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Complexity_C_Integer 2019-03-21 04.38 pair #429988844
details
property
value
status
complete
benchmark
speed_popl10_nested_multiple.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n082.star.cs.uiowa.edu
space
C4B_examples
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
2.11726 seconds
cpu usage
3.22635
user time
2.983
system time
0.243343
max virtual memory
1.8471736E7
max residence set size
187668.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^1))
output
3.15/2.08 WORST_CASE(?, O(n^1)) 3.15/2.09 proof of /export/starexec/sandbox2/output/output_files/bench.koat 3.15/2.09 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.15/2.09 3.15/2.09 3.15/2.09 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). 3.15/2.09 3.15/2.09 (0) CpxIntTrs 3.15/2.09 (1) Koat Proof [FINISHED, 882 ms] 3.15/2.09 (2) BOUNDS(1, n^1) 3.15/2.09 3.15/2.09 3.15/2.09 ---------------------------------------- 3.15/2.09 3.15/2.09 (0) 3.15/2.09 Obligation: 3.15/2.09 Complexity Int TRS consisting of the following rules: 3.15/2.09 eval_speed_popl10_nested_multiple_start(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y) -> Com_1(eval_speed_popl10_nested_multiple_bb0_in(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y)) :|: TRUE 3.15/2.09 eval_speed_popl10_nested_multiple_bb0_in(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y) -> Com_1(eval_speed_popl10_nested_multiple_bb1_in(v_x, v_y, v_.1, v_2, v_m, v_n, v_x, v_y)) :|: TRUE 3.15/2.09 eval_speed_popl10_nested_multiple_bb1_in(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y) -> Com_1(eval_speed_popl10_nested_multiple_bb2_in(v_.0, v_.01, v_.01, v_2, v_m, v_n, v_x, v_y)) :|: v_.0 < v_n 3.15/2.09 eval_speed_popl10_nested_multiple_bb1_in(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y) -> Com_1(eval_speed_popl10_nested_multiple_bb6_in(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y)) :|: v_.0 >= v_n 3.15/2.09 eval_speed_popl10_nested_multiple_bb2_in(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y) -> Com_1(eval_speed_popl10_nested_multiple_bb3_in(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y)) :|: v_.1 < v_m 3.15/2.09 eval_speed_popl10_nested_multiple_bb2_in(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y) -> Com_1(eval_speed_popl10_nested_multiple_bb5_in(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y)) :|: v_.1 >= v_m 3.15/2.09 eval_speed_popl10_nested_multiple_bb3_in(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y) -> Com_1(eval_speed_popl10_nested_multiple_0(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y)) :|: TRUE 3.15/2.09 eval_speed_popl10_nested_multiple_0(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y) -> Com_2(eval_nondet_start(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y), eval_speed_popl10_nested_multiple_1(v_.0, v_.01, v_.1, nondef.0, v_m, v_n, v_x, v_y)) :|: TRUE 3.15/2.09 eval_speed_popl10_nested_multiple_1(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y) -> Com_1(eval_speed_popl10_nested_multiple_bb5_in(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y)) :|: v_2 > 0 3.15/2.09 eval_speed_popl10_nested_multiple_1(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y) -> Com_1(eval_speed_popl10_nested_multiple_bb4_in(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y)) :|: v_2 <= 0 3.15/2.09 eval_speed_popl10_nested_multiple_bb4_in(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y) -> Com_1(eval_speed_popl10_nested_multiple_bb2_in(v_.0, v_.01, v_.1 + 1, v_2, v_m, v_n, v_x, v_y)) :|: TRUE 3.15/2.09 eval_speed_popl10_nested_multiple_bb5_in(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y) -> Com_1(eval_speed_popl10_nested_multiple_bb1_in(v_.0 + 1, v_.1, v_.1, v_2, v_m, v_n, v_x, v_y)) :|: TRUE 3.15/2.09 eval_speed_popl10_nested_multiple_bb6_in(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y) -> Com_1(eval_speed_popl10_nested_multiple_stop(v_.0, v_.01, v_.1, v_2, v_m, v_n, v_x, v_y)) :|: TRUE 3.15/2.09 3.15/2.09 The start-symbols are:[eval_speed_popl10_nested_multiple_start_8] 3.15/2.09 3.15/2.09 3.15/2.09 ---------------------------------------- 3.15/2.09 3.15/2.09 (1) Koat Proof (FINISHED) 3.15/2.09 YES(?, 47*ar_1 + 47*ar_4 + 49*ar_3 + 49*ar_6 + 24) 3.15/2.09 3.15/2.09 3.15/2.09 3.15/2.09 Initial complexity problem: 3.15/2.09 3.15/2.09 1: T: 3.15/2.09 3.15/2.09 (Comp: ?, Cost: 1) evalspeedpopl10nestedmultiplestart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalspeedpopl10nestedmultiplebb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 3.15/2.09 3.15/2.09 (Comp: ?, Cost: 1) evalspeedpopl10nestedmultiplebb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalspeedpopl10nestedmultiplebb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 