3.04/2.92 WORST_CASE(?, O(n^2)) 3.04/2.93 proof of /export/starexec/sandbox2/output/output_files/bench.koat 3.04/2.93 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.04/2.93 3.04/2.93 3.04/2.93 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 3.04/2.93 3.04/2.93 (0) CpxIntTrs 3.04/2.93 (1) Koat Proof [FINISHED, 840 ms] 3.04/2.93 (2) BOUNDS(1, n^2) 3.04/2.93 3.04/2.93 3.04/2.93 ---------------------------------------- 3.04/2.93 3.04/2.93 (0) 3.04/2.93 Obligation: 3.04/2.93 Complexity Int TRS consisting of the following rules: 3.04/2.93 eval_peed_pldi09_fig4_5_start(v_dir, v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_5_bb0_in(v_dir, v_i.0, v_m, v_n)) :|: TRUE 3.04/2.93 eval_peed_pldi09_fig4_5_bb0_in(v_dir, v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_5_bb3_in(v_dir, v_i.0, v_m, v_n)) :|: 0 >= v_m 3.04/2.93 eval_peed_pldi09_fig4_5_bb0_in(v_dir, v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_5_bb3_in(v_dir, v_i.0, v_m, v_n)) :|: v_m >= v_n 3.04/2.93 eval_peed_pldi09_fig4_5_bb0_in(v_dir, v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_5_bb1_in(v_dir, v_m, v_m, v_n)) :|: 0 < v_m && v_m < v_n 3.04/2.93 eval_peed_pldi09_fig4_5_bb1_in(v_dir, v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_5_bb2_in(v_dir, v_i.0, v_m, v_n)) :|: 0 < v_i.0 && v_i.0 < v_n 3.04/2.93 eval_peed_pldi09_fig4_5_bb1_in(v_dir, v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_5_bb3_in(v_dir, v_i.0, v_m, v_n)) :|: 0 >= v_i.0 3.04/2.93 eval_peed_pldi09_fig4_5_bb1_in(v_dir, v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_5_bb3_in(v_dir, v_i.0, v_m, v_n)) :|: v_i.0 >= v_n 3.04/2.93 eval_peed_pldi09_fig4_5_bb2_in(v_dir, v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_5_bb1_in(v_dir, v_i.0 + 1, v_m, v_n)) :|: v_dir >= 1 && v_dir <= 1 3.04/2.93 eval_peed_pldi09_fig4_5_bb2_in(v_dir, v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_5_bb1_in(v_dir, v_i.0 - 1, v_m, v_n)) :|: v_dir < 1 3.04/2.93 eval_peed_pldi09_fig4_5_bb2_in(v_dir, v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_5_bb1_in(v_dir, v_i.0 - 1, v_m, v_n)) :|: v_dir > 1 3.04/2.93 eval_peed_pldi09_fig4_5_bb3_in(v_dir, v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_5_stop(v_dir, v_i.0, v_m, v_n)) :|: TRUE 3.04/2.93 3.04/2.93 The start-symbols are:[eval_peed_pldi09_fig4_5_start_4] 3.04/2.93 3.04/2.93 3.04/2.93 ---------------------------------------- 3.04/2.93 3.04/2.93 (1) Koat Proof (FINISHED) 3.04/2.93 YES(?, 10*ar_0 + 4*ar_1 + 4*ar_0*ar_1 + 4*ar_0^2 + 17) 3.04/2.93 3.04/2.93 3.04/2.93 3.04/2.93 Initial complexity problem: 3.04/2.93 3.04/2.93 1: T: 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3)) 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 = 1 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ 0 >= ar_3 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_3 >= 2 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 3.04/2.93 3.04/2.93 start location: koat_start 3.04/2.93 3.04/2.93 leaf cost: 0 3.04/2.93 3.04/2.93 3.04/2.93 3.04/2.93 Repeatedly propagating knowledge in problem 1 produces the following problem: 3.04/2.93 3.04/2.93 2: T: 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 1) evalpeedpldi09fig45start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3)) 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 1) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 1) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 1) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 = 1 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ 0 >= ar_3 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_3 >= 2 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 3.04/2.93 3.04/2.93 start location: koat_start 3.04/2.93 3.04/2.93 leaf cost: 0 3.04/2.93 3.04/2.93 3.04/2.93 3.04/2.93 A polynomial rank function with 3.04/2.93 3.04/2.93 Pol(evalpeedpldi09fig45start) = 2 3.04/2.93 3.04/2.93 Pol(evalpeedpldi09fig45bb0in) = 2 3.04/2.93 3.04/2.93 Pol(evalpeedpldi09fig45bb3in) = 1 3.04/2.93 3.04/2.93 Pol(evalpeedpldi09fig45bb1in) = 2 3.04/2.93 3.04/2.93 Pol(evalpeedpldi09fig45bb2in) = 2 3.04/2.93 3.04/2.93 Pol(evalpeedpldi09fig45stop) = 0 3.04/2.93 3.04/2.93 Pol(koat_start) = 2 3.04/2.93 3.04/2.93 orients all transitions weakly and the transitions 3.04/2.93 3.04/2.93 evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) 3.04/2.93 3.04/2.93 evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 ] 3.04/2.93 3.04/2.93 evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ] 3.04/2.93 3.04/2.93 strictly and produces the following problem: 3.04/2.93 