/export/starexec/sandbox2/solver/bin/starexec_run_c_complexity /export/starexec/sandbox2/benchmark/theBenchmark.c /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^1)) proof of /export/starexec/sandbox2/output/output_files/bench.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 278 ms] (2) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_speed_popl10_fig2_1_start(v_.0, v_.01, v_m, v_n, v_x, v_y) -> Com_1(eval_speed_popl10_fig2_1_bb0_in(v_.0, v_.01, v_m, v_n, v_x, v_y)) :|: TRUE eval_speed_popl10_fig2_1_bb0_in(v_.0, v_.01, v_m, v_n, v_x, v_y) -> Com_1(eval_speed_popl10_fig2_1_bb1_in(v_x, v_y, v_m, v_n, v_x, v_y)) :|: TRUE eval_speed_popl10_fig2_1_bb1_in(v_.0, v_.01, v_m, v_n, v_x, v_y) -> Com_1(eval_speed_popl10_fig2_1_bb2_in(v_.0, v_.01, v_m, v_n, v_x, v_y)) :|: v_n > v_.0 eval_speed_popl10_fig2_1_bb1_in(v_.0, v_.01, v_m, v_n, v_x, v_y) -> Com_1(eval_speed_popl10_fig2_1_bb3_in(v_.0, v_.01, v_m, v_n, v_x, v_y)) :|: v_n <= v_.0 eval_speed_popl10_fig2_1_bb2_in(v_.0, v_.01, v_m, v_n, v_x, v_y) -> Com_1(eval_speed_popl10_fig2_1_bb1_in(v_.0, v_.01 + 1, v_m, v_n, v_x, v_y)) :|: v_m > v_.01 eval_speed_popl10_fig2_1_bb2_in(v_.0, v_.01, v_m, v_n, v_x, v_y) -> Com_1(eval_speed_popl10_fig2_1_bb1_in(v_.0 + 1, v_.01 + 1, v_m, v_n, v_x, v_y)) :|: v_m > v_.01 && v_m <= v_.01 eval_speed_popl10_fig2_1_bb2_in(v_.0, v_.01, v_m, v_n, v_x, v_y) -> Com_1(eval_speed_popl10_fig2_1_bb1_in(v_.0, v_.01, v_m, v_n, v_x, v_y)) :|: v_m <= v_.01 && v_m > v_.01 eval_speed_popl10_fig2_1_bb2_in(v_.0, v_.01, v_m, v_n, v_x, v_y) -> Com_1(eval_speed_popl10_fig2_1_bb1_in(v_.0 + 1, v_.01, v_m, v_n, v_x, v_y)) :|: v_m <= v_.01 eval_speed_popl10_fig2_1_bb3_in(v_.0, v_.01, v_m, v_n, v_x, v_y) -> Com_1(eval_speed_popl10_fig2_1_stop(v_.0, v_.01, v_m, v_n, v_x, v_y)) :|: TRUE The start-symbols are:[eval_speed_popl10_fig2_1_start_6] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 2*ar_1 + 2*ar_4 + 2*ar_3 + 2*ar_5 + 7) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalspeedpopl10fig21start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) (Comp: ?, Cost: 1) evalspeedpopl10fig21bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5)) (Comp: ?, Cost: 1) evalspeedpopl10fig21bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalspeedpopl10fig21bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_4 ] (Comp: ?, Cost: 1) evalspeedpopl10fig21bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_5 >= ar_2 + 1 ] (Comp: ?, Cost: 1) evalspeedpopl10fig21bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb1in(ar_0 + 1, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_5 >= ar_2 + 1 /\ ar_2 >= ar_5 ] (Comp: ?, Cost: 1) evalspeedpopl10fig21bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_5 /\ ar_5 >= ar_2 + 1 ] (Comp: ?, Cost: 1) evalspeedpopl10fig21bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_5 ] (Comp: ?, Cost: 1) evalspeedpopl10fig21bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21stop(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(evalspeedpopl10fig21start(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: evalspeedpopl10fig21bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb1in(ar_0 + 1, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_5 >= ar_2 + 1 /\ ar_2 >= ar_5 ] evalspeedpopl10fig21bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_5 /\ ar_5 >= ar_2 + 1 ] We thus obtain the following problem: 2: T: (Comp: ?, Cost: 1) evalspeedpopl10fig21bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) (Comp: ?, Cost: 1) evalspeedpopl10fig21bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_5 ] (Comp: ?, Cost: 1) evalspeedpopl10fig21bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_5 >= ar_2 + 1 ] (Comp: ?, Cost: 1) evalspeedpopl10fig21bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_4 ] (Comp: ?, Cost: 