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Compl Integ Trans Syste 26843 pair #381744573
details
property
value
status
complete
benchmark
ax.c.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n070.star.cs.uiowa.edu
space
Flores-Montoya_16
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
2.39504098892 seconds
cpu usage
5.311906689
max memory
3.2770048E8
stage attributes
key
value
output-size
48473
starexec-result
WORST_CASE(Omega(n^2), O(n^2))
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^2), O(n^2)) 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2). (0) CpxIntTrs (1) Koat Proof [FINISHED, 231 ms] (2) BOUNDS(1, n^2) (3) Loat Proof [FINISHED, 710 ms] (4) BOUNDS(n^2, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_ax_start(v__0, v__01, v_3, v_i, v_j, v_n) -> Com_1(eval_ax_bb0_in(v__0, v__01, v_3, v_i, v_j, v_n)) :|: TRUE eval_ax_bb0_in(v__0, v__01, v_3, v_i, v_j, v_n) -> Com_1(eval_ax_0(v__0, v__01, v_3, v_i, v_j, v_n)) :|: TRUE eval_ax_0(v__0, v__01, v_3, v_i, v_j, v_n) -> Com_1(eval_ax_1(v__0, v__01, v_3, v_i, v_j, v_n)) :|: TRUE eval_ax_1(v__0, v__01, v_3, v_i, v_j, v_n) -> Com_1(eval_ax_2(v__0, v__01, v_3, v_i, v_j, v_n)) :|: TRUE eval_ax_2(v__0, v__01, v_3, v_i, v_j, v_n) -> Com_1(eval_ax_3(v__0, v__01, v_3, v_i, v_j, v_n)) :|: TRUE eval_ax_3(v__0, v__01, v_3, v_i, v_j, v_n) -> Com_1(eval_ax_4(v__0, v__01, v_3, v_i, v_j, v_n)) :|: TRUE eval_ax_4(v__0, v__01, v_3, v_i, v_j, v_n) -> Com_1(eval_ax_5(v__0, v__01, v_3, v_i, v_j, v_n)) :|: TRUE eval_ax_5(v__0, v__01, v_3, v_i, v_j, v_n) -> Com_1(eval_ax_6(v__0, v__01, v_3, v_i, v_j, v_n)) :|: TRUE eval_ax_6(v__0, v__01, v_3, v_i, v_j, v_n) -> Com_1(eval_ax_bb1_in(0, v__01, v_3, v_i, v_j, v_n)) :|: TRUE eval_ax_bb1_in(v__0, v__01, v_3, v_i, v_j, v_n) -> Com_1(eval_ax_bb2_in(v__0, 0, v_3, v_i, v_j, v_n)) :|: TRUE eval_ax_bb2_in(v__0, v__01, v_3, v_i, v_j, v_n) -> Com_1(eval_ax_bb3_in(v__0, v__01, v_3, v_i, v_j, v_n)) :|: v__01 < v_n - 1 eval_ax_bb2_in(v__0, v__01, v_3, v_i, v_j, v_n) -> Com_1(eval_ax_bb4_in(v__0, v__01, v_3, v_i, v_j, v_n)) :|: v__01 >= v_n - 1 eval_ax_bb3_in(v__0, v__01, v_3, v_i, v_j, v_n) -> Com_1(eval_ax_bb2_in(v__0, v__01 + 1, v_3, v_i, v_j, v_n)) :|: TRUE eval_ax_bb4_in(v__0, v__01, v_3, v_i, v_j, v_n) -> Com_1(eval_ax_12(v__0, v__01, v__0 + 1, v_i, v_j, v_n)) :|: TRUE eval_ax_12(v__0, v__01, v_3, v_i, v_j, v_n) -> Com_1(eval_ax_13(v__0, v__01, v_3, v_i, v_j, v_n)) :|: TRUE eval_ax_13(v__0, v__01, v_3, v_i, v_j, v_n) -> Com_1(eval_ax_bb1_in(v_3, v__01, v_3, v_i, v_j, v_n)) :|: v__01 >= v_n - 1 && v_3 < v_n - 1 eval_ax_13(v__0, v__01, v_3, v_i, v_j, v_n) -> Com_1(eval_ax_bb5_in(v__0, v__01, v_3, v_i, v_j, v_n)) :|: v__01 < v_n - 1 eval_ax_13(v__0, v__01, v_3, v_i, v_j, v_n) -> Com_1(eval_ax_bb5_in(v__0, v__01, v_3, v_i, v_j, v_n)) :|: v_3 >= v_n - 1 eval_ax_bb5_in(v__0, v__01, v_3, v_i, v_j, v_n) -> Com_1(eval_ax_stop(v__0, v__01, v_3, v_i, v_j, v_n)) :|: TRUE The start-symbols are:[eval_ax_start_6] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 15*ar_2 + 2*ar_2^2 + 27) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalaxstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb0in(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalaxbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax0(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalax0(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax1(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalax1(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax2(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalax2(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax3(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalax3(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax4(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalax4(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax5(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalax5(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax6(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalax6(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb1in(0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalaxbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb2in(ar_0, 0, ar_2, ar_3)) (Comp: ?, Cost: 1) evalaxbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 2 ] (Comp: ?, Cost: 1) evalaxbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 + 1 >= ar_2 ] (Comp: ?, Cost: 1) evalaxbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb2in(ar_0, ar_1 + 1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalaxbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax12(ar_0, ar_1, ar_2, ar_0 + 1)) (Comp: ?, Cost: 1) evalax12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalax13(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb1in(ar_3, ar_1, ar_2, ar_3)) [ ar_1 + 1 >= ar_2 /\ ar_2 >= ar_3 + 2 ] (Comp: ?, Cost: 1) evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 2 ] (Comp: ?, Cost: 1) evalax13(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxbb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 + 1 >= ar_2 ] (Comp: ?, Cost: 1) evalaxbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxstop(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalaxstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] start location: koat_start
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