MAYBE Initial complexity problem: 1: T: (Comp: ?, Cost: 1) eval_speedFails4_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_speedFails4_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_1(Ar_0, Ar_1, Fresh_0, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_speedFails4_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_speedFails4_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_speedFails4_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_speedFails4_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_5(1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 1 ] (Comp: ?, Cost: 1) eval_speedFails4_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_5(-1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 < 1 ] (Comp: ?, Cost: 1) eval_speedFails4_5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_speedFails4_6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_speedFails4_7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_bb1_in(Ar_0, Ar_4, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_speedFails4_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 <= Ar_3 ] (Comp: ?, Cost: 1) eval_speedFails4_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 > Ar_3 ] (Comp: ?, Cost: 1) eval_speedFails4_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_bb1_in(Ar_0, Ar_1 + Ar_0, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 1 ] (Comp: ?, Cost: 1) eval_speedFails4_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_bb1_in(Ar_0, Ar_1 - Ar_0, Ar_2, Ar_3, Ar_4)) [ Ar_2 < 1 ] (Comp: ?, Cost: 1) eval_speedFails4_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 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) eval_speedFails4_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedFails4_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_1(Ar_0, Ar_1, Fresh_0, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedFails4_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedFails4_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedFails4_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedFails4_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_5(1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 1 ] (Comp: 1, Cost: 1) eval_speedFails4_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_5(-1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 < 1 ] (Comp: 2, Cost: 1) eval_speedFails4_5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 2, Cost: 1) eval_speedFails4_6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 2, Cost: 1) eval_speedFails4_7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_bb1_in(Ar_0, Ar_4, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_speedFails4_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 <= Ar_3 ] (Comp: ?, Cost: 1) eval_speedFails4_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 > Ar_3 ] (Comp: ?, Cost: 1) eval_speedFails4_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_bb1_in(Ar_0, Ar_1 + Ar_0, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 1 ] (Comp: ?, Cost: 1) eval_speedFails4_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_bb1_in(Ar_0, Ar_1 - Ar_0, Ar_2, Ar_3, Ar_4)) [ Ar_2 < 1 ] (Comp: ?, Cost: 1) eval_speedFails4_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(eval_speedFails4_start) = 2 Pol(eval_speedFails4_bb0_in) = 2 Pol(eval_speedFails4_1) = 2 Pol(eval_speedFails4_2) = 2 Pol(eval_speedFails4_3) = 2 Pol(eval_speedFails4_4) = 2 Pol(eval_speedFails4_5) = 2 Pol(eval_speedFails4_6) = 2 Pol(eval_speedFails4_7) = 2 Pol(eval_speedFails4_bb1_in) = 2 Pol(eval_speedFails4_bb2_in) = 2 Pol(eval_speedFails4_bb3_in) = 1 Pol(eval_speedFails4_stop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions eval_speedFails4_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) eval_speedFails4_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 > Ar_3 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) eval_speedFails4_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedFails4_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_1(Ar_0, Ar_1, Fresh_0, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedFails4_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedFails4_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedFails4_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedFails4_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_5(1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 1 ] (Comp: 1, Cost: 1) eval_speedFails4_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_5(-1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 < 1 ] (Comp: 2, Cost: 1) eval_speedFails4_5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 2, Cost: 1) eval_speedFails4_6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 2, Cost: 1) eval_speedFails4_7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_bb1_in(Ar_0, Ar_4, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_speedFails4_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 <= Ar_3 ] (Comp: 2, Cost: 1) eval_speedFails4_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 > Ar_3 ] (Comp: ?, Cost: 1) eval_speedFails4_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_bb1_in(Ar_0, Ar_1 + Ar_0, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 1 ] (Comp: ?, Cost: 1) eval_speedFails4_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_bb1_in(Ar_0, Ar_1 - Ar_0, Ar_2, Ar_3, Ar_4)) [ Ar_2 < 1 ] (Comp: 2, Cost: 1) eval_speedFails4_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 3 to obtain the following invariants: For symbol eval_speedFails4_5: -X_1 + 1 >= 0 /\ X_1 + 1 >= 0 For symbol eval_speedFails4_6: -X_1 + 1 >= 0 /\ X_1 + 1 >= 0 For symbol eval_speedFails4_7: -X_1 + 1 >= 0 /\ X_1 + 1 >= 0 For symbol eval_speedFails4_bb1_in: -X_1 + 1 >= 0 /\ X_1 + 1 >= 0 For symbol eval_speedFails4_bb2_in: -X_2 + X_4 >= 0 /\ -X_1 + 1 >= 0 /\ X_1 + 1 >= 0 For symbol eval_speedFails4_bb3_in: X_2 - X_4 - 1 >= 0 /\ -X_1 + 1 >= 0 /\ X_1 + 1 >= 0 This yielded the following problem: 4: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] (Comp: 2, Cost: 1) eval_speedFails4_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - Ar_3 - 1 >= 0 /\ -Ar_0 + 1 >= 0 /\ Ar_0 + 1 >= 0 ] (Comp: ?, Cost: 1) eval_speedFails4_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_bb1_in(Ar_0, Ar_1 - Ar_0, Ar_2, Ar_3, Ar_4)) [ -Ar_1 + Ar_3 >= 0 /\ -Ar_0 + 1 >= 0 /\ Ar_0 + 1 >= 0 /\ Ar_2 < 1 ] (Comp: ?, Cost: 1) eval_speedFails4_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_bb1_in(Ar_0, Ar_1 + Ar_0, Ar_2, Ar_3, Ar_4)) [ -Ar_1 + Ar_3 >= 0 /\ -Ar_0 + 1 >= 0 /\ Ar_0 + 1 >= 0 /\ Ar_2 >= 1 ] (Comp: 2, Cost: 1) eval_speedFails4_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_0 + 1 >= 0 /\ Ar_0 + 1 >= 0 /\ Ar_1 > Ar_3 ] (Comp: ?, Cost: 1) eval_speedFails4_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_0 + 1 >= 0 /\ Ar_0 + 1 >= 0 /\ Ar_1 <= Ar_3 ] (Comp: 2, Cost: 1) eval_speedFails4_7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_bb1_in(Ar_0, Ar_4, Ar_2, Ar_3, Ar_4)) [ -Ar_0 + 1 >= 0 /\ Ar_0 + 1 >= 0 ] (Comp: 2, Cost: 1) eval_speedFails4_6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_0 + 1 >= 0 /\ Ar_0 + 1 >= 0 ] (Comp: 2, Cost: 1) eval_speedFails4_5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_0 + 1 >= 0 /\ Ar_0 + 1 >= 0 ] (Comp: 1, Cost: 1) eval_speedFails4_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_5(-1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 < 1 ] (Comp: 1, Cost: 1) eval_speedFails4_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_5(1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 1 ] (Comp: 1, Cost: 1) eval_speedFails4_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedFails4_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedFails4_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedFails4_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_1(Ar_0, Ar_1, Fresh_0, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedFails4_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedFails4_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) start location: koat_start leaf cost: 0 Complexity upper bound ? Time: 4.827 sec (SMT: 4.667 sec)