MAYBE Initial complexity problem: 1: T: (1, 1) f1(a, b) -> f2(a, b) [ 0 >= a + b + 1 /\ a >= 1 ] (?, 1) f2(a, b) -> f2(a - b, b) [ a >= 0 ] (?, 1) f2(a, b) -> f3(a, b) [ 0 >= a + 1 ] start location: f1 leaf cost: 0 Repeatedly removing leaves of the complexity graph in problem 1 produces the following problem: 2: T: (1, 1) f1(a, b) -> f2(a, b) [ 0 >= a + b + 1 /\ a >= 1 ] (?, 1) f2(a, b) -> f2(a - b, b) [ a >= 0 ] start location: f1 leaf cost: 1 Applied AI with 'oct' on problem 2 to obtain the following invariants: For symbol f2: -X_2 - 2 >= 0 /\ X_1 - X_2 - 3 >= 0 /\ X_1 - 1 >= 0 This yielded the following problem: 3: T: (?, 1) f2(a, b) -> f2(a - b, b) [ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 ] (1, 1) f1(a, b) -> f2(a, b) [ 0 >= a + b + 1 /\ a >= 1 ] start location: f1 leaf cost: 1 By chaining the transition f1(a, b) -> f2(a, b) [ 0 >= a + b + 1 /\ a >= 1 ] with all transitions in problem 3, the following new transition is obtained: f1(a, b) -> f2(a - b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 ] We thus obtain the following problem: 4: T: (1, 2) f1(a, b) -> f2(a - b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 ] (?, 1) f2(a, b) -> f2(a - b, b) [ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 ] start location: f1 leaf cost: 1 By chaining the transition f1(a, b) -> f2(a - b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 ] with all transitions in problem 4, the following new transition is obtained: f1(a, b) -> f2(a - 2*b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 /\ a - 2*b - 3 >= 0 /\ a - b - 1 >= 0 /\ a - b >= 0 ] We thus obtain the following problem: 5: T: (1, 3) f1(a, b) -> f2(a - 2*b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 /\ a - 2*b - 3 >= 0 /\ a - b - 1 >= 0 /\ a - b >= 0 ] (?, 1) f2(a, b) -> f2(a - b, b) [ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 ] start location: f1 leaf cost: 1 By chaining the transition f1(a, b) -> f2(a - 2*b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 /\ a - 2*b - 3 >= 0 /\ a - b - 1 >= 0 /\ a - b >= 0 ] with all transitions in problem 5, the following new transition is obtained: f1(a, b) -> f2(a - 3*b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 /\ a - 2*b - 3 >= 0 /\ a - b - 1 >= 0 /\ a - b >= 0 /\ a - 3*b - 3 >= 0 /\ a - 2*b - 1 >= 0 /\ a - 2*b >= 0 ] We thus obtain the following problem: 6: T: (1, 4) f1(a, b) -> f2(a - 3*b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 /\ a - 2*b - 3 >= 0 /\ a - b - 1 >= 0 /\ a - b >= 0 /\ a - 3*b - 3 >= 0 /\ a - 2*b - 1 >= 0 /\ a - 2*b >= 0 ] (?, 1) f2(a, b) -> f2(a - b, b) [ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 ] start location: f1 leaf cost: 1 By chaining the transition f1(a, b) -> f2(a - 3*b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 /\ a - 2*b - 3 >= 0 /\ a - b - 1 >= 0 /\ a - b >= 0 /\ a - 3*b - 3 >= 0 /\ a - 2*b - 1 >= 0 /\ a - 2*b >= 0 ] with all transitions in problem 6, the following new transition is obtained: f1(a, b) -> f2(a - 4*b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 /\ a - 2*b - 3 >= 0 /\ a - b - 1 >= 0 /\ a - b >= 0 /\ a - 3*b - 3 >= 0 /\ a - 2*b - 1 >= 0 /\ a - 2*b >= 0 /\ a - 4*b - 3 >= 0 /\ a - 3*b - 1 >= 0 /\ a - 3*b >= 0 ] We thus obtain the following problem: 7: T: (1, 5) f1(a, b) -> f2(a - 4*b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 /\ a - 2*b - 3 >= 0 /\ a - b - 1 >= 0 /\ a - b >= 0 /\ a - 3*b - 3 >= 0 /\ a - 2*b - 1 >= 0 /\ a - 2*b >= 0 /\ a - 4*b - 3 >= 0 /\ a - 3*b - 1 >= 0 /\ a - 3*b >= 0 ] (?, 1) f2(a, b) -> f2(a - b, b) [ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 ] start location: f1 leaf cost: 1 By chaining the transition f1(a, b) -> f2(a - 4*b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 /\ a - 2*b - 3 >= 0 /\ a - b - 1 >= 0 /\ a - b >= 0 /\ a - 3*b - 3 >= 0 /\ a - 2*b - 1 >= 0 /\ a - 2*b >= 0 /\ a - 4*b - 3 >= 0 /\ a - 3*b - 1 >= 0 /\ a - 3*b >= 0 ] with all transitions in problem 7, the following new transition is obtained: f1(a, b) -> f2(a - 5*b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 /\ a - 2*b - 3 >= 0 /\ a - b - 1 >= 0 /\ a - b >= 0 /\ a - 3*b - 3 >= 0 /\ a - 2*b - 1 >= 0 /\ a - 2*b >= 0 /\ a - 4*b - 3 >= 0 /\ a - 3*b - 1 >= 0 /\ a - 3*b >= 0 /\ a - 5*b - 3 >= 0 /\ a - 4*b - 1 >= 0 /\ a - 4*b >= 0 ] We thus obtain the following problem: 8: T: (1, 6) f1(a, b) -> f2(a - 5*b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 /\ a - 2*b - 3 >= 0 /\ a - b - 1 >= 0 /\ a - b >= 0 /\ a - 3*b - 3 >= 0 /\ a - 2*b - 1 >= 0 /\ a - 2*b >= 0 /\ a - 4*b - 3 >= 0 /\ a - 3*b - 1 >= 0 /\ a - 3*b >= 0 /\ a - 5*b - 3 >= 0 /\ a - 4*b - 1 >= 0 /\ a - 4*b >= 0 ] (?, 1) f2(a, b) -> f2(a - b, b) [ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 ] start location: f1 leaf cost: 1 By chaining the transition f1(a, b) -> f2(a - 5*b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 /\ a - 2*b - 3 >= 0 /\ a - b - 1 >= 0 /\ a - b >= 0 /\ a - 3*b - 3 >= 0 /\ a - 2*b - 1 >= 0 /\ a - 2*b >= 0 /\ a - 4*b - 3 >= 0 /\ a - 3*b - 1 >= 0 /\ a - 3*b >= 0 /\ a - 5*b - 3 >= 0 /\ a - 4*b - 1 >= 0 /\ a - 4*b >= 0 ] with all transitions in problem 8, the following new transition is obtained: f1(a, b) -> f2(a - 6*b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 /\ a - 2*b - 3 >= 0 /\ a - b - 1 >= 0 /\ a - b >= 0 /\ a - 3*b - 3 >= 0 /\ a - 2*b - 1 >= 0 /\ a - 2*b >= 0 /\ a - 4*b - 3 >= 0 /\ a - 3*b - 1 >= 0 /\ a - 3*b >= 0 /\ a - 5*b - 3 >= 0 /\ a - 4*b - 1 >= 0 /\ a - 4*b >= 0 /\ a - 6*b - 3 >= 0 /\ a - 5*b - 1 >= 0 /\ a - 5*b >= 0 ] We thus obtain the following problem: 9: T: (1, 7) f1(a, b) -> f2(a - 6*b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 /\ a - 2*b - 3 >= 0 /\ a - b - 1 >= 0 /\ a - b >= 0 /\ a - 3*b - 3 >= 0 /\ a - 2*b - 1 >= 0 /\ a - 2*b >= 0 /\ a - 4*b - 3 >= 0 /\ a - 3*b - 1 >= 0 /\ a - 3*b >= 0 /\ a - 5*b - 3 >= 0 /\ a - 4*b - 1 >= 0 /\ a - 4*b >= 0 /\ a - 6*b - 3 >= 0 /\ a - 5*b - 1 >= 0 /\ a - 5*b >= 0 ] (?, 1) f2(a, b) -> f2(a - b, b) [ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 ] start location: f1 leaf cost: 1 By chaining the transition f1(a, b) -> f2(a - 6*b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 /\ a - 2*b - 3 >= 0 /\ a - b - 1 >= 0 /\ a - b >= 0 /\ a - 3*b - 3 >= 0 /\ a - 2*b - 1 >= 0 /\ a - 2*b >= 0 /\ a - 4*b - 3 >= 0 /\ a - 3*b - 1 >= 0 /\ a - 3*b >= 0 /\ a - 5*b - 3 >= 0 /\ a - 4*b - 1 >= 0 /\ a - 4*b >= 0 /\ a - 