MAYBE Initial complexity problem: 1: T: (?, 1) ack(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 ] (?, 1) ack(a, b) -> ack(a, b - 1) [ a >= 1 /\ b >= 1 ] (1, 1) start(a, b) -> ack(a, b) start location: start leaf cost: 0 A polynomial rank function with Pol(ack) = V_1 Pol(start) = V_1 orients all transitions weakly and the transition ack(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 ] strictly and produces the following problem: 2: T: (a, 1) ack(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 ] (?, 1) ack(a, b) -> ack(a, b - 1) [ a >= 1 /\ b >= 1 ] (1, 1) start(a, b) -> ack(a, b) start location: start leaf cost: 0 By chaining the transition start(a, b) -> ack(a, b) with all transitions in problem 2, the following new transitions are obtained: start(a, b) -> ack(a, b - 1) [ a >= 1 /\ b >= 1 ] start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 ] We thus obtain the following problem: 3: T: (1, 2) start(a, b) -> ack(a, b - 1) [ a >= 1 /\ b >= 1 ] (1, 2) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 ] (a, 1) ack(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 ] (?, 1) ack(a, b) -> ack(a, b - 1) [ a >= 1 /\ b >= 1 ] start location: start leaf cost: 0 By chaining the transition start(a, b) -> ack(a, b - 1) [ a >= 1 /\ b >= 1 ] with all transitions in problem 3, the following new transitions are obtained: start(a, b) -> ack(a, b - 2) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 ] start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 ] We thus obtain the following problem: 4: T: (1, 3) start(a, b) -> ack(a, b - 2) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 ] (1, 3) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 ] (1, 2) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 ] (a, 1) ack(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 ] (?, 1) ack(a, b) -> ack(a, b - 1) [ a >= 1 /\ b >= 1 ] start location: start leaf cost: 0 By chaining the transition start(a, b) -> ack(a, b - 2) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 ] with all transitions in problem 4, the following new transitions are obtained: start(a, b) -> ack(a, b - 3) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 ] start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 ] We thus obtain the following problem: 5: T: (1, 4) start(a, b) -> ack(a, b - 3) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 ] (1, 4) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 ] (1, 3) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 ] (1, 2) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 ] (a, 1) ack(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 ] (?, 1) ack(a, b) -> ack(a, b - 1) [ a >= 1 /\ b >= 1 ] start location: start leaf cost: 0 By chaining the transition start(a, b) -> ack(a, b - 3) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 ] with all transitions in problem 5, the following new transitions are obtained: start(a, b) -> ack(a, b - 4) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 ] start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 ] We thus obtain the following problem: 6: T: (1, 5) start(a, b) -> ack(a, b - 4) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 ] (1, 5) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 ] (1, 4) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 ] (1, 3) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 ] (1, 2) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 ] (a, 1) ack(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 ] (?, 1) ack(a, b) -> ack(a, b - 1) [ a >= 1 /\ b >= 1 ] start location: start leaf cost: 0 By chaining the transition start(a, b) -> ack(a, b - 4) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 ] with all transitions in problem 6, the following new transitions are obtained: start(a, b) -> ack(a, b - 5) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 ] start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 ] We thus obtain the following problem: 7: T: (1, 6) start(a, b) -> ack(a, b - 5) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 ] (1, 6) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 ] (1, 5) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 ] (1, 4) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 ] (1, 3) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 ] (1, 2) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 ] (a, 1) ack(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 ] (?, 1) ack(a, b) -> ack(a, b - 1) [ a >= 1 /\ b >= 1 ] start location: start leaf cost: 0 By chaining the transition start(a, b) -> ack(a, b - 5) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 ] with all transitions in problem 7, the following new transitions are obtained: start(a, b) -> ack(a, b - 6) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 ] start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 ] We thus obtain the following problem: 8: T: (1, 7) start(a, b) -> ack(a, b - 6) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 ] (1, 7) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 ] (1, 6) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 ] (1, 5) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 ] (1, 4) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 ] (1, 3) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 ] (1, 2) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 ] (a, 1) ack(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 ] (?, 1) ack(a, b) -> ack(a, b - 1) [ a >= 1 /\ b >= 1 ] start location: start leaf cost: 0 By chaining the transition start(a, b) -> ack(a, b - 6) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 ] with all transitions in problem 8, the following new transitions are obtained: start(a, b) -> ack(a, b - 7) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 ] start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 ] We thus obtain the following problem: 9: T: (1, 8) start(a, b) -> ack(a, b - 7) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 ] (1, 8) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 ] (1, 7) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 ] (1, 6) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 ] (1, 5) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 ] (1, 4) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 ] (1, 3) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 ] (1, 2) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 ] (a, 1) ack(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 ] (?, 1) ack(a, b) -> ack(a, b - 1) [ a >= 1 /\ b >= 1 ] start location: start leaf cost: 0 By chaining the transition start(a, b) -> ack(a, b - 7) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 ] with all transitions in problem 9, the following new transitions are obtained: start(a, b) -> ack(a, b - 8) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 ] start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 ] We thus obtain the following problem: 10: T: (1, 9) start(a, b) -> ack(a, b - 8) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 ] (1, 9) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 ] (1, 8) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 ] (1, 7) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 ] (1, 6) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 ] (1, 5) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 ] (1, 4) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 ] (1, 3) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 ] (1, 2) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 ] (a, 1) ack(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 ] (?, 1) ack(a, b) -> ack(a, b - 1) [ a >= 1 /\ b >= 1 ] start location: start leaf cost: 0 By chaining the transition start(a, b) -> ack(a, b - 8) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 ] with all transitions in problem 10, the following new transitions are obtained: start(a, b) -> ack(a, b - 9) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 ] start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 ] We thus obtain the following problem: 11: T: (1, 10) start(a, b) -> ack(a, b - 9) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 ] (1, 10) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 ] (1, 9) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 ] (1, 8) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 ] (1, 7) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 ] (1, 6) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 ] (1, 5) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 ] (1, 4) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 ] (1, 3) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 ] (1, 2) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 ] (a, 1) ack(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 ] (?, 1) ack(a, b) -> ack(a, b - 1) [ a >= 1 /\ b >= 1 ] start location: start leaf cost: 0 By chaining the transition start(a, b) -> ack(a, b - 9) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 ] with all transitions in problem 11, the following new transitions are obtained: start(a, b) -> ack(a, b - 10) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 ] start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 ] We thus obtain the following problem: 12: T: (1, 11) start(a, b) -> ack(a, b - 10) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 ] (1, 11) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 ] (1, 10) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 ] (1, 9) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 ] (1, 8) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 ] (1, 7) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 ] (1, 6) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 ] (1, 5) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 ] (1, 4) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 ] (1, 3) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 ] (1, 2) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 ] (a, 1) ack(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 ] (?, 1) ack(a, b) -> ack(a, b - 1) [ a >= 1 /\ b >= 1 ] start location: start leaf cost: 0 By chaining the transition start(a, b) -> ack(a, b - 10) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 ] with all transitions in problem 12, the following new transitions are obtained: start(a, b) -> ack(a, b - 11) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 /\ b - 10 >= 1 ] start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 /\ b - 10 >= 1 ] We thus obtain the following problem: 13: T: (1, 12) start(a, b) -> ack(a, b - 11) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 /\ b - 10 >= 1 ] (1, 12) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 /\ b - 10 >= 1 ] (1, 11) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 ] (1, 10) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 ] (1, 9) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 ] (1, 8) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 ] (1, 7) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 ] (1, 6) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 ] (1, 5) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 ] (1, 4) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 ] (1, 3) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 ] (1, 2) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 ] (a, 1) ack(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 ] (?, 1) ack(a, b) -> ack(a, b - 1) [ a >= 1 /\ b >= 1 ] start location: start leaf cost: 0 By chaining the transition start(a, b) -> ack(a, b - 11) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 /\ b - 10 >= 1 ] with all transitions in problem 13, the following new transitions are obtained: start(a, b) -> ack(a, b - 12) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 /\ b - 10 >= 1 /\ b - 11 >= 1 ] start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 /\ b - 10 >= 1 /\ b - 11 >= 1 ] We thus obtain the following problem: 14: T: (1, 13) start(a, b) -> ack(a, b - 12) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 /\ b - 10 >= 1 /\ b - 11 >= 1 ] (1, 13) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 /\ b - 10 >= 1 /\ b - 11 >= 1 ] (1, 12) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 /\ b - 10 >= 1 ] (1, 11) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 ] (1, 10) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 ] (1, 9) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 ] (1, 8) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 ] (1, 7) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 ] (1, 6) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 ] (1, 5) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 ] (1, 4) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 ] (1, 3) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 ] (1, 2) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 ] (a, 1) ack(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 ] (?, 1) ack(a, b) -> ack(a, b - 1) [ a >= 1 /\ b >= 1 ] start location: start leaf cost: 0 By chaining the transition start(a, b) -> ack(a, b - 12) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 /\ b - 10 >= 1 /\ b - 11 >= 1 ] with all transitions in problem 14, the following new transitions are obtained: start(a, b) -> ack(a, b - 13) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 /\ b - 10 >= 1 /\ b - 11 >= 1 /\ b - 12 >= 1 ] start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 /\ b - 10 >= 1 /\ b - 11 >= 1 /\ b - 12 >= 1 ] We thus obtain the following problem: 15: T: (1, 14) start(a, b) -> ack(a, b - 13) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 /\ b - 10 >= 1 /\ b - 11 >= 1 /\ b - 12 >= 1 ] (1, 14) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 /\ b - 10 >= 1 /\ b - 11 >= 1 /\ b - 12 >= 1 ] (1, 13) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 /\ b - 10 >= 1 /\ b - 11 >= 1 ] (1, 12) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 /\ b - 10 >= 1 ] (1, 11) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 ] (1, 10) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 ] (1, 9) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 ] (1, 8) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 ] (1, 7) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 ] (1, 6) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 ] (1, 5) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 ] (1, 4) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 ] (1, 3) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 ] (1, 2) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 ] (a, 1) ack(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 ] (?, 1) ack(a, b) -> ack(a, b - 1) [ a >= 1 /\ b >= 1 ] start location: start leaf cost: 0 By chaining the transition start(a, b) -> ack(a, b - 13) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 /\ b - 10 >= 1 /\ b - 11 >= 1 /\ b - 12 >= 1 ] with all transitions in problem 15, the following new transitions are obtained: start(a, b) -> ack(a, b - 14) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 /\ b - 10 >= 1 /\ b - 11 >= 1 /\ b - 12 >= 1 /\ b - 13 >= 1 ] start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 /\ b - 10 >= 1 /\ b - 11 >= 1 /\ b - 12 >= 1 /\ b - 13 >= 1 ] We thus obtain the following problem: 16: T: (1, 15) start(a, b) -> ack(a, b - 14) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 /\ b - 10 >= 1 /\ b - 11 >= 1 /\ b - 12 >= 1 /\ b - 13 >= 1 ] (1, 15) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 /\ b - 10 >= 1 /\ b - 11 >= 1 /\ b - 12 >= 1 /\ b - 13 >= 1 ] (1, 14) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 /\ b - 10 >= 1 /\ b - 11 >= 1 /\ b - 12 >= 1 ] (1, 13) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 /\ b - 10 >= 1 /\ b - 11 >= 1 ] (1, 12) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 /\ b - 10 >= 1 ] (1, 11) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 ] (1, 10) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 ] (1, 9) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 ] (1, 8) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 ] (1, 7) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 ] (1, 6) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 ] (1, 5) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 ] (1, 4) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 ] (1, 3) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 ] (1, 2) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 ] (a, 1) ack(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 ] (?, 1) ack(a, b) -> ack(a, b - 1) [ a >= 1 /\ b >= 1 ] start location: start leaf cost: 0 By chaining the transition start(a, b) -> ack(a, b - 14) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 /\ b - 10 >= 1 /\ b - 11 >= 1 /\ b - 12 >= 1 /\ b - 13 >= 1 ] with all transitions in problem 16, the following new transitions are obtained: start(a, b) -> ack(a, b - 15) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 /\ b - 10 >= 1 /\ b - 11 >= 1 /\ b - 12 >= 1 /\ b - 13 >= 1 /\ b - 14 >= 1 ] start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 /\ b - 10 >= 1 /\ b - 11 >= 1 /\ b - 12 >= 1 /\ b - 13 >= 1 /\ b - 14 >= 1 ] We thus obtain the following problem: 17: T: (1, 16) start(a, b) -> ack(a, b - 15) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 /\ b - 10 >= 1 /\ b - 11 >= 1 /\ b - 12 >= 1 /\ b - 13 >= 1 /\ b - 14 >= 1 ] (1, 16) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 /\ b - 10 >= 1 /\ b - 11 >= 1 /\ b - 12 >= 1 /\ b - 13 >= 1 /\ b - 14 >= 1 ] (1, 15) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 /\ b - 10 >= 1 /\ b - 11 >= 1 /\ b - 12 >= 1 /\ b - 13 >= 1 ] (1, 14) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 /\ b - 10 >= 1 /\ b - 11 >= 1 /\ b - 12 >= 1 ] (1, 13) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 /\ b - 10 >= 1 /\ b - 11 >= 1 ] (1, 12) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 /\ b - 10 >= 1 ] (1, 11) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 /\ b - 9 >= 1 ] (1, 10) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 /\ b - 8 >= 1 ] (1, 9) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 /\ b - 7 >= 1 ] (1, 8) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 /\ b - 6 >= 1 ] (1, 7) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 /\ b - 5 >= 1 ] (1, 6) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 /\ b - 4 >= 1 ] (1, 5) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 /\ b - 3 >= 1 ] (1, 4) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 /\ b - 2 >= 1 ] (1, 3) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 /\ b - 1 >= 1 ] (1, 2) start(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 ] (a, 1) ack(a, b) -> ack(a - 1, c) [ a >= 1 /\ b >= 1 ] (?, 1) ack(a, b) -> ack(a, b - 1) [ a >= 1 /\ b >= 1 ] start location: start leaf cost: 0 Complexity upper bound ? Time: 2.379 sec (SMT: 2.226 sec)