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Complexity_C_Integer 2019-03-21 04.38 pair #429989700
details
property
value
status
complete
benchmark
sipmabubble.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n080.star.cs.uiowa.edu
space
WTC_V2
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.69084 seconds
cpu usage
2.6268
user time
2.4248
system time
0.201995
max virtual memory
1.8273644E7
max residence set size
180660.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^2))
output
2.16/1.66 WORST_CASE(?, O(n^2)) 2.57/1.67 proof of /export/starexec/sandbox2/output/output_files/bench.koat 2.57/1.67 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.57/1.67 2.57/1.67 2.57/1.67 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 2.57/1.67 2.57/1.67 (0) CpxIntTrs 2.57/1.67 (1) Koat Proof [FINISHED, 377 ms] 2.57/1.67 (2) BOUNDS(1, n^2) 2.57/1.67 2.57/1.67 2.57/1.67 ---------------------------------------- 2.57/1.67 2.57/1.67 (0) 2.57/1.67 Obligation: 2.57/1.67 Complexity Int TRS consisting of the following rules: 2.57/1.67 eval_sipmabubble_start(v_i.0, v_j.0, v_n) -> Com_1(eval_sipmabubble_bb0_in(v_i.0, v_j.0, v_n)) :|: TRUE 2.57/1.67 eval_sipmabubble_bb0_in(v_i.0, v_j.0, v_n) -> Com_1(eval_sipmabubble_bb1_in(v_n, v_j.0, v_n)) :|: TRUE 2.57/1.67 eval_sipmabubble_bb1_in(v_i.0, v_j.0, v_n) -> Com_1(eval_sipmabubble_bb2_in(v_i.0, 0, v_n)) :|: v_i.0 >= 0 2.57/1.67 eval_sipmabubble_bb1_in(v_i.0, v_j.0, v_n) -> Com_1(eval_sipmabubble_bb5_in(v_i.0, v_j.0, v_n)) :|: v_i.0 < 0 2.57/1.67 eval_sipmabubble_bb2_in(v_i.0, v_j.0, v_n) -> Com_1(eval_sipmabubble_bb3_in(v_i.0, v_j.0, v_n)) :|: v_j.0 <= v_i.0 - 1 2.57/1.67 eval_sipmabubble_bb2_in(v_i.0, v_j.0, v_n) -> Com_1(eval_sipmabubble_bb4_in(v_i.0, v_j.0, v_n)) :|: v_j.0 > v_i.0 - 1 2.57/1.67 eval_sipmabubble_bb3_in(v_i.0, v_j.0, v_n) -> Com_1(eval_sipmabubble_2(v_i.0, v_j.0, v_n)) :|: TRUE 2.57/1.67 eval_sipmabubble_2(v_i.0, v_j.0, v_n) -> Com_2(eval_nondet_start(v_i.0, v_j.0, v_n), eval_sipmabubble_3(v_i.0, v_j.0, v_n)) :|: TRUE 2.57/1.67 eval_sipmabubble_3(v_i.0, v_j.0, v_n) -> Com_2(eval_nondet_start(v_i.0, v_j.0, v_n), eval_sipmabubble_4(v_i.0, v_j.0, v_n)) :|: TRUE 2.57/1.67 eval_sipmabubble_4(v_i.0, v_j.0, v_n) -> Com_1(eval_sipmabubble_bb2_in(v_i.0, v_j.0 + 1, v_n)) :|: TRUE 2.57/1.67 eval_sipmabubble_bb4_in(v_i.0, v_j.0, v_n) -> Com_1(eval_sipmabubble_bb1_in(v_i.0 - 1, v_j.0, v_n)) :|: TRUE 2.57/1.67 eval_sipmabubble_bb5_in(v_i.0, v_j.0, v_n) -> Com_1(eval_sipmabubble_stop(v_i.0, v_j.0, v_n)) :|: TRUE 2.57/1.67 2.57/1.67 The start-symbols are:[eval_sipmabubble_start_3] 2.57/1.67 2.57/1.67 2.57/1.67 ---------------------------------------- 2.57/1.67 2.57/1.67 (1) Koat Proof (FINISHED) 2.57/1.67 YES(?, 84*ar_1 + 75*ar_1^2 + 15) 2.57/1.67 2.57/1.67 2.57/1.67 2.57/1.67 Initial complexity problem: 2.57/1.67 2.57/1.67 1: T: 2.57/1.67 2.57/1.67 (Comp: ?, Cost: 1) evalsipmabubblestart(ar_0, ar_1, ar_2) -> Com_1(evalsipmabubblebb0in(ar_0, ar_1, ar_2)) 2.57/1.67 2.57/1.67 (Comp: ?, Cost: 1) evalsipmabubblebb0in(ar_0, ar_1, ar_2) -> Com_1(evalsipmabubblebb1in(ar_1, ar_1, ar_2)) 2.57/1.67 2.57/1.67 (Comp: ?, Cost: 1) evalsipmabubblebb1in(ar_0, ar_1, ar_2) -> Com_1(evalsipmabubblebb2in(ar_0, ar_1, 