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Compl Integ Trans Syste 26843 pair #381744897
details
property
value
status
complete
benchmark
loops.c.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n069.star.cs.uiowa.edu
space
Flores-Montoya_16
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
3.29869914055 seconds
cpu usage
6.589519141
max memory
3.52915456E8
stage attributes
key
value
output-size
40789
starexec-result
WORST_CASE(?, 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(?, 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). (0) CpxIntTrs (1) Koat Proof [FINISHED, 339 ms] (2) BOUNDS(1, n^2) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_loops_start(v_n, v_x_0, v_y_0) -> Com_1(eval_loops_bb0_in(v_n, v_x_0, v_y_0)) :|: TRUE eval_loops_bb0_in(v_n, v_x_0, v_y_0) -> Com_1(eval_loops_0(v_n, v_x_0, v_y_0)) :|: TRUE eval_loops_0(v_n, v_x_0, v_y_0) -> Com_1(eval_loops_1(v_n, v_x_0, v_y_0)) :|: TRUE eval_loops_1(v_n, v_x_0, v_y_0) -> Com_1(eval_loops_2(v_n, v_x_0, v_y_0)) :|: TRUE eval_loops_2(v_n, v_x_0, v_y_0) -> Com_1(eval_loops_bb1_in(v_n, v_n, v_y_0)) :|: v_n >= 0 eval_loops_2(v_n, v_x_0, v_y_0) -> Com_1(eval_loops_bb6_in(v_n, v_x_0, v_y_0)) :|: v_n < 0 eval_loops_bb1_in(v_n, v_x_0, v_y_0) -> Com_1(eval_loops_bb2_in(v_n, v_x_0, v_y_0)) :|: v_x_0 >= 0 eval_loops_bb1_in(v_n, v_x_0, v_y_0) -> Com_1(eval_loops_bb6_in(v_n, v_x_0, v_y_0)) :|: v_x_0 < 0 eval_loops_bb2_in(v_n, v_x_0, v_y_0) -> Com_1(eval_loops_bb3_in(v_n, v_x_0, 1)) :|: 1 < v_x_0 eval_loops_bb2_in(v_n, v_x_0, v_y_0) -> Com_1(eval_loops_bb5_in(v_n, v_x_0, v_y_0)) :|: 1 >= v_x_0 eval_loops_bb3_in(v_n, v_x_0, v_y_0) -> Com_1(eval_loops_bb4_in(v_n, v_x_0, v_y_0)) :|: v_y_0 < v_x_0 eval_loops_bb3_in(v_n, v_x_0, v_y_0) -> Com_1(eval_loops_bb5_in(v_n, v_x_0, v_y_0)) :|: v_y_0 >= v_x_0 eval_loops_bb4_in(v_n, v_x_0, v_y_0) -> Com_1(eval_loops_bb3_in(v_n, v_x_0, 2 * v_y_0)) :|: TRUE eval_loops_bb5_in(v_n, v_x_0, v_y_0) -> Com_1(eval_loops_bb1_in(v_n, v_x_0 - 1, v_y_0)) :|: TRUE eval_loops_bb6_in(v_n, v_x_0, v_y_0) -> Com_1(eval_loops_stop(v_n, v_x_0, v_y_0)) :|: TRUE The start-symbols are:[eval_loops_start_3] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 50*ar_0 + 8*ar_0^2 + 52) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalloopsstart(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb0in(ar_0, ar_1, ar_2)) (Comp: ?, Cost: 1) evalloopsbb0in(ar_0, ar_1, ar_2) -> Com_1(evalloops0(ar_0, ar_1, ar_2)) (Comp: ?, Cost: 1) evalloops0(ar_0, ar_1, ar_2) -> Com_1(evalloops1(ar_0, ar_1, ar_2)) (Comp: ?, Cost: 1) evalloops1(ar_0, ar_1, ar_2) -> Com_1(evalloops2(ar_0, ar_1, ar_2)) (Comp: ?, Cost: 1) evalloops2(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 0 ] (Comp: ?, Cost: 1) evalloops2(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 0 ] (Comp: ?, Cost: 1) evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 + 1 ] (Comp: ?, Cost: 1) evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 1)) [ ar_1 >= 2 ] (Comp: ?, Cost: 1) evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ 1 >= ar_1 ] (Comp: ?, Cost: 1) evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb4in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ] (Comp: ?, Cost: 1) evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ] (Comp: ?, Cost: 1) evalloopsbb4in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 2*ar_2)) (Comp: ?, Cost: 1) evalloopsbb5in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb1in(ar_0, ar_1 - 1, ar_2)) (Comp: ?, Cost: 1) evalloopsbb6in(ar_0, ar_1, ar_2) -> Com_1(evalloopsstop(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalloopsstart(ar_0, ar_1, ar_2)) [ 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) evalloopsstart(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb0in(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 1) evalloopsbb0in(ar_0, ar_1, ar_2) -> Com_1(evalloops0(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 1) evalloops0(ar_0, ar_1, ar_2) -> Com_1(evalloops1(ar_0, ar_1, ar_2))
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