6*b - 3 >= 0 /\ a - 5*b - 1 >= 0 /\ a - 5*b >= 0 ] with all transitions in problem 9, the following new transition is obtained: f1(a, b) -> f2(a - 7*b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 /\ a - 2*b - 3 >= 0 /\ a - b - 1 >= 0 /\ a - b >= 0 /\ a - 3*b - 3 >= 0 /\ a - 2*b - 1 >= 0 /\ a - 2*b >= 0 /\ a - 4*b - 3 >= 0 /\ a - 3*b - 1 >= 0 /\ a - 3*b >= 0 /\ a - 5*b - 3 >= 0 /\ a - 4*b - 1 >= 0 /\ a - 4*b >= 0 /\ a - 6*b - 3 >= 0 /\ a - 5*b - 1 >= 0 /\ a - 5*b >= 0 /\ a - 7*b - 3 >= 0 /\ a - 6*b - 1 >= 0 /\ a - 6*b >= 0 ] We thus obtain the following problem: 10: T: (1, 8) f1(a, b) -> f2(a - 7*b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 /\ a - 2*b - 3 >= 0 /\ a - b - 1 >= 0 /\ a - b >= 0 /\ a - 3*b - 3 >= 0 /\ a - 2*b - 1 >= 0 /\ a - 2*b >= 0 /\ a - 4*b - 3 >= 0 /\ a - 3*b - 1 >= 0 /\ a - 3*b >= 0 /\ a - 5*b - 3 >= 0 /\ a - 4*b - 1 >= 0 /\ a - 4*b >= 0 /\ a - 6*b - 3 >= 0 /\ a - 5*b - 1 >= 0 /\ a - 5*b >= 0 /\ a - 7*b - 3 >= 0 /\ a - 6*b - 1 >= 0 /\ a - 6*b >= 0 ] (?, 1) f2(a, b) -> f2(a - b, b) [ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 ] start location: f1 leaf cost: 1 By chaining the transition f1(a, b) -> f2(a - 7*b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 /\ a - 2*b - 3 >= 0 /\ a - b - 1 >= 0 /\ a - b >= 0 /\ a - 3*b - 3 >= 0 /\ a - 2*b - 1 >= 0 /\ a - 2*b >= 0 /\ a - 4*b - 3 >= 0 /\ a - 3*b - 1 >= 0 /\ a - 3*b >= 0 /\ a - 5*b - 3 >= 0 /\ a - 4*b - 1 >= 0 /\ a - 4*b >= 0 /\ a - 6*b - 3 >= 0 /\ a - 5*b - 1 >= 0 /\ a - 5*b >= 0 /\ a - 7*b - 3 >= 0 /\ a - 6*b - 1 >= 0 /\ a - 6*b >= 0 ] with all transitions in problem 10, the following new transition is obtained: f1(a, b) -> f2(a - 8*b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 /\ a - 2*b - 3 >= 0 /\ a - b - 1 >= 0 /\ a - b >= 0 /\ a - 3*b - 3 >= 0 /\ a - 2*b - 1 >= 0 /\ a - 2*b >= 0 /\ a - 4*b - 3 >= 0 /\ a - 3*b - 1 >= 0 /\ a - 3*b >= 0 /\ a - 5*b - 3 >= 0 /\ a - 4*b - 1 >= 0 /\ a - 4*b >= 0 /\ a - 6*b - 3 >= 0 /\ a - 5*b - 1 >= 0 /\ a - 5*b >= 0 /\ a - 7*b - 3 >= 0 /\ a - 6*b - 1 >= 0 /\ a - 6*b >= 0 /\ a - 8*b - 3 >= 0 /\ a - 7*b - 1 >= 0 /\ a - 7*b >= 0 ] We thus obtain the following problem: 11: T: (1, 9) f1(a, b) -> f2(a - 8*b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 /\ a - 2*b - 3 >= 0 /\ a - b - 1 >= 0 /\ a - b >= 0 /\ a - 3*b - 3 >= 0 /\ a - 2*b - 1 >= 0 /\ a - 2*b >= 0 /\ a - 4*b - 3 >= 0 /\ a - 3*b - 1 >= 0 /\ a - 3*b >= 0 /\ a - 5*b - 3 >= 0 /\ a - 4*b - 1 >= 0 /\ a - 4*b >= 0 /\ a - 6*b - 3 >= 0 /\ a - 5*b - 1 >= 0 /\ a - 5*b >= 0 /\ a - 7*b - 3 >= 0 /\ a - 6*b - 1 >= 0 /\ a - 6*b >= 0 /\ a - 8*b - 3 >= 0 /\ a - 7*b - 1 >= 0 /\ a - 7*b >= 0 ] (?, 1) f2(a, b) -> f2(a - b, b) [ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 ] start location: f1 leaf cost: 1 By chaining the transition f1(a, b) -> f2(a - 8*b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 /\ a - 2*b - 3 >= 0 /\ a - b - 1 >= 0 /\ a - b >= 0 /\ a - 3*b - 3 >= 0 /\ a - 2*b - 1 >= 0 /\ a - 2*b >= 0 /\ a - 4*b - 3 >= 0 /\ a - 3*b - 1 >= 0 /\ a - 3*b >= 0 /\ a - 5*b - 3 >= 0 /\ a - 4*b - 1 >= 0 /\ a - 4*b >= 0 /\ a - 6*b - 3 >= 0 /\ a - 5*b - 1 >= 0 /\ a - 5*b >= 0 /\ a - 7*b - 3 >= 0 /\ a - 6*b - 1 >= 0 /\ a - 6*b >= 0 /\ a - 8*b - 3 >= 0 /\ a - 7*b - 1 >= 0 /\ a - 7*b >= 0 ] with all transitions in problem 11, the following new transition is obtained: f1(a, b) -> f2(a - 9*b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 /\ a - 2*b - 3 >= 0 /\ a - b - 1 >= 0 /\ a - b >= 0 /\ a - 3*b - 3 >= 0 /\ a - 2*b - 1 >= 0 /\ a - 2*b >= 0 /\ a - 4*b - 3 >= 0 /\ a - 3*b - 1 >= 0 /\ a - 3*b >= 0 /\ a - 5*b - 3 >= 0 /\ a - 4*b - 1 >= 0 /\ a - 4*b >= 0 /\ a - 6*b - 3 >= 0 /\ a - 5*b - 1 >= 0 /\ a - 5*b >= 0 /\ a - 7*b - 3 >= 0 /\ a - 6*b - 1 >= 0 /\ a - 6*b >= 0 /\ a - 8*b - 3 >= 0 /\ a - 7*b - 1 >= 0 /\ a - 7*b >= 0 /\ a - 9*b - 3 >= 0 /\ a - 8*b - 1 >= 0 /\ a - 8*b >= 0 ] We thus obtain the following problem: 12: T: (1, 10) f1(a, b) -> f2(a - 9*b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 /\ a - 2*b - 3 >= 0 /\ a - b - 1 >= 0 /\ a - b >= 0 /\ a - 3*b - 3 >= 0 /\ a - 2*b - 1 >= 0 /\ a - 2*b >= 0 /\ a - 4*b - 3 >= 0 /\ a - 3*b - 1 >= 0 /\ a - 3*b >= 0 /\ a - 5*b - 3 >= 0 /\ a - 4*b - 1 >= 0 /\ a - 4*b >= 0 /\ a - 6*b - 3 >= 0 /\ a - 5*b - 1 >= 0 /\ a - 5*b >= 0 /\ a - 7*b - 3 >= 0 /\ a - 6*b - 1 >= 0 /\ a - 6*b >= 0 /\ a - 8*b - 3 >= 0 /\ a - 7*b - 1 >= 0 /\ a - 7*b >= 0 /\ a - 9*b - 3 >= 0 /\ a - 8*b - 1 >= 0 /\ a - 8*b >= 0 ] (?, 1) f2(a, b) -> f2(a - b, b) [ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 ] start location: f1 leaf cost: 1 By chaining the transition f1(a, b) -> f2(a - 9*b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 /\ a - 2*b - 3 >= 0 /\ a - b - 1 >= 0 /\ a - b >= 0 /\ a - 3*b - 3 >= 0 /\ a - 2*b - 1 >= 0 /\ a - 2*b >= 0 /\ a - 4*b - 3 >= 0 /\ a - 3*b - 1 >= 0 /\ a - 3*b >= 0 /\ a - 5*b - 3 >= 0 /\ a - 4*b - 1 >= 0 /\ a - 4*b >= 0 /\ a - 6*b - 3 >= 0 /\ a - 5*b - 1 >= 0 /\ a - 5*b >= 0 /\ a - 7*b - 3 >= 0 /\ a - 6*b - 1 >= 0 /\ a - 6*b >= 0 /\ a - 8*b - 3 >= 0 /\ a - 7*b - 1 >= 0 /\ a - 7*b >= 0 /\ a - 9*b - 3 >= 0 /\ a - 8*b - 1 >= 0 /\ a - 8*b >= 0 ] with all transitions in problem 12, the following new transition is obtained: f1(a, b) -> f2(a - 10*b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 /\ a - 2*b - 3 >= 0 /\ a - b - 1 >= 0 /\ a - b >= 0 /\ a - 3*b - 3 >= 0 /\ a - 2*b - 1 >= 0 /\ a - 2*b >= 0 /\ a - 4*b - 3 >= 0 /\ a - 3*b - 1 >= 0 /\ a - 3*b >= 0 /\ a - 5*b - 3 >= 0 /\ a - 4*b - 1 >= 0 /\ a - 4*b >= 0 /\ a - 6*b - 3 >= 0 /\ a - 5*b - 1 >= 0 /\ a - 5*b >= 0 /\ a - 7*b - 3 >= 0 /\ a - 6*b - 1 >= 0 /\ a - 6*b >= 0 /\ a - 8*b - 3 >= 0 /\ a - 7*b - 1 >= 0 /\ a - 7*b >= 0 /\ a - 9*b - 3 >= 0 /\ a - 8*b - 1 >= 0 /\ a - 8*b >= 0 /\ a - 10*b - 3 >= 0 /\ a - 9*b - 1 >= 0 /\ a - 9*b >= 0 ] We thus obtain the following problem: 13: T: (1, 11) f1(a, b) -> f2(a - 10*b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 /\ a - 2*b - 3 >= 0 /\ a - b - 1 >= 0 /\ a - b >= 0 /\ a - 3*b - 3 >= 0 /\ a - 2*b - 1 >= 0 /\ a - 2*b >= 0 /\ a - 4*b - 3 >= 0 /\ a - 3*b - 1 >= 0 /\ a - 3*b >= 0 /\ a - 5*b - 3 >= 0 /\ a - 4*b - 1 >= 0 /\ a - 4*b >= 0 /\ a - 6*b - 3 >= 0 /\ a - 5*b - 1 >= 0 /\ a - 5*b >= 0 /\ a - 7*b - 3 >= 0 /\ a - 6*b - 1 >= 0 /\ a - 6*b >= 0 /\ a - 8*b - 3 >= 0 /\ a - 7*b - 1 >= 0 /\ a - 7*b >= 0 /\ a - 9*b - 3 >= 0 /\ a - 8*b - 1 >= 0 /\ a - 8*b >= 0 /\ a - 10*b - 3 >= 0 /\ a - 9*b - 