MAYBE Initial complexity problem: 1: T: (Comp: ?, Cost: 1) f4(Ar_0, Ar_1, Ar_2) -> Com_1(f5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_1, Fresh_1 + 1, Ar_1)) (Comp: ?, Cost: 1) f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0, Fresh_0 + 1, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transition from problem 1: f4(Ar_0, Ar_1, Ar_2) -> Com_1(f5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ] We thus obtain the following problem: 2: T: (Comp: ?, Cost: 1) f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0, Fresh_0 + 1, Ar_1)) (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_1, Fresh_1 + 1, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 2 produces the following problem: 3: T: (Comp: ?, Cost: 1) f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0, Fresh_0 + 1, Ar_1)) (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_1, Fresh_1 + 1, Ar_1)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 3 to obtain the following invariants: For symbol f4: X_1 - X_2 + 1 >= 0 /\ -X_1 + X_2 - 1 >= 0 This yielded the following problem: 4: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_1, Fresh_1 + 1, Ar_1)) (Comp: ?, Cost: 1) f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0, Fresh_0 + 1, Ar_1)) [ Ar_0 - Ar_1 + 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound ? Time: 0.568 sec (SMT: 0.541 sec)