a, b) -> eval(b - 5, b - 4) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 ] (1, 6) start(a, b) -> eval(a - 3, a - 2) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 ] (1, 5) start(a, b) -> eval(b - 4, b - 3) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 ] (1, 4) start(a, b) -> eval(a - 2, a - 1) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 ] (1, 3) start(a, b) -> eval(b - 3, b - 2) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 ] (1, 2) start(a, b) -> eval(a - 1, a) [ a >= 1 /\ b >= 1 ] (?, 1) eval(a, b) -> eval(a - 1, a) [ a >= 1 /\ b >= 1 ] (?, 1) eval(a, b) -> eval(b - 2, a + 1) [ a >= 1 /\ b >= 1 ] start location: start leaf cost: 0 By chaining the transition start(a, b) -> eval(b - 6, a - 3) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 ] with all transitions in problem 10, the following new transitions are obtained: start(a, b) -> eval(a - 5, b - 5) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 ] start(a, b) -> eval(b - 7, b - 6) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 ] We thus obtain the following problem: 11: T: (1, 11) start(a, b) -> eval(a - 5, b - 5) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 ] (1, 11) start(a, b) -> eval(b - 7, b - 6) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 ] (1, 10) start(a, b) -> eval(a - 5, a - 4) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 ] (1, 9) start(a, b) -> eval(b - 6, b - 5) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 ] (1, 8) start(a, b) -> eval(a - 4, a - 3) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 ] (1, 7) start(a, b) -> eval(b - 5, b - 4) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 ] (1, 6) start(a, b) -> eval(a - 3, a - 2) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 ] (1, 5) start(a, b) -> eval(b - 4, b - 3) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 ] (1, 4) start(a, b) -> eval(a - 2, a - 1) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 ] (1, 3) start(a, b) -> eval(b - 3, b - 2) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 ] (1, 2) start(a, b) -> eval(a - 1, a) [ a >= 1 /\ b >= 1 ] (?, 1) eval(a, b) -> eval(a - 1, a) [ a >= 1 /\ b >= 1 ] (?, 1) eval(a, b) -> eval(b - 2, a + 1) [ a >= 1 /\ b >= 1 ] start location: start leaf cost: 0 By chaining the transition start(a, b) -> eval(a - 5, b - 5) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 ] with all transitions in problem 11, the following new transitions are obtained: start(a, b) -> eval(b - 7, a - 4) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 /\ a - 5 >= 1 ] start(a, b) -> eval(a - 6, a - 5) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 /\ a - 5 >= 1 ] We thus obtain the following problem: 12: T: (1, 12) start(a, b) -> eval(b - 7, a - 4) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 /\ a - 5 >= 1 ] (1, 12) start(a, b) -> eval(a - 6, a - 5) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 /\ a - 5 >= 1 ] (1, 11) start(a, b) -> eval(b - 7, b - 6) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 ] (1, 10) start(a, b) -> eval(a - 5, a - 4) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 ] (1, 9) start(a, b) -> eval(b - 6, b - 5) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 ] (1, 8) start(a, b) -> eval(a - 4, a - 3) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 ] (1, 7) start(a, b) -> eval(b - 5, b - 4) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 ] (1, 6) start(a, b) -> eval(a - 3, a - 2) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 ] (1, 5) start(a, b) -> eval(b - 4, b - 3) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 ] (1, 4) start(a, b) -> eval(a - 2, a - 1) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 ] (1, 3) start(a, b) -> eval(b - 3, b - 2) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 ] (1, 2) start(a, b) -> eval(a - 1, a) [ a >= 1 /\ b >= 1 ] (?, 1) eval(a, b) -> eval(a - 1, a) [ a >= 1 /\ b >= 1 ] (?, 1) eval(a, b) -> eval(b - 2, a + 1) [ a >= 1 /\ b >= 1 ] start location: start leaf cost: 0 By chaining the transition start(a, b) -> eval(b - 7, a - 4) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 /\ a - 5 >= 1 ] with all transitions in problem 12, the following new transitions are obtained: start(a, b) -> eval(a - 6, b - 6) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 /\ a - 5 >= 1 /\ b - 7 >= 1 ] start(a, b) -> eval(b - 8, b - 7) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 /\ a - 5 >= 1 /\ b - 7 >= 1 ] We thus obtain the following problem: 13: T: (1, 13) start(a, b) -> eval(a - 6, b - 6) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 /\ a - 5 >= 1 /\ b - 7 >= 1 ] (1, 13) start(a, b) -> eval(b - 8, b - 7) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 /\ a - 5 >= 1 /\ b - 7 >= 1 ] (1, 12) start(a, b) -> eval(a - 6, a - 5) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 /\ a - 5 >= 1 ] (1, 11) start(a, b) -> eval(b - 7, b - 6) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 ] (1, 10) start(a, b) -> eval(a - 5, a - 4) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 ] (1, 9) start(a, b) -> eval(b - 6, b - 5) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 ] (1, 8) start(a, b) -> eval(a - 4, a - 3) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 ] (1, 7) start(a, b) -> eval(b - 5, b - 4) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 ] (1, 6) start(a, b) -> eval(a - 3, a - 2) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 ] (1, 5) start(a, b) -> eval(b - 4, b - 3) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 ] (1, 4) start(a, b) -> eval(a - 2, a - 1) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 ] (1, 3) start(a, b) -> eval(b - 3, b - 2) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 ] (1, 2) start(a, b) -> eval(a - 1, a) [ a >= 1 /\ b >= 1 ] (?, 1) eval(a, b) -> eval(a - 1, a) [ a >= 1 /\ b >= 1 ] (?, 1) eval(a, b) -> eval(b - 2, a + 1) [ a >= 1 /\ b >= 1 ] start location: start leaf cost: 0 By chaining the transition start(a, b) -> eval(a - 6, b - 6) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 /\ a - 5 >= 1 /\ b - 7 >= 1 ] with all transitions in problem 13, the following new transitions are obtained: start(a, b) -> eval(b - 8, a - 5) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 /\ a - 5 >= 1 /\ b - 7 >= 1 /\ a - 6 >= 1 ] start(a, b) -> eval(a - 7, a - 6) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 /\ a - 5 >= 1 /\ b - 7 >= 1 /\ a - 6 >= 1 ] We thus obtain the following problem: 14: T: (1, 14) start(a, b) -> eval(b - 8, a - 5) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 /\ a - 5 >= 1 /\ b - 7 >= 1 /\ a - 6 >= 1 ] (1, 14) start(a, b) -> eval(a - 7, a - 6) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 /\ a - 5 >= 1 /\ b - 7 >= 1 /\ a - 6 >= 1 ] (1, 13) start(a, b) -> eval(b - 8, b - 7) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 /\ a - 5 >= 1 /\ b - 7 >= 1 ] (1, 12) start(a, b) -> eval(a - 6, a - 5) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 /\ a - 5 >= 1 ] (1, 11) start(a, b) -> eval(b - 7, b - 6) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 ] (1, 10) start(a, b) -> eval(a - 5, a - 4) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 ] (1, 9) start(a, b) -> eval(b - 6, b - 5) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 ] (1, 8) start(a, b) -> eval(a - 4, a - 3) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 ] (1, 7) start(a, b) -> eval(b - 5, b - 4) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 ] (1, 6) start(a, b) -> eval(a - 3, a - 2) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 ] (1, 5) start(a, b) -> eval(b - 4, b - 3) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 ] (1, 4) start(a, b) -> eval(a - 2, a - 1) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 ] (1, 3) start(a, b) -> eval(b - 3, b - 2) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 ] (1, 2) start(a, b) -> eval(a - 1, a) [ a >= 1 /\ b >= 1 ] (?, 1) eval(a, b) -> eval(a - 1, a) [ a >= 1 /\ b >= 1 ] (?, 1) eval(a, b) -> eval(b - 2, a + 1) [ a >= 1 /\ b >= 1 ] start location: start leaf cost: 0 By chaining the transition start(a, b) -> eval(b - 8, a - 5) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 /\ a - 5 >= 1 /\ b - 7 >= 1 /\ a - 6 >= 1 ] with all transitions in problem 14, the following new transitions are obtained: start(a, b) -> eval(a - 7, b - 7) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 /\ a - 5 >= 1 /\ b - 7 >= 1 /\ a - 6 >= 1 /\ b - 8 >= 1 ] start(a, b) -> eval(b - 9, b - 8) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 /\ a - 5 >= 1 /\ b - 7 >= 1 /\ a - 6 >= 1 /\ b - 8 >= 1 ] We thus obtain the following problem: 15: T: (1, 15) start(a, b) -> eval(a - 7, b - 7) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 /\ a - 5 >= 1 /\ b - 7 >= 1 /\ a - 6 >= 1 /\ b - 8 >= 1 ] (1, 15) start(a, b) -> eval(b - 9, b - 8) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 /\ a - 5 >= 1 /\ b - 7 >= 1 /\ a - 6 >= 1 /\ b - 8 >= 1 ] (1, 14) start(a, b) -> eval(a - 7, a - 6) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 /\ a - 5 >= 1 /\ b - 7 >= 1 /\ a - 6 >= 1 ] (1, 13) start(a, b) -> eval(b - 8, b - 7) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 /\ a - 5 >= 1 /\ b - 7 >= 1 ] (1, 12) start(a, b) -> eval(a - 6, a - 5) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 /\ a - 5 >= 1 ] (1, 11) start(a, b) -> eval(b - 7, b - 6) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 ] (1, 10) start(a, b) -> eval(a - 5, a - 4) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 ] (1, 9) start(a, b) -> eval(b - 6, b - 5) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 ] (1, 8) start(a, b) -> eval(a - 4, a - 3) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 ] (1, 7) start(a, b) -> eval(b - 5, b - 4) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 ] (1, 6) start(a, b) -> eval(a - 3, a - 2) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 ] (1, 5) start(a, b) -> eval(b - 4, b - 3) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 ] (1, 4) start(a, b) -> eval(a - 2, a - 1) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 ] (1, 3) start(a, b) -> eval(b - 3, b - 2) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 ] (1, 2) start(a, b) -> eval(a - 1, a) [ a >= 1 /\ b >= 1 ] (?, 1) eval(a, b) -> eval(a - 1, a) [ a >= 1 /\ b >= 1 ] (?, 1) eval(a, b) -> eval(b - 2, a + 1) [ a >= 1 /\ b >= 1 ] start location: start leaf cost: 0 By chaining the transition start(a, b) -> eval(a - 7, b - 7) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 /\ a - 5 >= 1 /\ b - 7 >= 1 /\ a - 6 >= 1 /\ b - 8 >= 1 ] with all transitions in problem 15, the following new transitions are obtained: start(a, b) -> eval(b - 9, a - 6) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 /\ a - 5 >= 1 /\ b - 7 >= 1 /\ a - 6 >= 1 /\ b - 8 >= 1 /\ a - 7 >= 1 ] start(a, b) -> eval(a - 8, a - 7) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 /\ a - 5 >= 1 /\ b - 7 >= 1 /\ a - 6 >= 1 /\ b - 8 >= 1 /\ a - 7 >= 1 ] We thus obtain the following problem: 16: T: (1, 16) start(a, b) -> eval(b - 9, a - 6) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 /\ a - 5 >= 1 /\ b - 7 >= 1 /\ a - 6 >= 1 /\ b - 8 >= 1 /\ a - 7 >= 1 ] (1, 16) start(a, b) -> eval(a - 8, a - 7) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 /\ a - 5 >= 1 /\ b - 7 >= 1 /\ a - 6 >= 1 /\ b - 8 >= 1 /\ a - 7 >= 1 ] (1, 15) start(a, b) -> eval(b - 9, b - 8) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 /\ a - 5 >= 1 /\ b - 7 >= 1 /\ a - 6 >= 1 /\ b - 8 >= 1 ] (1, 14) start(a, b) -> eval(a - 7, a - 6) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 /\ a - 5 >= 1 /\ b - 7 >= 1 /\ a - 6 >= 1 ] (1, 13) start(a, b) -> eval(b - 8, b - 7) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 /\ a - 5 >= 1 /\ b - 7 >= 1 ] (1, 12) start(a, b) -> eval(a - 6, a - 5) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 /\ a - 5 >= 1 ] (1, 11) start(a, b) -> eval(b - 7, b - 6) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 /\ b - 6 >= 1 ] (1, 10) start(a, b) -> eval(a - 5, a - 4) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 /\ a - 4 >= 1 ] (1, 9) start(a, b) -> eval(b - 6, b - 5) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 /\ b - 5 >= 1 ] (1, 8) start(a, b) -> eval(a - 4, a - 3) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 /\ a - 3 >= 1 ] (1, 7) start(a, b) -> eval(b - 5, b - 4) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 /\ b - 4 >= 1 ] (1, 6) start(a, b) -> eval(a - 3, a - 2) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 /\ a - 2 >= 1 ] (1, 5) start(a, b) -> eval(b - 4, b - 3) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 /\ b - 3 >= 1 ] (1, 4) start(a, b) -> eval(a - 2, a - 1) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 /\ a - 1 >= 1 /\ b - 1 >= 1 ] (1, 3) start(a, b) -> eval(b - 3, b - 2) [ a >= 1 /\ b >= 1 /\ b - 2 >= 1 /\ a + 1 >= 1 ] (1, 2) start(a, b) -> eval(a - 1, a) [ a >= 1 /\ b >= 1 ] (?, 1) eval(a, b) -> eval(a - 1, a) [ a >= 1 /\ b >= 1 ] (?, 1) eval(a, b) -> eval(b - 2, a + 1) [ a >= 1 /\ b >= 1 ] start location: start leaf cost: 0 Complexity upper bound ? Time: 3.502 sec (SMT: 3.305 sec)