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Complexity_C_Integer 2019-03-21 04.38 pair #429989632
details
property
value
status
complete
benchmark
rank1.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n082.star.cs.uiowa.edu
space
WTC_V2
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
10.5547 seconds
cpu usage
11.8544
user time
11.186
system time
0.668478
max virtual memory
1.8648296E7
max residence set size
213456.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^2))
output
11.63/10.49 WORST_CASE(?, O(n^2)) 11.77/10.50 proof of /export/starexec/sandbox2/output/output_files/bench.koat 11.77/10.50 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 11.77/10.50 11.77/10.50 11.77/10.50 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 11.77/10.50 11.77/10.50 (0) CpxIntTrs 11.77/10.50 (1) Koat Proof [FINISHED, 9220 ms] 11.77/10.50 (2) BOUNDS(1, n^2) 11.77/10.50 11.77/10.50 11.77/10.50 ---------------------------------------- 11.77/10.50 11.77/10.50 (0) 11.77/10.50 Obligation: 11.77/10.50 Complexity Int TRS consisting of the following rules: 11.77/10.50 eval_rank1_start(v_3, v_6, v_m, v_x.0, v_x.1, v_y.0, v_y.1, v_y.2) -> Com_1(eval_rank1_bb0_in(v_3, v_6, v_m, v_x.0, v_x.1, v_y.0, v_y.1, v_y.2)) :|: TRUE 11.77/10.50 eval_rank1_bb0_in(v_3, v_6, v_m, v_x.0, v_x.1, v_y.0, v_y.1, v_y.2) -> Com_1(eval_rank1_bb1_in(v_3, v_6, v_m, v_m, v_x.1, 0, v_y.1, v_y.2)) :|: TRUE 11.77/10.50 eval_rank1_bb1_in(v_3, v_6, v_m, v_x.0, v_x.1, v_y.0, v_y.1, v_y.2) -> Com_1(eval_rank1_bb2_in(v_3, v_6, v_m, v_x.0, v_x.1, v_y.0, v_y.1, v_y.2)) :|: v_x.0 >= 0 && v_y.0 >= 0 11.77/10.50 eval_rank1_bb1_in(v_3, v_6, v_m, v_x.0, v_x.1, v_y.0, v_y.1, v_y.2) -> Com_1(eval_rank1_bb7_in(v_3, v_6, v_m, v_x.0, v_x.1, v_y.0, v_y.1, v_y.2)) :|: v_x.0 < 0 11.77/10.50 eval_rank1_bb1_in(v_3, v_6, v_m, v_x.0, v_x.1, v_y.0, v_y.1, v_y.2) -> Com_1(eval_rank1_bb7_in(v_3, v_6, v_m, v_x.0, v_x.1, v_y.0, v_y.1, v_y.2)) :|: v_y.0 < 0 11.77/10.50 eval_rank1_bb2_in(v_3, v_6, v_m, v_x.0, v_x.1, v_y.0, v_y.1, v_y.2) -> Com_1(eval_rank1_0(v_3, v_6, v_m, v_x.0, v_x.1, v_y.0, v_y.1, v_y.2)) :|: TRUE 11.77/10.50 eval_rank1_0(v_3, v_6, v_m, v_x.0, v_x.1, v_y.0, v_y.1, v_y.2) -> Com_2(eval_nondet_start(v_3, v_6, v_m, v_x.0, v_x.1, v_y.0, v_y.1, v_y.2), eval_rank1_1(nondef.0, v_6, v_m, v_x.0, v_x.1, v_y.0, v_y.1, v_y.2)) :|: TRUE 11.77/10.50 eval_rank1_1(v_3, v_6, v_m, v_x.0, v_x.1, v_y.0, v_y.1, v_y.2) -> Com_1(eval_rank1_bb3_in(v_3, v_6, v_m, v_x.0, v_x.1, v_y.0, v_y.0, v_y.2)) :|: v_3 > 0 11.77/10.50 eval_rank1_1(v_3, v_6, v_m, v_x.0, v_x.1, v_y.0, v_y.1, v_y.2) -> Com_1(eval_rank1_bb6_in(v_3, v_6, v_m, v_x.0, v_x.0, v_y.0, v_y.1, v_y.0)) :|: v_3 <= 0 11.77/10.50 eval_rank1_bb3_in(v_3, v_6, v_m, v_x.0, v_x.1, v_y.0, v_y.1, v_y.2) -> Com_1(eval_rank1_bb4_in(v_3, v_6, v_m, v_x.0, v_x.1, v_y.0, v_y.1, v_y.2)) :|: v_y.1 <= v_m 11.77/10.50 eval_rank1_bb3_in(v_3, v_6, v_m, v_x.0, v_x.1, v_y.0, v_y.1, v_y.2) -> Com_1(eval_rank1_.critedge_in(v_3, v_6, v_m, v_x.0, v_x.1, v_y.0, v_y.1, v_y.2)) :|: v_y.1 > v_m 11.77/10.50 