MAYBE Initial complexity problem: 1: T: (Comp: ?, Cost: 1) f3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f1(0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f2(Ar_0, Ar_1, Ar_2, Fresh_1)) [ Ar_1 >= Ar_2 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f2(1, Ar_1 + 1, Ar_2, Fresh_0)) [ Ar_1 + 1 = Ar_2 /\ Ar_0 = 0 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f1(0, Ar_1 + 1, Ar_2 + 1, Ar_3)) [ Ar_2 >= Ar_1 + 2 /\ Ar_2 >= Ar_1 + 1 /\ Ar_0 = 0 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f3(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 1 produces the following problem: 2: T: (Comp: 1, Cost: 1) f3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f1(0, Ar_1, Ar_2, Ar_3)) (Comp: 1, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f2(Ar_0, Ar_1, Ar_2, Fresh_1)) [ Ar_1 >= Ar_2 ] (Comp: 1, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f2(1, Ar_1 + 1, Ar_2, Fresh_0)) [ Ar_1 + 1 = Ar_2 /\ Ar_0 = 0 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f1(0, Ar_1 + 1, Ar_2 + 1, Ar_3)) [ Ar_2 >= Ar_1 + 2 /\ Ar_2 >= Ar_1 + 1 /\ Ar_0 = 0 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f3(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 2 to obtain the following invariants: For symbol f1: -X_1 >= 0 /\ X_1 >= 0 This yielded the following problem: 3: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f3(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f1(0, Ar_1 + 1, Ar_2 + 1, Ar_3)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_1 + 2 /\ Ar_2 >= Ar_1 + 1 /\ Ar_0 = 0 ] (Comp: 1, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f2(1, Ar_1 + 1, Ar_2, Fresh_0)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ Ar_1 + 1 = Ar_2 /\ Ar_0 = 0 ] (Comp: 1, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f2(Ar_0, Ar_1, Ar_2, Fresh_1)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_2 ] (Comp: 1, Cost: 1) f3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f1(0, Ar_1, Ar_2, Ar_3)) start location: koat_start leaf cost: 0 Complexity upper bound ? Time: 1.637 sec (SMT: 1.573 sec)