WORST_CASE(?, O(n^2)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) eval_start_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb0_in(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) eval_start_bb0_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_0(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) eval_start_0(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_1(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) eval_start_1(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_2(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) eval_start_2(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_3(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) eval_start_3(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_4(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) eval_start_4(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_5(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) eval_start_5(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_6(Ar_0, Ar_1, Ar_2)) (Comp: ?, Cost: 1) eval_start_6(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb1_in(Ar_0, 0, 0)) (Comp: ?, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 < Ar_0 ] (Comp: ?, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) eval_start_bb2_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1 + 1, Ar_2 + 1)) (Comp: ?, Cost: 1) eval_start_bb3_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2)) [ Ar_2 > 0 ] (Comp: ?, Cost: 1) eval_start_bb3_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb5_in(Ar_0, Ar_1, Ar_2)) [ Ar_2 <= 0 ] (Comp: ?, Cost: 1) eval_start_bb4_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 - 1)) (Comp: ?, Cost: 1) eval_start_bb5_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_stop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_start(Ar_0, Ar_1, Ar_2)) [ 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_start_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb0_in(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_bb0_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_0(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_0(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_1(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_1(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_2(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_2(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_3(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_3(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_4(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_4(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_5(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_5(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_6(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_6(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb1_in(Ar_0, 0, 0)) (Comp: ?, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 < Ar_0 ] (Comp: ?, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) eval_start_bb2_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1 + 1, Ar_2 + 1)) (Comp: ?, Cost: 1) eval_start_bb3_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2)) [ Ar_2 > 0 ] (Comp: ?, Cost: 1) eval_start_bb3_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb5_in(Ar_0, Ar_1, Ar_2)) [ Ar_2 <= 0 ] (Comp: ?, Cost: 1) eval_start_bb4_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 - 1)) (Comp: ?, Cost: 1) eval_start_bb5_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_stop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(eval_start_start) = 2 Pol(eval_start_bb0_in) = 2 Pol(eval_start_0) = 2 Pol(eval_start_1) = 2 Pol(eval_start_2) = 2 Pol(eval_start_3) = 2 Pol(eval_start_4) = 2 Pol(eval_start_5) = 2 Pol(eval_start_6) = 2 Pol(eval_start_bb1_in) = 2 Pol(eval_start_bb2_in) = 2 Pol(eval_start_bb3_in) = 2 Pol(eval_start_bb4_in) = 2 Pol(eval_start_bb5_in) = 1 Pol(eval_start_stop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions eval_start_bb5_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_stop(Ar_0, Ar_1, Ar_2)) eval_start_bb3_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb5_in(Ar_0, Ar_1, Ar_2)) [ Ar_2 <= 0 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) eval_start_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb0_in(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_bb0_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_0(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_0(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_1(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_1(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_2(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_2(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_3(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_3(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_4(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_4(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_5(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_5(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_6(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_6(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb1_in(Ar_0, 0, 0)) (Comp: ?, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 < Ar_0 ] (Comp: ?, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) eval_start_bb2_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1 + 1, Ar_2 + 1)) (Comp: ?, Cost: 1) eval_start_bb3_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2)) [ Ar_2 > 0 ] (Comp: 2, Cost: 1) eval_start_bb3_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb5_in(Ar_0, Ar_1, Ar_2)) [ Ar_2 <= 0 ] (Comp: ?, Cost: 1) eval_start_bb4_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 - 1)) (Comp: 2, Cost: 1) eval_start_bb5_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_stop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(eval_start_start) = 2*V_1 Pol(eval_start_bb0_in) = 2*V_1 Pol(eval_start_0) = 2*V_1 Pol(eval_start_1) = 2*V_1 Pol(eval_start_2) = 2*V_1 Pol(eval_start_3) = 2*V_1 Pol(eval_start_4) = 2*V_1 Pol(eval_start_5) = 2*V_1 Pol(eval_start_6) = 2*V_1 Pol(eval_start_bb1_in) = 2*V_1 - 2*V_2 Pol(eval_start_bb2_in) = 2*V_1 - 2*V_2 - 2 Pol(eval_start_bb3_in) = 2*V_1 - 2*V_2 Pol(eval_start_bb4_in) = 2*V_1 - 2*V_2 Pol(eval_start_bb5_in) = 2*V_1 - 2*V_2 Pol(eval_start_stop) = 2*V_1 - 2*V_2 Pol(koat_start) = 2*V_1 orients all transitions weakly and the transition eval_start_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 < Ar_0 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) eval_start_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb0_in(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_bb0_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_0(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_0(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_1(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_1(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_2(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_2(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_3(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_3(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_4(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_4(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_5(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_5(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_6(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_6(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb1_in(Ar_0, 0, 0)) (Comp: 2*Ar_0, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 < Ar_0 ] (Comp: ?, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) eval_start_bb2_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1 + 1, Ar_2 + 1)) (Comp: ?, Cost: 1) eval_start_bb3_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2)) [ Ar_2 > 0 ] (Comp: 2, Cost: 1) eval_start_bb3_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb5_in(Ar_0, Ar_1, Ar_2)) [ Ar_2 <= 0 ] (Comp: ?, Cost: 1) eval_start_bb4_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 - 1)) (Comp: 2, Cost: 1) eval_start_bb5_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_stop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 4 produces the following problem: 5: T: (Comp: 1, Cost: 1) eval_start_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb0_in(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_bb0_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_0(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_0(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_1(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_1(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_2(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_2(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_3(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_3(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_4(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_4(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_5(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_5(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_6(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_6(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb1_in(Ar_0, 0, 0)) (Comp: 2*Ar_0, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 < Ar_0 ] (Comp: ?, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_0 ] (Comp: 2*Ar_0, Cost: 1) eval_start_bb2_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1 + 1, Ar_2 + 1)) (Comp: ?, Cost: 1) eval_start_bb3_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2)) [ Ar_2 > 0 ] (Comp: 2, Cost: 1) eval_start_bb3_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb5_in(Ar_0, Ar_1, Ar_2)) [ Ar_2 <= 0 ] (Comp: ?, Cost: 1) eval_start_bb4_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 - 1)) (Comp: 2, Cost: 1) eval_start_bb5_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_stop(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 5 to obtain the following invariants: For symbol eval_start_bb1_in: X_2 - X_3 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_2 >= 0 For symbol eval_start_bb2_in: X_2 - X_3 >= 0 /\ X_1 - X_3 - 1 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_1 - X_2 - 1 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ X_1 - 1 >= 0 For symbol eval_start_bb3_in: X_2 - X_3 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_2 >= 0 /\ -X_1 + X_2 >= 0 For symbol eval_start_bb4_in: X_2 - X_3 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ X_2 - 1 >= 0 /\ -X_1 + X_2 >= 0 For symbol eval_start_bb5_in: -X_3 >= 0 /\ X_2 - X_3 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 >= 0 /\ X_2 >= 0 /\ -X_1 + X_2 >= 0 This yielded the following problem: 6: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] (Comp: 