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Complexity_ITS 2019-03-21 04.46 pair #429990002
details
property
value
status
complete
benchmark
textbook_ex3.c.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n069.star.cs.uiowa.edu
space
Flores-Montoya_16
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
25.2192 seconds
cpu usage
31.1947
user time
29.4775
system time
1.71726
max virtual memory
1.8787256E7
max residence set size
243240.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^4), O(n^6))
output
31.04/25.17 WORST_CASE(Omega(n^4), O(n^6)) 31.04/25.18 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 31.04/25.18 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 31.04/25.18 31.04/25.18 31.04/25.18 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^4, n^6). 31.04/25.18 31.04/25.18 (0) CpxIntTrs 31.04/25.18 (1) Koat Proof [FINISHED, 925 ms] 31.04/25.18 (2) BOUNDS(1, n^6) 31.04/25.18 (3) Loat Proof [FINISHED, 2527 ms] 31.04/25.18 (4) BOUNDS(n^4, INF) 31.04/25.18 31.04/25.18 31.04/25.18 ---------------------------------------- 31.04/25.18 31.04/25.18 (0) 31.04/25.18 Obligation: 31.04/25.18 Complexity Int TRS consisting of the following rules: 31.04/25.18 eval_abc_start(v_2, v_6, v_7, v_i_0, v_i_0_sink, v_j_0, v_l_0, v_m) -> Com_1(eval_abc_bb0_in(v_2, v_6, v_7, v_i_0, v_i_0_sink, v_j_0, v_l_0, v_m)) :|: TRUE 31.04/25.18 eval_abc_bb0_in(v_2, v_6, v_7, v_i_0, v_i_0_sink, v_j_0, v_l_0, v_m) -> Com_1(eval_abc_0(v_2, v_6, v_7, v_i_0, v_i_0_sink, v_j_0, v_l_0, v_m)) :|: TRUE 31.04/25.18 eval_abc_0(v_2, v_6, v_7, v_i_0, v_i_0_sink, v_j_0, v_l_0, v_m) -> Com_1(eval_abc_1(v_2, v_6, v_7, v_i_0, v_i_0_sink, v_j_0, v_l_0, v_m)) :|: TRUE 31.04/25.18 eval_abc_1(v_2, v_6, v_7, v_i_0, v_i_0_sink, v_j_0, v_l_0, v_m) -> Com_1(eval_abc_2(v_2, v_6, v_7, v_i_0, v_i_0_sink, v_j_0, v_l_0, v_m)) :|: TRUE 31.04/25.18 eval_abc_2(v_2, v_6, v_7, v_i_0, v_i_0_sink, v_j_0, v_l_0, v_m) -> Com_1(eval_abc_3(v_2, v_6, v_7, v_i_0, v_i_0_sink, v_j_0, v_l_0, v_m)) :|: TRUE 31.04/25.18 eval_abc_3(v_2, v_6, v_7, v_i_0, v_i_0_sink, v_j_0, v_l_0, v_m) -> Com_1(eval_abc_4(v_2, v_6, v_7, v_i_0, v_i_0_sink, v_j_0, v_l_0, v_m)) :|: TRUE 31.04/25.18 eval_abc_4(v_2, v_6, v_7, v_i_0, v_i_0_sink, v_j_0, v_l_0, v_m) -> Com_1(eval_abc_5(v_2, v_6, v_7, v_i_0, v_i_0_sink, v_j_0, v_l_0, v_m)) :|: TRUE 31.04/25.18 eval_abc_5(v_2, v_6, v_7, v_i_0, v_i_0_sink, v_j_0, v_l_0, v_m) -> Com_1(eval_abc_6(v_2, v_6, v_7, v_i_0, v_i_0_sink, v_j_0, v_l_0, v_m)) :|: TRUE 31.04/25.18 eval_abc_6(v_2, v_6, v_7, v_i_0, v_i_0_sink, v_j_0, v_l_0, v_m) -> Com_1(eval_abc_bb1_in(v_2, v_6, v_7, 1, v_i_0_sink, v_j_0, v_l_0, v_m)) :|: TRUE 31.04/25.18 eval_abc_bb1_in(v_2, v_6, v_7, v_i_0, v_i_0_sink, v_j_0, v_l_0, v_m) -> Com_1(eval_abc_bb2_in(v_2, v_6, v_7, v_i_0, v_i_0_sink, 1, v_l_0, v_m)) :|: v_i_0 <= v_m 31.04/25.18 eval_abc_bb1_in(v_2, v_6, v_7, v_i_0, v_i_0_sink, v_j_0, v_l_0, v_m) -> Com_1(eval_abc_bb8_in(v_2, v_6, v_7, v_i_0, v_i_0_sink, v_j_0, v_l_0, v_m)) :|: v_i_0 > v_m 31.04/25.18 eval_abc_bb2_in(v_2, v_6, v_7, v_i_0, v_i_0_sink, v_j_0, v_l_0, v_m) -> Com_1(eval_abc_bb3_in(v_2, v_6, v_7, v_i_0, v_i_0, v_j_0, v_l_0, v_m)) :|: v_j_0 <= v_i_0 31.04/25.18 eval_abc_bb2_in(v_2, v_6, v_7, v_i_0, v_i_0_sink, v_j_0, v_l_0, v_m) -> Com_1(eval_abc_bb7_in(v_2, v_6, v_7, v_i_0, v_i_0_sink, v_j_0, v_l_0, v_m)) :|: v_j_0 > v_i_0 31.04/25.18 eval_abc_bb3_in(v_2, v_6, v_7, v_i_0, v_i_0_sink, v_j_0, v_l_0, v_m) -> Com_1(eval_abc_bb4_in(v_i_0_sink + 1, v_6, v_7, v_i_0, v_i_0_sink, v_j_0, 1, v_m)) :|: v_i_0_sink + 1 <= v_m 31.04/25.18 eval_abc_bb3_in(v_2, v_6, v_7, v_i_0, v_i_0_sink, v_j_0, v_l_0, v_m) -> Com_1(eval_abc_bb6_in(v_i_0_sink + 1, v_6, v_7, v_i_0, v_i_0_sink, v_j_0, v_l_0, v_m)) :|: v_i_0_sink + 1 > v_m 31.04/25.18 eval_abc_bb4_in(v_2, v_6, v_7, v_i_0, v_i_0_sink, v_j_0, v_l_0, v_m) -> Com_1(eval_abc_bb5_in(v_2, v_6, v_7, v_i_0, v_i_0_sink, v_j_0, v_l_0, v_m)) :|: v_l_0 <= v_2 31.04/25.18 eval_abc_bb4_in(v_2, v_6, v_7, v_i_0, v_i_0_sink, v_j_0, v_l_0, v_m) -> Com_1(eval_abc_bb3_in(v_2, v_6, v_7, v_i_0, v_2, v_j_0, v_l_0, v_m)) :|: v_l_0 > v_2 31.04/25.18 eval_abc_bb5_in(v_2, v_6, v_7, v_i_0, v_i_0_sink, v_j_0, v_l_0, v_m) -> Com_1(eval_abc_bb4_in(v_2, v_6, v_7, v_i_0, v_i_0_sink, v_j_0, v_l_0 + 1, v_m)) :|: TRUE 31.04/25.18 eval_abc_bb6_in(v_2, v_6, v_7, v_i_0, v_i_0_sink, v_j_0, v_l_0, v_m) -> Com_1(eval_abc_12(v_2, v_j_0 + 1, v_7, v_i_0, v_i_0_sink, v_j_0, v_l_0, v_m)) :|: TRUE 31.04/25.18 eval_abc_12(v_2, v_6, v_7, v_i_0, v_i_0_sink, v_j_0, v_l_0, v_m) -> Com_1(eval_abc_13(v_2, v_6, v_7, v_i_0, v_i_0_sink, v_j_0, v_l_0, v_m)) :|: TRUE 31.04/25.18 eval_abc_13(v_2, v_6, v_7, v_i_0, v_i_0_sink, v_j_0, v_l_0, v_m) -> Com_1(eval_abc_bb2_in(v_2, v_6, v_7, v_i_0, v_i_0_sink, v_6, v_l_0, v_m)) :|: TRUE 31.04/25.18 eval_abc_bb7_in(v_2, v_6, v_7, v_i_0, v_i_0_sink, v_j_0, v_l_0, v_m) -> Com_1(eval_abc_15(v_2, v_6, v_i_0 + 1, v_i_0, v_i_0_sink, v_j_0, v_l_0, v_m)) :|: TRUE 31.04/25.18 eval_abc_15(v_2, v_6, v_7, v_i_0, v_i_0_sink, v_j_0, v_l_0, v_m) -> Com_1(eval_abc_16(v_2, v_6, v_7, v_i_0, v_i_0_sink, v_j_0, v_l_0, v_m)) :|: TRUE 31.04/25.18 eval_abc_16(v_2, v_6, v_7, v_i_0, v_i_0_sink, v_j_0, v_l_0, v_m) -> Com_1(eval_abc_bb1_in(v_2, v_6, v_7, v_7, v_i_0_sink, v_j_0, v_l_0, v_m)) :|: TRUE 31.04/25.18 eval_abc_bb8_in(v_2, v_6, v_7, v_i_0, v_i_0_sink, v_j_0, v_l_0, v_m) -> Com_1(eval_abc_stop(v_2, v_6, v_7, v_i_0, v_i_0_sink, v_j_0, v_l_0, v_m)) :|: TRUE 31.04/25.18 31.04/25.18 The start-symbols are:[eval_abc_start_8] 31.04/25.18 31.04/25.18 31.04/25.18 ---------------------------------------- 31.04/25.18 31.04/25.18 (1) Koat Proof (FINISHED) 31.04/25.18 YES(?, 44099*ar_1 + 2669728*ar_1^2 + 1595820*ar_1^3 + 331632*ar_1^4 + 800*ar_1^6 + 27680*ar_1^5 + 13) 31.04/25.18 31.04/25.18 31.04/25.18 31.04/25.18 Initial complexity problem: 31.04/25.18 31.04/25.18 1: T: 31.04/25.18 31.04/25.18 (Comp: ?, Cost: 1) evalabcstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 