1 >= 0 /\ a - 9*b >= 0 ] (?, 1) f2(a, b) -> f2(a - b, b) [ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 ] start location: f1 leaf cost: 1 By chaining the transition f1(a, b) -> f2(a - 10*b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 /\ a - 2*b - 3 >= 0 /\ a - b - 1 >= 0 /\ a - b >= 0 /\ a - 3*b - 3 >= 0 /\ a - 2*b - 1 >= 0 /\ a - 2*b >= 0 /\ a - 4*b - 3 >= 0 /\ a - 3*b - 1 >= 0 /\ a - 3*b >= 0 /\ a - 5*b - 3 >= 0 /\ a - 4*b - 1 >= 0 /\ a - 4*b >= 0 /\ a - 6*b - 3 >= 0 /\ a - 5*b - 1 >= 0 /\ a - 5*b >= 0 /\ a - 7*b - 3 >= 0 /\ a - 6*b - 1 >= 0 /\ a - 6*b >= 0 /\ a - 8*b - 3 >= 0 /\ a - 7*b - 1 >= 0 /\ a - 7*b >= 0 /\ a - 9*b - 3 >= 0 /\ a - 8*b - 1 >= 0 /\ a - 8*b >= 0 /\ a - 10*b - 3 >= 0 /\ a - 9*b - 1 >= 0 /\ a - 9*b >= 0 ] with all transitions in problem 13, the following new transition is obtained: f1(a, b) -> f2(a - 11*b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 /\ a - 2*b - 3 >= 0 /\ a - b - 1 >= 0 /\ a - b >= 0 /\ a - 3*b - 3 >= 0 /\ a - 2*b - 1 >= 0 /\ a - 2*b >= 0 /\ a - 4*b - 3 >= 0 /\ a - 3*b - 1 >= 0 /\ a - 3*b >= 0 /\ a - 5*b - 3 >= 0 /\ a - 4*b - 1 >= 0 /\ a - 4*b >= 0 /\ a - 6*b - 3 >= 0 /\ a - 5*b - 1 >= 0 /\ a - 5*b >= 0 /\ a - 7*b - 3 >= 0 /\ a - 6*b - 1 >= 0 /\ a - 6*b >= 0 /\ a - 8*b - 3 >= 0 /\ a - 7*b - 1 >= 0 /\ a - 7*b >= 0 /\ a - 9*b - 3 >= 0 /\ a - 8*b - 1 >= 0 /\ a - 8*b >= 0 /\ a - 10*b - 3 >= 0 /\ a - 9*b - 1 >= 0 /\ a - 9*b >= 0 /\ a - 11*b - 3 >= 0 /\ a - 10*b - 1 >= 0 /\ a - 10*b >= 0 ] We thus obtain the following problem: 14: T: (1, 12) f1(a, b) -> f2(a - 11*b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 /\ a - 2*b - 3 >= 0 /\ a - b - 1 >= 0 /\ a - b >= 0 /\ a - 3*b - 3 >= 0 /\ a - 2*b - 1 >= 0 /\ a - 2*b >= 0 /\ a - 4*b - 3 >= 0 /\ a - 3*b - 1 >= 0 /\ a - 3*b >= 0 /\ a - 5*b - 3 >= 0 /\ a - 4*b - 1 >= 0 /\ a - 4*b >= 0 /\ a - 6*b - 3 >= 0 /\ a - 5*b - 1 >= 0 /\ a - 5*b >= 0 /\ a - 7*b - 3 >= 0 /\ a - 6*b - 1 >= 0 /\ a - 6*b >= 0 /\ a - 8*b - 3 >= 0 /\ a - 7*b - 1 >= 0 /\ a - 7*b >= 0 /\ a - 9*b - 3 >= 0 /\ a - 8*b - 1 >= 0 /\ a - 8*b >= 0 /\ a - 10*b - 3 >= 0 /\ a - 9*b - 1 >= 0 /\ a - 9*b >= 0 /\ a - 11*b - 3 >= 0 /\ a - 10*b - 1 >= 0 /\ a - 10*b >= 0 ] (?, 1) f2(a, b) -> f2(a - b, b) [ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 ] start location: f1 leaf cost: 1 By chaining the transition f1(a, b) -> f2(a - 11*b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 /\ a - 2*b - 3 >= 0 /\ a - b - 1 >= 0 /\ a - b >= 0 /\ a - 3*b - 3 >= 0 /\ a - 2*b - 1 >= 0 /\ a - 2*b >= 0 /\ a - 4*b - 3 >= 0 /\ a - 3*b - 1 >= 0 /\ a - 3*b >= 0 /\ a - 5*b - 3 >= 0 /\ a - 4*b - 1 >= 0 /\ a - 4*b >= 0 /\ a - 6*b - 3 >= 0 /\ a - 5*b - 1 >= 0 /\ a - 5*b >= 0 /\ a - 7*b - 3 >= 0 /\ a - 6*b - 1 >= 0 /\ a - 6*b >= 0 /\ a - 8*b - 3 >= 0 /\ a - 7*b - 1 >= 0 /\ a - 7*b >= 0 /\ a - 9*b - 3 >= 0 /\ a - 8*b - 1 >= 0 /\ a - 8*b >= 0 /\ a - 10*b - 3 >= 0 /\ a - 9*b - 1 >= 0 /\ a - 9*b >= 0 /\ a - 11*b - 3 >= 0 /\ a - 10*b - 1 >= 0 /\ a - 10*b >= 0 ] with all transitions in problem 14, the following new transition is obtained: f1(a, b) -> f2(a - 12*b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 /\ a - 2*b - 3 >= 0 /\ a - b - 1 >= 0 /\ a - b >= 0 /\ a - 3*b - 3 >= 