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Complexity_C_Integer 2019-03-21 04.38 pair #429988824
details
property
value
status
complete
benchmark
speed_popl10_nested_single.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n144.star.cs.uiowa.edu
space
C4B_examples
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.74849 seconds
cpu usage
2.82796
user time
2.59259
system time
0.235373
max virtual memory
1.84537E7
max residence set size
183200.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^1))
output
2.74/1.71 WORST_CASE(?, O(n^1)) 2.74/1.72 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.74/1.72 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.74/1.72 2.74/1.72 2.74/1.72 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). 2.74/1.72 2.74/1.72 (0) CpxIntTrs 2.74/1.72 (1) Koat Proof [FINISHED, 481 ms] 2.74/1.72 (2) BOUNDS(1, n^1) 2.74/1.72 2.74/1.72 2.74/1.72 ---------------------------------------- 2.74/1.72 2.74/1.72 (0) 2.74/1.72 Obligation: 2.74/1.72 Complexity Int TRS consisting of the following rules: 2.74/1.72 eval_speed_popl10_nested_single_start(v_3, v_n, v_x.0, v_x.1) -> Com_1(eval_speed_popl10_nested_single_bb0_in(v_3, v_n, v_x.0, v_x.1)) :|: TRUE 2.74/1.72 eval_speed_popl10_nested_single_bb0_in(v_3, v_n, v_x.0, v_x.1) -> Com_1(eval_speed_popl10_nested_single_bb1_in(v_3, v_n, 0, v_x.1)) :|: TRUE 2.74/1.72 eval_speed_popl10_nested_single_bb1_in(v_3, v_n, v_x.0, v_x.1) -> Com_1(eval_speed_popl10_nested_single_bb2_in(v_3, v_n, v_x.0, v_x.1)) :|: v_x.0 < v_n 2.74/1.72 eval_speed_popl10_nested_single_bb1_in(v_3, v_n, v_x.0, v_x.1) -> Com_1(eval_speed_popl10_nested_single_bb6_in(v_3, v_n, v_x.0, v_x.1)) :|: v_x.0 >= v_n 2.74/1.72 eval_speed_popl10_nested_single_bb2_in(v_3, v_n, v_x.0, v_x.1) -> Com_1(eval_speed_popl10_nested_single_bb3_in(v_3, v_n, v_x.0, v_x.0 + 1)) :|: TRUE 2.74/1.72 eval_speed_popl10_nested_single_bb3_in(v_3, v_n, v_x.0, v_x.1) -> Com_1(eval_speed_popl10_nested_single_bb4_in(v_3, v_n, v_x.0, v_x.1)) :|: v_x.1 < v_n 2.74/1.72 eval_speed_popl10_nested_single_bb3_in(v_3, v_n, v_x.0, v_x.1) -> Com_1(eval_speed_popl10_nested_single_bb1_in(v_3, v_n, v_x.1, v_x.1)) :|: v_x.1 >= v_n 2.74/1.72 eval_speed_popl10_nested_single_bb4_in(v_3, v_n, v_x.0, v_x.1) -> Com_1(eval_speed_popl10_nested_single_2(v_3, v_n, v_x.0, v_x.1)) :|: TRUE 2.74/1.72 eval_speed_popl10_nested_single_2(v_3, v_n, v_x.0, v_x.1) -> Com_2(eval_nondet_start(v_3, v_n, v_x.0, v_x.1), eval_speed_popl10_nested_single_3(nondef.0, v_n, v_x.0, v_x.1)) :|: TRUE 2.74/1.72 eval_speed_popl10_nested_single_3(v_3, v_n, v_x.0, v_x.1) -> Com_1(eval_speed_popl10_nested_single_bb1_in(v_3, v_n, v_x.1, v_x.1)) :|: v_3 > 0 2.74/1.72 eval_speed_popl10_nested_single_3(v_3, v_n, v_x.0, v_x.1) -> Com_1(eval_speed_popl10_nested_single_bb5_in(v_3, v_n, v_x.0, v_x.1)) :|: v_3 <= 0 2.74/1.72 eval_speed_popl10_nested_single_bb5_in(v_3, v_n, v_x.0, v_x.1) -> Com_1(eval_speed_popl10_nested_single_bb3_in(v_3, v_n, v_x.0, v_x.1 + 1)) :|: TRUE 2.74/1.72 eval_speed_popl10_nested_single_bb6_in(v_3, v_n, v_x.0, v_x.1) -> Com_1(eval_speed_popl10_nested_single_stop(v_3, v_n, v_x.0, v_x.1)) :|: TRUE 2.74/1.72 2.74/1.72 The start-symbols are:[eval_speed_popl10_nested_single_start_4] 2.74/1.72 2.74/1.72 2.74/1.72 ---------------------------------------- 2.74/1.72 2.74/1.72 (1) Koat Proof (FINISHED) 2.74/1.72 YES(?, 88*ar_1 + 6) 2.74/1.72 2.74/1.72 2.74/1.72 2.74/1.72 Initial complexity problem: 2.74/1.72 2.74/1.72 1: T: 2.74/1.72 2.74/1.72 (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglestart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10nestedsinglebb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.74/1.72 2.74/1.72 (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10nestedsinglebb1in(0, ar_1, ar_2, ar_3, ar_4)) 2.74/1.72 2.74/1.72 (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10nestedsinglebb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ] 2.74/1.72 2.74/1.72 (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10nestedsinglebb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ] 2.74/1.72 2.74/1.72 (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10nestedsinglebb3in(ar_0, ar_1, ar_0 + 1, ar_3, ar_4)) 2.74/1.72 2.74/1.72 (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10nestedsinglebb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_2 + 1 ] 2.74/1.72 2.74/1.72 (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10nestedsinglebb1in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_1 ] 2.74/1.72 2.74/1.72 (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10nestedsingle2(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.74/1.72 2.74/1.72 (Comp: ?, Cost: 1) evalspeedpopl10nestedsingle20(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.74/1.72 2.74/1.72 (Comp: ?, Cost: 1) evalspeedpopl10nestedsingle21(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10nestedsingle3(ar_0, ar_1, ar_2, ar_4, ar_4)) 2.74/1.72 2.74/1.72 (Comp: ?, Cost: 1) evalspeedpopl10nestedsingle2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_2(evalspeedpopl10nestedsingle20(ar_0, ar_1, ar_2, ar_3, f), evalspeedpopl10nestedsingle21(ar_0, ar_1, ar_2, ar_3, f)) 2.74/1.72 2.74/1.72 (Comp: ?, Cost: 1) evalspeedpopl10nestedsingle3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10nestedsinglebb1in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 1 ] 2.74/1.72 2.74/1.72 (Comp: ?, Cost: 1) evalspeedpopl10nestedsingle3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10nestedsinglebb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 ] 2.74/1.72 2.74/1.72 (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10nestedsinglebb3in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) 2.74/1.72 2.74/1.72 (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10nestedsinglestop(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.74/1.72 2.74/1.72 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10nestedsinglestart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 2.74/1.72 2.74/1.72 start location: koat_start 2.74/1.72 2.74/1.72 leaf cost: 0 2.74/1.72 2.74/1.72 2.74/1.72 2.74/1.72 Repeatedly propagating knowledge in problem 1 produces the following problem: 2.74/1.72 2.74/1.72 2: T: 2.74/1.72 2.74/1.72 (Comp: 1, Cost: 1) evalspeedpopl10nestedsinglestart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10nestedsinglebb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.74/1.72 2.74/1.72 (Comp: 1, Cost: 1) evalspeedpopl10nestedsinglebb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10nestedsinglebb1in(0, ar_1, ar_2, ar_3, ar_4)) 2.74/1.72 2.74/1.72 (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10nestedsinglebb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ] 2.74/1.72 2.74/1.72 (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10nestedsinglebb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ] 2.74/1.72 2.74/1.72 (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10nestedsinglebb3in(ar_0, ar_1, ar_0 + 1, ar_3, ar_4)) 2.74/1.72 2.74/1.72 (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10nestedsinglebb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_2 + 1 ] 2.74/1.72 2.74/1.72 (Comp: ?, Cost: 1) evalspeedpopl10nestedsinglebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedpopl10nestedsinglebb1in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_1 ]
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