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Compl C Integ Progr 85445 pair #381745664
details
property
value
status
complete
benchmark
Loopus2015_ex1.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n034.star.cs.uiowa.edu
space
Loopus
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
2.16971802711 seconds
cpu usage
3.328046598
max memory
3.09866496E8
stage attributes
key
value
output-size
123197
starexec-result
WORST_CASE(?, O(n^2))
output
/export/starexec/sandbox/solver/bin/starexec_run_c_complexity /export/starexec/sandbox/benchmark/theBenchmark.c /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^2)) proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). (0) CpxIntTrs (1) Koat Proof [FINISHED, 982 ms] (2) BOUNDS(1, n^2) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_Loopus2015_ex1_start(v_1, v_2, v_3, v_n, v_p.0, v_r.0, v_x.0) -> Com_1(eval_Loopus2015_ex1_bb0_in(v_1, v_2, v_3, v_n, v_p.0, v_r.0, v_x.0)) :|: TRUE eval_Loopus2015_ex1_bb0_in(v_1, v_2, v_3, v_n, v_p.0, v_r.0, v_x.0) -> Com_1(eval_Loopus2015_ex1_bb1_in(v_1, v_2, v_3, v_n, v_p.0, 0, v_n)) :|: TRUE eval_Loopus2015_ex1_bb1_in(v_1, v_2, v_3, v_n, v_p.0, v_r.0, v_x.0) -> Com_1(eval_Loopus2015_ex1_bb2_in(v_1, v_2, v_3, v_n, v_p.0, v_r.0, v_x.0)) :|: v_x.0 > 0 eval_Loopus2015_ex1_bb1_in(v_1, v_2, v_3, v_n, v_p.0, v_r.0, v_x.0) -> Com_1(eval_Loopus2015_ex1_bb5_in(v_1, v_2, v_3, v_n, v_p.0, v_r.0, v_x.0)) :|: v_x.0 <= 0 eval_Loopus2015_ex1_bb2_in(v_1, v_2, v_3, v_n, v_p.0, v_r.0, v_x.0) -> Com_1(eval_Loopus2015_ex1_2(v_x.0 - 1, v_r.0 + 1, v_3, v_n, v_p.0, v_r.0, v_x.0)) :|: TRUE eval_Loopus2015_ex1_2(v_1, v_2, v_3, v_n, v_p.0, v_r.0, v_x.0) -> Com_2(eval_nondet_start(v_1, v_2, v_3, v_n, v_p.0, v_r.0, v_x.0), eval_Loopus2015_ex1_3(v_1, v_2, nondef.0, v_n, v_p.0, v_r.0, v_x.0)) :|: TRUE eval_Loopus2015_ex1_3(v_1, v_2, v_3, v_n, v_p.0, v_r.0, v_x.0) -> Com_1(eval_Loopus2015_ex1_bb3_in(v_1, v_2, v_3, v_n, v_2, v_r.0, v_x.0)) :|: v_3 > 0 eval_Loopus2015_ex1_3(v_1, v_2, v_3, v_n, v_p.0, v_r.0, v_x.0) -> Com_1(eval_Loopus2015_ex1_bb1_in(v_1, v_2, v_3, v_n, v_p.0, v_2, v_1)) :|: v_3 <= 0 eval_Loopus2015_ex1_bb3_in(v_1, v_2, v_3, v_n, v_p.0, v_r.0, v_x.0) -> Com_1(eval_Loopus2015_ex1_bb4_in(v_1, v_2, v_3, v_n, v_p.0, v_r.0, v_x.0)) :|: v_p.0 > 0 eval_Loopus2015_ex1_bb3_in(v_1, v_2, v_3, v_n, v_p.0, v_r.0, v_x.0) -> Com_1(eval_Loopus2015_ex1_bb1_in(v_1, v_2, v_3, v_n, v_p.0, 0, v_1)) :|: v_p.0 <= 0 eval_Loopus2015_ex1_bb4_in(v_1, v_2, v_3, v_n, v_p.0, v_r.0, v_x.0) -> Com_1(eval_Loopus2015_ex1_bb3_in(v_1, v_2, v_3, v_n, v_p.0 - 1, v_r.0, v_x.0)) :|: TRUE eval_Loopus2015_ex1_bb5_in(v_1, v_2, v_3, v_n, v_p.0, v_r.0, v_x.0) -> Com_1(eval_Loopus2015_ex1_stop(v_1, v_2, v_3, v_n, v_p.0, v_r.0, v_x.0)) :|: TRUE The start-symbols are:[eval_Loopus2015_ex1_start_7] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 196*ar_2^2 + 70*ar_2 + 6) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalLoopus2015ex1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalLoopus2015ex1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: ?, Cost: 1) evalLoopus2015ex1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalLoopus2015ex1bb1in(0, ar_2, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: ?, Cost: 1) evalLoopus2015ex1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalLoopus2015ex1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 >= 1 ] (Comp: ?, Cost: 1) evalLoopus2015ex1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalLoopus2015ex1bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_1 ] (Comp: ?, Cost: 1) evalLoopus2015ex1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalLoopus2015ex12(ar_0, ar_1, ar_2, ar_1 - 1, ar_0 + 1, ar_5, ar_6, ar_7)) (Comp: ?, Cost: 1) evalLoopus2015ex120(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: ?, Cost: 1) evalLoopus2015ex121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalLoopus2015ex13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_6, ar_6, ar_7)) (Comp: ?, Cost: 1) evalLoopus2015ex12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_2(evalLoopus2015ex120(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, i, ar_7), evalLoopus2015ex121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, i, ar_7)) (Comp: ?, Cost: 1) evalLoopus2015ex13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalLoopus2015ex1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_4)) [ ar_5 >= 1 ] (Comp: ?, Cost: 1) evalLoopus2015ex13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalLoopus2015ex1bb1in(ar_4, ar_3, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_5 ] (Comp: ?, Cost: 1) evalLoopus2015ex1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalLoopus2015ex1bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_7 >= 1 ] (Comp: ?, Cost: 1) evalLoopus2015ex1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalLoopus2015ex1bb1in(0, ar_3, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_7 ] (Comp: ?, Cost: 1) evalLoopus2015ex1bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalLoopus2015ex1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7 - 1)) (Comp: ?, Cost: 1) evalLoopus2015ex1bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalLoopus2015ex1stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalLoopus2015ex1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 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) evalLoopus2015ex1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalLoopus2015ex1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: 1, Cost: 1) evalLoopus2015ex1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalLoopus2015ex1bb1in(0, ar_2, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: ?, Cost: 1) evalLoopus2015ex1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalLoopus2015ex1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 >= 1 ] (Comp: ?, Cost: 1) evalLoopus2015ex1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalLoopus2015ex1bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_1 ] (Comp: ?, Cost: 1) evalLoopus2015ex1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalLoopus2015ex12(ar_0, ar_1, ar_2, ar_1 - 1, ar_0 + 1, ar_5, ar_6, ar_7))
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