MAYBE Initial complexity problem: 1: T: (?, 1) f8(a) -> f8(2) (1, 1) f1(a) -> f4(3) (?, 1) f4(a) -> f4(3) start location: f1 leaf cost: 0 Testing for reachability in the complexity graph removes the following transition from problem 1: f8(a) -> f8(2) We thus obtain the following problem: 2: T: (?, 1) f4(a) -> f4(3) (1, 1) f1(a) -> f4(3) start location: f1 leaf cost: 0 Applied AI with 'oct' on problem 2 to obtain the following invariants: For symbol f4: -X_1 + 3 >= 0 /\ X_1 - 3 >= 0 This yielded the following problem: 3: T: (1, 1) f1(a) -> f4(3) (?, 1) f4(a) -> f4(3) [ -a + 3 >= 0 /\ a - 3 >= 0 ] start location: f1 leaf cost: 0 By chaining the transition f1(a) -> f4(3) with all transitions in problem 3, the following new transition is obtained: f1(a) -> f4(3) [ 0 >= 0 ] We thus obtain the following problem: 4: T: (1, 2) f1(a) -> f4(3) [ 0 >= 0 ] (?, 1) f4(a) -> f4(3) [ -a + 3 >= 0 /\ a - 3 >= 0 ] start location: f1 leaf cost: 0 Complexity upper bound ? Time: 0.111 sec (SMT: 0.103 sec)