3.04/2.93 3: T: 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 1) evalpeedpldi09fig45start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3)) 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 1) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 1) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 1) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 3.04/2.93 3.04/2.93 (Comp: 2, Cost: 1) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ] 3.04/2.93 3.04/2.93 (Comp: 2, Cost: 1) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 = 1 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ 0 >= ar_3 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_3 >= 2 ] 3.04/2.93 3.04/2.93 (Comp: 2, Cost: 1) evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 3.04/2.93 3.04/2.93 start location: koat_start 3.04/2.93 3.04/2.93 leaf cost: 0 3.04/2.93 3.04/2.93 3.04/2.93 3.04/2.93 Applied AI with 'oct' on problem 3 to obtain the following invariants: 3.04/2.93 3.04/2.93 For symbol evalpeedpldi09fig45bb1in: X_2 - 2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 - 1 >= 0 3.04/2.93 3.04/2.93 For symbol evalpeedpldi09fig45bb2in: X_2 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ X_1 + X_3 - 2 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 - 1 >= 0 3.04/2.93 3.04/2.93 3.04/2.93 3.04/2.93 3.04/2.93 3.04/2.93 This yielded the following problem: 3.04/2.93 3.04/2.93 4: T: 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 3.04/2.93 3.04/2.93 (Comp: 2, Cost: 1) evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 ] 3.04/2.93 3.04/2.93 (Comp: 2, Cost: 1) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] 3.04/2.93 3.04/2.93 (Comp: 2, Cost: 1) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 1) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 1) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 1) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 1) evalpeedpldi09fig45start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3)) 3.04/2.93 3.04/2.93 start location: koat_start 3.04/2.93 3.04/2.93 leaf cost: 0 3.04/2.93 3.04/2.93 3.04/2.93 3.04/2.93 By chaining the transition koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] with all transitions in problem 4, the following new transition is obtained: 3.04/2.93 3.04/2.93 koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 3.04/2.93 3.04/2.93 We thus obtain the following problem: 3.04/2.93 3.04/2.93 5: T: 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 3.04/2.93 3.04/2.93 (Comp: 2, Cost: 1) evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 ] 3.04/2.93 3.04/2.93 (Comp: 2, Cost: 1) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] 3.04/2.93 3.04/2.93 (Comp: 2, Cost: 1) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 1) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 1) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 1) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 1) evalpeedpldi09fig45start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3)) 3.04/2.93 3.04/2.93 start location: koat_start 3.04/2.93 3.04/2.93 leaf cost: 0 3.04/2.93 3.04/2.93 3.04/2.93 3.04/2.93 Testing for reachability in the complexity graph removes the following transition from problem 5: 3.04/2.93 3.04/2.93 evalpeedpldi09fig45start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3)) 3.04/2.93 3.04/2.93 We thus obtain the following problem: 3.04/2.93 3.04/2.93 6: T: 3.04/2.93 3.04/2.93 (Comp: 2, Cost: 1) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] 3.04/2.93 3.04/2.93 (Comp: 2, Cost: 1) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 3.04/2.93 3.04/2.93 (Comp: 2, Cost: 1) evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 1) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 1) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 1) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 3.04/2.93 3.04/2.93 start location: koat_start 3.04/2.93 3.04/2.93 leaf cost: 0 3.04/2.93 3.04/2.93 3.04/2.93 3.04/2.93 By chaining the transition evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] with all transitions in problem 6, the following new transition is obtained: 3.04/2.93 3.04/2.93 evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] 3.04/2.93 3.04/2.93 We thus obtain the following problem: 3.04/2.93 3.04/2.93 7: T: 3.04/2.93 3.04/2.93 (Comp: 2, Cost: 2) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] 3.04/2.93 3.04/2.93 (Comp: 2, Cost: 1) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 3.04/2.93 3.04/2.93 (Comp: 2, Cost: 1) evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 1) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 1) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 1) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 3.04/2.93 3.04/2.93 start location: koat_start 3.04/2.93 3.04/2.93 leaf cost: 0 3.04/2.93 3.04/2.93 3.04/2.93 3.04/2.93 By chaining the transition evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] with all transitions in problem 7, the following new transition is obtained: 3.04/2.93 3.04/2.93 evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 3.04/2.93 3.04/2.93 We thus obtain the following problem: 3.04/2.93 3.04/2.93 8: T: 3.04/2.93 3.04/2.93 (Comp: 2, Cost: 2) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 3.04/2.93 3.04/2.93 (Comp: 2, Cost: 2) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 3.04/2.93 3.04/2.93 (Comp: 2, Cost: 1) evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 1) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 1) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 1) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 3.04/2.93 3.04/2.93 start location: koat_start 3.04/2.93 3.04/2.93 leaf cost: 0 3.04/2.93 3.04/2.93 3.04/2.93 3.04/2.93 By chaining the transition evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] with all transitions in problem 8, the following new transition is obtained: 3.04/2.93 3.04/2.93 evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 3.04/2.93 3.04/2.93 We thus obtain the following problem: 3.04/2.93 3.04/2.93 9: T: 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 2) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 3.04/2.93 3.04/2.93 (Comp: 2, Cost: 2) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 3.04/2.93 3.04/2.93 (Comp: 2, Cost: 2) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 3.04/2.93 3.04/2.93 (Comp: 2, Cost: 1) evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 1) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 1) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 3.04/2.93 3.04/2.93 start location: koat_start 3.04/2.93 3.04/2.93 leaf cost: 0 3.04/2.93 3.04/2.93 3.04/2.93 3.04/2.93 By chaining the transition evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ] with all transitions in problem 9, the following new transition is obtained: 3.04/2.93 3.04/2.93 evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ] 3.04/2.93 3.04/2.93 We thus obtain the following problem: 3.04/2.93 3.04/2.93 10: T: 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 2) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 2) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 3.04/2.93 3.04/2.93 (Comp: 2, Cost: 2) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 3.04/2.93 3.04/2.93 (Comp: 2, Cost: 2) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 3.04/2.93 3.04/2.93 (Comp: 2, Cost: 1) evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 1) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 3.04/2.93 3.04/2.93 start location: koat_start 3.04/2.93 3.04/2.93 leaf cost: 0 3.04/2.93 3.04/2.93 3.04/2.93 3.04/2.93 Testing for reachability in the complexity graph removes the following transition from problem 10: 3.04/2.93 3.04/2.93 evalpeedpldi09fig45bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) 3.04/2.93 3.04/2.93 We thus obtain the following problem: 3.04/2.93 3.04/2.93 11: T: 3.04/2.93 3.04/2.93 (Comp: 2, Cost: 2) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] 3.04/2.93 3.04/2.93 (Comp: 2, Cost: 2) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 2) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 2) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 1) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 3.04/2.93 3.04/2.93 start location: koat_start 3.04/2.93 3.04/2.93 leaf cost: 0 3.04/2.93 3.04/2.93 3.04/2.93 3.04/2.93 By chaining the transition evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ] with all transitions in problem 11, the following new transition is obtained: 3.04/2.93 3.04/2.93 evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ] 3.04/2.93 3.04/2.93 We thus obtain the following problem: 3.04/2.93 3.04/2.93 12: T: 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 2) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ] 3.04/2.93 3.04/2.93 (Comp: 2, Cost: 2) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] 3.04/2.93 3.04/2.93 (Comp: 2, Cost: 2) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 2) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 2) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 3.04/2.93 3.04/2.93 start location: koat_start 3.04/2.93 3.04/2.93 leaf cost: 0 3.04/2.93 3.04/2.93 3.04/2.93 3.04/2.93 By chaining the transition evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 ] with all transitions in problem 12, the following new transitions are obtained: 3.04/2.93 3.04/2.93 evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 /\ ar_2 + 1 >= ar_1 ] 3.04/2.93 3.04/2.93 evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 /\ ar_2 + 1 >= 1 /\ ar_1 >= ar_2 + 2 ] 3.04/2.93 3.04/2.93 We thus obtain the following problem: 3.04/2.93 3.04/2.93 13: T: 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 3) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 /\ ar_2 + 1 >= ar_1 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 2) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 /\ ar_2 + 1 >= 1 /\ ar_1 >= ar_2 + 2 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 2) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ] 3.04/2.93 3.04/2.93 (Comp: 2, Cost: 2) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] 3.04/2.93 3.04/2.93 (Comp: 2, Cost: 2) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 2) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 2) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 3.04/2.93 3.04/2.93 start location: koat_start 3.04/2.93 3.04/2.93 leaf cost: 0 3.04/2.93 3.04/2.93 3.04/2.93 3.04/2.93 Testing for reachability in the complexity graph removes the following transition from problem 13: 3.04/2.93 3.04/2.93 evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 ] 3.04/2.93 3.04/2.93 We thus obtain the following problem: 3.04/2.93 3.04/2.93 14: T: 3.04/2.93 3.04/2.93 (Comp: 2, Cost: 2) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 2) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 /\ ar_2 + 1 >= 1 /\ ar_1 >= ar_2 + 2 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 3) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 /\ ar_2 + 1 >= ar_1 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 2) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 2) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 2) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 3.04/2.93 3.04/2.93 start location: koat_start 3.04/2.93 3.04/2.93 leaf cost: 0 3.04/2.93 3.04/2.93 3.04/2.93 3.04/2.93 A polynomial rank function with 3.04/2.93 3.04/2.93 Pol(evalpeedpldi09fig45bb1in) = 1 3.04/2.93 3.04/2.93 Pol(evalpeedpldi09fig45stop) = 0 3.04/2.93 3.04/2.93 Pol(evalpeedpldi09fig45bb2in) = 1 3.04/2.93 3.04/2.93 Pol(evalpeedpldi09fig45bb0in) = 1 3.04/2.93 3.04/2.93 Pol(koat_start) = 1 3.04/2.93 3.04/2.93 orients all transitions weakly and the transition 3.04/2.93 3.04/2.93 evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 /\ ar_2 + 1 >= ar_1 ] 3.04/2.93 3.04/2.93 strictly and produces the following problem: 3.04/2.93 3.04/2.93 15: T: 3.04/2.93 3.04/2.93 (Comp: 2, Cost: 2) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 2) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 /\ ar_2 + 1 >= 1 /\ ar_1 >= ar_2 + 2 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 3) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 /\ ar_2 + 1 >= ar_1 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 2) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 2) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 2) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 3.04/2.93 3.04/2.93 start location: koat_start 3.04/2.93 3.04/2.93 leaf cost: 0 3.04/2.93 3.04/2.93 3.04/2.93 3.04/2.93 A polynomial rank function with 3.04/2.93 3.04/2.93 Pol(evalpeedpldi09fig45bb2in) = 2*V_3 - 1 3.04/2.93 3.04/2.93 Pol(evalpeedpldi09fig45bb1in) = 2*V_3 3.04/2.93 3.04/2.93 and size complexities 3.04/2.93 3.04/2.93 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0 3.04/2.93 3.04/2.93 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1 3.04/2.93 3.04/2.93 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2 3.04/2.93 3.04/2.93 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-0) = ar_0 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-1) = ar_1 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-2) = ar_2 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-3) = ar_3 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-0) = ar_0 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-1) = ar_1 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-2) = ar_2 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-3) = ar_3 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-0) = ar_0 