MAYBE Initial complexity problem: 1: T: (Comp: ?, Cost: 1) f0(Ar_0) -> Com_1(f1(100)) (Comp: ?, Cost: 1) f1(Ar_0) -> Com_1(f1(Ar_0 - 1)) [ Ar_0 >= 302 ] (Comp: ?, Cost: 1) f1(Ar_0) -> Com_1(f1(Ar_0 - 1)) [ 300 >= Ar_0 ] (Comp: 1, Cost: 0) koat_start(Ar_0) -> Com_1(f0(Ar_0)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transition from problem 1: f1(Ar_0) -> Com_1(f1(Ar_0 - 1)) [ Ar_0 >= 302 ] We thus obtain the following problem: 2: T: (Comp: ?, Cost: 1) f1(Ar_0) -> Com_1(f1(Ar_0 - 1)) [ 300 >= Ar_0 ] (Comp: ?, Cost: 1) f0(Ar_0) -> Com_1(f1(100)) (Comp: 1, Cost: 0) koat_start(Ar_0) -> Com_1(f0(Ar_0)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 2 produces the following problem: 3: T: (Comp: ?, Cost: 1) f1(Ar_0) -> Com_1(f1(Ar_0 - 1)) [ 300 >= Ar_0 ] (Comp: 1, Cost: 1) f0(Ar_0) -> Com_1(f1(100)) (Comp: 1, Cost: 0) koat_start(Ar_0) -> Com_1(f0(Ar_0)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 3 to obtain the following invariants: For symbol f1: -X_1 + 100 >= 0 This yielded the following problem: 4: T: (Comp: 1, Cost: 0) koat_start(Ar_0) -> Com_1(f0(Ar_0)) [ 0 <= 0 ] (Comp: 1, Cost: 1) f0(Ar_0) -> Com_1(f1(100)) (Comp: ?, Cost: 1) f1(Ar_0) -> Com_1(f1(Ar_0 - 1)) [ -Ar_0 + 100 >= 0 /\ 300 >= Ar_0 ] start location: koat_start leaf cost: 0 Complexity upper bound ? Time: 0.463 sec (SMT: 0.440 sec)