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Complexity_C_Integer 2019-03-21 04.38 pair #429989696
details
property
value
status
complete
benchmark
unperfect.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n065.star.cs.uiowa.edu
space
WTC_V2
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
2.0857 seconds
cpu usage
6.09664
user time
5.59983
system time
0.496812
max virtual memory
1.8531212E7
max residence set size
201220.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^2))
output
2.98/2.05 WORST_CASE(?, O(n^2)) 2.98/2.06 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.98/2.06 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.98/2.06 2.98/2.06 2.98/2.06 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 2.98/2.06 2.98/2.06 (0) CpxIntTrs 2.98/2.06 (1) Koat Proof [FINISHED, 784 ms] 2.98/2.06 (2) BOUNDS(1, n^2) 2.98/2.06 2.98/2.06 2.98/2.06 ---------------------------------------- 2.98/2.06 2.98/2.06 (0) 2.98/2.06 Obligation: 2.98/2.06 Complexity Int TRS consisting of the following rules: 2.98/2.06 eval_unperfect_start(v_1, v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_unperfect_bb0_in(v_1, v_x, v_y1.0, v_y2.1, v_y3.0)) :|: TRUE 2.98/2.06 eval_unperfect_bb0_in(v_1, v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_unperfect_bb3_in(v_1, v_x, v_y1.0, v_y2.1, v_y3.0)) :|: v_x <= 0 2.98/2.06 eval_unperfect_bb0_in(v_1, v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_unperfect_bb1_in(v_1, v_x, v_x, v_y2.1, v_x)) :|: v_x > 0 2.98/2.06 eval_unperfect_bb1_in(v_1, v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_unperfect_bb2_in(v_1, v_x, v_y1.0, v_y2.1, v_y3.0)) :|: v_y1.0 - 1 >= 0 && v_y1.0 - 1 <= 0 2.98/2.06 eval_unperfect_bb1_in(v_1, v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_unperfect_bb4_in(v_y1.0 - 1, v_x, v_y1.0, v_x, v_y3.0)) :|: v_y1.0 - 1 < 0 2.98/2.06 eval_unperfect_bb1_in(v_1, v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_unperfect_bb4_in(v_y1.0 - 1, v_x, v_y1.0, v_x, v_y3.0)) :|: v_y1.0 - 1 > 0 2.98/2.06 eval_unperfect_bb2_in(v_1, v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_unperfect_bb3_in(v_1, v_x, v_y1.0, v_y2.1, v_y3.0)) :|: v_y3.0 < 0 2.98/2.06 eval_unperfect_bb2_in(v_1, v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_unperfect_bb3_in(v_1, v_x, v_y1.0, v_y2.1, v_y3.0)) :|: v_y3.0 > 0 2.98/2.06 eval_unperfect_bb2_in(v_1, v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_unperfect_bb3_in(v_1, v_x, v_y1.0, v_y2.1, v_y3.0)) :|: v_y3.0 >= 0 && v_y3.0 <= 0 2.98/2.06 eval_unperfect_bb3_in(v_1, v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_unperfect_stop(v_1, v_x, v_y1.0, v_y2.1, v_y3.0)) :|: TRUE 2.98/2.06 eval_unperfect_bb4_in(v_1, v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_unperfect_bb5_in(v_1, v_x, v_y1.0, v_y2.1, v_y3.0)) :|: v_y2.1 >= v_1 2.98/2.06 eval_unperfect_bb4_in(v_1, v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_unperfect_bb6_in(v_1, v_x, v_y1.0, v_y2.1, v_y3.0)) :|: v_y2.1 < v_1 2.98/2.06 eval_unperfect_bb5_in(v_1, v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_unperfect_bb4_in(v_1, v_x, v_y1.0, v_y2.1 - v_1, v_y3.0)) :|: TRUE 2.98/2.06 eval_unperfect_bb6_in(v_1, v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_unperfect_bb1_in(v_1, v_x, v_1, v_y2.1, v_y3.0 - v_1)) :|: v_y2.1 >= 0 && v_y2.1 <= 0 2.98/2.06 eval_unperfect_bb6_in(v_1, v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_unperfect_bb1_in(v_1, v_x, v_1, v_y2.1, v_y3.0)) :|: v_y2.1 < 0 2.98/2.06 eval_unperfect_bb6_in(v_1, v_x, v_y1.0, v_y2.1, v_y3.0) -> Com_1(eval_unperfect_bb1_in(v_1, v_x, v_1, v_y2.1, v_y3.0)) :|: v_y2.1 > 0 2.98/2.06 2.98/2.06 The start-symbols are:[eval_unperfect_start_5] 2.98/2.06 2.98/2.06 2.98/2.06 ---------------------------------------- 2.98/2.06 2.98/2.06 (1) Koat Proof (FINISHED) 2.98/2.06 YES(?, 13*ar_0 + 8*ar_0^2 + 18) 2.98/2.06 2.98/2.06 2.98/2.06 2.98/2.06 Initial complexity problem: 2.98/2.06 