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Complexity_ITS 2019-03-21 04.46 pair #429989886
details
property
value
status
complete
benchmark
random2d.c.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n140.star.cs.uiowa.edu
space
Flores-Montoya_16
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
4.77437 seconds
cpu usage
10.7389
user time
10.2755
system time
0.463427
max virtual memory
1.8812984E7
max residence set size
240204.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
10.62/4.72 WORST_CASE(Omega(n^1), O(n^1)) 10.68/4.73 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 10.68/4.73 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 10.68/4.73 10.68/4.73 10.68/4.73 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1). 10.68/4.73 10.68/4.73 (0) CpxIntTrs 10.68/4.73 (1) Koat Proof [FINISHED, 524 ms] 10.68/4.73 (2) BOUNDS(1, n^1) 10.68/4.73 (3) Loat Proof [FINISHED, 3041 ms] 10.68/4.73 (4) BOUNDS(n^1, INF) 10.68/4.73 10.68/4.73 10.68/4.73 ---------------------------------------- 10.68/4.73 10.68/4.73 (0) 10.68/4.73 Obligation: 10.68/4.73 Complexity Int TRS consisting of the following rules: 10.68/4.73 eval_random2d_start(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_bb0_in(v_1, v_2, v_N, v_i_0)) :|: TRUE 10.68/4.73 eval_random2d_bb0_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_0(v_1, v_2, v_N, v_i_0)) :|: TRUE 10.68/4.73 eval_random2d_0(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_1(v_1, v_2, v_N, v_i_0)) :|: TRUE 10.68/4.73 eval_random2d_1(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_2(v_1, v_2, v_N, v_i_0)) :|: TRUE 10.68/4.73 eval_random2d_2(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_3(v_1, v_2, v_N, v_i_0)) :|: TRUE 10.68/4.73 eval_random2d_3(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_4(v_1, v_2, v_N, v_i_0)) :|: TRUE 10.68/4.73 eval_random2d_4(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_5(v_1, v_2, v_N, v_i_0)) :|: TRUE 10.68/4.73 eval_random2d_5(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_6(v_1, v_2, v_N, v_i_0)) :|: TRUE 10.68/4.73 eval_random2d_6(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_7(v_1, v_2, v_N, v_i_0)) :|: TRUE 10.68/4.73 eval_random2d_7(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_8(v_1, v_2, v_N, v_i_0)) :|: TRUE 10.68/4.73 eval_random2d_8(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_9(v_1, v_2, v_N, v_i_0)) :|: TRUE 10.68/4.73 eval_random2d_9(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_10(v_1, v_2, v_N, v_i_0)) :|: TRUE 10.68/4.73 eval_random2d_10(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_bb1_in(v_1, v_2, v_N, 0)) :|: TRUE 10.68/4.73 eval_random2d_bb1_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_bb2_in(v_1, v_2, v_N, v_i_0)) :|: v_i_0 < v_N 10.68/4.73 eval_random2d_bb1_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_bb8_in(v_1, v_2, v_N, v_i_0)) :|: v_i_0 >= v_N 10.68/4.73 eval_random2d_bb2_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_12(v_i_0 + 1, v_2, v_N, v_i_0)) :|: TRUE 10.68/4.73 eval_random2d_12(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_13(v_1, nondef_0, v_N, v_i_0)) :|: TRUE 10.68/4.73 eval_random2d_13(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_bb3_in(v_1, v_2, v_N, v_i_0)) :|: v_2 >= 0 && v_2 <= 3 10.68/4.73 eval_random2d_13(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_bb1_in(v_1, v_2, v_N, v_1)) :|: v_2 < 0 10.68/4.73 eval_random2d_13(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_bb1_in(v_1, v_2, v_N, v_1)) :|: v_2 > 3 10.68/4.73 eval_random2d_bb3_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_NodeBlock9_in(v_1, v_2, v_N, v_i_0)) :|: TRUE 10.68/4.73 eval_random2d_NodeBlock9_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_NodeBlock_in(v_1, v_2, v_N, v_i_0)) :|: v_2 < 2 10.68/4.73 eval_random2d_NodeBlock9_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_NodeBlock7_in(v_1, v_2, v_N, v_i_0)) :|: v_2 >= 2 10.68/4.73 eval_random2d_NodeBlock_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_LeafBlock_in(v_1, v_2, v_N, v_i_0)) :|: v_2 < 1 10.68/4.73 eval_random2d_NodeBlock_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_LeafBlock1_in(v_1, v_2, v_N, v_i_0)) :|: v_2 >= 1 10.68/4.73 eval_random2d_LeafBlock_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_bb4_in(v_1, v_2, v_N, v_i_0)) :|: v_2 >= 0 && v_2 <= 0 10.68/4.73 