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Complexity_ITS 2019-03-21 04.46 pair #429989984
details
property
value
status
complete
benchmark
Loopus2014_ex1.c.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n141.star.cs.uiowa.edu
space
Flores-Montoya_16
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
12.6312 seconds
cpu usage
20.0566
user time
19.2163
system time
0.840309
max virtual memory
1.9038168E7
max residence set size
349108.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), O(n^2))
output
19.90/7.43 WORST_CASE(Omega(n^2), O(n^2)) 19.90/7.44 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 19.90/7.44 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 19.90/7.44 19.90/7.44 19.90/7.44 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2). 19.90/7.44 19.90/7.44 (0) CpxIntTrs 19.90/7.44 (1) Koat Proof [FINISHED, 5570 ms] 19.90/7.44 (2) BOUNDS(1, n^2) 19.90/7.44 (3) Loat Proof [FINISHED, 4590 ms] 19.90/7.44 (4) BOUNDS(n^2, INF) 19.90/7.44 19.90/7.44 19.90/7.44 ---------------------------------------- 19.90/7.44 19.90/7.44 (0) 19.90/7.44 Obligation: 19.90/7.44 Complexity Int TRS consisting of the following rules: 19.90/7.44 eval_start_start(v_4, 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_start_bb0_in(v_4, 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 19.90/7.44 eval_start_bb0_in(v_4, 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_start_0(v_4, 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 19.90/7.44 eval_start_0(v_4, 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_start_1(v_4, 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 19.90/7.44 eval_start_1(v_4, 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_start_2(v_4, 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 19.90/7.44 eval_start_2(v_4, 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_start_3(v_4, 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 19.90/7.44 eval_start_3(v_4, 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_start_4(v_4, 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 19.90/7.44 eval_start_4(v_4, 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_start_5(v_4, 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 19.90/7.44 eval_start_5(v_4, 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_start_6(v_4, 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 19.90/7.44 eval_start_6(v_4, 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_start_7(v_4, 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 19.90/7.44 eval_start_7(v_4, 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_start_8(v_4, 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 19.90/7.44 eval_start_8(v_4, 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_start_9(v_4, 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 19.90/7.44 eval_start_9(v_4, 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_start_10(v_4, 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 19.90/7.44 eval_start_10(v_4, 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_start_bb1_in(v_4, 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 19.90/7.44 eval_start_bb1_in(v_4, 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_start_bb2_in(v_4, 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 19.90/7.44 eval_start_bb1_in(v_4, 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_start_bb10_in(v_4, 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 19.90/7.44 eval_start_bb2_in(v_4, 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_start_bb3_in(v_4, 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 19.90/7.44 eval_start_bb3_in(v_4, 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_start_bb4_in(v_4, 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 19.90/7.44 eval_start_bb3_in(v_4, 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_start_bb1_in(v_4, 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 19.90/7.44 eval_start_bb4_in(v_4, 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_start_15(v_b_1 - 1, 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 19.90/7.44 eval_start_15(v_4, 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_start_16(v_4, 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 19.90/7.44 eval_start_16(v_4, 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_start_bb5_in(v_4, v_8, v_a_0, v_a_1, v_a_1, v_a_3, v_b_0, v_b_1, v_4, v_b_3, v_n - 1, v_n)) :|: TRUE 19.90/7.44 eval_start_bb5_in(v_4, 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_start_bb6_in(v_4, 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 19.90/7.44 eval_start_bb5_in(v_4, 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_start_bb3_in(v_4, 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 19.90/7.44 eval_start_bb6_in(v_4, 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_start_bb7_in(v_4, 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 19.90/7.44 eval_start_bb6_in(v_4, 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_start_bb9_in(v_4, 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 19.90/7.44 eval_start_bb7_in(v_4, 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_start_18(v_4, 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 19.90/7.44 eval_start_18(v_4, 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_start_19(v_4, 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 19.90/7.44 eval_start_19(v_4, 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_start_bb8_in(v_4, 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 19.90/7.44 eval_start_19(v_4, 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_start_bb9_in(v_4, 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 19.90/7.44 eval_start_bb8_in(v_4, 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_start_bb9_in(v_4, 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 19.90/7.44 eval_start_bb9_in(v_4, 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_start_bb5_in(v_4, 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 19.90/7.44 eval_start_bb10_in(v_4, 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_start_stop(v_4, 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 19.90/7.44 19.90/7.44 The start-symbols are:[eval_start_start_12] 19.90/7.44 19.90/7.44 19.90/7.44 ---------------------------------------- 19.90/7.44 19.90/7.44 (1) Koat Proof (FINISHED) 19.90/7.44 YES(?, 3276*ar_1^2 + 918921*ar_1 + 17) 19.90/7.44 19.90/7.44 19.90/7.44 19.90/7.44 Initial complexity problem: 19.90/7.44 19.90/7.44 1: T: 19.90/7.44 19.90/7.44 (Comp: ?, Cost: 1) evalstartstart(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(evalstartbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) 19.90/7.44 19.90/7.44 (Comp: ?, Cost: 1) evalstartbb0in(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(evalstart0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) 19.90/7.44 19.90/7.44 (Comp: ?, Cost: 1) evalstart0(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(evalstart1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) 19.90/7.44 19.90/7.44 (Comp: ?, Cost: 1) evalstart1(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(evalstart2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) 19.90/7.44 19.90/7.44 (Comp: ?, Cost: 1) evalstart2(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(evalstart3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) 19.90/7.44 19.90/7.44 (Comp: ?, Cost: 1) evalstart3(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(evalstart4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) 19.90/7.44 19.90/7.44 (Comp: ?, Cost: 1) evalstart4(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(evalstart5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) 19.90/7.44 19.90/7.44 (Comp: ?, Cost: 1) evalstart5(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(evalstart6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) 19.90/7.44 19.90/7.44 (Comp: ?, Cost: 1) evalstart6(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(evalstart7(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) 19.90/7.44 19.90/7.44 (Comp: ?, Cost: 1) evalstart7(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(evalstart8(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) 19.90/7.44 19.90/7.44 (Comp: ?, Cost: 1) evalstart8(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(evalstart9(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) 19.90/7.44 19.90/7.44 (Comp: ?, Cost: 1) evalstart9(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(evalstart10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) 19.90/7.44 19.90/7.44 (Comp: ?, Cost: 1) evalstart10(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(evalstartbb1in(ar_1, ar_1, 0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) 19.90/7.44 19.90/7.44 (Comp: ?, Cost: 1) evalstartbb1in(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(evalstartbb2in(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 ] 19.90/7.44 19.90/7.44 (Comp: ?, Cost: 1) evalstartbb1in(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(evalstartbb10in(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 ] 19.90/7.44 19.90/7.44 (Comp: ?, Cost: 1) evalstartbb2in(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(evalstartbb3in(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)) 19.90/7.44 19.90/7.44 (Comp: ?, Cost: 1) evalstartbb3in(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(evalstartbb4in(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 ] 19.90/7.44
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