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Compl Integ Trans Syste 26843 pair #381744625
details
property
value
status
complete
benchmark
wise.c.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n082.star.cs.uiowa.edu
space
Flores-Montoya_16
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
2.30532717705 seconds
cpu usage
5.009490286
max memory
3.11803904E8
stage attributes
key
value
output-size
37024
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1).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, 107 ms] (2) BOUNDS(1, n^1) (3) Loat Proof [FINISHED, 624 ms] (4) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_wise_start(v__0, v__01, v_x, v_y) -> Com_1(eval_wise_bb0_in(v__0, v__01, v_x, v_y)) :|: TRUE eval_wise_bb0_in(v__0, v__01, v_x, v_y) -> Com_1(eval_wise_0(v__0, v__01, v_x, v_y)) :|: TRUE eval_wise_0(v__0, v__01, v_x, v_y) -> Com_1(eval_wise_1(v__0, v__01, v_x, v_y)) :|: TRUE eval_wise_1(v__0, v__01, v_x, v_y) -> Com_1(eval_wise_2(v__0, v__01, v_x, v_y)) :|: TRUE eval_wise_2(v__0, v__01, v_x, v_y) -> Com_1(eval_wise_bb2_in(v__0, v__01, v_x, v_y)) :|: v_x < 0 eval_wise_2(v__0, v__01, v_x, v_y) -> Com_1(eval_wise_bb2_in(v__0, v__01, v_x, v_y)) :|: v_y < 0 eval_wise_2(v__0, v__01, v_x, v_y) -> Com_1(eval_wise_bb1_in(v_x, v_y, v_x, v_y)) :|: v_x >= 0 && v_y >= 0 eval_wise_bb1_in(v__0, v__01, v_x, v_y) -> Com_1(eval_wise__critedge_in(v__0, v__01, v_x, v_y)) :|: v__0 - v__01 > 2 eval_wise_bb1_in(v__0, v__01, v_x, v_y) -> Com_1(eval_wise__critedge_in(v__0, v__01, v_x, v_y)) :|: v__01 - v__0 > 2 eval_wise_bb1_in(v__0, v__01, v_x, v_y) -> Com_1(eval_wise_bb2_in(v__0, v__01, v_x, v_y)) :|: v__0 - v__01 <= 2 && v__01 - v__0 <= 2 eval_wise__critedge_in(v__0, v__01, v_x, v_y) -> Com_1(eval_wise_bb1_in(v__0 + 1, v__01, v_x, v_y)) :|: v__0 < v__01 eval_wise__critedge_in(v__0, v__01, v_x, v_y) -> Com_1(eval_wise_bb1_in(v__0, v__01, v_x, v_y)) :|: v__0 < v__01 && v__0 >= v__01 eval_wise__critedge_in(v__0, v__01, v_x, v_y) -> Com_1(eval_wise_bb1_in(v__0 + 1, v__01 + 1, v_x, v_y)) :|: v__0 >= v__01 && v__0 < v__01 eval_wise__critedge_in(v__0, v__01, v_x, v_y) -> Com_1(eval_wise_bb1_in(v__0, v__01 + 1, v_x, v_y)) :|: v__0 >= v__01 eval_wise_bb2_in(v__0, v__01, v_x, v_y) -> Com_1(eval_wise_stop(v__0, v__01, v_x, v_y)) :|: TRUE The start-symbols are:[eval_wise_start_4] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 8*ar_0 + 8*ar_1 + 17) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalwisestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb0in(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalwisebb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise0(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalwise0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise1(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalwise1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwise2(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_1 + 1 ] (Comp: ?, Cost: 1) evalwise2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_0, ar_1)) [ ar_0 >= 0 /\ ar_1 >= 0 ] (Comp: ?, Cost: 1) evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisecritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 + 3 ] (Comp: ?, Cost: 1) evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisecritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 3 ] (Comp: ?, Cost: 1) evalwisebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 2 >= ar_2 /\ ar_2 + 2 >= ar_3 ] (Comp: ?, Cost: 1) evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_3 >= ar_2 + 1 ] (Comp: ?, Cost: 1) evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 1 /\ ar_2 >= ar_3 ] (Comp: ?, Cost: 1) evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2 + 1, ar_3 + 1)) [ ar_2 >= ar_3 /\ ar_3 >= ar_2 + 1 ] (Comp: ?, Cost: 1) evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2, ar_3 + 1)) [ ar_2 >= ar_3 ] (Comp: ?, Cost: 1) evalwisebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisestop(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transitions from problem 1: evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 1 /\ ar_2 >= ar_3 ] evalwisecritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalwisebb1in(ar_0, ar_1, ar_2 + 1, ar_3 + 1)) [ ar_2 >= ar_3 /\ ar_3 >= ar_2 + 1 ] We thus obtain the following problem:
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