eval_rank1_bb4_in(v_3, v_6, v_m, v_x.0, v_x.1, v_y.0, v_y.1, v_y.2) -> Com_1(eval_rank1_2(v_3, v_6, v_m, v_x.0, v_x.1, v_y.0, v_y.1, v_y.2)) :|: TRUE 11.77/10.50 eval_rank1_2(v_3, v_6, v_m, v_x.0, v_x.1, v_y.0, v_y.1, v_y.2) -> Com_2(eval_nondet_start(v_3, v_6, v_m, v_x.0, v_x.1, v_y.0, v_y.1, v_y.2), eval_rank1_3(v_3, nondef.1, v_m, v_x.0, v_x.1, v_y.0, v_y.1, v_y.2)) :|: TRUE 11.77/10.50 eval_rank1_3(v_3, v_6, v_m, v_x.0, v_x.1, v_y.0, v_y.1, v_y.2) -> Com_1(eval_rank1_bb5_in(v_3, v_6, v_m, v_x.0, v_x.1, v_y.0, v_y.1, v_y.2)) :|: v_6 > 0 11.77/10.50 eval_rank1_3(v_3, v_6, v_m, v_x.0, v_x.1, v_y.0, v_y.1, v_y.2) -> Com_1(eval_rank1_.critedge_in(v_3, v_6, v_m, v_x.0, v_x.1, v_y.0, v_y.1, v_y.2)) :|: v_6 <= 0 11.77/10.50 eval_rank1_bb5_in(v_3, v_6, v_m, v_x.0, v_x.1, v_y.0, v_y.1, v_y.2) -> Com_1(eval_rank1_bb3_in(v_3, v_6, v_m, v_x.0, v_x.1, v_y.0, v_y.1 + 1, v_y.2)) :|: TRUE 11.77/10.50 eval_rank1_.critedge_in(v_3, v_6, v_m, v_x.0, v_x.1, v_y.0, v_y.1, v_y.2) -> Com_1(eval_rank1_bb6_in(v_3, v_6, v_m, v_x.0, v_x.0 - 1, v_y.0, v_y.1, v_y.1)) :|: TRUE 11.77/10.50 eval_rank1_bb6_in(v_3, v_6, v_m, v_x.0, v_x.1, v_y.0, v_y.1, v_y.2) -> Com_1(eval_rank1_bb1_in(v_3, v_6, v_m, v_x.1, v_x.1, v_y.2 - 1, v_y.1, v_y.2)) :|: TRUE 11.77/10.50 eval_rank1_bb7_in(v_3, v_6, v_m, v_x.0, v_x.1, v_y.0, v_y.1, v_y.2) -> Com_1(eval_rank1_stop(v_3, v_6, v_m, v_x.0, v_x.1, v_y.0, v_y.1, v_y.2)) :|: TRUE 11.77/10.50 11.77/10.50 The start-symbols are:[eval_rank1_start_8] 11.77/10.50 11.77/10.50 11.77/10.50 ---------------------------------------- 11.77/10.50 11.77/10.50 (1) Koat Proof (FINISHED) 11.77/10.50 YES(?, 2649*ar_1 + 756*ar_1^2 + 1959) 11.77/10.50 11.77/10.50 11.77/10.50 11.77/10.50 Initial complexity problem: 11.77/10.50 11.77/10.50 1: T: 11.77/10.50 11.77/10.50 (Comp: ?, Cost: 1) evalrank1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrank1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 11.77/10.50 11.77/10.50 (Comp: ?, Cost: 1) evalrank1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrank1bb1in(ar_1, ar_1, 0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 11.77/10.50 11.77/10.50 (Comp: ?, Cost: 1) evalrank1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrank1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_0 >= 0 /\ ar_2 >= 0 ] 11.77/10.50 11.77/10.50 (Comp: ?, Cost: 1) evalrank1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrank1bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ 0 >= ar_0 + 1 ] 11.77/10.50 11.77/10.50 (Comp: ?, Cost: 1) evalrank1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrank1bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ 0 >= ar_2 + 1 ] 11.77/10.50 11.77/10.50 (Comp: ?, Cost: 1) evalrank1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrank10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 11.77/10.50 11.77/10.50 (Comp: ?, Cost: 1) evalrank100(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 11.77/10.50 11.77/10.50 (Comp: ?, Cost: 1) evalrank101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrank11(ar_0, ar_1, ar_2, ar_4, ar_4, ar_5, ar_6, ar_7, ar_8)) 