eval_random2d_LeafBlock_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_NewDefault_in(v_1, v_2, v_N, v_i_0)) :|: v_2 < 0 10.68/4.73 eval_random2d_LeafBlock_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_NewDefault_in(v_1, v_2, v_N, v_i_0)) :|: v_2 > 0 10.68/4.73 eval_random2d_bb4_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_bb1_in(v_1, v_2, v_N, v_1)) :|: TRUE 10.68/4.73 eval_random2d_LeafBlock1_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_bb5_in(v_1, v_2, v_N, v_i_0)) :|: v_2 >= 1 && v_2 <= 1 10.68/4.73 eval_random2d_LeafBlock1_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_NewDefault_in(v_1, v_2, v_N, v_i_0)) :|: v_2 < 1 10.68/4.73 eval_random2d_LeafBlock1_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_NewDefault_in(v_1, v_2, v_N, v_i_0)) :|: v_2 > 1 10.68/4.73 eval_random2d_bb5_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_bb1_in(v_1, v_2, v_N, v_1)) :|: TRUE 10.68/4.73 eval_random2d_NodeBlock7_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_LeafBlock3_in(v_1, v_2, v_N, v_i_0)) :|: v_2 < 3 10.68/4.73 eval_random2d_NodeBlock7_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_LeafBlock5_in(v_1, v_2, v_N, v_i_0)) :|: v_2 >= 3 10.68/4.73 eval_random2d_LeafBlock3_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_bb6_in(v_1, v_2, v_N, v_i_0)) :|: v_2 >= 2 && v_2 <= 2 10.68/4.73 eval_random2d_LeafBlock3_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_NewDefault_in(v_1, v_2, v_N, v_i_0)) :|: v_2 < 2 10.68/4.73 eval_random2d_LeafBlock3_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_NewDefault_in(v_1, v_2, v_N, v_i_0)) :|: v_2 > 2 10.68/4.73 eval_random2d_bb6_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_bb1_in(v_1, v_2, v_N, v_1)) :|: TRUE 10.68/4.73 eval_random2d_LeafBlock5_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_bb7_in(v_1, v_2, v_N, v_i_0)) :|: v_2 >= 3 && v_2 <= 3 10.68/4.73 eval_random2d_LeafBlock5_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_NewDefault_in(v_1, v_2, v_N, v_i_0)) :|: v_2 < 3 10.68/4.73 eval_random2d_LeafBlock5_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_NewDefault_in(v_1, v_2, v_N, v_i_0)) :|: v_2 > 3 10.68/4.73 eval_random2d_bb7_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_bb1_in(v_1, v_2, v_N, v_1)) :|: TRUE 10.68/4.73 eval_random2d_NewDefault_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_bb1_in(v_1, v_2, v_N, v_1)) :|: TRUE 10.68/4.73 eval_random2d_bb8_in(v_1, v_2, v_N, v_i_0) -> Com_1(eval_random2d_stop(v_1, v_2, v_N, v_i_0)) :|: TRUE 10.68/4.73 10.68/4.73 The start-symbols are:[eval_random2d_start_4] 10.68/4.73 10.68/4.73 10.68/4.73 ---------------------------------------- 10.68/4.73 10.68/4.73 (1) Koat Proof (FINISHED) 10.68/4.73 YES(?, 29*ar_1 + 17) 10.68/4.73 10.68/4.73 10.68/4.73 10.68/4.73 Initial complexity problem: 10.68/4.73 10.68/4.73 1: T: 10.68/4.73 10.68/4.73 (Comp: ?, Cost: 1) evalrandom2dstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2dbb0in(ar_0, ar_1, ar_2, ar_3)) 10.68/4.73 10.68/4.73 (Comp: ?, Cost: 1) evalrandom2dbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d0(ar_0, ar_1, ar_2, ar_3)) 10.68/4.73 10.68/4.73 (Comp: ?, Cost: 1) evalrandom2d0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d1(ar_0, ar_1, ar_2, ar_3)) 10.68/4.73 10.68/4.73 (Comp: ?, Cost: 1) evalrandom2d1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d2(ar_0, ar_1, ar_2, ar_3)) 10.68/4.73 10.68/4.73 (Comp: ?, Cost: 1) evalrandom2d2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d3(ar_0, ar_1, ar_2, ar_3)) 10.68/4.73 10.68/4.73 (Comp: ?, Cost: 1) evalrandom2d3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d4(ar_0, ar_1, ar_2, ar_3)) 10.68/4.73 10.68/4.73 (Comp: ?, Cost: 1) evalrandom2d4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d5(ar_0, ar_1, ar_2, ar_3)) 10.68/4.73 10.68/4.73 (Comp: ?, Cost: 1) evalrandom2d5(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d6(ar_0, ar_1, ar_2, ar_3)) 10.68/4.73 10.68/4.73 (Comp: ?, Cost: 1) evalrandom2d6(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d7(ar_0, ar_1, ar_2, ar_3)) 10.68/4.73 10.68/4.73 (Comp: ?, Cost: 1) evalrandom2d7(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d8(ar_0, ar_1, ar_2, ar_3)) 10.68/4.73 10.68/4.73 (Comp: ?, Cost: 1) evalrandom2d8(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrandom2d9(ar_0, ar_1, ar_2, ar_3))
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