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-1) = ar_1 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-2) = ar_0 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-3) = ar_3 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= 2 ]", 0-0) = ar_0 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= 2 ]", 0-1) = ar_1 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= 2 ]", 0-2) = ar_0 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= 2 ]", 0-3) = ar_3 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_3 ]", 0-0) = ar_0 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_3 ]", 0-1) = ar_1 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_3 ]", 0-2) = ar_0 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_3 ]", 0-3) = ar_3 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 = 1 /\\ ar_2 + 1 >= ar_1 ]", 0-0) = ar_0 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 = 1 /\\ ar_2 + 1 >= ar_1 ]", 0-1) = ar_1 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 = 1 /\\ ar_2 + 1 >= ar_1 ]", 0-2) = ar_1 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 = 1 /\\ ar_2 + 1 >= ar_1 ]", 0-3) = 1 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 = 1 /\\ ar_2 + 1 >= 1 /\\ ar_1 >= ar_2 + 2 ]", 0-0) = ar_0 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 = 1 /\\ ar_2 + 1 >= 1 /\\ ar_1 >= ar_2 + 2 ]", 0-1) = ar_1 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 = 1 /\\ ar_2 + 1 >= 1 /\\ ar_1 >= ar_2 + 2 ]", 0-2) = ar_1 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 = 1 /\\ ar_2 + 1 >= 1 /\\ ar_1 >= ar_2 + 2 ]", 0-3) = 1 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 /\\ ar_1 >= ar_2 + 1 ]", 0-0) = ar_0 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 /\\ ar_1 >= ar_2 + 1 ]", 0-1) = ar_1 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 /\\ ar_1 >= ar_2 + 1 ]", 0-2) = ar_0 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 /\\ ar_1 >= ar_2 + 1 ]", 0-3) = ar_3 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 ]", 0-0) = ar_0 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 ]", 0-1) = ar_1 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 ]", 0-2) = ar_0 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 ]", 0-3) = ar_3 3.04/2.93 3.04/2.93 orients the transitions 3.04/2.93 3.04/2.93 evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 3.04/2.93 3.04/2.93 evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 3.04/2.93 3.04/2.93 evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 3.04/2.93 3.04/2.93 weakly and the transitions 3.04/2.93 3.04/2.93 evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 3.04/2.93 3.04/2.93 evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 3.04/2.93 3.04/2.93 evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 3.04/2.93 3.04/2.93 strictly and produces the following problem: 3.04/2.93 3.04/2.93 16: T: 3.04/2.93 3.04/2.93 (Comp: 2, Cost: 2) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 3.04/2.93 3.04/2.93 (Comp: 2*ar_0 + 1, Cost: 1) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 3.04/2.93 3.04/2.93 (Comp: ?, Cost: 2) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 /\ ar_2 + 1 >= 1 /\ ar_1 >= ar_2 + 2 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 3) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 /\ ar_2 + 1 >= ar_1 ] 3.04/2.93 3.04/2.93 (Comp: 2*ar_0 + 1, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 3.04/2.93 3.04/2.93 (Comp: 2*ar_0 + 1, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 2) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 2) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 2) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 3.04/2.93 3.04/2.93 start location: koat_start 3.04/2.93 3.04/2.93 leaf cost: 0 3.04/2.93 3.04/2.93 3.04/2.93 3.04/2.93 A polynomial rank function with 3.04/2.93 3.04/2.93 Pol(evalpeedpldi09fig45bb2in) = V_2 - V_3 3.04/2.93 3.04/2.93 and size complexities 3.04/2.93 3.04/2.93 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0 3.04/2.93 3.04/2.93 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1 3.04/2.93 3.04/2.93 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2 3.04/2.93 3.04/2.93 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-0) = ar_0 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-1) = ar_1 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-2) = ar_2 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-3) = ar_3 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-0) = ar_0 