MAYBE Initial complexity problem: 1: T: (1, 1) f0(a, b) -> f1(a, b) (?, 1) f1(a, b) -> f1(c + 1, c + 1) start location: f0 leaf cost: 0 By chaining the transition f0(a, b) -> f1(a, b) with all transitions in problem 1, the following new transition is obtained: f0(a, b) -> f1(c + 1, c + 1) We thus obtain the following problem: 2: T: (1, 2) f0(a, b) -> f1(c + 1, c + 1) (?, 1) f1(a, b) -> f1(c + 1, c + 1) start location: f0 leaf cost: 0 By chaining the transition f0(a, b) -> f1(c + 1, c + 1) with all transitions in problem 2, the following new transition is obtained: f0(a, b) -> f1(c' + 1, c' + 1) We thus obtain the following problem: 3: T: (1, 3) f0(a, b) -> f1(c' + 1, c' + 1) (?, 1) f1(a, b) -> f1(c + 1, c + 1) start location: f0 leaf cost: 0 By chaining the transition f0(a, b) -> f1(c' + 1, c' + 1) with all transitions in problem 3, the following new transition is obtained: f0(a, b) -> f1(c + 1, c + 1) We thus obtain the following problem: 4: T: (1, 4) f0(a, b) -> f1(c + 1, c + 1) (?, 1) f1(a, b) -> f1(c + 1, c + 1) start location: f0 leaf cost: 0 By chaining the transition f0(a, b) -> f1(c + 1, c + 1) with all transitions in problem 4, the following new transition is obtained: f0(a, b) -> f1(c' + 1, c' + 1) We thus obtain the following problem: 5: T: (1, 5) f0(a, b) -> f1(c' + 1, c' + 1) (?, 1) f1(a, b) -> f1(c + 1, c + 1) start location: f0 leaf cost: 0 By chaining the transition f0(a, b) -> f1(c' + 1, c' + 1) with all transitions in problem 5, the following new transition is obtained: f0(a, b) -> f1(c + 1, c + 1) We thus obtain the following problem: 6: T: (1, 6) f0(a, b) -> f1(c + 1, c + 1) (?, 1) f1(a, b) -> f1(c + 1, c + 1) start location: f0 leaf cost: 0 By chaining the transition f0(a, b) -> f1(c + 1, c + 1) with all transitions in problem 6, the following new transition is obtained: f0(a, b) -> f1(c' + 1, c' + 1) We thus obtain the following problem: 7: T: (1, 7) f0(a, b) -> f1(c' + 1, c' + 1) (?, 1) f1(a, b) -> f1(c + 1, c + 1) start location: f0 leaf cost: 0 By chaining the transition f0(a, b) -> f1(c' + 1, c' + 1) with all transitions in problem 7, the following new transition is obtained: f0(a, b) -> f1(c + 1, c + 1) We thus obtain the following problem: 8: T: (1, 8) f0(a, b) -> f1(c + 1, c + 1) (?, 1) f1(a, b) -> f1(c + 1, c + 1) start location: f0 leaf cost: 0 By chaining the transition f0(a, b) -> f1(c + 1, c + 1) with all transitions in problem 8, the following new transition is obtained: f0(a, b) -> f1(c' + 1, c' + 1) We thus obtain the following problem: 9: T: (1, 9) f0(a, b) -> f1(c' + 1, c' + 1) (?, 1) f1(a, b) -> f1(c + 1, c + 1) start location: f0 leaf cost: 0 By chaining the transition f0(a, b) -> f1(c' + 1, c' + 1) with all transitions in problem 9, the following new transition is obtained: f0(a, b) -> f1(c + 1, c + 1) We thus obtain the following problem: 10: T: (1, 10) f0(a, b) -> f1(c + 1, c + 1) (?, 1) f1(a, b) -> f1(c + 1, c + 1) start location: f0 leaf cost: 0 By chaining the transition f0(a, b) -> f1(c + 1, c + 1) with all transitions in problem 10, the following new transition is obtained: f0(a, b) -> f1(c' + 1, c' + 1) We thus obtain the following problem: 11: T: (1, 11) f0(a, b) -> f1(c' + 1, c' + 1) (?, 1) f1(a, b) -> f1(c + 1, c + 1) start location: f0 leaf cost: 0 By chaining the transition f0(a, b) -> f1(c' + 1, c' + 1) with all transitions in problem 11, the following new transition is obtained: f0(a, b) -> f1(c + 1, c + 1) We thus obtain the following problem: 12: T: (1, 12) f0(a, b) -> f1(c + 1, c + 1) (?, 1) f1(a, b) -> f1(c + 1, c + 1) start location: f0 leaf cost: 0 By chaining the transition f0(a, b) -> f1(c + 1, c + 1) with all transitions in problem 12, the following new transition is obtained: f0(a, b) -> f1(c' + 1, c' + 1) We thus obtain the following problem: 13: T: (1, 13) f0(a, b) -> f1(c' + 1, c' + 1) (?, 1) f1(a, b) -> f1(c + 1, c + 1) start location: f0 leaf cost: 0 By chaining the transition f0(a, b) -> f1(c' + 1, c' + 1) with all transitions in problem 13, the following new transition is obtained: f0(a, b) -> f1(c + 1, c + 1) We thus obtain the following problem: 14: T: (1, 14) f0(a, b) -> f1(c + 1, c + 1) (?, 1) f1(a, b) -> f1(c + 1, c + 1) start location: f0 leaf cost: 0 By chaining the transition f0(a, b) -> f1(c + 1, c + 1) with all transitions in problem 14, the following new transition is obtained: f0(a, b) -> f1(c' + 1, c' + 1) We thus obtain the following problem: 15: T: (1, 15) f0(a, b) -> f1(c' + 1, c' + 1) (?, 1) f1(a, b) -> f1(c + 1, c + 1) start location: f0 leaf cost: 0 By chaining the transition f0(a, b) -> f1(c' + 1, c' + 1) with all transitions in problem 15, the following new transition is obtained: f0(a, b) -> f1(c + 1, c + 1) We thus obtain the following problem: 16: T: (1, 16) f0(a, b) -> f1(c + 1, c + 1) (?, 1) f1(a, b) -> f1(c + 1, c + 1) start location: f0 leaf cost: 0 Complexity upper bound ? Time: 0.520 sec (SMT: 0.480 sec)