details

property	value
status	complete
benchmark	CPU2006_SingleLinkCluster.c
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n050.star.cs.uiowa.edu
space	Sinn_2016

run statistics

property	value
solver	AProVE
configuration	c_complexity
runtime (wallclock)	5.958 seconds
cpu usage	7.36238
user time	6.89736
system time	0.465023
max virtual memory	1.8606252E7
max residence set size	259468.0

stage attributes

key	value
starexec-result	WORST_CASE(?, O(n^2))

output

7.22/5.88 WORST_CASE(?, O(n^2)) 7.22/5.89 proof of /export/starexec/sandbox/output/output_files/bench.koat 7.22/5.89 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 7.22/5.89 7.22/5.89 7.22/5.89 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 7.22/5.89 7.22/5.89 (0) CpxIntTrs 7.22/5.89 (1) Koat Proof [FINISHED, 4593 ms] 7.22/5.89 (2) BOUNDS(1, n^2) 7.22/5.89 7.22/5.89 7.22/5.89 ---------------------------------------- 7.22/5.89 7.22/5.89 (0) 7.22/5.89 Obligation: 7.22/5.89 Complexity Int TRS consisting of the following rules: 7.22/5.89 eval_SingleLinkCluster_start(v_8, v_a.0, v_a.1, v_a.2, v_a.3, v_b.0, v_b.1, v_b.2, v_b.3, v_i.0, v_n) -> Com_1(eval_SingleLinkCluster_bb0_in(v_8, v_a.0, v_a.1, v_a.2, v_a.3, v_b.0, v_b.1, v_b.2, v_b.3, v_i.0, v_n)) :|: TRUE 7.22/5.89 eval_SingleLinkCluster_bb0_in(v_8, v_a.0, v_a.1, v_a.2, v_a.3, v_b.0, v_b.1, v_b.2, v_b.3, v_i.0, v_n) -> Com_1(eval_SingleLinkCluster_bb1_in(v_8, v_n, v_a.1, v_a.2, v_a.3, 0, v_b.1, v_b.2, v_b.3, v_i.0, v_n)) :|: TRUE 7.22/5.89 eval_SingleLinkCluster_bb1_in(v_8, v_a.0, v_a.1, v_a.2, v_a.3, v_b.0, v_b.1, v_b.2, v_b.3, v_i.0, v_n) -> Com_1(eval_SingleLinkCluster_bb2_in(v_8, v_a.0, v_a.1, v_a.2, v_a.3, v_b.0, v_b.1, v_b.2, v_b.3, v_i.0, v_n)) :|: v_a.0 > 0 7.22/5.89 eval_SingleLinkCluster_bb1_in(v_8, v_a.0, v_a.1, v_a.2, v_a.3, v_b.0, v_b.1, v_b.2, v_b.3, v_i.0, v_n) -> Com_1(eval_SingleLinkCluster_bb10_in(v_8, v_a.0, v_a.1, v_a.2, v_a.3, v_b.0, v_b.1, v_b.2, v_b.3, v_i.0, v_n)) :|: v_a.0 <= 0 7.22/5.89 eval_SingleLinkCluster_bb2_in(v_8, v_a.0, v_a.1, v_a.2, v_a.3, v_b.0, v_b.1, v_b.2, v_b.3, v_i.0, v_n) -> Com_1(eval_SingleLinkCluster_bb3_in(v_8, v_a.0, v_a.0 - 1, v_a.2, v_a.3, v_b.0, v_b.0 + 1, v_b.2, v_b.3, v_i.0, v_n)) :|: TRUE 7.22/5.89 eval_SingleLinkCluster_bb3_in(v_8, v_a.0, v_a.1, v_a.2, v_a.3, v_b.0, v_b.1, v_b.2, v_b.3, v_i.0, v_n) -> Com_1(eval_SingleLinkCluster_bb4_in(v_8, v_a.0, v_a.1, v_a.2, v_a.3, v_b.0, v_b.1, v_b.2, v_b.3, v_i.0, v_n)) :|: v_b.1 > 0 7.22/5.89 eval_SingleLinkCluster_bb3_in(v_8, v_a.0, v_a.1, v_a.2, v_a.3, v_b.0, v_b.1, v_b.2, v_b.3, v_i.0, v_n) -> Com_1(eval_SingleLinkCluster_bb1_in(v_8, v_a.1, v_a.1, v_a.2, v_a.3, v_b.1, v_b.1, v_b.2, v_b.3, v_i.0, v_n)) :|: v_b.1 <= 0 7.22/5.89 eval_SingleLinkCluster_bb4_in(v_8, v_a.0, v_a.1, v_a.2, v_a.3, v_b.0, v_b.1, v_b.2, v_b.3, v_i.0, v_n) -> Com_1(eval_SingleLinkCluster_bb5_in(v_8, v_a.0, v_a.1, v_a.1, v_a.3, v_b.0, v_b.1, v_b.1 - 1, v_b.3, v_n - 1, v_n)) :|: TRUE 7.22/5.89 eval_SingleLinkCluster_bb5_in(v_8, v_a.0, v_a.1, v_a.2, v_a.3, v_b.0, v_b.1, v_b.2, v_b.3, v_i.0, v_n) -> Com_1(eval_SingleLinkCluster_bb6_in(v_8, v_a.0, v_a.1, v_a.2, v_a.3, v_b.0, v_b.1, v_b.2, v_b.3, v_i.0, v_n)) :|: v_i.0 > 0 7.22/5.89 eval_SingleLinkCluster_bb5_in(v_8, v_a.0, v_a.1, v_a.2, v_a.3, v_b.0, v_b.1, v_b.2, v_b.3, v_i.0, v_n) -> Com_1(eval_SingleLinkCluster_bb3_in(v_8, v_a.0, v_a.2, v_a.2, v_a.3, v_b.0, v_b.2, v_b.2, v_b.3, v_i.0, v_n)) :|: v_i.0 <= 0 7.22/5.89 eval_SingleLinkCluster_bb6_in(v_8, v_a.0, v_a.1, v_a.2, v_a.3, v_b.0, v_b.1, v_b.2, v_b.3, v_i.0, v_n) -> Com_1(eval_SingleLinkCluster_bb7_in(v_8, v_a.0, v_a.1, v_a.2, v_a.3, v_b.0, v_b.1, v_b.2, v_b.3, v_i.0, v_n)) :|: v_a.2 > 0 7.22/5.89 eval_SingleLinkCluster_bb6_in(v_8, v_a.0, v_a.1, v_a.2, v_a.3, v_b.0, v_b.1, v_b.2, v_b.3, v_i.0, v_n) -> Com_1(eval_SingleLinkCluster_bb9_in(v_8, v_a.0, v_a.1, v_a.2, v_a.2, v_b.0, v_b.1, v_b.2, v_b.2, v_i.0, v_n)) :|: v_a.2 <= 0 7.22/5.89 eval_SingleLinkCluster_bb7_in(v_8, v_a.0, v_a.1, v_a.2, v_a.3, v_b.0, v_b.1, v_b.2, v_b.3, v_i.0, v_n) -> Com_1(eval_SingleLinkCluster_6(v_8, v_a.0, v_a.1, v_a.2, v_a.3, v_b.0, v_b.1, v_b.2, v_b.3, v_i.0, v_n)) :|: TRUE 7.22/5.89 eval_SingleLinkCluster_6(v_8, v_a.0, v_a.1, v_a.2, v_a.3, v_b.0, v_b.1, v_b.2, v_b.3, v_i.0, v_n) -> Com_2(eval_nondet_start(v_8, v_a.0, v_a.1, v_a.2, v_a.3, v_b.0, v_b.1, v_b.2, v_b.3, v_i.0, v_n), eval_SingleLinkCluster_7(nondef.0, v_a.0, v_a.1, v_a.2, v_a.3, v_b.0, v_b.1, v_b.2, v_b.3, v_i.0, v_n)) :|: TRUE 7.22/5.89 eval_SingleLinkCluster_7(v_8, v_a.0, v_a.1, v_a.2, v_a.3, v_b.0, v_b.1, v_b.2, v_b.3, v_i.0, v_n) -> Com_1(eval_SingleLinkCluster_bb8_in(v_8, v_a.0, v_a.1, v_a.2, v_a.3, v_b.0, v_b.1, v_b.2, v_b.3, v_i.0, v_n)) :|: v_8 < 0 7.22/5.89 eval_SingleLinkCluster_7(v_8, v_a.0, v_a.1, v_a.2, v_a.3, v_b.0, v_b.1, v_b.2, v_b.3, v_i.0, v_n) -> Com_1(eval_SingleLinkCluster_bb8_in(v_8, v_a.0, v_a.1, v_a.2, v_a.3, v_b.0, v_b.1, v_b.2, v_b.3, v_i.0, v_n)) :|: v_8 > 0 7.22/5.89 eval_SingleLinkCluster_7(v_8, v_a.0, v_a.1, v_a.2, v_a.3, v_b.0, v_b.1, v_b.2, v_b.3, v_i.0, v_n) -> Com_1(eval_SingleLinkCluster_bb9_in(v_8, v_a.0, v_a.1, v_a.2, v_a.2, v_b.0, v_b.1, v_b.2, v_b.2, v_i.0, v_n)) :|: v_8 >= 0 && v_8 <= 0 7.22/5.89 eval_SingleLinkCluster_bb8_in(v_8, v_a.0, v_a.1, v_a.2, v_a.3, v_b.0, v_b.1, v_b.2, v_b.3, v_i.0, v_n) -> Com_1(eval_SingleLinkCluster_bb9_in(v_8, v_a.0, v_a.1, v_a.2, v_a.2 - 1, v_b.0, v_b.1, v_b.2, v_b.2 + 1, v_i.0, v_n)) :|: TRUE 7.22/5.89 eval_SingleLinkCluster_bb9_in(v_8, v_a.0, v_a.1, v_a.2, v_a.3, v_b.0, v_b.1, v_b.2, v_b.3, v_i.0, v_n) -> Com_1(eval_SingleLinkCluster_bb5_in(v_8, v_a.0, v_a.1, v_a.3, v_a.3, v_b.0, v_b.1, v_b.3, v_b.3, v_i.0 - 1, v_n)) :|: TRUE 7.22/5.89 eval_SingleLinkCluster_bb10_in(v_8, v_a.0, v_a.1, v_a.2, v_a.3, v_b.0, v_b.1, v_b.2, v_b.3, v_i.0, v_n) -> Com_1(eval_SingleLinkCluster_stop(v_8, v_a.0, v_a.1, v_a.2, v_a.3, v_b.0, v_b.1, v_b.2, v_b.3, v_i.0, v_n)) :|: TRUE 7.22/5.89 7.22/5.89 The start-symbols are:[eval_SingleLinkCluster_start_11] 7.22/5.89 7.22/5.89 7.22/5.89 ---------------------------------------- 7.22/5.89 7.22/5.89 (1) Koat Proof (FINISHED) 7.22/5.89 YES(?, 720*ar_1^2 + 354*ar_1 + 6) 7.22/5.89 7.22/5.89 7.22/5.89 7.22/5.89 Initial complexity problem: 7.22/5.89 7.22/5.89 1: T: 7.22/5.89 7.22/5.89 (Comp: ?, Cost: 1) evalSingleLinkClusterstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalSingleLinkClusterbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) 7.22/5.89 7.22/5.89 (Comp: ?, Cost: 1) evalSingleLinkClusterbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalSingleLinkClusterbb1in(ar_1, ar_1, 0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) 7.22/5.89 7.22/5.89 (Comp: ?, Cost: 1) evalSingleLinkClusterbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalSingleLinkClusterbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ ar_0 >= 1 ] 7.22/5.89 7.22/5.89 (Comp: ?, Cost: 1) evalSingleLinkClusterbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalSingleLinkClusterbb10in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ 0 >= ar_0 ] 7.22/5.89 7.22/5.89 (Comp: ?, Cost: 1) evalSingleLinkClusterbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalSingleLinkClusterbb3in(ar_0, ar_1, ar_2, ar_0 - 1, ar_2 + 1, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) 7.22/5.89 7.22/5.89 (Comp: ?, Cost: 1) evalSingleLinkClusterbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalSingleLinkClusterbb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ ar_4 >= 1 ] 7.22/5.89 7.22/5.89 (Comp: ?, Cost: 1) evalSingleLinkClusterbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalSingleLinkClusterbb1in(ar_3, ar_1, ar_4, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ 0 >= ar_4 ] 7.22/5.89 7.22/5.89 (Comp: ?, Cost: 1) evalSingleLinkClusterbb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalSingleLinkClusterbb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_3, ar_4 - 1, ar_1 - 1, ar_8, ar_9, ar_10, ar_11)) 7.22/5.89 7.22/5.89 (Comp: ?, Cost: 1) evalSingleLinkClusterbb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalSingleLinkClusterbb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ ar_7 >= 1 ] 7.22/5.89 7.22/5.89 (Comp: ?, Cost: 1) evalSingleLinkClusterbb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalSingleLinkClusterbb3in(ar_0, ar_1, ar_2, ar_5, ar_6, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ 0 >= ar_7 ] 7.22/5.89 7.22/5.89 (Comp: ?, Cost: 