11.77/10.50 11.77/10.50 (Comp: ?, Cost: 1) evalrank10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_2(evalrank100(ar_0, ar_1, ar_2, ar_3, j, ar_5, ar_6, ar_7, ar_8), evalrank101(ar_0, ar_1, ar_2, ar_3, j, ar_5, ar_6, ar_7, ar_8)) 11.77/10.50 11.77/10.50 (Comp: ?, Cost: 1) evalrank11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrank1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_2, ar_6, ar_7, ar_8)) [ ar_3 >= 1 ] 11.77/10.50 11.77/10.50 (Comp: ?, Cost: 1) evalrank11(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrank1bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_0, ar_2, ar_8)) [ 0 >= ar_3 ] 11.77/10.50 11.77/10.50 (Comp: ?, Cost: 1) evalrank1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrank1bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_1 >= ar_5 ] 11.77/10.50 11.77/10.50 (Comp: ?, Cost: 1) evalrank1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrank1critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_5 >= ar_1 + 1 ] 11.77/10.50 11.77/10.50 (Comp: ?, Cost: 1) evalrank1bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrank12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 11.77/10.50 11.77/10.50 (Comp: ?, Cost: 1) evalrank120(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 11.77/10.50 11.77/10.50 (Comp: ?, Cost: 1) evalrank121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrank13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_4)) 11.77/10.50 11.77/10.50 (Comp: ?, Cost: 1) evalrank12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_2(evalrank120(ar_0, ar_1, ar_2, ar_3, j, ar_5, ar_6, ar_7, ar_8), evalrank121(ar_0, ar_1, ar_2, ar_3, j, ar_5, ar_6, ar_7, ar_8)) 11.77/10.50 11.77/10.50 (Comp: ?, Cost: 1) evalrank13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrank1bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_8 >= 1 ] 11.77/10.50 11.77/10.50 (Comp: ?, Cost: 1) evalrank13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrank1critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ 0 >= ar_8 ] 11.77/10.50 11.77/10.50 (Comp: ?, Cost: 1) evalrank1bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrank1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1, ar_6, ar_7, ar_8)) 11.77/10.50 11.77/10.50 (Comp: ?, Cost: 1) evalrank1critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrank1bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_0 - 1, ar_5, ar_8)) 11.77/10.50 11.77/10.50 (Comp: ?, Cost: 1) evalrank1bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrank1bb1in(ar_6, ar_1, ar_7 - 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 11.77/10.50 11.77/10.50 (Comp: ?, Cost: 1) evalrank1bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrank1stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 11.77/10.50 11.77/10.50 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalrank1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ 0 <= 0 ] 11.77/10.50 11.77/10.50 start location: koat_start
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return to Complexity_C_Integer 2019-03-21 04.38