/export/starexec/sandbox/solver/bin/starexec_run_c_complexity /export/starexec/sandbox/benchmark/theBenchmark.c /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^1)) proof of /export/starexec/sandbox/output/output_files/bench.koat # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 180 ms] (2) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_speed_popl10_fig2_2_start(v_.0, v_.01, v_n, v_x, v_z) -> Com_1(eval_speed_popl10_fig2_2_bb0_in(v_.0, v_.01, v_n, v_x, v_z)) :|: TRUE eval_speed_popl10_fig2_2_bb0_in(v_.0, v_.01, v_n, v_x, v_z) -> Com_1(eval_speed_popl10_fig2_2_bb1_in(v_x, v_z, v_n, v_x, v_z)) :|: TRUE eval_speed_popl10_fig2_2_bb1_in(v_.0, v_.01, v_n, v_x, v_z) -> Com_1(eval_speed_popl10_fig2_2_bb2_in(v_.0, v_.01, v_n, v_x, v_z)) :|: v_.0 < v_n eval_speed_popl10_fig2_2_bb1_in(v_.0, v_.01, v_n, v_x, v_z) -> Com_1(eval_speed_popl10_fig2_2_bb3_in(v_.0, v_.01, v_n, v_x, v_z)) :|: v_.0 >= v_n eval_speed_popl10_fig2_2_bb2_in(v_.0, v_.01, v_n, v_x, v_z) -> Com_1(eval_speed_popl10_fig2_2_bb1_in(v_.0 + 1, v_.01, v_n, v_x, v_z)) :|: v_.01 > v_.0 eval_speed_popl10_fig2_2_bb2_in(v_.0, v_.01, v_n, v_x, v_z) -> Com_1(eval_speed_popl10_fig2_2_bb1_in(v_.0, v_.01, v_n, v_x, v_z)) :|: v_.01 > v_.0 && v_.01 <= v_.0 eval_speed_popl10_fig2_2_bb2_in(v_.0, v_.01, v_n, v_x, v_z) -> Com_1(eval_speed_popl10_fig2_2_bb1_in(v_.0 + 1, v_.01 + 1, v_n, v_x, v_z)) :|: v_.01 <= v_.0 && v_.01 > v_.0 eval_speed_popl10_fig2_2_bb2_in(v_.0, v_.01, v_n, v_x, v_z) -> Com_1(eval_speed_popl10_fig2_2_bb1_in(v_.0, v_.01 + 1, v_n, v_x, v_z)) :|: v_.01 <= v_.0 eval_speed_popl10_fig2_2_bb3_in(v_.0, v_.01, v_n, v_x, v_z) -> Com_1(eval_speed_popl10_fig2_2_stop(v_.0, v_.01, v_n, v_x, v_z)) :|: TRUE The start-symbols are:[eval_speed_popl10_fig2_2_start_5] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 2*Ar_3 + 4*Ar_4 + 2*Ar_1 + 7) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalspeedpopl10fig22start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10fig22bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10fig22bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalspeedpopl10fig22bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_4 ] (Comp: ?, Cost: 1) evalspeedpopl10fig22bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalspeedpopl10fig22bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 /\ Ar_0 >= Ar_2 ] (Comp: ?, Cost: 1) evalspeedpopl10fig22bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb1in(Ar_0 + 1, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) [ Ar_0 >= Ar_2 /\ Ar_2 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalspeedpopl10fig22bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) [ Ar_0 >= Ar_2 ] (Comp: ?, Cost: 1) evalspeedpopl10fig22bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22stop(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(evalspeedpopl10fig22start(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: evalspeedpopl10fig22bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 /\ Ar_0 >= Ar_2 ] evalspeedpopl10fig22bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb1in(Ar_0 + 1, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) [ Ar_0 >= Ar_2 /\ Ar_2 >= Ar_0 + 1 ] We thus obtain the following problem: 2: T: (Comp: ?, Cost: 1) evalspeedpopl10fig22bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10fig22bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) [ Ar_0 >= Ar_2 ] (Comp: ?, Cost: 1) evalspeedpopl10fig22bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalspeedpopl10fig22bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_4 ] (Comp: ?, Cost: 1) evalspeedpopl10fig22bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalspeedpopl10fig22bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10fig22start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb0in(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(evalspeedpopl10fig22start(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) evalspeedpopl10fig22bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10fig22bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) [ Ar_0 >= Ar_2 ] (Comp: ?, Cost: 1) evalspeedpopl10fig22bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalspeedpopl10fig22bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_4 ] (Comp: ?, Cost: 1) evalspeedpopl10fig22bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalspeedpopl10fig22bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedpopl10fig22start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb0in(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(evalspeedpopl10fig22start(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(evalspeedpopl10fig22bb3in) = 1 Pol(evalspeedpopl10fig22stop) = 0 Pol(evalspeedpopl10fig22bb2in) = 2 Pol(evalspeedpopl10fig22bb1in) = 2 Pol(evalspeedpopl10fig22bb0in) = 2 Pol(evalspeedpopl10fig22start) = 2 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalspeedpopl10fig22bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) evalspeedpopl10fig22bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_4 ] strictly and produces the following problem: 4: T: (Comp: 2, Cost: 1) evalspeedpopl10fig22bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10fig22bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) [ Ar_0 >= Ar_2 ] (Comp: ?, Cost: 1) evalspeedpopl10fig22bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evalspeedpopl10fig22bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_4 ] (Comp: ?, Cost: 