1) evalspeedpopl10fig21bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalspeedpopl10fig21bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5)) (Comp: ?, Cost: 1) evalspeedpopl10fig21start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb0in(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(evalspeedpopl10fig21start(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) evalspeedpopl10fig21bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) (Comp: ?, Cost: 1) evalspeedpopl10fig21bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_5 ] (Comp: ?, Cost: 1) evalspeedpopl10fig21bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_5 >= ar_2 + 1 ] (Comp: ?, Cost: 1) evalspeedpopl10fig21bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_4 ] (Comp: ?, Cost: 1) evalspeedpopl10fig21bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= ar_0 + 1 ] (Comp: 1, Cost: 1) evalspeedpopl10fig21bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5)) (Comp: 1, Cost: 1) evalspeedpopl10fig21start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb0in(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(evalspeedpopl10fig21start(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(evalspeedpopl10fig21bb3in) = 1 Pol(evalspeedpopl10fig21stop) = 0 Pol(evalspeedpopl10fig21bb2in) = 2 Pol(evalspeedpopl10fig21bb1in) = 2 Pol(evalspeedpopl10fig21bb0in) = 2 Pol(evalspeedpopl10fig21start) = 2 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalspeedpopl10fig21bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) evalspeedpopl10fig21bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_4 ] strictly and produces the following problem: 4: T: (Comp: 2, Cost: 1) evalspeedpopl10fig21bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) (Comp: ?, Cost: 1) evalspeedpopl10fig21bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_5 ] (Comp: ?, Cost: 1) evalspeedpopl10fig21bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_5 >= ar_2 + 1 ] (Comp: 2, Cost: 1) evalspeedpopl10fig21bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_4 ] (Comp: ?, Cost: 1) evalspeedpopl10fig21bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= ar_0 + 1 ] (Comp: 1, Cost: 1) evalspeedpopl10fig21bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5)) (Comp: 1, Cost: 1) evalspeedpopl10fig21start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb0in(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(evalspeedpopl10fig21start(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(evalspeedpopl10fig21bb3in) = -V_3 + V_6 Pol(evalspeedpopl10fig21stop) = -V_3 + V_6 Pol(evalspeedpopl10fig21bb2in) = -V_3 + V_6 Pol(evalspeedpopl10fig21bb1in) = -V_3 + V_6 Pol(evalspeedpopl10fig21bb0in) = -V_4 + V_6 Pol(evalspeedpopl10fig21start) = -V_4 + V_6 Pol(koat_start) = -V_4 + V_6 orients all transitions weakly and the transition evalspeedpopl10fig21bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_5 >= ar_2 + 1 ] strictly and produces the following problem: 5: T: (Comp: 2, Cost: 1) evalspeedpopl10fig21bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) (Comp: ?, Cost: 1) evalspeedpopl10fig21bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_5 ] (Comp: ar_3 + ar_5, Cost: 1) evalspeedpopl10fig21bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_5 >= ar_2 + 1 ] (Comp: 2, Cost: 1) evalspeedpopl10fig21bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_4 ] (Comp: ?, Cost: 1) evalspeedpopl10fig21bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= ar_0 + 1 ] (Comp: 1, Cost: 1) evalspeedpopl10fig21bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5)) (Comp: 1, Cost: 1) evalspeedpopl10fig21start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb0in(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(evalspeedpopl10fig21start(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 