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Compl Integ Trans Syste 26843 pair #381744745
details
property
value
status
complete
benchmark
t47.c.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n087.star.cs.uiowa.edu
space
Flores-Montoya_16
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
2.18374800682 seconds
cpu usage
4.69193058
max memory
2.96124416E8
stage attributes
key
value
output-size
21034
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 136 ms] (2) BOUNDS(1, n^1) (3) Loat Proof [FINISHED, 628 ms] (4) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_start_start(v__0, v_flag_0, v_n) -> Com_1(eval_start_bb0_in(v__0, v_flag_0, v_n)) :|: TRUE eval_start_bb0_in(v__0, v_flag_0, v_n) -> Com_1(eval_start_0(v__0, v_flag_0, v_n)) :|: TRUE eval_start_0(v__0, v_flag_0, v_n) -> Com_1(eval_start_1(v__0, v_flag_0, v_n)) :|: TRUE eval_start_1(v__0, v_flag_0, v_n) -> Com_1(eval_start_2(v__0, v_flag_0, v_n)) :|: TRUE eval_start_2(v__0, v_flag_0, v_n) -> Com_1(eval_start_3(v__0, v_flag_0, v_n)) :|: TRUE eval_start_3(v__0, v_flag_0, v_n) -> Com_1(eval_start_4(v__0, v_flag_0, v_n)) :|: TRUE eval_start_4(v__0, v_flag_0, v_n) -> Com_1(eval_start_5(v__0, v_flag_0, v_n)) :|: TRUE eval_start_5(v__0, v_flag_0, v_n) -> Com_1(eval_start_bb1_in(v_n, 1, v_n)) :|: TRUE eval_start_bb1_in(v__0, v_flag_0, v_n) -> Com_1(eval_start_bb2_in(v__0, v_flag_0, v_n)) :|: v_flag_0 > 0 eval_start_bb1_in(v__0, v_flag_0, v_n) -> Com_1(eval_start_bb3_in(v__0, v_flag_0, v_n)) :|: v_flag_0 <= 0 eval_start_bb2_in(v__0, v_flag_0, v_n) -> Com_1(eval_start_bb1_in(v__0 - 1, 1, v_n)) :|: v__0 > 0 eval_start_bb2_in(v__0, v_flag_0, v_n) -> Com_1(eval_start_bb1_in(v__0, 1, v_n)) :|: v__0 > 0 && v__0 <= 0 eval_start_bb2_in(v__0, v_flag_0, v_n) -> Com_1(eval_start_bb1_in(v__0 - 1, 0, v_n)) :|: v__0 <= 0 && v__0 > 0 eval_start_bb2_in(v__0, v_flag_0, v_n) -> Com_1(eval_start_bb1_in(v__0, 0, v_n)) :|: v__0 <= 0 eval_start_bb3_in(v__0, v_flag_0, v_n) -> Com_1(eval_start_stop(v__0, v_flag_0, v_n)) :|: TRUE The start-symbols are:[eval_start_start_3] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 2*ar_1 + 14) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalstartstart(ar_0, ar_1, ar_2) -> Com_1(evalstartbb0in(ar_0, ar_1, ar_2)) (Comp: ?, Cost: 1) evalstartbb0in(ar_0, ar_1, ar_2) -> Com_1(evalstart0(ar_0, ar_1, ar_2)) (Comp: ?, Cost: 1) evalstart0(ar_0, ar_1, ar_2) -> Com_1(evalstart1(ar_0, ar_1, ar_2)) (Comp: ?, Cost: 1) evalstart1(ar_0, ar_1, ar_2) -> Com_1(evalstart2(ar_0, ar_1, ar_2)) (Comp: ?, Cost: 1) evalstart2(ar_0, ar_1, ar_2) -> Com_1(evalstart3(ar_0, ar_1, ar_2)) (Comp: ?, Cost: 1) evalstart3(ar_0, ar_1, ar_2) -> Com_1(evalstart4(ar_0, ar_1, ar_2)) (Comp: ?, Cost: 1) evalstart4(ar_0, ar_1, ar_2) -> Com_1(evalstart5(ar_0, ar_1, ar_2)) (Comp: ?, Cost: 1) evalstart5(ar_0, ar_1, ar_2) -> Com_1(evalstartbb1in(ar_1, ar_1, 1)) (Comp: ?, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2) -> Com_1(evalstartbb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 1 ] (Comp: ?, Cost: 1) evalstartbb1in(ar_0, ar_1, ar_2) -> Com_1(evalstartbb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ] (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2) -> Com_1(evalstartbb1in(ar_0 - 1, ar_1, 1)) [ ar_0 >= 1 ] (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2) -> Com_1(evalstartbb1in(ar_0, ar_1, 1)) [ ar_0 >= 1 /\ 0 >= ar_0 ] (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2) -> Com_1(evalstartbb1in(ar_0 - 1, ar_1, 0)) [ 0 >= ar_0 /\ ar_0 >= 1 ] (Comp: ?, Cost: 1) evalstartbb2in(ar_0, ar_1, ar_2) -> Com_1(evalstartbb1in(ar_0, ar_1, 0)) [ 0 >= ar_0 ] (Comp: ?, Cost: 1) evalstartbb3in(ar_0, ar_1, ar_2) -> Com_1(evalstartstop(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalstartstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transitions from problem 1: evalstartbb2in(ar_0, ar_1, ar_2) -> Com_1(evalstartbb1in(ar_0, ar_1, 1)) [ ar_0 >= 1 /\ 0 >= ar_0 ] evalstartbb2in(ar_0, ar_1, ar_2) -> Com_1(evalstartbb1in(ar_0 - 1, ar_1, 0)) [ 0 >= ar_0 /\ ar_0 >= 1 ] We thus obtain the following problem:
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