Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Complexity_C_Integer 2019-03-21 04.38 pair #429989636
details
property
value
status
complete
benchmark
nested_loop.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n099.star.cs.uiowa.edu
space
WTC_V2
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
11.411 seconds
cpu usage
12.8675
user time
12.1483
system time
0.719173
max virtual memory
1.8819664E7
max residence set size
366016.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^3))
output
12.66/11.34 WORST_CASE(?, O(n^3)) 12.66/11.36 proof of /export/starexec/sandbox2/output/output_files/bench.koat 12.66/11.36 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 12.66/11.36 12.66/11.36 12.66/11.36 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^3). 12.66/11.36 12.66/11.36 (0) CpxIntTrs 12.66/11.36 (1) Koat Proof [FINISHED, 10.0 s] 12.66/11.36 (2) BOUNDS(1, n^3) 12.66/11.36 12.66/11.36 12.66/11.36 ---------------------------------------- 12.66/11.36 12.66/11.36 (0) 12.66/11.36 Obligation: 12.66/11.36 Complexity Int TRS consisting of the following rules: 12.66/11.36 eval_nested_loop_start(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_bb0_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: TRUE 12.66/11.36 eval_nested_loop_bb0_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_bb1_in(v_11, v_4, v_7, v_9, v_N, 0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: 0 <= v_n && 0 <= v_m && 0 <= v_N 12.66/11.36 eval_nested_loop_bb0_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_.critedge_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: 0 > v_n 12.66/11.36 eval_nested_loop_bb0_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_.critedge_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: 0 > v_m 12.66/11.36 eval_nested_loop_bb0_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_.critedge_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: 0 > v_N 12.66/11.36 eval_nested_loop_bb1_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_bb2_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: v_i.0 < v_n 12.66/11.36 eval_nested_loop_bb1_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_.critedge_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: v_i.0 >= v_n 12.66/11.36 eval_nested_loop_bb2_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_0(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: TRUE 12.66/11.36 eval_nested_loop_0(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_2(eval_nondet_start(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n), eval_nested_loop_1(v_11, nondef.0, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: TRUE 12.66/11.36 eval_nested_loop_1(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_.critedge3_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.0, 0, v_k.0, v_m, v_n)) :|: v_4 > 0 12.66/11.36 eval_nested_loop_1(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_.critedge_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: v_4 <= 0 12.66/11.36 eval_nested_loop_.critedge3_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_bb3_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: v_j.0 < v_m 12.66/11.36 eval_nested_loop_.critedge3_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_.critedge2_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: v_j.0 >= v_m 12.66/11.36 eval_nested_loop_bb3_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_2(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: TRUE 12.66/11.36 eval_nested_loop_2(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_2(eval_nondet_start(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n), eval_nested_loop_3(v_11, v_4, nondef.1, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: TRUE 12.66/11.36 eval_nested_loop_3(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_bb4_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: v_7 > 0 12.66/11.36 eval_nested_loop_3(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_.critedge2_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: v_7 <= 0 12.66/11.36 eval_nested_loop_bb4_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_bb5_in(v_11, v_4, v_7, v_j.0 + 1, v_N, v_i.0, v_i.1, v_j.0, v_i.1, v_m, v_n)) :|: TRUE 12.66/11.36 eval_nested_loop_bb5_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_bb6_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: v_k.0 < v_N 12.66/11.36 eval_nested_loop_bb5_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_.critedge3_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_k.0, v_9, v_k.0, v_m, v_n)) :|: v_k.0 >= v_N 12.66/11.36 eval_nested_loop_bb6_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_6(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: TRUE 12.66/11.36 eval_nested_loop_6(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_2(eval_nondet_start(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n), eval_nested_loop_7(nondef.2, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: TRUE 12.66/11.36 eval_nested_loop_7(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_bb7_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: v_11 > 0 12.66/11.36 eval_nested_loop_7(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_.critedge3_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_k.0, v_9, v_k.0, v_m, v_n)) :|: v_11 <= 0 12.66/11.36 