0)) [ ar_0 >= 0 ] 2.57/1.67 2.57/1.67 (Comp: ?, Cost: 1) evalsipmabubblebb1in(ar_0, ar_1, ar_2) -> Com_1(evalsipmabubblebb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ] 2.57/1.67 2.57/1.67 (Comp: ?, Cost: 1) evalsipmabubblebb2in(ar_0, ar_1, ar_2) -> Com_1(evalsipmabubblebb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ] 2.57/1.67 2.57/1.67 (Comp: ?, Cost: 1) evalsipmabubblebb2in(ar_0, ar_1, ar_2) -> Com_1(evalsipmabubblebb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 ] 2.57/1.67 2.57/1.67 (Comp: ?, Cost: 1) evalsipmabubblebb3in(ar_0, ar_1, ar_2) -> Com_1(evalsipmabubble2(ar_0, ar_1, ar_2)) 2.57/1.67 2.57/1.67 (Comp: ?, Cost: 1) evalsipmabubble2(ar_0, ar_1, ar_2) -> Com_2(evalnondetstart(ar_0, ar_1, ar_2), evalsipmabubble3(ar_0, ar_1, ar_2)) 2.57/1.67 2.57/1.67 (Comp: ?, Cost: 1) evalsipmabubble3(ar_0, ar_1, ar_2) -> Com_2(evalnondetstart(ar_0, ar_1, ar_2), evalsipmabubble4(ar_0, ar_1, ar_2)) 2.57/1.67 2.57/1.67 (Comp: ?, Cost: 1) evalsipmabubble4(ar_0, ar_1, ar_2) -> Com_1(evalsipmabubblebb2in(ar_0, ar_1, ar_2 + 1)) 2.57/1.67 2.57/1.67 (Comp: ?, Cost: 1) evalsipmabubblebb4in(ar_0, ar_1, ar_2) -> Com_1(evalsipmabubblebb1in(ar_0 - 1, ar_1, ar_2)) 2.57/1.67 2.57/1.67 (Comp: ?, Cost: 1) evalsipmabubblebb5in(ar_0, ar_1, ar_2) -> Com_1(evalsipmabubblestop(ar_0, ar_1, ar_2)) 2.57/1.67 2.57/1.67 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalsipmabubblestart(ar_0, ar_1, ar_2)) [ 0 <= 0 ] 2.57/1.67 2.57/1.67 start location: koat_start 2.57/1.67 2.57/1.67 leaf cost: 0 2.57/1.67 2.57/1.67 2.57/1.67 2.57/1.67 Repeatedly propagating knowledge in problem 1 produces the following problem: 2.57/1.67 2.57/1.67 2: T: 2.57/1.67 2.57/1.67 (Comp: 1, Cost: 1) evalsipmabubblestart(ar_0, ar_1, ar_2) -> Com_1(evalsipmabubblebb0in(ar_0, ar_1, ar_2)) 2.57/1.67 2.57/1.67 (Comp: 1, Cost: 1) evalsipmabubblebb0in(ar_0, ar_1, ar_2) -> Com_1(evalsipmabubblebb1in(ar_1, ar_1, ar_2)) 2.57/1.67 2.57/1.67 (Comp: ?, Cost: 1) evalsipmabubblebb1in(ar_0, ar_1, ar_2) -> Com_1(evalsipmabubblebb2in(ar_0, ar_1, 0)) [ ar_0 >= 0 ] 2.57/1.67 2.57/1.67 (Comp: ?, Cost: 1) evalsipmabubblebb1in(ar_0, ar_1, ar_2) -> Com_1(evalsipmabubblebb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ] 2.57/1.67 2.57/1.67 (Comp: ?, Cost: 1) evalsipmabubblebb2in(ar_0, ar_1, ar_2) -> Com_1(evalsipmabubblebb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ] 2.57/1.67 2.57/1.67 (Comp: ?, Cost: 1) evalsipmabubblebb2in(ar_0, ar_1, ar_2) -> Com_1(evalsipmabubblebb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 ] 2.57/1.67 2.57/1.67 (Comp: ?, Cost: 1) evalsipmabubblebb3in(ar_0, ar_1, ar_2) -> Com_1(evalsipmabubble2(ar_0, ar_1, ar_2)) 2.57/1.67 2.57/1.67 (Comp: ?, Cost: 1) evalsipmabubble2(ar_0, ar_1, ar_2) -> Com_2(evalnondetstart(ar_0, ar_1, ar_2), evalsipmabubble3(ar_0, ar_1, ar_2)) 2.57/1.67 2.57/1.67 (Comp: ?, Cost: 1) evalsipmabubble3(ar_0, ar_1, ar_2) -> Com_2(evalnondetstart(ar_0, ar_1, ar_2), evalsipmabubble4(ar_0, ar_1, ar_2)) 2.57/1.67 2.57/1.67 (Comp: ?, Cost: 1) evalsipmabubble4(ar_0, ar_1, ar_2) -> Com_1(evalsipmabubblebb2in(ar_0, ar_1, ar_2 + 1)) 2.57/1.67
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