WORST_CASE(?, O(n^1)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) eval_speedDis1_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) eval_speedDis1_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) eval_speedDis1_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) eval_speedDis1_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) eval_speedDis1_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) eval_speedDis1_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) eval_speedDis1_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) eval_speedDis1_5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) eval_speedDis1_6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb1_in(Ar_4, Ar_5, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) eval_speedDis1_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 < Ar_3 ] (Comp: ?, Cost: 1) eval_speedDis1_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) eval_speedDis1_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb1_in(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 < Ar_2 ] (Comp: ?, Cost: 1) eval_speedDis1_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb1_in(Ar_0 + 1, Ar_1 + 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 < Ar_2 /\ Ar_1 >= Ar_2 ] (Comp: ?, Cost: 1) eval_speedDis1_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= Ar_2 /\ Ar_1 < Ar_2 ] (Comp: ?, Cost: 1) eval_speedDis1_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb1_in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= Ar_2 ] (Comp: ?, Cost: 1) eval_speedDis1_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transitions from problem 1: eval_speedDis1_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb1_in(Ar_0 + 1, Ar_1 + 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 < Ar_2 /\ Ar_1 >= Ar_2 ] eval_speedDis1_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= Ar_2 /\ Ar_1 < Ar_2 ] We thus obtain the following problem: 2: T: (Comp: ?, Cost: 1) eval_speedDis1_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) eval_speedDis1_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb1_in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= Ar_2 ] (Comp: ?, Cost: 1) eval_speedDis1_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb1_in(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 < Ar_2 ] (Comp: ?, Cost: 1) eval_speedDis1_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) eval_speedDis1_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 < Ar_3 ] (Comp: ?, Cost: 1) eval_speedDis1_6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb1_in(Ar_4, Ar_5, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) eval_speedDis1_5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) eval_speedDis1_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) eval_speedDis1_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) eval_speedDis1_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) eval_speedDis1_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) eval_speedDis1_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) eval_speedDis1_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) eval_speedDis1_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 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_speedDis1_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) eval_speedDis1_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb1_in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= Ar_2 ] (Comp: ?, Cost: 1) eval_speedDis1_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb1_in(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 < Ar_2 ] (Comp: ?, Cost: 1) eval_speedDis1_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) eval_speedDis1_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 < Ar_3 ] (Comp: 1, Cost: 1) eval_speedDis1_6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb1_in(Ar_4, Ar_5, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(eval_speedDis1_bb3_in) = 1 Pol(eval_speedDis1_stop) = 0 Pol(eval_speedDis1_bb2_in) = 2 Pol(eval_speedDis1_bb1_in) = 2 Pol(eval_speedDis1_6) = 2 Pol(eval_speedDis1_5) = 2 Pol(eval_speedDis1_4) = 2 Pol(eval_speedDis1_3) = 2 Pol(eval_speedDis1_2) = 2 Pol(eval_speedDis1_1) = 2 Pol(eval_speedDis1_0) = 2 Pol(eval_speedDis1_bb0_in) = 2 Pol(eval_speedDis1_start) = 2 Pol(koat_start) = 2 orients all transitions weakly and the transitions eval_speedDis1_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) eval_speedDis1_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_3 ] strictly and produces the following problem: 4: T: (Comp: 2, Cost: 1) eval_speedDis1_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) eval_speedDis1_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb1_in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= Ar_2 ] (Comp: ?, Cost: 1) eval_speedDis1_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb1_in(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 < Ar_2 ] (Comp: 2, Cost: 1) eval_speedDis1_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) eval_speedDis1_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 < Ar_3 ] (Comp: 1, Cost: 1) eval_speedDis1_6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb1_in(Ar_4, Ar_5, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(eval_speedDis1_bb3_in) = -V_2 + V_3 + 1 Pol(eval_speedDis1_stop) = -V_2 + V_3 + 1 Pol(eval_speedDis1_bb2_in) = -V_2 + V_3 + 1 Pol(eval_speedDis1_bb1_in) = -V_2 + V_3 + 1 Pol(eval_speedDis1_6) = V_3 - V_6 + 1 Pol(eval_speedDis1_5) = V_3 - V_6 + 1 Pol(eval_speedDis1_4) = V_3 - V_6 + 1 Pol(eval_speedDis1_3) = V_3 - V_6 + 1 Pol(eval_speedDis1_2) = V_3 - V_6 + 1 Pol(eval_speedDis1_1) = V_3 - V_6 + 1 Pol(eval_speedDis1_0) = V_3 - V_6 + 1 Pol(eval_speedDis1_bb0_in) = V_3 - V_6 + 1 Pol(eval_speedDis1_start) = V_3 - V_6 + 1 Pol(koat_start) = V_3 - V_6 + 1 orients all transitions weakly and the transition