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Complexity_C_Integer 2019-03-21 04.38 pair #429989734
details
property
value
status
complete
benchmark
rank2.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n036.star.cs.uiowa.edu
space
WTC_V2
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
2.33142 seconds
cpu usage
3.17917
user time
2.88542
system time
0.29375
max virtual memory
1.8510644E7
max residence set size
182720.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^1))
output
3.03/2.29 WORST_CASE(?, O(n^1)) 3.03/2.30 proof of /export/starexec/sandbox/output/output_files/bench.koat 3.03/2.30 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.03/2.30 3.03/2.30 3.03/2.30 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). 3.03/2.30 3.03/2.30 (0) CpxIntTrs 3.03/2.30 (1) Koat Proof [FINISHED, 1083 ms] 3.03/2.30 (2) BOUNDS(1, n^1) 3.03/2.30 3.03/2.30 3.03/2.30 ---------------------------------------- 3.03/2.30 3.03/2.30 (0) 3.03/2.30 Obligation: 3.03/2.30 Complexity Int TRS consisting of the following rules: 3.03/2.30 eval_rank2_start(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1) -> Com_1(eval_rank2_bb0_in(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1)) :|: TRUE 3.03/2.30 eval_rank2_bb0_in(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1) -> Com_1(eval_rank2_bb1_in(v_1, v_4, v_m, v_m, v_m, v_y.1)) :|: TRUE 3.03/2.30 eval_rank2_bb1_in(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1) -> Com_1(eval_rank2_bb2_in(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1)) :|: v_x.0 >= 2 3.03/2.30 eval_rank2_bb1_in(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1) -> Com_1(eval_rank2_bb6_in(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1)) :|: v_x.0 < 2 3.03/2.30 eval_rank2_bb2_in(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1) -> Com_1(eval_rank2_bb3_in(v_x.0 - 1, v_4, v_m, v_x.0, v_y.0, v_y.0 + v_x.0 - 1)) :|: TRUE 3.03/2.30 eval_rank2_bb3_in(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1) -> Com_1(eval_rank2_bb4_in(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1)) :|: v_y.1 >= v_1 3.03/2.30 eval_rank2_bb3_in(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1) -> Com_1(eval_rank2_.critedge_in(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1)) :|: v_y.1 < v_1 3.03/2.30 eval_rank2_bb4_in(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1) -> Com_1(eval_rank2_3(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1)) :|: TRUE 3.03/2.30 eval_rank2_3(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1) -> Com_2(eval_nondet_start(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1), eval_rank2_4(v_1, nondef.0, v_m, v_x.0, v_y.0, v_y.1)) :|: TRUE 3.03/2.30 eval_rank2_4(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1) -> Com_1(eval_rank2_bb5_in(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1)) :|: v_4 > 0 3.03/2.30 eval_rank2_4(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1) -> Com_1(eval_rank2_.critedge_in(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1)) :|: v_4 <= 0 3.03/2.30 eval_rank2_bb5_in(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1) -> Com_1(eval_rank2_bb3_in(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1 - 1)) :|: TRUE 3.03/2.30 eval_rank2_.critedge_in(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1) -> Com_1(eval_rank2_bb1_in(v_1, v_4, v_m, v_1 - 1, v_y.1 - v_1 + 1, v_y.1)) :|: TRUE 3.03/2.30 eval_rank2_bb6_in(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1) -> Com_1(eval_rank2_stop(v_1, v_4, v_m, v_x.0, v_y.0, v_y.1)) :|: TRUE 3.03/2.30 3.03/2.30 The start-symbols are:[eval_rank2_start_6] 3.03/2.30 3.03/2.30 3.03/2.30 ---------------------------------------- 3.03/2.30 3.03/2.30 (1) Koat Proof (FINISHED) 3.03/2.30 YES(?, 113*ar_1 + 6) 3.03/2.30 3.03/2.30 3.03/2.30 3.03/2.30 Initial complexity problem: 3.03/2.30 3.03/2.30 1: T: 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb1in(ar_1, ar_1, ar_1, ar_3, ar_4, ar_5, ar_6)) 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_0 >= 2 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 1 >= ar_0 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb3in(ar_0, ar_1, ar_2, ar_0 - 1, ar_2 + ar_0 - 1, ar_5, ar_6)) 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_4 >= ar_3 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_3 >= ar_4 + 1 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank23(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank230(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank231(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank24(ar_0, ar_1, ar_2, ar_3, ar_4, ar_6, ar_6)) 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank23(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_2(evalrank230(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h), evalrank231(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, h)) 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank24(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_5 >= 1 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank24(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_5 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5, ar_6)) 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb1in(ar_3 - 1, ar_1, ar_4 - ar_3 + 1, ar_3, ar_4, ar_5, ar_6)) 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 3.03/2.30 3.03/2.30 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 <= 0 ] 3.03/2.30 3.03/2.30 start location: koat_start 3.03/2.30 3.03/2.30 leaf cost: 0 3.03/2.30 3.03/2.30 3.03/2.30 3.03/2.30 Repeatedly propagating knowledge in problem 1 produces the following problem: 3.03/2.30 3.03/2.30 2: T: 3.03/2.30 3.03/2.30 (Comp: 1, Cost: 1) evalrank2start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 3.03/2.30 3.03/2.30 (Comp: 1, Cost: 1) evalrank2bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb1in(ar_1, ar_1, ar_1, ar_3, ar_4, ar_5, ar_6)) 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_0 >= 2 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 1 >= ar_0 ] 3.03/2.30 3.03/2.30 (Comp: ?, Cost: 1) evalrank2bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrank2bb3in(ar_0, ar_1, ar_2, ar_0 - 1, ar_2 + ar_0 - 1, ar_5, ar_6)) 3.03/2.30
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