1) evalspeedpopl10fig22bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalspeedpopl10fig22bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedpopl10fig22start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb0in(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(evalspeedpopl10fig22start(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 evalspeedpopl10fig22bb1in: X_3 - X_4 >= 0 /\ X_1 - X_2 >= 0 For symbol evalspeedpopl10fig22bb2in: -X_2 + X_5 - 1 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_3 - X_4 >= 0 /\ X_1 - X_2 >= 0 For symbol evalspeedpopl10fig22bb3in: X_1 - X_5 >= 0 /\ X_3 - X_4 >= 0 /\ X_1 - X_2 >= 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(evalspeedpopl10fig22start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] (Comp: 1, Cost: 1) evalspeedpopl10fig22start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedpopl10fig22bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10fig22bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_4 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evalspeedpopl10fig22bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= Ar_4 ] (Comp: ?, Cost: 1) evalspeedpopl10fig22bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ -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_0 + 1 ] (Comp: ?, Cost: 1) evalspeedpopl10fig22bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) [ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= Ar_2 ] (Comp: 2, Cost: 1) evalspeedpopl10fig22bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 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(evalspeedpopl10fig22start) = -V_2 + V_5 Pol(evalspeedpopl10fig22bb0in) = -V_2 + V_5 Pol(evalspeedpopl10fig22bb1in) = -V_1 + V_5 Pol(evalspeedpopl10fig22bb2in) = -V_1 + V_5 Pol(evalspeedpopl10fig22bb3in) = -V_1 + V_5 Pol(evalspeedpopl10fig22stop) = -V_1 + V_5 orients all transitions weakly and the transition evalspeedpopl10fig22bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ -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_0 + 1 ] 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(evalspeedpopl10fig22start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] (Comp: 1, Cost: 1) evalspeedpopl10fig22start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedpopl10fig22bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10fig22bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_4 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evalspeedpopl10fig22bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= Ar_4 ] (Comp: Ar_1 + Ar_4, Cost: 1) evalspeedpopl10fig22bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ -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_0 + 1 ] (Comp: ?, Cost: 1) evalspeedpopl10fig22bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) [ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= Ar_2 ] (Comp: 2, Cost: 1) evalspeedpopl10fig22bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 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_4 + V_5 Pol(evalspeedpopl10fig22start) = -V_4 + V_5 Pol(evalspeedpopl10fig22bb0in) = -V_4 + V_5 Pol(evalspeedpopl10fig22bb1in) = -V_3 + V_5 Pol(evalspeedpopl10fig22bb2in) = -V_3 + V_5 Pol(evalspeedpopl10fig22bb3in) = -V_3 + V_5 Pol(evalspeedpopl10fig22stop) = -V_3 + V_5 orients all transitions weakly and the transition evalspeedpopl10fig22bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) [ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 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) -> Com_1(evalspeedpopl10fig22start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] (Comp: 1, Cost: 1) evalspeedpopl10fig22start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedpopl10fig22bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10fig22bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_4 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evalspeedpopl10fig22bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= Ar_4 ] (Comp: Ar_1 + Ar_4, Cost: 1) evalspeedpopl10fig22bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ -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_0 + 1 ] (Comp: Ar_3 + Ar_4, Cost: 1) evalspeedpopl10fig22bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) [ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= Ar_2 ] (Comp: 2, Cost: 1) evalspeedpopl10fig22bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 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) -> Com_1(evalspeedpopl10fig22start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] (Comp: 1, Cost: 1) evalspeedpopl10fig22start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedpopl10fig22bb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4)) (Comp: Ar_3 + 2*Ar_4 + Ar_1 + 1, Cost: 1) evalspeedpopl10fig22bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_4 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evalspeedpopl10fig22bb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= Ar_4 ] (Comp: Ar_1 + Ar_4, Cost: 1) evalspeedpopl10fig22bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ -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_0 + 1 ] (Comp: Ar_3 + Ar_4, Cost: 1) evalspeedpopl10fig22bb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22bb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) [ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= Ar_2 ] (Comp: 2, Cost: 1) evalspeedpopl10fig22bb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10fig22stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 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_3 + 4*Ar_4 + 2*Ar_1 + 7 Time: 0.166 sec (SMT: 0.140 sec) ---------------------------------------- (2) BOUNDS(1, n^1)