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Complexity_C_Integer 2019-03-21 04.38 pair #429988858
details
property
value
status
complete
benchmark
speed_pldi09_fig4_5.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n007.star.cs.uiowa.edu
space
C4B_examples
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
2.97053 seconds
cpu usage
3.13035
user time
2.87351
system time
0.256843
max virtual memory
1.8480744E7
max residence set size
183460.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^2))
output
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3.04/2.93 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.04/2.93 3.04/2.93 3.04/2.93 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 3.04/2.93 3.04/2.93 (0) CpxIntTrs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 ]
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