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Complexity_ITS 2019-03-21 04.46 pair #429989962
details
property
value
status
complete
benchmark
perfect1.c.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n061.star.cs.uiowa.edu
space
Flores-Montoya_16
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
20.8061 seconds
cpu usage
27.5914
user time
25.6946
system time
1.89675
max virtual memory
1.8987308E7
max residence set size
277644.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
27.38/20.77 WORST_CASE(Omega(n^1), O(n^2)) 27.38/20.78 proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat 27.38/20.78 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 27.38/20.78 27.38/20.78 27.38/20.78 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, max(23, 15 + 4 * Arg_0) + max(4, 2 * Arg_0) * nat(Arg_0) + nat(Arg_0) + nat(Arg_0 * max(4, 2 * Arg_0) + min(-2 * Arg_0, -4)) * nat(Arg_0) + nat(Arg_0 * max(4, 2 * Arg_0) + min(-2 * Arg_0, -4)) + max(3, 2 + Arg_0) + max(10, -10 + 10 * Arg_0) + max(9, -9 + 9 * Arg_0) + max(5, -5 + 5 * Arg_0) + nat(-2 + 2 * Arg_0) + max(-14 + 14 * Arg_0, 14) + max(8, -8 + 8 * Arg_0)). 27.38/20.78 27.38/20.78 (0) CpxIntTrs 27.38/20.78 (1) Loat Proof [FINISHED, 2116 ms] 27.38/20.78 (2) BOUNDS(n^1, INF) 27.38/20.78 27.38/20.78 27.38/20.78 ---------------------------------------- 27.38/20.78 27.38/20.78 (0) 27.38/20.78 Obligation: 27.38/20.78 Complexity Int TRS consisting of the following rules: 27.38/20.78 eval_perfect1_start(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect1_bb0_in(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: TRUE 27.38/20.78 eval_perfect1_bb0_in(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect1_0(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: TRUE 27.38/20.78 eval_perfect1_0(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect1_1(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: TRUE 27.38/20.78 eval_perfect1_1(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect1_bb7_in(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: v_x <= 1 27.38/20.78 eval_perfect1_1(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect1_bb1_in(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: v_x > 1 27.38/20.78 eval_perfect1_bb1_in(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect1_2(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: TRUE 27.38/20.78 eval_perfect1_2(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect1_3(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: TRUE 27.38/20.78 eval_perfect1_3(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect1_4(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: TRUE 27.38/20.78 eval_perfect1_4(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect1_5(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: TRUE 27.38/20.78 eval_perfect1_5(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect1_6(v__y3_0, v_x - 1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: TRUE 27.38/20.78 eval_perfect1_6(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect1_7(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: TRUE 27.38/20.78 eval_perfect1_7(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect1_8(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: TRUE 27.38/20.78 eval_perfect1_8(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect1_bb2_in(v__y3_0, v_1, v_6, v_7, v_x, v_1, v_y2_1, v_x)) :|: TRUE 27.38/20.78 eval_perfect1_bb2_in(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect1_bb3_in(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_x, v_y3_0)) :|: v_y1_0 > 0 27.38/20.78 eval_perfect1_bb2_in(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect1_bb6_in(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: v_y1_0 <= 0 27.38/20.78 eval_perfect1_bb3_in(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect1_bb4_in(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: v_y2_1 >= v_y1_0 27.38/20.78 eval_perfect1_bb3_in(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect1_bb5_in(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: v_y2_1 < v_y1_0 27.38/20.78 