WORST_CASE(?, O(n^1)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) eval_speedDis2_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_speedDis2_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_speedDis2_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_speedDis2_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_speedDis2_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_speedDis2_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_speedDis2_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_speedDis2_5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb1_in(Ar_3, Ar_4, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_speedDis2_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 < Ar_2 ] (Comp: ?, Cost: 1) eval_speedDis2_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_2 ] (Comp: ?, Cost: 1) eval_speedDis2_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb1_in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 > Ar_0 ] (Comp: ?, Cost: 1) eval_speedDis2_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 > Ar_0 /\ Ar_1 <= Ar_0 ] (Comp: ?, Cost: 1) eval_speedDis2_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb1_in(Ar_0 + 1, Ar_1 + 1, Ar_2, Ar_3, Ar_4)) [ Ar_1 <= Ar_0 /\ Ar_1 > Ar_0 ] (Comp: ?, Cost: 1) eval_speedDis2_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb1_in(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4)) [ Ar_1 <= Ar_0 ] (Comp: ?, Cost: 1) eval_speedDis2_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_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_speedDis2_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transitions from problem 1: eval_speedDis2_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 > Ar_0 /\ Ar_1 <= Ar_0 ] eval_speedDis2_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb1_in(Ar_0 + 1, Ar_1 + 1, Ar_2, Ar_3, Ar_4)) [ Ar_1 <= Ar_0 /\ Ar_1 > Ar_0 ] We thus obtain the following problem: 2: T: (Comp: ?, Cost: 1) eval_speedDis2_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_speedDis2_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb1_in(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4)) [ Ar_1 <= Ar_0 ] (Comp: ?, Cost: 1) eval_speedDis2_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb1_in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 > Ar_0 ] (Comp: ?, Cost: 1) eval_speedDis2_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_2 ] (Comp: ?, Cost: 1) eval_speedDis2_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 < Ar_2 ] (Comp: ?, Cost: 1) eval_speedDis2_5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb1_in(Ar_3, Ar_4, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_speedDis2_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_speedDis2_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_speedDis2_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_speedDis2_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_speedDis2_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_speedDis2_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_speedDis2_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb0_in(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_speedDis2_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 2 produces the following problem: 3: T: (Comp: ?, Cost: 1) eval_speedDis2_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_speedDis2_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb1_in(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4)) [ Ar_1 <= Ar_0 ] (Comp: ?, Cost: 1) eval_speedDis2_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb1_in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 > Ar_0 ] (Comp: ?, Cost: 1) eval_speedDis2_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_2 ] (Comp: ?, Cost: 1) eval_speedDis2_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 < Ar_2 ] (Comp: 1, Cost: 1) eval_speedDis2_5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb1_in(Ar_3, Ar_4, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedDis2_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedDis2_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedDis2_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedDis2_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedDis2_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedDis2_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedDis2_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb0_in(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_speedDis2_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_speedDis2_bb3_in) = 1 Pol(eval_speedDis2_stop) = 0 Pol(eval_speedDis2_bb2_in) = 2 Pol(eval_speedDis2_bb1_in) = 2 Pol(eval_speedDis2_5) = 2 Pol(eval_speedDis2_4) = 2 Pol(eval_speedDis2_3) = 2 Pol(eval_speedDis2_2) = 2 Pol(eval_speedDis2_1) = 2 Pol(eval_speedDis2_0) = 2 Pol(eval_speedDis2_bb0_in) = 2 Pol(eval_speedDis2_start) = 2 Pol(koat_start) = 2 orients all transitions weakly and the transitions eval_speedDis2_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) eval_speedDis2_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_2 ] strictly and produces the following problem: 4: T: (Comp: 2, Cost: 1) eval_speedDis2_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_speedDis2_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb1_in(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4)) [ Ar_1 <= Ar_0 ] (Comp: ?, Cost: 1) eval_speedDis2_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb1_in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 > Ar_0 ] (Comp: 2, Cost: 1) eval_speedDis2_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_2 ] (Comp: ?, Cost: 1) eval_speedDis2_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 < Ar_2 ] (Comp: 1, Cost: 1) eval_speedDis2_5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb1_in(Ar_3, Ar_4, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedDis2_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedDis2_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedDis2_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedDis2_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedDis2_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedDis2_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedDis2_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb0_in(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_speedDis2_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 4 to obtain the following invariants: For symbol eval_speedDis2_bb1_in: X_2 - X_5 >= 0 /\ X_1 - X_4 >= 0 For symbol eval_speedDis2_bb2_in: X_2 - X_5 >= 0 /\ X_3 - X_4 - 1 >= 0 /\ X_1 - X_4 >= 0 /\ -X_1 + X_3 - 1 >= 0 For symbol eval_speedDis2_bb3_in: X_2 - X_5 >= 0 /\ X_1 - X_4 >= 0 /\ X_1 - X_3 >= 0 This yielded the following problem: 5: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] (Comp: 1, Cost: 1) eval_speedDis2_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedDis2_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedDis2_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedDis2_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedDis2_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedDis2_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedDis2_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedDis2_5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb1_in(Ar_3, Ar_4, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_speedDis2_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - Ar_4 >= 0 /\ Ar_0 - Ar_3 >= 0 /\ Ar_0 < Ar_2 ] (Comp: 2, Cost: 1) eval_speedDis2_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - Ar_4 >= 0 /\ Ar_0 - Ar_3 >= 0 /\ Ar_0 >= Ar_2 ] (Comp: ?, Cost: 1) eval_speedDis2_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb1_in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - Ar_4 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_0 - Ar_3 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 > Ar_0 ] (Comp: ?, Cost: 1) eval_speedDis2_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb1_in(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - Ar_4 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_0 - Ar_3 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 <= Ar_0 ] (Comp: 2, Cost: 1) eval_speedDis2_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - Ar_4 >= 0 /\ Ar_0 - Ar_3 >= 0 /\ Ar_0 - Ar_2 >= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = V_3 - V_4 Pol(eval_speedDis2_start) = V_3 - V_4 Pol(eval_speedDis2_bb0_in) = V_3 - V_4 Pol(eval_speedDis2_0) = V_3 - V_4 Pol(eval_speedDis2_1) = V_3 - V_4 Pol(eval_speedDis2_2) = V_3 - V_4 Pol(eval_speedDis2_3) = V_3 - V_4 Pol(eval_speedDis2_4) = V_3 - V_4 Pol(eval_speedDis2_5) = V_3 - V_4 Pol(eval_speedDis2_bb1_in) = -V_1 + V_3 Pol(eval_speedDis2_bb2_in) = -V_1 + V_3 Pol(eval_speedDis2_bb3_in) = -V_1 + V_3 Pol(eval_speedDis2_stop) = -V_1 + V_3 orients all transitions weakly and the transition eval_speedDis2_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb1_in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - Ar_4 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_0 - Ar_3 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 > Ar_0 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] (Comp: 1, Cost: 1) eval_speedDis2_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedDis2_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedDis2_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedDis2_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedDis2_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedDis2_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedDis2_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedDis2_5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb1_in(Ar_3, Ar_4, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_speedDis2_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - Ar_4 >= 0 /\ Ar_0 - Ar_3 >= 0 /\ Ar_0 < Ar_2 ] (Comp: 2, Cost: 1) eval_speedDis2_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - Ar_4 >= 0 /\ Ar_0 - Ar_3 >= 0 /\ Ar_0 >= Ar_2 ] (Comp: Ar_2 + Ar_3, Cost: 1) eval_speedDis2_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb1_in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - Ar_4 