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Compl Integ Trans Syste 26843 pair #381744459
details
property
value
status
complete
benchmark
sipmabubble.c.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n113.star.cs.uiowa.edu
space
Flores-Montoya_16
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
2.63365888596 seconds
cpu usage
5.787596681
max memory
3.07912704E8
stage attributes
key
value
output-size
61723
starexec-result
WORST_CASE(Omega(n^2), O(n^2))
output
/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^2), O(n^2)) proof of /export/starexec/sandbox/benchmark/theBenchmark.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2). (0) CpxIntTrs (1) Koat Proof [FINISHED, 226 ms] (2) BOUNDS(1, n^2) (3) Loat Proof [FINISHED, 915 ms] (4) BOUNDS(n^2, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_sipmabubble_start(v_24, v_i_0, v_j_0, v_n) -> Com_1(eval_sipmabubble_bb0_in(v_24, v_i_0, v_j_0, v_n)) :|: TRUE eval_sipmabubble_bb0_in(v_24, v_i_0, v_j_0, v_n) -> Com_1(eval_sipmabubble_0(v_24, v_i_0, v_j_0, v_n)) :|: TRUE eval_sipmabubble_0(v_24, v_i_0, v_j_0, v_n) -> Com_1(eval_sipmabubble_1(v_24, v_i_0, v_j_0, v_n)) :|: TRUE eval_sipmabubble_1(v_24, v_i_0, v_j_0, v_n) -> Com_1(eval_sipmabubble_2(v_24, v_i_0, v_j_0, v_n)) :|: TRUE eval_sipmabubble_2(v_24, v_i_0, v_j_0, v_n) -> Com_1(eval_sipmabubble_3(v_24, v_i_0, v_j_0, v_n)) :|: TRUE eval_sipmabubble_3(v_24, v_i_0, v_j_0, v_n) -> Com_1(eval_sipmabubble_4(v_24, v_i_0, v_j_0, v_n)) :|: TRUE eval_sipmabubble_4(v_24, v_i_0, v_j_0, v_n) -> Com_1(eval_sipmabubble_5(v_24, v_i_0, v_j_0, v_n)) :|: TRUE eval_sipmabubble_5(v_24, v_i_0, v_j_0, v_n) -> Com_1(eval_sipmabubble_6(v_24, v_i_0, v_j_0, v_n)) :|: TRUE eval_sipmabubble_6(v_24, v_i_0, v_j_0, v_n) -> Com_1(eval_sipmabubble_bb1_in(v_24, v_n, v_j_0, v_n)) :|: TRUE eval_sipmabubble_bb1_in(v_24, v_i_0, v_j_0, v_n) -> Com_1(eval_sipmabubble_bb2_in(v_24, v_i_0, 0, v_n)) :|: v_i_0 >= 0 eval_sipmabubble_bb1_in(v_24, v_i_0, v_j_0, v_n) -> Com_1(eval_sipmabubble_bb7_in(v_24, v_i_0, v_j_0, v_n)) :|: v_i_0 < 0 eval_sipmabubble_bb2_in(v_24, v_i_0, v_j_0, v_n) -> Com_1(eval_sipmabubble_bb3_in(v_24, v_i_0, v_j_0, v_n)) :|: v_j_0 <= v_i_0 - 1 eval_sipmabubble_bb2_in(v_24, v_i_0, v_j_0, v_n) -> Com_1(eval_sipmabubble_bb6_in(v_24, v_i_0, v_j_0, v_n)) :|: v_j_0 > v_i_0 - 1 eval_sipmabubble_bb3_in(v_24, v_i_0, v_j_0, v_n) -> Com_1(eval_sipmabubble_bb4_in(v_24, v_i_0, v_j_0, v_n)) :|: nondef_0 > nondef_1 eval_sipmabubble_bb3_in(v_24, v_i_0, v_j_0, v_n) -> Com_1(eval_sipmabubble_bb5_in(v_24, v_i_0, v_j_0, v_n)) :|: nondef_0 <= nondef_1 eval_sipmabubble_bb4_in(v_24, v_i_0, v_j_0, v_n) -> Com_1(eval_sipmabubble_bb5_in(v_24, v_i_0, v_j_0, v_n)) :|: TRUE eval_sipmabubble_bb5_in(v_24, v_i_0, v_j_0, v_n) -> Com_1(eval_sipmabubble_bb2_in(v_24, v_i_0, v_j_0 + 1, v_n)) :|: TRUE eval_sipmabubble_bb6_in(v_24, v_i_0, v_j_0, v_n) -> Com_1(eval_sipmabubble_29(v_i_0 - 1, v_i_0, v_j_0, v_n)) :|: TRUE eval_sipmabubble_29(v_24, v_i_0, v_j_0, v_n) -> Com_1(eval_sipmabubble_30(v_24, v_i_0, v_j_0, v_n)) :|: TRUE eval_sipmabubble_30(v_24, v_i_0, v_j_0, v_n) -> Com_1(eval_sipmabubble_bb1_in(v_24, v_24, v_j_0, v_n)) :|: TRUE eval_sipmabubble_bb7_in(v_24, v_i_0, v_j_0, v_n) -> Com_1(eval_sipmabubble_stop(v_24, v_i_0, v_j_0, v_n)) :|: TRUE The start-symbols are:[eval_sipmabubble_start_4] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 653*ar_1 + 30*ar_1^2 + 636) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalsipmabubblestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalsipmabubblebb0in(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalsipmabubblebb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalsipmabubble0(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalsipmabubble0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalsipmabubble1(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalsipmabubble1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalsipmabubble2(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalsipmabubble2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalsipmabubble3(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalsipmabubble3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalsipmabubble4(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalsipmabubble4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalsipmabubble5(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalsipmabubble5(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalsipmabubble6(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalsipmabubble6(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalsipmabubblebb1in(ar_1, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalsipmabubblebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalsipmabubblebb2in(ar_0, ar_1, 0, ar_3)) [ ar_0 >= 0 ] (Comp: ?, Cost: 1) evalsipmabubblebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalsipmabubblebb7in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalsipmabubblebb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalsipmabubblebb6in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ] (Comp: ?, Cost: 1) evalsipmabubblebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalsipmabubblebb4in(ar_0, ar_1, ar_2, ar_3)) [ e >= f + 1 ] (Comp: ?, Cost: 1) evalsipmabubblebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalsipmabubblebb5in(ar_0, ar_1, ar_2, ar_3)) [ f >= e ] (Comp: ?, Cost: 1) evalsipmabubblebb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalsipmabubblebb5in(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalsipmabubblebb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalsipmabubblebb2in(ar_0, ar_1, ar_2 + 1, ar_3)) (Comp: ?, Cost: 1) evalsipmabubblebb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalsipmabubble29(ar_0, ar_1, ar_2, ar_0 - 1)) (Comp: ?, Cost: 1) evalsipmabubble29(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalsipmabubble30(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalsipmabubble30(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalsipmabubblebb1in(ar_3, ar_1, ar_2, ar_3))
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