eval_perfect1_bb4_in(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect1_bb3_in(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1 - v_y1_0, v_y3_0)) :|: TRUE 27.38/20.78 eval_perfect1_bb5_in(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect1_12(v__y3_0, v_1, v_y3_0 - v_y1_0, v_7, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: TRUE 27.38/20.78 eval_perfect1_12(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect1_13(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: TRUE 27.38/20.78 eval_perfect1_13(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect1_14(v_6, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: v_y2_1 >= 0 && v_y2_1 <= 0 27.38/20.78 eval_perfect1_13(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect1_14(v_y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: v_y2_1 < 0 27.38/20.78 eval_perfect1_13(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect1_14(v_y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: v_y2_1 > 0 27.38/20.78 eval_perfect1_14(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect1_15(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: TRUE 27.38/20.78 eval_perfect1_15(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect1_16(v__y3_0, v_1, v_6, v_y1_0 - 1, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: TRUE 27.38/20.78 eval_perfect1_16(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect1_17(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: TRUE 27.38/20.78 eval_perfect1_17(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect1_bb2_in(v__y3_0, v_1, v_6, v_7, v_x, v_7, v_y2_1, v__y3_0)) :|: TRUE 27.38/20.78 eval_perfect1_bb6_in(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect1_bb7_in(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: v_y3_0 < 0 27.38/20.78 eval_perfect1_bb6_in(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect1_bb7_in(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: v_y3_0 > 0 27.38/20.78 eval_perfect1_bb6_in(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect1_bb7_in(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: v_y3_0 >= 0 && v_y3_0 <= 0 27.38/20.78 eval_perfect1_bb7_in(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0) -> Com_1(eval_perfect1_stop(v__y3_0, v_1, v_6, v_7, v_x, v_y1_0, v_y2_1, v_y3_0)) :|: TRUE 27.38/20.78 27.38/20.78 The start-symbols are:[eval_perfect1_start_8] 27.38/20.78 27.38/20.78 27.38/20.78 ---------------------------------------- 27.38/20.78 27.38/20.78 (1) Loat Proof (FINISHED) 27.38/20.78 27.38/20.78 27.38/20.78 ### Pre-processing the ITS problem ### 27.38/20.78 27.38/20.78 27.38/20.78 27.38/20.78 Initial linear ITS problem 27.38/20.78 27.38/20.78 Start location: evalperfect1start 27.38/20.78 27.38/20.78 0: evalperfect1start -> evalperfect1bb0in : [], cost: 1 27.38/20.78 27.38/20.78 1: evalperfect1bb0in -> evalperfect10 : [], cost: 1 27.38/20.78 27.38/20.78 2: evalperfect10 -> evalperfect11 : [], cost: 1 27.38/20.78 27.38/20.78 3: evalperfect11 -> evalperfect1bb7in : [ 1>=A ], cost: 1 27.38/20.78 27.38/20.78 4: evalperfect11 -> evalperfect1bb1in : [ A>=2 ], cost: 1 27.38/20.78 27.38/20.78 5: evalperfect1bb1in -> evalperfect12 : [], cost: 1 27.38/20.78 27.38/20.78 6: evalperfect12 -> evalperfect13 : [], cost: 1 27.38/20.78 27.38/20.78 7: evalperfect13 -> evalperfect14 : [], cost: 1 27.38/20.78 27.38/20.78 8: evalperfect14 -> evalperfect15 : [], cost: 1 27.38/20.78 27.38/20.78 9: evalperfect15 -> evalperfect16 : B'=-1+A, [], cost: 1 27.38/20.78 27.38/20.78 10: evalperfect16 -> evalperfect17 : [], cost: 1 27.38/20.78 27.38/20.78 11: evalperfect17 -> evalperfect18 : [], cost: 1 27.38/20.78 27.38/20.78 12: evalperfect18 -> evalperfect1bb2in : C'=B, D'=A, [], cost: 1 27.38/20.78 27.38/20.78 13: evalperfect1bb2in -> evalperfect1bb3in : E'=A, [ C>=1 ], cost: 1 27.38/20.78 27.38/20.78 14: evalperfect1bb2in -> evalperfect1bb6in : [ 0>=C ], cost: 1 27.38/20.78 27.38/20.78 15: evalperfect1bb3in -> evalperfect1bb4in : [ E>=C ], cost: 1 27.38/20.78 27.38/20.78 16: evalperfect1bb3in -> evalperfect1bb5in : [ C>=1+E ], cost: 1 27.38/20.78 27.38/20.78 17: evalperfect1bb4in -> evalperfect1bb3in : E'=-C+E, [], cost: 1
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