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_0 - Ar_3 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 > Ar_0 ] (Comp: ?, Cost: 1) eval_speedDis2_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb1_in(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - Ar_4 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_0 - Ar_3 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 <= Ar_0 ] (Comp: 2, Cost: 1) eval_speedDis2_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - Ar_4 >= 0 /\ Ar_0 - Ar_3 >= 0 /\ Ar_0 - Ar_2 >= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = 3*V_3 - V_4 - 2*V_5 Pol(eval_speedDis2_start) = 3*V_3 - V_4 - 2*V_5 Pol(eval_speedDis2_bb0_in) = 3*V_3 - V_4 - 2*V_5 Pol(eval_speedDis2_0) = 3*V_3 - V_4 - 2*V_5 Pol(eval_speedDis2_1) = 3*V_3 - V_4 - 2*V_5 Pol(eval_speedDis2_2) = 3*V_3 - V_4 - 2*V_5 Pol(eval_speedDis2_3) = 3*V_3 - V_4 - 2*V_5 Pol(eval_speedDis2_4) = 3*V_3 - V_4 - 2*V_5 Pol(eval_speedDis2_5) = 3*V_3 - V_4 - 2*V_5 Pol(eval_speedDis2_bb1_in) = -V_1 - 2*V_2 + 3*V_3 Pol(eval_speedDis2_bb2_in) = -V_1 - 2*V_2 + 3*V_3 - 1 Pol(eval_speedDis2_bb3_in) = -V_1 - 2*V_2 + 3*V_3 Pol(eval_speedDis2_stop) = -V_1 - 2*V_2 + 3*V_3 orients all transitions weakly and the transition eval_speedDis2_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb1_in(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - Ar_4 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_0 - Ar_3 >= 0 /\ -Ar_0 + Ar_2 - 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, Ar_3, Ar_4) -> Com_1(eval_speedDis2_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] (Comp: 1, Cost: 1) eval_speedDis2_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedDis2_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedDis2_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedDis2_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedDis2_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedDis2_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedDis2_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedDis2_5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb1_in(Ar_3, Ar_4, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) eval_speedDis2_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - Ar_4 >= 0 /\ Ar_0 - Ar_3 >= 0 /\ Ar_0 < Ar_2 ] (Comp: 2, Cost: 1) eval_speedDis2_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - Ar_4 >= 0 /\ Ar_0 - Ar_3 >= 0 /\ Ar_0 >= Ar_2 ] (Comp: Ar_2 + Ar_3, Cost: 1) eval_speedDis2_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb1_in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - Ar_4 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_0 - Ar_3 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 > Ar_0 ] (Comp: 3*Ar_2 + Ar_3 + 2*Ar_4, Cost: 1) eval_speedDis2_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb1_in(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - Ar_4 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_0 - Ar_3 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 <= Ar_0 ] (Comp: 2, Cost: 1) eval_speedDis2_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - Ar_4 >= 0 /\ Ar_0 - Ar_3 >= 0 /\ Ar_0 - Ar_2 >= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 7 produces the following problem: 8: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] (Comp: 1, Cost: 1) eval_speedDis2_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedDis2_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedDis2_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedDis2_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedDis2_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedDis2_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedDis2_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) eval_speedDis2_5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb1_in(Ar_3, Ar_4, Ar_2, Ar_3, Ar_4)) (Comp: 4*Ar_2 + 2*Ar_3 + 2*Ar_4 + 1, Cost: 1) eval_speedDis2_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - Ar_4 >= 0 /\ Ar_0 - Ar_3 >= 0 /\ Ar_0 < Ar_2 ] (Comp: 2, Cost: 1) eval_speedDis2_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - Ar_4 >= 0 /\ Ar_0 - Ar_3 >= 0 /\ Ar_0 >= Ar_2 ] (Comp: Ar_2 + Ar_3, Cost: 1) eval_speedDis2_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb1_in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - Ar_4 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_0 - Ar_3 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 > Ar_0 ] (Comp: 3*Ar_2 + Ar_3 + 2*Ar_4, Cost: 1) eval_speedDis2_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_bb1_in(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - Ar_4 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_0 - Ar_3 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 <= Ar_0 ] (Comp: 2, Cost: 1) eval_speedDis2_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval_speedDis2_stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - Ar_4 >= 0 /\ Ar_0 - Ar_3 >= 0 /\ Ar_0 - Ar_2 >= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 8*Ar_2 + 4*Ar_3 + 4*Ar_4 + 13 Time: 2.801 sec (SMT: 2.693 sec)