3.15/2.09 3.15/2.09 (Comp: ?, Cost: 1) evalspeedpopl10nestedmultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalspeedpopl10nestedmultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_2, ar_6, ar_7, ar_8)) [ ar_4 >= ar_0 + 1 ] 3.15/2.09 3.15/2.09 (Comp: ?, Cost: 1) evalspeedpopl10nestedmultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalspeedpopl10nestedmultiplebb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_0 >= ar_4 ] 3.15/2.09 3.15/2.09 (Comp: ?, Cost: 1) evalspeedpopl10nestedmultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalspeedpopl10nestedmultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_6 >= ar_5 + 1 ] 3.15/2.09 3.15/2.09 (Comp: ?, Cost: 1) evalspeedpopl10nestedmultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalspeedpopl10nestedmultiplebb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_5 >= ar_6 ] 3.15/2.09 3.15/2.09 (Comp: ?, Cost: 1) evalspeedpopl10nestedmultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalspeedpopl10nestedmultiple0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 3.15/2.09 3.15/2.09 (Comp: ?, Cost: 1) evalspeedpopl10nestedmultiple00(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 3.15/2.09 3.15/2.09 (Comp: ?, Cost: 1) evalspeedpopl10nestedmultiple01(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalspeedpopl10nestedmultiple1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_8, ar_8)) 3.15/2.09 3.15/2.09 (Comp: ?, Cost: 1) evalspeedpopl10nestedmultiple0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_2(evalspeedpopl10nestedmultiple00(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, j), evalspeedpopl10nestedmultiple01(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, j)) 3.15/2.09 3.15/2.09 (Comp: ?, Cost: 1) evalspeedpopl10nestedmultiple1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalspeedpopl10nestedmultiplebb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_7 >= 1 ] 3.15/2.09 3.15/2.09 (Comp: ?, Cost: 1) evalspeedpopl10nestedmultiple1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalspeedpopl10nestedmultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ 0 >= ar_7 ] 3.15/2.09 3.15/2.09 (Comp: ?, Cost: 1) evalspeedpopl10nestedmultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalspeedpopl10nestedmultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1, ar_6, ar_7, ar_8)) 3.15/2.09 3.15/2.09 (Comp: ?, Cost: 1) evalspeedpopl10nestedmultiplebb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalspeedpopl10nestedmultiplebb1in(ar_0 + 1, ar_1, ar_5, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 3.15/2.09 3.15/2.09 (Comp: ?, Cost: 1) evalspeedpopl10nestedmultiplebb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalspeedpopl10nestedmultiplestop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 3.15/2.09 3.15/2.09 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalspeedpopl10nestedmultiplestart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ 0 <= 0 ] 3.15/2.09 3.15/2.09 start location: koat_start 3.15/2.09 3.15/2.09 leaf cost: 0 3.15/2.09 3.15/2.09 3.15/2.09 3.15/2.09 Repeatedly propagating knowledge in problem 1 produces the following problem: 3.15/2.09 3.15/2.09 2: T: 3.15/2.09 3.15/2.09 (Comp: 1, Cost: 1) evalspeedpopl10nestedmultiplestart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalspeedpopl10nestedmultiplebb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 3.15/2.09 3.15/2.09 (Comp: 1, Cost: 1) evalspeedpopl10nestedmultiplebb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalspeedpopl10nestedmultiplebb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 3.15/2.09 3.15/2.09 (Comp: ?, Cost: 1) evalspeedpopl10nestedmultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalspeedpopl10nestedmultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_2, ar_6, ar_7, ar_8)) [ ar_4 >= ar_0 + 1 ] 3.15/2.09 3.15/2.09 (Comp: ?, Cost: 1) evalspeedpopl10nestedmultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalspeedpopl10nestedmultiplebb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_0 >= ar_4 ] 3.15/2.09 3.15/2.09 (Comp: ?, Cost: 1) evalspeedpopl10nestedmultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalspeedpopl10nestedmultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_6 >= ar_5 + 1 ] 3.15/2.09 3.15/2.09 (Comp: ?, Cost: 1) evalspeedpopl10nestedmultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalspeedpopl10nestedmultiplebb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_5 >= ar_6 ] 3.15/2.09 3.15/2.09 (Comp: ?, Cost: 1) evalspeedpopl10nestedmultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalspeedpopl10nestedmultiple0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8))
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