2, Cost: 1) eval_start_bb5_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_stop(Ar_0, Ar_1, Ar_2)) [ -Ar_2 >= 0 /\ Ar_1 - Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: ?, Cost: 1) eval_start_bb4_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 - 1)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: 2, Cost: 1) eval_start_bb3_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb5_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_2 <= 0 ] (Comp: ?, Cost: 1) eval_start_bb3_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_2 > 0 ] (Comp: 2*Ar_0, Cost: 1) eval_start_bb2_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1 + 1, Ar_2 + 1)) [ Ar_1 - Ar_2 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: ?, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_1 >= Ar_0 ] (Comp: 2*Ar_0, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_1 < Ar_0 ] (Comp: 1, Cost: 1) eval_start_6(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb1_in(Ar_0, 0, 0)) (Comp: 1, Cost: 1) eval_start_5(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_6(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_4(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_5(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_3(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_4(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_2(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_3(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_1(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_2(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_0(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_1(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_bb0_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_0(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb0_in(Ar_0, Ar_1, Ar_2)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(eval_start_bb4_in) = 3*V_3 Pol(eval_start_bb1_in) = 3*V_3 + 2 Pol(eval_start_bb3_in) = 3*V_3 + 1 and size complexities S("eval_start_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb0_in(Ar_0, Ar_1, Ar_2))", 0-0) = Ar_0 S("eval_start_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb0_in(Ar_0, Ar_1, Ar_2))", 0-1) = Ar_1 S("eval_start_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb0_in(Ar_0, Ar_1, Ar_2))", 0-2) = Ar_2 S("eval_start_bb0_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_0(Ar_0, Ar_1, Ar_2))", 0-0) = Ar_0 S("eval_start_bb0_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_0(Ar_0, Ar_1, Ar_2))", 0-1) = Ar_1 S("eval_start_bb0_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_0(Ar_0, Ar_1, Ar_2))", 0-2) = Ar_2 S("eval_start_0(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_1(Ar_0, Ar_1, Ar_2))", 0-0) = Ar_0 S("eval_start_0(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_1(Ar_0, Ar_1, Ar_2))", 0-1) = Ar_1 S("eval_start_0(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_1(Ar_0, Ar_1, Ar_2))", 0-2) = Ar_2 S("eval_start_1(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_2(Ar_0, Ar_1, Ar_2))", 0-0) = Ar_0 S("eval_start_1(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_2(Ar_0, Ar_1, Ar_2))", 0-1) = Ar_1 S("eval_start_1(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_2(Ar_0, Ar_1, Ar_2))", 0-2) = Ar_2 S("eval_start_2(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_3(Ar_0, Ar_1, Ar_2))", 0-0) = Ar_0 S("eval_start_2(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_3(Ar_0, Ar_1, Ar_2))", 0-1) = Ar_1 S("eval_start_2(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_3(Ar_0, Ar_1, Ar_2))", 0-2) = Ar_2 S("eval_start_3(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_4(Ar_0, Ar_1, Ar_2))", 0-0) = Ar_0 S("eval_start_3(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_4(Ar_0, Ar_1, Ar_2))", 0-1) = Ar_1 S("eval_start_3(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_4(Ar_0, Ar_1, Ar_2))", 0-2) = Ar_2 S("eval_start_4(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_5(Ar_0, Ar_1, Ar_2))", 0-0) = Ar_0 S("eval_start_4(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_5(Ar_0, Ar_1, Ar_2))", 0-1) = Ar_1 S("eval_start_4(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_5(Ar_0, Ar_1, Ar_2))", 0-2) = Ar_2 S("eval_start_5(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_6(Ar_0, Ar_1, Ar_2))", 0-0) = Ar_0 S("eval_start_5(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_6(Ar_0, Ar_1, Ar_2))", 0-1) = Ar_1 S("eval_start_5(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_6(Ar_0, Ar_1, Ar_2))", 0-2) = Ar_2 S("eval_start_6(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb1_in(Ar_0, 0, 0))", 0-0) = Ar_0 S("eval_start_6(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb1_in(Ar_0, 0, 0))", 0-1) = 0 S("eval_start_6(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb1_in(Ar_0, 0, 0))", 0-2) = 0 S("eval_start_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_1 < Ar_0 ]", 0-0) = Ar_0 S("eval_start_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_1 < Ar_0 ]", 0-1) = Ar_0 S("eval_start_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_1 < Ar_0 ]", 0-2) = Ar_0 S("eval_start_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_1 >= Ar_0 ]", 0-0) = Ar_0 S("eval_start_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_1 >= Ar_0 ]", 0-1) = Ar_0 S("eval_start_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ Ar_1 >= Ar_0 ]", 0-2) = Ar_0 