0 /\ a - 2*b - 1 >= 0 /\ a - 2*b >= 0 /\ a - 4*b - 3 >= 0 /\ a - 3*b - 1 >= 0 /\ a - 3*b >= 0 /\ a - 5*b - 3 >= 0 /\ a - 4*b - 1 >= 0 /\ a - 4*b >= 0 /\ a - 6*b - 3 >= 0 /\ a - 5*b - 1 >= 0 /\ a - 5*b >= 0 /\ a - 7*b - 3 >= 0 /\ a - 6*b - 1 >= 0 /\ a - 6*b >= 0 /\ a - 8*b - 3 >= 0 /\ a - 7*b - 1 >= 0 /\ a - 7*b >= 0 /\ a - 9*b - 3 >= 0 /\ a - 8*b - 1 >= 0 /\ a - 8*b >= 0 /\ a - 10*b - 3 >= 0 /\ a - 9*b - 1 >= 0 /\ a - 9*b >= 0 /\ a - 11*b - 3 >= 0 /\ a - 10*b - 1 >= 0 /\ a - 10*b >= 0 /\ a - 12*b - 3 >= 0 /\ a - 11*b - 1 >= 0 /\ a - 11*b >= 0 ] We thus obtain the following problem: 15: T: (1, 13) f1(a, b) -> f2(a - 12*b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 /\ a - 2*b - 3 >= 0 /\ a - b - 1 >= 0 /\ a - b >= 0 /\ a - 3*b - 3 >= 0 /\ a - 2*b - 1 >= 0 /\ a - 2*b >= 0 /\ a - 4*b - 3 >= 0 /\ a - 3*b - 1 >= 0 /\ a - 3*b >= 0 /\ a - 5*b - 3 >= 0 /\ a - 4*b - 1 >= 0 /\ a - 4*b >= 0 /\ a - 6*b - 3 >= 0 /\ a - 5*b - 1 >= 0 /\ a - 5*b >= 0 /\ a - 7*b - 3 >= 0 /\ a - 6*b - 1 >= 0 /\ a - 6*b >= 0 /\ a - 8*b - 3 >= 0 /\ a - 7*b - 1 >= 0 /\ a - 7*b >= 0 /\ a - 9*b - 3 >= 0 /\ a - 8*b - 1 >= 0 /\ a - 8*b >= 0 /\ a - 10*b - 3 >= 0 /\ a - 9*b - 1 >= 0 /\ a - 9*b >= 0 /\ a - 11*b - 3 >= 0 /\ a - 10*b - 1 >= 0 /\ a - 10*b >= 0 /\ a - 12*b - 3 >= 0 /\ a - 11*b - 1 >= 0 /\ a - 11*b >= 0 ] (?, 1) f2(a, b) -> f2(a - b, b) [ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 ] start location: f1 leaf cost: 1 By chaining the transition f1(a, b) -> f2(a - 12*b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 /\ a - 2*b - 3 >= 0 /\ a - b - 1 >= 0 /\ a - b >= 0 /\ a - 3*b - 3 >= 0 /\ a - 2*b - 1 >= 0 /\ a - 2*b >= 0 /\ a - 4*b - 3 >= 0 /\ a - 3*b - 1 >= 0 /\ a - 3*b >= 0 /\ a - 5*b - 3 >= 0 /\ a - 4*b - 1 >= 0 /\ a - 4*b >= 0 /\ a - 6*b - 3 >= 0 /\ a - 5*b - 1 >= 0 /\ a - 5*b >= 0 /\ a - 7*b - 3 >= 0 /\ a - 6*b - 1 >= 0 /\ a - 6*b >= 0 /\ a - 8*b - 3 >= 0 /\ a - 7*b - 1 >= 0 /\ a - 7*b >= 0 /\ a - 9*b - 3 >= 0 /\ a - 8*b - 1 >= 0 /\ a - 8*b >= 0 /\ a - 10*b - 3 >= 0 /\ a - 9*b - 1 >= 0 /\ a - 9*b >= 0 /\ a - 11*b - 3 >= 0 /\ a - 10*b - 1 >= 0 /\ a - 10*b >= 0 /\ a - 12*b - 3 >= 0 /\ a - 11*b - 1 >= 0 /\ a - 11*b >= 0 ] with all transitions in problem 15, the following new transition is obtained: f1(a, b) -> f2(a - 13*b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 /\ a - 2*b - 3 >= 0 /\ a - b - 1 >= 0 /\ a - b >= 0 /\ a - 3*b - 3 >= 0 /\ a - 2*b - 1 >= 0 /\ a - 2*b >= 0 /\ a - 4*b - 3 >= 0 /\ a - 3*b - 1 >= 0 /\ a - 3*b >= 0 /\ a - 5*b - 3 >= 0 /\ a - 4*b - 1 >= 0 /\ a - 4*b >= 0 /\ a - 6*b - 3 >= 0 /\ a - 5*b - 1 >= 0 /\ a - 5*b >= 0 /\ a - 7*b - 3 >= 0 /\ a - 6*b - 1 >= 0 /\ a - 6*b >= 0 /\ a - 8*b - 3 >= 0 /\ a - 7*b - 1 >= 0 /\ a - 7*b >= 0 /\ a - 9*b - 3 >= 0 /\ a - 8*b - 1 >= 0 /\ a - 8*b >= 0 /\ a - 10*b - 3 >= 0 /\ a - 9*b - 1 >= 0 /\ a - 9*b >= 0 /\ a - 11*b - 3 >= 0 /\ a - 10*b - 1 >= 0 /\ a - 10*b >= 0 /\ a - 12*b - 3 >= 0 /\ a - 11*b - 1 >= 0 /\ a - 11*b >= 0 /\ a - 13*b - 3 >= 0 /\ a - 12*b - 1 >= 0 /\ a - 12*b >= 0 ] We thus obtain the following problem: 16: T: (1, 14) f1(a, b) -> f2(a - 13*b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 /\ a - 2*b - 3 >= 0 /\ a - b - 1 >= 0 /\ a - b >= 0 /\ a - 