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Compl C Integ Progr 85445 pair #381745594
details
property
value
status
complete
benchmark
nestedLoop.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n090.star.cs.uiowa.edu
space
WTC_V2
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
46.8618550301 seconds
cpu usage
48.647253493
max memory
5.36236032E8
stage attributes
key
value
output-size
2092955
starexec-result
WORST_CASE(?, O(n^3))
output
/export/starexec/sandbox2/solver/bin/starexec_run_c_complexity /export/starexec/sandbox2/benchmark/theBenchmark.c /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^3)) proof of /export/starexec/sandbox2/output/output_files/bench.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^3). (0) CpxIntTrs (1) Koat Proof [FINISHED, 45.7 s] (2) BOUNDS(1, n^3) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_nestedLoop_start(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nestedLoop_bb0_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: TRUE eval_nestedLoop_bb0_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nestedLoop_bb1_in(v_11, v_12, v_3, v_7, v_N, 0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: 0 <= v_n && 0 <= v_m && 0 <= v_N eval_nestedLoop_bb0_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nestedLoop_bb7_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: 0 > v_n eval_nestedLoop_bb0_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nestedLoop_bb7_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: 0 > v_m eval_nestedLoop_bb0_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nestedLoop_bb7_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: 0 > v_N eval_nestedLoop_bb1_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nestedLoop_0(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: TRUE eval_nestedLoop_0(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_2(eval_nondet_start(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n), eval_nestedLoop_1(v_11, v_12, nondef.0, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: TRUE eval_nestedLoop_1(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nestedLoop_bb2_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.0, 0, v_k.0, v_m, v_n)) :|: v_3 > 0 && v_i.0 < v_n eval_nestedLoop_1(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nestedLoop_bb7_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: v_3 <= 0 eval_nestedLoop_1(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nestedLoop_bb7_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: v_i.0 >= v_n eval_nestedLoop_bb2_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nestedLoop_2(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: TRUE eval_nestedLoop_2(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_2(eval_nondet_start(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n), eval_nestedLoop_3(v_11, v_12, v_3, nondef.1, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: TRUE eval_nestedLoop_3(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nestedLoop_bb3_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: v_7 > 0 && v_j.0 < v_m eval_nestedLoop_3(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nestedLoop_bb6_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: v_7 <= 0 eval_nestedLoop_3(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nestedLoop_bb6_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: v_j.0 >= v_m eval_nestedLoop_bb3_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nestedLoop_bb4_in(v_j.0 + 1, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_i.1, v_m, v_n)) :|: TRUE eval_nestedLoop_bb4_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nestedLoop_6(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: TRUE eval_nestedLoop_6(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_2(eval_nondet_start(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n), eval_nestedLoop_7(v_11, nondef.2, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: TRUE eval_nestedLoop_7(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nestedLoop_bb5_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: v_12 > 0 && v_k.0 < v_N eval_nestedLoop_7(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nestedLoop_bb2_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_k.0, v_11, v_k.0, v_m, v_n)) :|: v_12 <= 0 eval_nestedLoop_7(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nestedLoop_bb2_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_k.0, v_11, v_k.0, v_m, v_n)) :|: v_k.0 >= v_N eval_nestedLoop_bb5_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nestedLoop_bb4_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0 + 1, v_m, v_n)) :|: TRUE eval_nestedLoop_bb6_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nestedLoop_bb1_in(v_11, v_12, v_3, v_7, v_N, v_i.1 + 1, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: TRUE eval_nestedLoop_bb7_in(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nestedLoop_stop(v_11, v_12, v_3, v_7, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: TRUE The start-symbols are:[eval_nestedLoop_start_11] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 7512*ar_0 + 18630*ar_0*ar_1 + 3035*ar_1 + 2880*ar_0*ar_1*ar_2 + 480*ar_1*ar_2 + 1152*ar_0*ar_2 + 2520*ar_0^2*ar_1 + 1008*ar_0^2 + 192*ar_2 + 1238) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalnestedLoopstart(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(evalnestedLoopbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) (Comp: ?, Cost: 1) evalnestedLoopbb0in(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(evalnestedLoopbb1in(ar_0, ar_1, ar_2, 0, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ ar_0 >= 0 /\ ar_1 >= 0 /\ ar_2 >= 0 ] (Comp: ?, Cost: 1) evalnestedLoopbb0in(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(evalnestedLoopbb7in(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 + 1 ] (Comp: ?, Cost: 1) evalnestedLoopbb0in(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(evalnestedLoopbb7in(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_1 + 1 ] (Comp: ?, Cost: 1) evalnestedLoopbb0in(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(evalnestedLoopbb7in(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_2 + 1 ] (Comp: ?, Cost: 1) evalnestedLoopbb1in(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(evalnestedLoop0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) (Comp: ?, Cost: 1) evalnestedLoop00(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(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) (Comp: ?, Cost: 1) evalnestedLoop01(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(evalnestedLoop1(ar_0, ar_1, ar_2, ar_3, ar_5, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) (Comp: ?, Cost: 1) evalnestedLoop0(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_2(evalnestedLoop00(ar_0, ar_1, ar_2, ar_3, ar_4, m, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11), evalnestedLoop01(ar_0, ar_1, ar_2, ar_3, ar_4, m, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) (Comp: ?, Cost: 1) evalnestedLoop1(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(evalnestedLoopbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_3, 0, ar_8, ar_9, ar_10, ar_11)) [ ar_4 >= 1 /\ ar_0 >= ar_3 + 1 ] (Comp: ?, Cost: 1) evalnestedLoop1(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(evalnestedLoopbb7in(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_4 ] (Comp: ?, Cost: 1) evalnestedLoop1(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(evalnestedLoopbb7in(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_3 >= ar_0 ] (Comp: ?, Cost: 1) evalnestedLoopbb2in(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(evalnestedLoop2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) (Comp: ?, Cost: 1) evalnestedLoop20(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(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) (Comp: ?, Cost: 1) evalnestedLoop21(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(evalnestedLoop3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_5, ar_9, ar_10, ar_11)) (Comp: ?, Cost: 1) evalnestedLoop2(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_2(evalnestedLoop20(ar_0, ar_1, ar_2, ar_3, ar_4, m, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11), evalnestedLoop21(ar_0, ar_1, ar_2, ar_3, ar_4, m, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) (Comp: ?, Cost: 1) evalnestedLoop3(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(evalnestedLoopbb3in(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_8 >= 1 /\ ar_1 >= ar_7 + 1 ] (Comp: ?, Cost: 1) evalnestedLoop3(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(evalnestedLoopbb6in(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_8 ] (Comp: ?, Cost: 1) evalnestedLoop3(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(evalnestedLoopbb6in(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_7 >= ar_1 ]
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