eval_nested_loop_bb7_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_bb5_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0 + 1, v_m, v_n)) :|: TRUE 12.66/11.36 eval_nested_loop_.critedge2_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_bb1_in(v_11, v_4, v_7, v_9, v_N, v_i.1 + 1, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: TRUE 12.66/11.36 eval_nested_loop_.critedge_in(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n) -> Com_1(eval_nested_loop_stop(v_11, v_4, v_7, v_9, v_N, v_i.0, v_i.1, v_j.0, v_k.0, v_m, v_n)) :|: TRUE 12.66/11.36 12.66/11.36 The start-symbols are:[eval_nested_loop_start_11] 12.66/11.36 12.66/11.36 12.66/11.36 ---------------------------------------- 12.66/11.36 12.66/11.36 (1) Koat Proof (FINISHED) 12.66/11.36 YES(?, 664*ar_0 + 31360*ar_0*ar_1*ar_2 + 7840*ar_0*ar_2 + 1792*ar_0*ar_1^2 + 2816*ar_0*ar_1 + 28224*ar_0^2*ar_1 + 7056*ar_0^2 + 11) 12.66/11.36 12.66/11.36 12.66/11.36 12.66/11.36 Initial complexity problem: 12.66/11.36 12.66/11.36 1: T: 12.66/11.36 12.66/11.36 (Comp: ?, Cost: 1) evalnestedloopstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalnestedloopbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) 12.66/11.36 12.66/11.36 (Comp: ?, Cost: 1) evalnestedloopbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalnestedloopbb1in(ar_0, ar_1, ar_2, 0, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ ar_0 >= 0 /\ ar_1 >= 0 /\ ar_2 >= 0 ] 12.66/11.36 12.66/11.36 (Comp: ?, Cost: 1) evalnestedloopbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalnestedloopcritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ 0 >= ar_0 + 1 ] 12.66/11.36 12.66/11.36 (Comp: ?, Cost: 1) evalnestedloopbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalnestedloopcritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ 0 >= ar_1 + 1 ] 12.66/11.36 12.66/11.36 (Comp: ?, Cost: 1) evalnestedloopbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalnestedloopcritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ 0 >= ar_2 + 1 ] 12.66/11.36 12.66/11.36 (Comp: ?, Cost: 1) evalnestedloopbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalnestedloopbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ ar_0 >= ar_3 + 1 ] 12.66/11.36 12.66/11.36 (Comp: ?, Cost: 1) evalnestedloopbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalnestedloopcritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ ar_3 >= ar_0 ] 12.66/11.36 12.66/11.36 (Comp: ?, Cost: 1) evalnestedloopbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalnestedloop0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) 12.66/11.36 12.66/11.36 (Comp: ?, Cost: 1) evalnestedloop00(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) 12.66/11.36 12.66/11.36 (Comp: ?, Cost: 1) evalnestedloop01(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalnestedloop1(ar_0, ar_1, ar_2, ar_3, ar_5, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) 12.66/11.36 12.66/11.36 (Comp: ?, Cost: 1) evalnestedloop0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_2(evalnestedloop00(ar_0, ar_1, ar_2, ar_3, ar_4, m, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11), evalnestedloop01(ar_0, ar_1, ar_2, ar_3, ar_4, m, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) 12.66/11.36 12.66/11.36 (Comp: ?, Cost: 1) evalnestedloop1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalnestedloopcritedge3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_3, 0, ar_8, ar_9, ar_10, ar_11)) [ ar_4 >= 1 ] 12.66/11.36 12.66/11.36 (Comp: ?, Cost: 1) evalnestedloop1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalnestedloopcritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ 0 >= ar_4 ] 12.66/11.36 12.66/11.36 (Comp: ?, Cost: 1) evalnestedloopcritedge3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalnestedloopbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ ar_1 >= ar_7 + 1 ] 12.66/11.36 12.66/11.36 (Comp: ?, Cost: 1) evalnestedloopcritedge3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalnestedloopcritedge2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ ar_7 >= ar_1 ] 12.66/11.36 12.66/11.36 (Comp: ?, Cost: 1) evalnestedloopbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalnestedloop2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) 12.66/11.36 12.66/11.36 (Comp: ?, Cost: 1) evalnestedloop20(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) 12.66/11.36 12.66/11.36 (Comp: ?, Cost: 1) evalnestedloop21(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalnestedloop3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_5, ar_9, ar_10, ar_11)) 12.66/11.36 12.66/11.36 (Comp: ?, Cost: 1) evalnestedloop2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_2(evalnestedloop20(ar_0, ar_1, ar_2, ar_3, ar_4, m, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11), evalnestedloop21(ar_0, ar_1, ar_2, ar_3, ar_4, m, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) 12.66/11.36 12.66/11.36 (Comp: ?, Cost: 1) evalnestedloop3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalnestedloopbb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ ar_8 >= 1 ] 12.66/11.36 12.66/11.36 (Comp: ?, Cost: 1) evalnestedloop3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11) -> Com_1(evalnestedloopcritedge2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11)) [ 0 >= ar_8 ]
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