3*b - 3 >= 0 /\ a - 2*b - 1 >= 0 /\ a - 2*b >= 0 /\ a - 4*b - 3 >= 0 /\ a - 3*b - 1 >= 0 /\ a - 3*b >= 0 /\ a - 5*b - 3 >= 0 /\ a - 4*b - 1 >= 0 /\ a - 4*b >= 0 /\ a - 6*b - 3 >= 0 /\ a - 5*b - 1 >= 0 /\ a - 5*b >= 0 /\ a - 7*b - 3 >= 0 /\ a - 6*b - 1 >= 0 /\ a - 6*b >= 0 /\ a - 8*b - 3 >= 0 /\ a - 7*b - 1 >= 0 /\ a - 7*b >= 0 /\ a - 9*b - 3 >= 0 /\ a - 8*b - 1 >= 0 /\ a - 8*b >= 0 /\ a - 10*b - 3 >= 0 /\ a - 9*b - 1 >= 0 /\ a - 9*b >= 0 /\ a - 11*b - 3 >= 0 /\ a - 10*b - 1 >= 0 /\ a - 10*b >= 0 /\ a - 12*b - 3 >= 0 /\ a - 11*b - 1 >= 0 /\ a - 11*b >= 0 /\ a - 13*b - 3 >= 0 /\ a - 12*b - 1 >= 0 /\ a - 12*b >= 0 ] (?, 1) f2(a, b) -> f2(a - b, b) [ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 ] start location: f1 leaf cost: 1 By chaining the transition f1(a, b) -> f2(a - 13*b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 /\ a - 2*b - 3 >= 0 /\ a - b - 1 >= 0 /\ a - b >= 0 /\ a - 3*b - 3 >= 0 /\ a - 2*b - 1 >= 0 /\ a - 2*b >= 0 /\ a - 4*b - 3 >= 0 /\ a - 3*b - 1 >= 0 /\ a - 3*b >= 0 /\ a - 5*b - 3 >= 0 /\ a - 4*b - 1 >= 0 /\ a - 4*b >= 0 /\ a - 6*b - 3 >= 0 /\ a - 5*b - 1 >= 0 /\ a - 5*b >= 0 /\ a - 7*b - 3 >= 0 /\ a - 6*b - 1 >= 0 /\ a - 6*b >= 0 /\ a - 8*b - 3 >= 0 /\ a - 7*b - 1 >= 0 /\ a - 7*b >= 0 /\ a - 9*b - 3 >= 0 /\ a - 8*b - 1 >= 0 /\ a - 8*b >= 0 /\ a - 10*b - 3 >= 0 /\ a - 9*b - 1 >= 0 /\ a - 9*b >= 0 /\ a - 11*b - 3 >= 0 /\ a - 10*b - 1 >= 0 /\ a - 10*b >= 0 /\ a - 12*b - 3 >= 0 /\ a - 11*b - 1 >= 0 /\ a - 11*b >= 0 /\ a - 13*b - 3 >= 0 /\ a - 12*b - 1 >= 0 /\ a - 12*b >= 0 ] with all transitions in problem 16, the following new transition is obtained: f1(a, b) -> f2(a - 14*b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 /\ a - 2*b - 3 >= 0 /\ a - b - 1 >= 0 /\ a - b >= 0 /\ a - 3*b - 3 >= 0 /\ a - 2*b - 1 >= 0 /\ a - 2*b >= 0 /\ a - 4*b - 3 >= 0 /\ a - 3*b - 1 >= 0 /\ a - 3*b >= 0 /\ a - 5*b - 3 >= 0 /\ a - 4*b - 1 >= 0 /\ a - 4*b >= 0 /\ a - 6*b - 3 >= 0 /\ a - 5*b - 1 >= 0 /\ a - 5*b >= 0 /\ a - 7*b - 3 >= 0 /\ a - 6*b - 1 >= 0 /\ a - 6*b >= 0 /\ a - 8*b - 3 >= 0 /\ a - 7*b - 1 >= 0 /\ a - 7*b >= 0 /\ a - 9*b - 3 >= 0 /\ a - 8*b - 1 >= 0 /\ a - 8*b >= 0 /\ a - 10*b - 3 >= 0 /\ a - 9*b - 1 >= 0 /\ a - 9*b >= 0 /\ a - 11*b - 3 >= 0 /\ a - 10*b - 1 >= 0 /\ a - 10*b >= 0 /\ a - 12*b - 3 >= 0 /\ a - 11*b - 1 >= 0 /\ a - 11*b >= 0 /\ a - 13*b - 3 >= 0 /\ a - 12*b - 1 >= 0 /\ a - 12*b >= 0 /\ a - 14*b - 3 >= 0 /\ a - 13*b - 1 >= 0 /\ a - 13*b >= 0 ] We thus obtain the following problem: 17: T: (1, 15) f1(a, b) -> f2(a - 14*b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 /\ a - 2*b - 3 >= 0 /\ a - b - 1 >= 0 /\ a - b >= 0 /\ a - 3*b - 3 >= 0 /\ a - 2*b - 1 >= 0 /\ a - 2*b >= 0 /\ a - 4*b - 3 >= 0 /\ a - 3*b - 1 >= 0 /\ a - 3*b >= 0 /\ a - 5*b - 3 >= 0 /\ a - 4*b - 1 >= 0 /\ a - 4*b >= 0 /\ a - 6*b - 3 >= 0 /\ a - 5*b - 1 >= 0 /\ a - 5*b >= 0 /\ a - 7*b - 3 >= 0 /\ a - 6*b - 1 >= 0 /\ a - 6*b >= 0 /\ a - 8*b - 3 >= 0 /\ a - 7*b - 1 >= 0 /\ a - 7*b >= 0 /\ a - 9*b - 3 >= 0 /\ a - 8*b - 1 >= 0 /\ a - 8*b >= 0 /\ a - 10*b - 3 >= 0 /\ a - 9*b - 1 >= 0 /\ a - 9*b >= 0 /\ a - 11*b - 3 >= 0 /\ a - 10*b - 1 >= 0 /\ a - 10*b >= 0 /\ a - 12*b - 3 >= 0 /\ a - 11*b - 1 >= 0 /\ a - 11*b >= 0 /\ a - 13*b - 3 >= 0 /\ a - 12*b - 1 >= 0 /\ a - 12*b >= 0 /\ a - 14*b - 3 >= 0 /\ a - 13*b - 1 >= 0 /\ a - 13*b >= 0 ] (?, 1) f2(a, b) -> f2(a - b, b) [ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 ] start location: f1 leaf cost: 1 By chaining the transition f1(a, b) -> f2(a - 14*b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 /\ a - 2*b - 3 >= 0 /\ a - b - 1 >= 0 /\ a - b >= 0 /\ a - 3*b - 3 >= 0 /\ a - 2*b - 1 >= 0 /\ a - 2*b >= 0 /\ a - 4*b - 3 >= 0 /\ a - 3*b - 1 >= 0 /\ a - 3*b >= 0 /\ a - 5*b - 3 >= 0 /\ a - 4*b - 1 >= 0 /\ a - 4*b >= 0 /\ a - 6*b - 3 >= 0 /\ a - 5*b - 1 >= 0 /\ a - 5*b >= 0 /\ a - 7*b - 3 >= 0 /\ a - 6*b - 1 >= 0 /\ a - 6*b >= 0 /\ a - 8*b - 3 >= 0 /\ a - 7*b - 1 >= 0 /\ a - 7*b >= 0 /\ a - 9*b - 3 >= 0 /\ a - 8*b - 1 >= 0 /\ a - 8*b >= 0 /\ a - 10*b - 3 >= 0 /\ a - 9*b - 1 >= 0 /\ a - 9*b >= 0 /\ a - 11*b - 3 >= 0 /\ a - 10*b - 1 >= 0 /\ a - 10*b >= 0 /\ a - 12*b - 3 >= 0 /\ a - 11*b - 1 >= 0 /\ a - 11*b >= 0 /\ a - 13*b - 3 >= 0 /\ a - 12*b - 1 >= 0 /\ a - 12*b >= 0 /\ a - 14*b - 3 >= 0 /\ a - 13*b - 1 >= 0 /\ a - 13*b >= 0 ] with all transitions in problem 17, the following new transition is obtained: f1(a, b) -> f2(a - 15*b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 /\ a - 2*b - 3 >= 0 /\ a - b - 1 >= 0 /\ a - b >= 0 /\ a - 3*b - 3 >= 0 /\ a - 2*b - 1 >= 0 /\ a - 2*b >= 0 /\ a - 4*b - 3 >= 0 /\ a - 3*b - 1 >= 0 /\ a - 3*b >= 0 /\ a - 5*b - 3 >= 0 /\ a - 4*b - 1 >= 0 /\ a - 4*b >= 0 /\ a - 6*b - 3 >= 0 /\ a - 5*b - 1 >= 0 /\ a - 5*b >= 0 /\ a - 7*b - 3 >= 0 /\ a - 6*b - 1 >= 0 /\ a - 6*b >= 0 /\ a - 8*b - 3 >= 0 /\ a - 7*b - 1 >= 0 /\ a - 7*b >= 0 /\ a - 9*b - 3 >= 0 /\ a - 8*b - 1 >= 0 /\ a - 8*b >= 0 /\ a - 10*b - 3 >= 0 /\ a - 9*b - 1 >= 0 /\ a - 9*b >= 0 /\ a - 11*b - 3 >= 0 /\ a - 10*b - 1 >= 0 /\ a - 10*b >= 0 /\ a - 12*b - 3 >= 0 /\ a - 11*b - 1 >= 0 /\ a - 11*b >= 0 /\ a - 13*b - 3 >= 0 /\ a - 12*b - 1 >= 0 /\ a - 12*b >= 0 /\ a - 14*b - 3 >= 0 /\ a - 13*b - 1 >= 0 /\ a - 13*b >= 0 /\ a - 15*b - 3 >= 0 /\ a - 14*b - 1 >= 0 /\ a - 14*b >= 0 ] We thus obtain the following problem: 18: T: (1, 16) f1(a, b) -> f2(a - 15*b, b) [ 0 >= a + b + 1 /\ a >= 1 /\ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 /\ a - 2*b - 3 >= 0 /\ a - b - 1 >= 0 /\ a - b >= 0 /\ a - 3*b - 3 >= 0 /\ a - 2*b - 1 >= 0 /\ a - 2*b >= 0 /\ a - 4*b - 3 >= 0 /\ a - 3*b - 1 >= 0 /\ a - 3*b >= 0 /\ a - 5*b - 3 >= 0 /\ a - 4*b - 1 >= 0 /\ a - 4*b >= 0 /\ a - 6*b - 3 >= 0 /\ a - 5*b - 1 >= 0 /\ a - 5*b >= 0 /\ a - 7*b - 3 >= 0 /\ a - 6*b - 1 >= 0 /\ a - 6*b >= 0 /\ a - 8*b - 3 >= 0 /\ a - 7*b - 1 >= 0 /\ a - 7*b >= 0 /\ a - 9*b - 3 >= 0 /\ a - 8*b - 1 >= 0 /\ a - 8*b >= 0 /\ a - 10*b - 3 >= 0 /\ a - 9*b - 1 >= 0 /\ a - 9*b >= 0 /\ a - 11*b - 3 >= 0 /\ a - 10*b - 1 >= 0 /\ a - 10*b >= 0 /\ a - 12*b - 3 >= 0 /\ a - 11*b - 1 >= 0 /\ a - 11*b >= 0 /\ a - 13*b - 3 >= 0 /\ a - 12*b - 1 >= 0 /\ a - 12*b >= 0 /\ a - 14*b - 3 >= 0 /\ a - 13*b - 1 >= 0 /\ a - 13*b >= 0 /\ a - 15*b - 3 >= 0 /\ a - 14*b - 1 >= 0 /\ a - 14*b >= 0 ] (?, 1) f2(a, b) -> f2(a - b, b) [ -b - 2 >= 0 /\ a - b - 3 >= 0 /\ a - 1 >= 0 /\ a >= 0 ] start location: f1 leaf cost: 1 Complexity upper bound ? Time: 2.698 sec (SMT: 2.517 sec)