eval_speedDis1_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb1_in(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 < Ar_2 ] strictly and produces the following problem: 5: T: (Comp: 2, Cost: 1) eval_speedDis1_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) eval_speedDis1_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb1_in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= Ar_2 ] (Comp: Ar_2 + Ar_5 + 1, Cost: 1) eval_speedDis1_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb1_in(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 < Ar_2 ] (Comp: 2, Cost: 1) eval_speedDis1_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) eval_speedDis1_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 < Ar_3 ] (Comp: 1, Cost: 1) eval_speedDis1_6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb1_in(Ar_4, Ar_5, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 5 to obtain the following invariants: For symbol eval_speedDis1_bb1_in: X_2 - X_6 >= 0 /\ X_1 - X_5 >= 0 For symbol eval_speedDis1_bb2_in: X_2 - X_6 >= 0 /\ X_4 - X_5 - 1 >= 0 /\ X_1 - X_5 >= 0 /\ -X_1 + X_4 - 1 >= 0 For symbol eval_speedDis1_bb3_in: X_2 - X_6 >= 0 /\ X_1 - X_5 >= 0 /\ X_1 - X_4 >= 0 This yielded the following problem: 6: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] (Comp: 1, Cost: 1) eval_speedDis1_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb1_in(Ar_4, Ar_5, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) eval_speedDis1_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 - Ar_5 >= 0 /\ Ar_0 - Ar_4 >= 0 /\ Ar_0 < Ar_3 ] (Comp: 2, Cost: 1) eval_speedDis1_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 - Ar_5 >= 0 /\ Ar_0 - Ar_4 >= 0 /\ Ar_0 >= Ar_3 ] (Comp: Ar_2 + Ar_5 + 1, Cost: 1) eval_speedDis1_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb1_in(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 - Ar_5 >= 0 /\ Ar_3 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 >= 0 /\ -Ar_0 + Ar_3 - 1 >= 0 /\ Ar_1 < Ar_2 ] (Comp: ?, Cost: 1) eval_speedDis1_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb1_in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 - Ar_5 >= 0 /\ Ar_3 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 >= 0 /\ -Ar_0 + Ar_3 - 1 >= 0 /\ Ar_1 >= Ar_2 ] (Comp: 2, Cost: 1) eval_speedDis1_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 - Ar_5 >= 0 /\ Ar_0 - Ar_4 >= 0 /\ Ar_0 - Ar_3 >= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = V_4 - V_5 Pol(eval_speedDis1_start) = V_4 - V_5 Pol(eval_speedDis1_bb0_in) = V_4 - V_5 Pol(eval_speedDis1_0) = V_4 - V_5 Pol(eval_speedDis1_1) = V_4 - V_5 Pol(eval_speedDis1_2) = V_4 - V_5 Pol(eval_speedDis1_3) = V_4 - V_5 Pol(eval_speedDis1_4) = V_4 - V_5 Pol(eval_speedDis1_5) = V_4 - V_5 Pol(eval_speedDis1_6) = V_4 - V_5 Pol(eval_speedDis1_bb1_in) = -V_1 + V_4 Pol(eval_speedDis1_bb2_in) = -V_1 + V_4 Pol(eval_speedDis1_bb3_in) = -V_1 + V_4 Pol(eval_speedDis1_stop) = -V_1 + V_4 orients all transitions weakly and the transition eval_speedDis1_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb1_in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 - Ar_5 >= 0 /\ Ar_3 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 >= 0 /\ -Ar_0 + Ar_3 - 1 >= 0 /\ Ar_1 >= Ar_2 ] strictly and produces the following problem: 7: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] (Comp: 1, Cost: 1) eval_speedDis1_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb1_in(Ar_4, Ar_5, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: ?, Cost: 1) eval_speedDis1_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 - Ar_5 >= 0 /\ Ar_0 - Ar_4 >= 0 /\ Ar_0 < Ar_3 ] (Comp: 2, Cost: 1) eval_speedDis1_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 - Ar_5 >= 0 /\ Ar_0 - Ar_4 >= 0 /\ Ar_0 >= Ar_3 ] (Comp: Ar_2 + Ar_5 + 1, Cost: 1) eval_speedDis1_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb1_in(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 - Ar_5 >= 0 /\ Ar_3 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 >= 0 /\ -Ar_0 + Ar_3 - 1 >= 0 /\ Ar_1 < Ar_2 ] (Comp: Ar_3 + Ar_4, Cost: 1) eval_speedDis1_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb1_in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 - Ar_5 >= 0 /\ Ar_3 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 >= 0 /\ -Ar_0 + Ar_3 - 1 >= 0 /\ Ar_1 >= Ar_2 ] (Comp: 2, Cost: 1) eval_speedDis1_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 - Ar_5 >= 0 /\ Ar_0 - Ar_4 >= 0 /\ Ar_0 - Ar_3 >= 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, Ar_5) -> Com_1(eval_speedDis1_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] (Comp: 1, Cost: 1) eval_speedDis1_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: 1, Cost: 1) eval_speedDis1_6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb1_in(Ar_4, Ar_5, Ar_2, Ar_3, Ar_4, Ar_5)) (Comp: Ar_3 + Ar_4 + Ar_2 + Ar_5 + 2, Cost: 1) eval_speedDis1_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 - Ar_5 >= 0 /\ Ar_0 - Ar_4 >= 0 /\ Ar_0 < Ar_3 ] (Comp: 2, Cost: 1) eval_speedDis1_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 - Ar_5 >= 0 /\ Ar_0 - Ar_4 >= 0 /\ Ar_0 >= Ar_3 ] (Comp: Ar_2 + Ar_5 + 1, Cost: 1) eval_speedDis1_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb1_in(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 - Ar_5 >= 0 /\ Ar_3 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 >= 0 /\ -Ar_0 + Ar_3 - 1 >= 0 /\ Ar_1 < Ar_2 ] (Comp: Ar_3 + Ar_4, Cost: 1) eval_speedDis1_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_bb1_in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 - Ar_5 >= 0 /\ Ar_3 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 >= 0 /\ -Ar_0 + Ar_3 - 1 >= 0 /\ Ar_1 >= Ar_2 ] (Comp: 2, Cost: 1) eval_speedDis1_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(eval_speedDis1_stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 - Ar_5 >= 0 /\ Ar_0 - Ar_4 >= 0 /\ Ar_0 - Ar_3 >= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 2*Ar_3 + 2*Ar_4 + 2*Ar_2 + 2*Ar_5 + 16 Time: 3.373 sec (SMT: 3.233 sec)