S("eval_start_bb2_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1 + 1, Ar_2 + 1)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-0) = Ar_0 S("eval_start_bb2_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1 + 1, Ar_2 + 1)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-1) = Ar_0 S("eval_start_bb2_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1 + 1, Ar_2 + 1)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_0 + Ar_2 - 1 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 - 1 >= 0 /\\ Ar_0 - 1 >= 0 ]", 0-2) = Ar_0 S("eval_start_bb3_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_2 > 0 ]", 0-0) = Ar_0 S("eval_start_bb3_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_2 > 0 ]", 0-1) = Ar_0 S("eval_start_bb3_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_2 > 0 ]", 0-2) = Ar_0 S("eval_start_bb3_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb5_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_2 <= 0 ]", 0-0) = Ar_0 S("eval_start_bb3_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb5_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_2 <= 0 ]", 0-1) = Ar_0 S("eval_start_bb3_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb5_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_2 <= 0 ]", 0-2) = 0 S("eval_start_bb4_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 - 1)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 ]", 0-0) = Ar_0 S("eval_start_bb4_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 - 1)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 ]", 0-1) = Ar_0 S("eval_start_bb4_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 - 1)) [ Ar_1 - Ar_2 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_1 + Ar_2 - 2 >= 0 /\\ Ar_1 - 1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 ]", 0-2) = Ar_0 S("eval_start_bb5_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_stop(Ar_0, Ar_1, Ar_2)) [ -Ar_2 >= 0 /\\ Ar_1 - Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 ]", 0-0) = Ar_0 S("eval_start_bb5_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_stop(Ar_0, Ar_1, Ar_2)) [ -Ar_2 >= 0 /\\ Ar_1 - Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 ]", 0-1) = Ar_0 S("eval_start_bb5_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_stop(Ar_0, Ar_1, Ar_2)) [ -Ar_2 >= 0 /\\ Ar_1 - Ar_2 >= 0 /\\ Ar_2 >= 0 /\\ Ar_1 + Ar_2 >= 0 /\\ Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 ]", 0-2) = 0 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-2) = Ar_2 orients the transitions eval_start_bb4_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 - 1)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] eval_start_bb3_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_2 > 0 ] eval_start_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_1 >= Ar_0 ] weakly and the transitions eval_start_bb4_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 - 1)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] eval_start_bb3_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_2 > 0 ] eval_start_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_1 >= Ar_0 ] strictly and produces the following problem: 7: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] (Comp: 2, Cost: 1) eval_start_bb5_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_stop(Ar_0, Ar_1, Ar_2)) [ -Ar_2 >= 0 /\ Ar_1 - Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: 6*Ar_0^2 + 4*Ar_0 + 2, Cost: 1) eval_start_bb4_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 - 1)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 2 >= 0 /\ Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ] (Comp: 2, Cost: 1) eval_start_bb3_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb5_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_2 <= 0 ] (Comp: 6*Ar_0^2 + 4*Ar_0 + 2, Cost: 1) eval_start_bb3_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_2 > 0 ] (Comp: 2*Ar_0, Cost: 1) eval_start_bb2_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1 + 1, Ar_2 + 1)) [ Ar_1 - Ar_2 >= 0 /\ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 - 1 >= 0 ] (Comp: 6*Ar_0^2 + 4*Ar_0 + 2, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_1 >= Ar_0 ] (Comp: 2*Ar_0, Cost: 1) eval_start_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_1 < Ar_0 ] (Comp: 1, Cost: 1) eval_start_6(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb1_in(Ar_0, 0, 0)) (Comp: 1, Cost: 1) eval_start_5(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_6(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_4(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_5(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_3(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_4(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_2(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_3(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_1(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_2(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_0(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_1(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_bb0_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_0(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 1) eval_start_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb0_in(Ar_0, Ar_1, Ar_2)) start location: koat_start leaf cost: 0 Complexity upper bound 18*Ar_0^2 + 16*Ar_0 + 19 Time: 2.858 sec (SMT: 2.756 sec)