evalspeedpopl10fig21bb1in: X_3 - X_4 >= 0 /\ X_1 - X_2 >= 0 For symbol evalspeedpopl10fig21bb2in: -X_2 + X_5 - 1 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_3 - X_4 >= 0 /\ X_1 - X_2 >= 0 For symbol evalspeedpopl10fig21bb3in: X_1 - X_5 >= 0 /\ X_3 - X_4 >= 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, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] (Comp: 1, Cost: 1) evalspeedpopl10fig21start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) (Comp: 1, Cost: 1) evalspeedpopl10fig21bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5)) (Comp: ?, Cost: 1) evalspeedpopl10fig21bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_4 >= ar_0 + 1 ] (Comp: 2, Cost: 1) evalspeedpopl10fig21bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_0 >= ar_4 ] (Comp: ar_3 + ar_5, Cost: 1) evalspeedpopl10fig21bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_5 >= ar_2 + 1 ] (Comp: ?, Cost: 1) evalspeedpopl10fig21bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_2 >= ar_5 ] (Comp: 2, Cost: 1) evalspeedpopl10fig21bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 - ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = -V_2 + V_5 Pol(evalspeedpopl10fig21start) = -V_2 + V_5 Pol(evalspeedpopl10fig21bb0in) = -V_2 + V_5 Pol(evalspeedpopl10fig21bb1in) = -V_1 + V_5 Pol(evalspeedpopl10fig21bb2in) = -V_1 + V_5 Pol(evalspeedpopl10fig21bb3in) = -V_1 + V_5 Pol(evalspeedpopl10fig21stop) = -V_1 + V_5 orients all transitions weakly and the transition evalspeedpopl10fig21bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_2 >= ar_5 ] 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(evalspeedpopl10fig21start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] (Comp: 1, Cost: 1) evalspeedpopl10fig21start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) (Comp: 1, Cost: 1) evalspeedpopl10fig21bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5)) (Comp: ?, Cost: 1) evalspeedpopl10fig21bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_4 >= ar_0 + 1 ] (Comp: 2, Cost: 1) evalspeedpopl10fig21bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_0 >= ar_4 ] (Comp: ar_3 + ar_5, Cost: 1) evalspeedpopl10fig21bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_5 >= ar_2 + 1 ] (Comp: ar_1 + ar_4, Cost: 1) evalspeedpopl10fig21bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_2 >= ar_5 ] (Comp: 2, Cost: 1) evalspeedpopl10fig21bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 - ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 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(evalspeedpopl10fig21start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] (Comp: 1, Cost: 1) evalspeedpopl10fig21start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) (Comp: 1, Cost: 1) evalspeedpopl10fig21bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5)) (Comp: ar_1 + ar_4 + ar_3 + ar_5 + 1, Cost: 1) evalspeedpopl10fig21bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_4 >= ar_0 + 1 ] (Comp: 2, Cost: 1) evalspeedpopl10fig21bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_0 >= ar_4 ] (Comp: ar_3 + ar_5, Cost: 1) evalspeedpopl10fig21bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_5 >= ar_2 + 1 ] (Comp: ar_1 + ar_4, Cost: 1) evalspeedpopl10fig21bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ -ar_1 + ar_4 - 1 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_2 >= ar_5 ] (Comp: 2, Cost: 1) evalspeedpopl10fig21bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalspeedpopl10fig21stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 - ar_4 >= 0 /\ ar_2 - ar_3 >= 0 /\ ar_0 - ar_1 >= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 2*ar_1 + 2*ar_4 + 2*ar_3 + 2*ar_5 + 7 Time: 0.235 sec (SMT: 0.195 sec) ---------------------------------------- (2) BOUNDS(1, n^1)