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Complexity_C_Integer 2019-03-21 04.38 pair #429989544
details
property
value
status
complete
benchmark
Loopus2014_ex1.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n075.star.cs.uiowa.edu
space
Loopus
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
5.55089 seconds
cpu usage
6.90853
user time
6.50776
system time
0.400771
max virtual memory
1.8684276E7
max residence set size
241256.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^2))
output
6.70/5.50 WORST_CASE(?, O(n^2)) 6.85/5.51 proof of /export/starexec/sandbox/output/output_files/bench.koat 6.85/5.51 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 6.85/5.51 6.85/5.51 6.85/5.51 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 6.85/5.51 6.85/5.51 (0) CpxIntTrs 6.85/5.51 (1) Koat Proof [FINISHED, 4198 ms] 6.85/5.51 (2) BOUNDS(1, n^2) 6.85/5.51 6.85/5.51 6.85/5.51 ---------------------------------------- 6.85/5.51 6.85/5.51 (0) 6.85/5.51 Obligation: 6.85/5.51 Complexity Int TRS consisting of the following rules: 6.85/5.51 eval_Loopus2014_ex1_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_Loopus2014_ex1_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 6.85/5.51 eval_Loopus2014_ex1_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_Loopus2014_ex1_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 6.85/5.51 eval_Loopus2014_ex1_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_Loopus2014_ex1_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 6.85/5.51 eval_Loopus2014_ex1_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_Loopus2014_ex1_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 6.85/5.51 eval_Loopus2014_ex1_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_Loopus2014_ex1_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 6.85/5.51 eval_Loopus2014_ex1_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_Loopus2014_ex1_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 6.85/5.51 eval_Loopus2014_ex1_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_Loopus2014_ex1_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 6.85/5.51 eval_Loopus2014_ex1_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_Loopus2014_ex1_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 6.85/5.51 eval_Loopus2014_ex1_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_Loopus2014_ex1_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 6.85/5.51 eval_Loopus2014_ex1_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_Loopus2014_ex1_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 6.85/5.51 eval_Loopus2014_ex1_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_Loopus2014_ex1_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 6.85/5.51 eval_Loopus2014_ex1_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_Loopus2014_ex1_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 6.85/5.51 eval_Loopus2014_ex1_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_Loopus2014_ex1_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 6.85/5.51 eval_Loopus2014_ex1_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_Loopus2014_ex1_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 6.85/5.51 eval_Loopus2014_ex1_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_Loopus2014_ex1_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 6.85/5.51 eval_Loopus2014_ex1_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_Loopus2014_ex1_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 6.85/5.51 eval_Loopus2014_ex1_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_Loopus2014_ex1_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 6.85/5.51 eval_Loopus2014_ex1_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_Loopus2014_ex1_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 6.85/5.51 eval_Loopus2014_ex1_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_Loopus2014_ex1_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 6.85/5.51 6.85/5.51 The start-symbols are:[eval_Loopus2014_ex1_start_11] 6.85/5.51 6.85/5.51 6.85/5.51 ---------------------------------------- 6.85/5.51 6.85/5.51 (1) Koat Proof (FINISHED) 6.85/5.51 YES(?, 1152*ar_1^2 + 553*ar_1 + 6) 6.85/5.51 6.85/5.51 6.85/5.51 6.85/5.51 Initial complexity problem: 6.85/5.51 6.85/5.51 1: T: 6.85/5.51 6.85/5.51 (Comp: ?, Cost: 1) evalLoopus2014ex1start(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(evalLoopus2014ex1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) 6.85/5.51 6.85/5.51 (Comp: ?, Cost: 1) evalLoopus2014ex1bb0in(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(evalLoopus2014ex1bb1in(ar_1, ar_1, 0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) 6.85/5.51 6.85/5.51 (Comp: ?, Cost: 1) evalLoopus2014ex1bb1in(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(evalLoopus2014ex1bb2in(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 ] 6.85/5.51 6.85/5.51 (Comp: ?, Cost: 1) evalLoopus2014ex1bb1in(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(evalLoopus2014ex1bb10in(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 ] 6.85/5.51 6.85/5.51 (Comp: ?, Cost: 1) evalLoopus2014ex1bb2in(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(evalLoopus2014ex1bb3in(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)) 6.85/5.51 6.85/5.51 (Comp: ?, Cost: 1) evalLoopus2014ex1bb3in(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(evalLoopus2014ex1bb4in(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 ] 6.85/5.51 6.85/5.51 (Comp: ?, Cost: 1) evalLoopus2014ex1bb3in(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(evalLoopus2014ex1bb1in(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 ] 6.85/5.51 6.85/5.51 (Comp: ?, Cost: 1) evalLoopus2014ex1bb4in(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(evalLoopus2014ex1bb5in(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)) 6.85/5.51 6.85/5.51 (Comp: ?, Cost: 1) evalLoopus2014ex1bb5in(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(evalLoopus2014ex1bb6in(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 ] 6.85/5.51 6.85/5.51 (Comp: ?, Cost: 1) evalLoopus2014ex1bb5in(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(evalLoopus2014ex1bb3in(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 ] 6.85/5.51 6.85/5.51 (Comp: ?, Cost: 1) evalLoopus2014ex1bb6in(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(evalLoopus2014ex1bb7in(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 ] 6.85/5.51 6.85/5.51 (Comp: ?, Cost: 1) evalLoopus2014ex1bb6in(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(evalLoopus2014ex1bb9in(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 ] 6.85/5.51 6.85/5.51 (Comp: ?, Cost: 1) evalLoopus2014ex1bb7in(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(evalLoopus2014ex16(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) 6.85/5.51 6.85/5.51 (Comp: ?, Cost: 1) evalLoopus2014ex160(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)) 6.85/5.51 6.85/5.51 (Comp: ?, Cost: 1) evalLoopus2014ex161(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(evalLoopus2014ex17(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_11, ar_11)) 6.85/5.51 6.85/5.51 (Comp: ?, Cost: 1) evalLoopus2014ex16(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(evalLoopus2014ex160(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, m), evalLoopus2014ex161(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, m)) 6.85/5.51 6.85/5.51 (Comp: ?, Cost: 1) evalLoopus2014ex17(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(evalLoopus2014ex1bb8in(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 ] 6.85/5.51 6.85/5.51 (Comp: ?, Cost: 1) evalLoopus2014ex17(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(evalLoopus2014ex1bb9in(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_10 ] 6.85/5.51 6.85/5.51 (Comp: ?, Cost: 1) evalLoopus2014ex1bb8in(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(evalLoopus2014ex1bb9in(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)) 6.85/5.51 6.85/5.51 (Comp: ?, Cost: 1) evalLoopus2014ex1bb9in(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(evalLoopus2014ex1bb5in(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)) 6.85/5.51 6.85/5.51 (Comp: ?, Cost: 1) evalLoopus2014ex1bb10in(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(evalLoopus2014ex1stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) 6.85/5.51 6.85/5.51 (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(evalLoopus2014ex1start(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 ] 6.85/5.51 6.85/5.51 start location: koat_start 6.85/5.51 6.85/5.51 leaf cost: 0 6.85/5.51 6.85/5.51
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