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-1) = ar_1 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-2) = ar_2 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-3) = ar_3 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-0) = ar_0 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-1) = ar_1 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-2) = ar_0 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-3) = ar_3 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= 2 ]", 0-0) = ar_0 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= 2 ]", 0-1) = ar_1 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= 2 ]", 0-2) = ar_0 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= 2 ]", 0-3) = ar_3 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_3 ]", 0-0) = ar_0 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_3 ]", 0-1) = ar_1 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_3 ]", 0-2) = ar_0 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_3 ]", 0-3) = ar_3 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 = 1 /\\ ar_2 + 1 >= ar_1 ]", 0-0) = ar_0 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 = 1 /\\ ar_2 + 1 >= ar_1 ]", 0-1) = ar_1 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 = 1 /\\ ar_2 + 1 >= ar_1 ]", 0-2) = ar_1 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 = 1 /\\ ar_2 + 1 >= ar_1 ]", 0-3) = 1 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 = 1 /\\ ar_2 + 1 >= 1 /\\ ar_1 >= ar_2 + 2 ]", 0-0) = ar_0 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 = 1 /\\ ar_2 + 1 >= 1 /\\ ar_1 >= ar_2 + 2 ]", 0-1) = ar_1 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 = 1 /\\ ar_2 + 1 >= 1 /\\ ar_1 >= ar_2 + 2 ]", 0-2) = ar_1 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 = 1 /\\ ar_2 + 1 >= 1 /\\ ar_1 >= ar_2 + 2 ]", 0-3) = 1 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 /\\ ar_1 >= ar_2 + 1 ]", 0-0) = ar_0 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 /\\ ar_1 >= ar_2 + 1 ]", 0-1) = ar_1 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 /\\ ar_1 >= ar_2 + 1 ]", 0-2) = ar_0 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 /\\ ar_1 >= ar_2 + 1 ]", 0-3) = ar_3 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 ]", 0-0) = ar_0 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 ]", 0-1) = ar_1 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 ]", 0-2) = ar_0 3.04/2.93 3.04/2.93 S("evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 ]", 0-3) = ar_3 3.04/2.93 3.04/2.93 orients the transitions 3.04/2.93 3.04/2.93 evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 /\ ar_2 + 1 >= 1 /\ ar_1 >= ar_2 + 2 ] 3.04/2.93 3.04/2.93 weakly and the transition 3.04/2.93 3.04/2.93 evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 /\ ar_2 + 1 >= 1 /\ ar_1 >= ar_2 + 2 ] 3.04/2.93 3.04/2.93 strictly and produces the following problem: 3.04/2.93 3.04/2.93 17: T: 3.04/2.93 3.04/2.93 (Comp: 2, Cost: 2) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ] 3.04/2.93 3.04/2.93 (Comp: 2*ar_0 + 1, Cost: 1) evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] 3.04/2.93 3.04/2.93 (Comp: 2*ar_1 + 2*ar_0 + 2*ar_0*ar_1 + 2*ar_0^2, Cost: 2) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 /\ ar_2 + 1 >= 1 /\ ar_1 >= ar_2 + 2 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 3) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 = 1 /\ ar_2 + 1 >= ar_1 ] 3.04/2.93 3.04/2.93 (Comp: 2*ar_0 + 1, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ] 3.04/2.93 3.04/2.93 (Comp: 2*ar_0 + 1, Cost: 1) evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 2 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 2) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb2in(ar_0, ar_1, ar_0, ar_3)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 2) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 2) evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45stop(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 3.04/2.93 3.04/2.93 (Comp: 1, Cost: 1) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalpeedpldi09fig45bb0in(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 3.04/2.93 3.04/2.93 start location: koat_start 3.04/2.93 3.04/2.93 leaf cost: 0 3.04/2.93 3.04/2.93 3.04/2.93 3.04/2.93 Complexity upper bound 10*ar_0 + 4*ar_1 + 4*ar_0*ar_1 + 4*ar_0^2 + 17 3.04/2.93 3.04/2.93 3.04/2.93 3.04/2.93 Time: 0.854 sec (SMT: 0.681 sec) 3.04/2.93 3.04/2.93 3.04/2.93 ---------------------------------------- 3.04/2.93 3.04/2.93 (2) 3.04/2.93 BOUNDS(1, n^2) 3.08/2.97 EOF