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Compl C Integ Progr 85445 pair #381745669
details
property
value
status
complete
benchmark
textbook_ex3.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n056.star.cs.uiowa.edu
space
ABC
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.47788000107 seconds
cpu usage
2.464596676
max memory
2.50232832E8
stage attributes
key
value
output-size
105078
starexec-result
WORST_CASE(?, O(n^6))
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^6)) 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^6). (0) CpxIntTrs (1) Koat Proof [FINISHED, 281 ms] (2) BOUNDS(1, n^6) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_textbook_ex3_start(v_i.0, v_j.0, v_k.0, v_l.0, v_m) -> Com_1(eval_textbook_ex3_bb0_in(v_i.0, v_j.0, v_k.0, v_l.0, v_m)) :|: TRUE eval_textbook_ex3_bb0_in(v_i.0, v_j.0, v_k.0, v_l.0, v_m) -> Com_1(eval_textbook_ex3_bb1_in(1, v_j.0, v_k.0, v_l.0, v_m)) :|: TRUE eval_textbook_ex3_bb1_in(v_i.0, v_j.0, v_k.0, v_l.0, v_m) -> Com_1(eval_textbook_ex3_bb2_in(v_i.0, 1, v_k.0, v_l.0, v_m)) :|: v_i.0 <= v_m eval_textbook_ex3_bb1_in(v_i.0, v_j.0, v_k.0, v_l.0, v_m) -> Com_1(eval_textbook_ex3_bb8_in(v_i.0, v_j.0, v_k.0, v_l.0, v_m)) :|: v_i.0 > v_m eval_textbook_ex3_bb2_in(v_i.0, v_j.0, v_k.0, v_l.0, v_m) -> Com_1(eval_textbook_ex3_bb3_in(v_i.0, v_j.0, v_i.0 + 1, v_l.0, v_m)) :|: v_j.0 <= v_i.0 eval_textbook_ex3_bb2_in(v_i.0, v_j.0, v_k.0, v_l.0, v_m) -> Com_1(eval_textbook_ex3_bb1_in(v_i.0 + 1, v_j.0, v_k.0, v_l.0, v_m)) :|: v_j.0 > v_i.0 eval_textbook_ex3_bb3_in(v_i.0, v_j.0, v_k.0, v_l.0, v_m) -> Com_1(eval_textbook_ex3_bb4_in(v_i.0, v_j.0, v_k.0, 1, v_m)) :|: v_k.0 <= v_m eval_textbook_ex3_bb3_in(v_i.0, v_j.0, v_k.0, v_l.0, v_m) -> Com_1(eval_textbook_ex3_bb7_in(v_i.0, v_j.0, v_k.0, v_l.0, v_m)) :|: v_k.0 > v_m eval_textbook_ex3_bb4_in(v_i.0, v_j.0, v_k.0, v_l.0, v_m) -> Com_1(eval_textbook_ex3_bb5_in(v_i.0, v_j.0, v_k.0, v_l.0, v_m)) :|: v_l.0 <= v_k.0 eval_textbook_ex3_bb4_in(v_i.0, v_j.0, v_k.0, v_l.0, v_m) -> Com_1(eval_textbook_ex3_bb6_in(v_i.0, v_j.0, v_k.0, v_l.0, v_m)) :|: v_l.0 > v_k.0 eval_textbook_ex3_bb5_in(v_i.0, v_j.0, v_k.0, v_l.0, v_m) -> Com_1(eval_textbook_ex3_bb4_in(v_i.0, v_j.0, v_k.0, v_l.0 + 1, v_m)) :|: TRUE eval_textbook_ex3_bb6_in(v_i.0, v_j.0, v_k.0, v_l.0, v_m) -> Com_1(eval_textbook_ex3_bb3_in(v_i.0, v_j.0, v_k.0 + 1, v_l.0, v_m)) :|: TRUE eval_textbook_ex3_bb7_in(v_i.0, v_j.0, v_k.0, v_l.0, v_m) -> Com_1(eval_textbook_ex3_bb2_in(v_i.0, v_j.0 + 1, v_k.0, v_l.0, v_m)) :|: TRUE eval_textbook_ex3_bb8_in(v_i.0, v_j.0, v_k.0, v_l.0, v_m) -> Com_1(eval_textbook_ex3_stop(v_i.0, v_j.0, v_k.0, v_l.0, v_m)) :|: TRUE The start-symbols are:[eval_textbook_ex3_start_5] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 134*ar_1 + 464*ar_1^2 + 692*ar_1^3 + 472*ar_1^4 + 16*ar_1^6 + 144*ar_1^5 + 6) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evaltextbookex3start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evaltextbookex3bb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: ?, Cost: 1) evaltextbookex3bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evaltextbookex3bb1in(1, ar_1, ar_2, ar_3, ar_4)) (Comp: ?, Cost: 1) evaltextbookex3bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evaltextbookex3bb2in(ar_0, ar_1, 1, ar_3, ar_4)) [ ar_1 >= ar_0 ] (Comp: ?, Cost: 1) evaltextbookex3bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evaltextbookex3bb8in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 + 1 ] (Comp: ?, Cost: 1) evaltextbookex3bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evaltextbookex3bb3in(ar_0, ar_1, ar_2, ar_0 + 1, ar_4)) [ ar_0 >= ar_2 ] (Comp: ?, Cost: 1) evaltextbookex3bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evaltextbookex3bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evaltextbookex3bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evaltextbookex3bb4in(ar_0, ar_1, ar_2, ar_3, 1)) [ ar_1 >= ar_3 ] (Comp: ?, Cost: 1) evaltextbookex3bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evaltextbookex3bb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 ] (Comp: ?, Cost: 1) evaltextbookex3bb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evaltextbookex3bb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ] (Comp: ?, Cost: 1) evaltextbookex3bb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evaltextbookex3bb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ] (Comp: ?, Cost: 1) evaltextbookex3bb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evaltextbookex3bb4in(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) (Comp: ?, Cost: 1) evaltextbookex3bb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evaltextbookex3bb3in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) (Comp: ?, Cost: 1) evaltextbookex3bb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evaltextbookex3bb2in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) (Comp: ?, Cost: 1) evaltextbookex3bb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evaltextbookex3stop(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evaltextbookex3start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 1 produces the following problem: 2: T: (Comp: 1, Cost: 1) evaltextbookex3start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evaltextbookex3bb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) evaltextbookex3bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evaltextbookex3bb1in(1, ar_1, ar_2, ar_3, ar_4)) (Comp: ?, Cost: 1) evaltextbookex3bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evaltextbookex3bb2in(ar_0, ar_1, 1, ar_3, ar_4)) [ ar_1 >= ar_0 ] (Comp: ?, Cost: 1) evaltextbookex3bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evaltextbookex3bb8in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 + 1 ]
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