2.98/2.06 1: T: 2.98/2.06 2.98/2.06 (Comp: ?, Cost: 1) evalunperfectstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalunperfectbb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.98/2.06 2.98/2.06 (Comp: ?, Cost: 1) evalunperfectbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalunperfectbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 ] 2.98/2.06 2.98/2.06 (Comp: ?, Cost: 1) evalunperfectbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalunperfectbb1in(ar_0, ar_0, ar_0, ar_3, ar_4)) [ ar_0 >= 1 ] 2.98/2.06 2.98/2.06 (Comp: ?, Cost: 1) evalunperfectbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalunperfectbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 = 1 ] 2.98/2.06 2.98/2.06 (Comp: ?, Cost: 1) evalunperfectbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalunperfectbb4in(ar_0, ar_1, ar_2, ar_1 - 1, ar_0)) [ 0 >= ar_1 ] 2.98/2.06 2.98/2.06 (Comp: ?, Cost: 1) evalunperfectbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalunperfectbb4in(ar_0, ar_1, ar_2, ar_1 - 1, ar_0)) [ ar_1 >= 2 ] 2.98/2.06 2.98/2.06 (Comp: ?, Cost: 1) evalunperfectbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalunperfectbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ] 2.98/2.06 2.98/2.06 (Comp: ?, Cost: 1) evalunperfectbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalunperfectbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ] 2.98/2.06 2.98/2.06 (Comp: ?, Cost: 1) evalunperfectbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalunperfectbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 = 0 ] 2.98/2.06 2.98/2.06 (Comp: ?, Cost: 1) evalunperfectbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalunperfectstop(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.98/2.06 2.98/2.06 (Comp: ?, Cost: 1) evalunperfectbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalunperfectbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 ] 2.98/2.06 2.98/2.06 (Comp: ?, Cost: 1) evalunperfectbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalunperfectbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 + 1 ] 2.98/2.06 2.98/2.06 (Comp: ?, Cost: 1) evalunperfectbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalunperfectbb4in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_3)) 2.98/2.06 2.98/2.06 (Comp: ?, Cost: 1) evalunperfectbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalunperfectbb1in(ar_0, ar_3, ar_2 - ar_3, ar_3, ar_4)) [ ar_4 = 0 ] 2.98/2.06 2.98/2.06 (Comp: ?, Cost: 1) evalunperfectbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalunperfectbb1in(ar_0, ar_3, ar_2, ar_3, ar_4)) [ 0 >= ar_4 + 1 ] 2.98/2.06 2.98/2.06 (Comp: ?, Cost: 1) evalunperfectbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalunperfectbb1in(ar_0, ar_3, ar_2, ar_3, ar_4)) [ ar_4 >= 1 ] 2.98/2.06 2.98/2.06 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalunperfectstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 2.98/2.06 2.98/2.06 start location: koat_start 2.98/2.06 2.98/2.06 leaf cost: 0 2.98/2.06 2.98/2.06 2.98/2.06 2.98/2.06 Repeatedly propagating knowledge in problem 1 produces the following problem: 2.98/2.06 2.98/2.06 2: T: 2.98/2.06 2.98/2.06 (Comp: 1, Cost: 1) evalunperfectstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalunperfectbb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.98/2.06 2.98/2.06 (Comp: 1, Cost: 1) evalunperfectbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalunperfectbb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 ] 2.98/2.06 2.98/2.06 (Comp: 1, Cost: 1) evalunperfectbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalunperfectbb1in(ar_0, ar_0, ar_0, ar_3, ar_4)) [ ar_0 >= 1 ] 2.98/2.06 2.98/2.06 (Comp: ?, Cost: 1) evalunperfectbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalunperfectbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 = 1 ] 2.98/2.06
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