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Compl C Integ Progr 85445 pair #381745811
details
property
value
status
complete
benchmark
speed_popl10_fig2_2.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n048.star.cs.uiowa.edu
space
C4B_examples
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.44010877609 seconds
cpu usage
2.537767743
max memory
2.48201216E8
stage attributes
key
value
output-size
17859
starexec-result
WORST_CASE(?, O(n^1))
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^1)) 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 179 ms] (2) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_speed_popl10_fig2_2_start(v_.0, v_.01, v_n, v_x, v_z) -> Com_1(eval_speed_popl10_fig2_2_bb0_in(v_.0, v_.01, v_n, v_x, v_z)) :|: TRUE eval_speed_popl10_fig2_2_bb0_in(v_.0, v_.01, v_n, v_x, v_z) -> Com_1(eval_speed_popl10_fig2_2_bb1_in(v_x, v_z, v_n, v_x, v_z)) :|: TRUE eval_speed_popl10_fig2_2_bb1_in(v_.0, v_.01, v_n, v_x, v_z) -> Com_1(eval_speed_popl10_fig2_2_bb2_in(v_.0, v_.01, v_n, v_x, v_z)) :|: v_.0 < v_n eval_speed_popl10_fig2_2_bb1_in(v_.0, v_.01, v_n, v_x, v_z) -> Com_1(eval_speed_popl10_fig2_2_bb3_in(v_.0, v_.01, v_n, v_x, v_z)) :|: v_.0 >= v_n eval_speed_popl10_fig2_2_bb2_in(v_.0, v_.01, v_n, v_x, v_z) -> Com_1(eval_speed_popl10_fig2_2_bb1_in(v_.0 + 1, v_.01, v_n, v_x, v_z)) :|: v_.01 > v_.0 eval_speed_popl10_fig2_2_bb2_in(v_.0, v_.01, v_n, v_x, v_z) -> Com_1(eval_speed_popl10_fig2_2_bb1_in(v_.0, v_.01, v_n, v_x, v_z)) :|: v_.01 > v_.0 && v_.01 <= v_.0 eval_speed_popl10_fig2_2_bb2_in(v_.0, v_.01, v_n, v_x, v_z) -> Com_1(eval_speed_popl10_fig2_2_bb1_in(v_.0 + 1, v_.01 + 1, v_n, v_x, v_z)) :|: v_.01 <= v_.0 && v_.01 > v_.0 eval_speed_popl10_fig2_2_bb2_in(v_.0, v_.01, v_n, v_x, v_z) -> Com_1(eval_speed_popl10_fig2_2_bb1_in(v_.0, v_.01 + 1, v_n, v_x, v_z)) :|: v_.01 <= v_.0 eval_speed_popl10_fig2_2_bb3_in(v_.0, v_.01, v_n, v_x, v_z) -> Com_1(eval_speed_popl10_fig2_2_stop(v_.0, v_.01, v_n, v_x, v_z)) :|: TRUE The start-symbols are:[eval_speed_popl10_fig2_2_start_5] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 2*ar_3 + 4*ar_4 + 2*ar_1 + 7) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalspeedpopl10fig22start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10fig22bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb1in(ar_1, ar_1, ar_3, ar_3, ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10fig22bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalspeedpopl10fig22bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_4 ] (Comp: ?, Cost: 1) evalspeedpopl10fig22bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalspeedpopl10fig22bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 + 1 /\ ar_0 >= ar_2 ] (Comp: ?, Cost: 1) evalspeedpopl10fig22bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb1in(ar_0 + 1, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_0 >= ar_2 /\ ar_2 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalspeedpopl10fig22bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_0 >= ar_2 ] (Comp: ?, Cost: 1) evalspeedpopl10fig22bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22stop(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(evalspeedpopl10fig22start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transitions from problem 1: evalspeedpopl10fig22bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 + 1 /\ ar_0 >= ar_2 ] evalspeedpopl10fig22bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb1in(ar_0 + 1, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_0 >= ar_2 /\ ar_2 >= ar_0 + 1 ] We thus obtain the following problem: 2: T: (Comp: ?, Cost: 1) evalspeedpopl10fig22bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22stop(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10fig22bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_0 >= ar_2 ] (Comp: ?, Cost: 1) evalspeedpopl10fig22bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalspeedpopl10fig22bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_4 ] (Comp: ?, Cost: 1) evalspeedpopl10fig22bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalspeedpopl10fig22bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb1in(ar_1, ar_1, ar_3, ar_3, ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10fig22start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10fig22bb0in(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(evalspeedpopl10fig22start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] start location: koat_start
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