31.04/25.18 31.04/25.18 (Comp: ?, Cost: 1) evalabcbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 31.04/25.18 31.04/25.18 (Comp: ?, Cost: 1) evalabc0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 31.04/25.18 31.04/25.18 (Comp: ?, Cost: 1) evalabc1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 31.04/25.18 31.04/25.18 (Comp: ?, Cost: 1) evalabc2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 31.04/25.18 31.04/25.18 (Comp: ?, Cost: 1) evalabc3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 31.04/25.18 31.04/25.18 (Comp: ?, Cost: 1) evalabc4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalabc5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 31.04/25.18 31.04/25.18 (Comp: ?, Cost: 1) evalabc5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalabc6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 31.04/25.18 31.04/25.18 (Comp: ?, Cost: 1) evalabc6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalabcbb1in(1, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 31.04/25.18 31.04/25.18 (Comp: ?, Cost: 1) evalabcbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalabcbb2in(ar_0, ar_1, 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 >= ar_0 ] 31.04/25.18 31.04/25.18 (Comp: ?, Cost: 1) evalabcbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalabcbb8in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_1 + 1 ] 31.04/25.18 31.04/25.18 (Comp: ?, Cost: 1) evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_0, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_2 ] 31.04/25.18 31.04/25.18 (Comp: ?, Cost: 1) evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalabcbb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_2 >= ar_0 + 1 ] 31.04/25.18 31.04/25.18 (Comp: ?, Cost: 1) evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_3 + 1, 1, ar_6, ar_7)) [ ar_1 >= ar_3 + 1 ] 31.04/25.18 31.04/25.18 (Comp: ?, Cost: 1) evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalabcbb6in(ar_0, ar_1, ar_2, ar_3, ar_3 + 1, ar_5, ar_6, ar_7)) [ ar_3 >= ar_1 ] 31.04/25.18 31.04/25.18 (Comp: ?, Cost: 1) evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_4 >= ar_5 ] 31.04/25.18 31.04/25.18 (Comp: ?, Cost: 1) evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_4, ar_4, ar_5, ar_6, ar_7)) [ ar_5 >= ar_4 + 1 ] 31.04/25.18 31.04/25.18 (Comp: ?, Cost: 1) evalabcbb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1, ar_6, ar_7)) 31.04/25.18 31.04/25.18 (Comp: ?, Cost: 1) evalabcbb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalabc12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_2 + 1, ar_7)) 31.04/25.18 31.04/25.18 (Comp: ?, Cost: 1) evalabc12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalabc13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 31.04/25.18 31.04/25.18 (Comp: ?, Cost: 1) evalabc13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_6, ar_3, ar_4, ar_5, ar_6, ar_7))
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