1) evalSingleLinkClusterbb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalSingleLinkClusterbb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ ar_5 >= 1 ] 7.22/5.89 7.22/5.89 (Comp: ?, Cost: 1) evalSingleLinkClusterbb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalSingleLinkClusterbb9in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_5, ar_6, ar_10, ar_11)) [ 0 >= ar_5 ] 7.22/5.89 7.22/5.89 (Comp: ?, Cost: 1) evalSingleLinkClusterbb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalSingleLinkCluster6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) 7.22/5.89 7.22/5.89 (Comp: ?, Cost: 1) evalSingleLinkCluster60(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) 7.22/5.89 7.22/5.89 (Comp: ?, Cost: 1) evalSingleLinkCluster61(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalSingleLinkCluster7(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_11, ar_11)) 7.22/5.89 7.22/5.89 (Comp: ?, Cost: 1) evalSingleLinkCluster6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_2(evalSingleLinkCluster60(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, m), evalSingleLinkCluster61(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, m)) 7.22/5.89 7.22/5.89 (Comp: ?, Cost: 1) evalSingleLinkCluster7(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalSingleLinkClusterbb8in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ 0 >= ar_10 + 1 ] 7.22/5.89 7.22/5.89 (Comp: ?, Cost: 1) evalSingleLinkCluster7(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalSingleLinkClusterbb8in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ ar_10 >= 1 ] 7.22/5.89 7.22/5.89 (Comp: ?, Cost: 1) evalSingleLinkCluster7(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalSingleLinkClusterbb9in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_5, ar_6, ar_10, ar_11)) [ ar_10 = 0 ] 7.22/5.89 7.22/5.89 (Comp: ?, Cost: 1) evalSingleLinkClusterbb8in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalSingleLinkClusterbb9in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_5 - 1, ar_6 + 1, ar_10, ar_11)) 7.22/5.89 7.22/5.89 (Comp: ?, Cost: 1) evalSingleLinkClusterbb9in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalSingleLinkClusterbb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_8, ar_9, ar_7 - 1, ar_8, ar_9, ar_10, ar_11)) 7.22/5.89 7.22/5.89 (Comp: ?, Cost: 1) evalSingleLinkClusterbb10in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalSingleLinkClusterstop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) 7.22/5.89 7.22/5.89 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalSingleLinkClusterstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ 0 <= 0 ] 7.22/5.89 7.22/5.89 start location: koat_start 7.22/5.89 popout

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all output return to Complexity_C_Integer 2019-03-21 04.38