Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Complexity_C_Integer 2019-03-21 04.38 pair #429989620
details
property
value
status
complete
benchmark
loops.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n034.star.cs.uiowa.edu
space
WTC_V2
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
2.29072 seconds
cpu usage
2.55918
user time
2.33796
system time
0.221223
max virtual memory
1.846756E7
max residence set size
181116.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^2))
output
2.39/1.57 WORST_CASE(?, O(n^2)) 2.51/1.98 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.51/1.98 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.51/1.98 2.51/1.98 2.51/1.98 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 2.51/1.98 2.51/1.98 (0) CpxIntTrs 2.51/1.98 (1) Koat Proof [FINISHED, 370 ms] 2.51/1.98 (2) BOUNDS(1, n^2) 2.51/1.98 2.51/1.98 2.51/1.98 ---------------------------------------- 2.51/1.98 2.51/1.98 (0) 2.51/1.98 Obligation: 2.51/1.98 Complexity Int TRS consisting of the following rules: 2.51/1.98 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 2.51/1.98 eval_loops_bb0_in(v_n, v_x.0, v_y.0) -> Com_1(eval_loops_bb1_in(v_n, v_n, v_y.0)) :|: v_n >= 0 2.51/1.98 eval_loops_bb0_in(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 2.51/1.98 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 2.51/1.98 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 2.51/1.98 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 2.51/1.98 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 2.51/1.98 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 2.51/1.98 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 2.51/1.98 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 2.51/1.98 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 2.51/1.98 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 2.51/1.98 2.51/1.98 The start-symbols are:[eval_loops_start_3] 2.51/1.98 2.51/1.98 2.51/1.98 ---------------------------------------- 2.51/1.98 2.51/1.98 (1) Koat Proof (FINISHED) 2.51/1.98 YES(?, 50*ar_0 + 8*ar_0^2 + 49) 2.51/1.98 2.51/1.98 2.51/1.98 2.51/1.98 Initial complexity problem: 2.51/1.98 2.51/1.98 1: T: 2.51/1.98 2.51/1.98 (Comp: ?, Cost: 1) evalloopsstart(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb0in(ar_0, ar_1, ar_2)) 2.51/1.98 2.51/1.98 (Comp: ?, Cost: 1) evalloopsbb0in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 0 ] 2.51/1.98 2.51/1.98 (Comp: ?, Cost: 1) evalloopsbb0in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ] 2.51/1.98 2.51/1.98 (Comp: ?, Cost: 1) evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 0 ] 2.51/1.98 2.51/1.98 (Comp: ?, Cost: 1) evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 + 1 ] 2.51/1.98 2.51/1.98 (Comp: ?, Cost: 1) evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 1)) [ ar_1 >= 2 ] 2.51/1.98 2.51/1.98 (Comp: ?, Cost: 1) evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ 1 >= ar_1 ] 2.51/1.98 2.51/1.98 (Comp: ?, Cost: 1) evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb4in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ] 2.51/1.98 2.51/1.98 (Comp: ?, Cost: 1) evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ] 2.51/1.98 2.51/1.98 (Comp: ?, Cost: 1) evalloopsbb4in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 2*ar_2)) 2.51/1.98 2.51/1.98 (Comp: ?, Cost: 1) evalloopsbb5in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb1in(ar_0, ar_1 - 1, ar_2)) 2.51/1.98 2.51/1.98 (Comp: ?, Cost: 1) evalloopsbb6in(ar_0, ar_1, ar_2) -> Com_1(evalloopsstop(ar_0, ar_1, ar_2)) 2.51/1.98 2.51/1.98 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalloopsstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ] 2.51/1.98 2.51/1.98 start location: koat_start 2.51/1.98 2.51/1.98 leaf cost: 0 2.51/1.98 2.51/1.98 2.51/1.98 2.51/1.98 Repeatedly propagating knowledge in problem 1 produces the following problem: 2.51/1.98 2.51/1.98 2: T: 2.51/1.98 2.51/1.98 (Comp: 1, Cost: 1) evalloopsstart(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb0in(ar_0, ar_1, ar_2)) 2.51/1.98 2.51/1.98 (Comp: 1, Cost: 1) evalloopsbb0in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 0 ] 2.51/1.98 2.51/1.98 (Comp: 1, Cost: 1) evalloopsbb0in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ] 2.51/1.98 2.51/1.98 (Comp: ?, Cost: 1) evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 0 ] 2.51/1.98 2.51/1.98 (Comp: ?, Cost: 1) evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 + 1 ] 2.51/1.98 2.51/1.98 (Comp: ?, Cost: 1) evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 1)) [ ar_1 >= 2 ] 2.51/1.98 2.51/1.98 (Comp: ?, Cost: 1) evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ 1 >= ar_1 ] 2.51/1.98 2.51/1.98 (Comp: ?, Cost: 1) evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb4in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ] 2.51/1.98 2.51/1.98 (Comp: ?, Cost: 1) evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ] 2.51/1.98 2.51/1.98 (Comp: ?, Cost: 1) evalloopsbb4in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 2*ar_2)) 2.51/1.98
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to Complexity_C_Integer 2019-03-21 04.38