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Complexity_ITS 2019-03-21 04.46 pair #429990000
details
property
value
status
complete
benchmark
knuth_morris_pratt.c.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n077.star.cs.uiowa.edu
space
Flores-Montoya_16
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
35.7004 seconds
cpu usage
44.9667
user time
41.2738
system time
3.69285
max virtual memory
1.903152E7
max residence set size
330720.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
44.76/35.66 WORST_CASE(Omega(n^1), O(n^1)) 44.76/35.67 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 44.76/35.67 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 44.76/35.67 44.76/35.67 44.76/35.67 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, max(15 + 7 * Arg_2, 15) + nat(1 + 7 * Arg_2) + nat(3 * Arg_2) + nat(30 * Arg_2) + max(9, 9 + Arg_2) + nat(2 + 2 * Arg_2) + nat(10 * Arg_2) + nat(18 * Arg_2) + nat(2 * Arg_2)). 44.76/35.67 44.76/35.67 (0) CpxIntTrs 44.76/35.67 (1) Koat2 Proof [FINISHED, 33.8 s] 44.76/35.67 (2) BOUNDS(1, max(15 + 7 * Arg_2, 15) + nat(1 + 7 * Arg_2) + nat(3 * Arg_2) + nat(30 * Arg_2) + max(9, 9 + Arg_2) + nat(2 + 2 * Arg_2) + nat(10 * Arg_2) + nat(18 * Arg_2) + nat(2 * Arg_2)) 44.76/35.67 (3) Loat Proof [FINISHED, 3096 ms] 44.76/35.67 (4) BOUNDS(n^1, INF) 44.76/35.67 44.76/35.67 44.76/35.67 ---------------------------------------- 44.76/35.67 44.76/35.67 (0) 44.76/35.67 Obligation: 44.76/35.67 Complexity Int TRS consisting of the following rules: 44.76/35.67 eval_srch_start(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n) -> Com_1(eval_srch_bb0_in(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n)) :|: TRUE 44.76/35.67 eval_srch_bb0_in(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n) -> Com_1(eval_srch_0(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n)) :|: TRUE 44.76/35.67 eval_srch_0(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n) -> Com_1(eval_srch_1(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n)) :|: TRUE 44.76/35.67 eval_srch_1(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n) -> Com_1(eval_srch_2(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n)) :|: TRUE 44.76/35.67 eval_srch_2(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n) -> Com_1(eval_srch_3(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n)) :|: TRUE 44.76/35.67 eval_srch_3(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n) -> Com_1(eval_srch_4(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n)) :|: TRUE 44.76/35.67 eval_srch_4(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n) -> Com_1(eval_srch_5(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n)) :|: TRUE 44.76/35.67 eval_srch_5(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n) -> Com_1(eval_srch_6(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n)) :|: TRUE 44.76/35.67 eval_srch_6(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n) -> Com_1(eval_srch_7(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n)) :|: TRUE 44.76/35.67 eval_srch_7(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n) -> Com_1(eval_srch_8(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n)) :|: TRUE 44.76/35.67 eval_srch_8(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n) -> Com_1(eval_srch_9(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n)) :|: TRUE 44.76/35.67 eval_srch_9(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n) -> Com_1(eval_srch_10(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n)) :|: TRUE 44.76/35.67 eval_srch_10(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n) -> Com_1(eval_srch_bb1_in(v_11, v_22, v_23, v_3, 0, 0, v_j_1, v_m, v_n)) :|: TRUE 44.76/35.67 eval_srch_bb1_in(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n) -> Com_1(eval_srch_bb2_in(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n)) :|: v_i_0 < v_n 44.76/35.67 eval_srch_bb1_in(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n) -> Com_1(eval_srch_bb10_in(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n)) :|: v_i_0 >= v_n 44.76/35.67 eval_srch_bb2_in(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n) -> Com_1(eval_srch_bb3_in(v_11, v_22, v_23, nondef_0, v_i_0, v_j_0, v_j_0, v_m, v_n)) :|: TRUE 44.76/35.67 eval_srch_bb3_in(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n) -> Com_1(eval_srch_bb4_in(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n)) :|: v_j_1 >= 0 44.76/35.67 eval_srch_bb3_in(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n) -> Com_1(eval_srch__critedge_in(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n)) :|: v_j_1 < 0 44.76/35.67 eval_srch_bb4_in(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n) -> Com_1(eval_srch_bb5_in(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n)) :|: v_3 < nondef_1 44.76/35.67 eval_srch_bb4_in(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n) -> Com_1(eval_srch_bb5_in(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n)) :|: v_3 > nondef_1 44.76/35.67 eval_srch_bb4_in(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n) -> Com_1(eval_srch__critedge_in(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n)) :|: v_3 >= nondef_1 && v_3 <= nondef_1 44.76/35.67 eval_srch_bb5_in(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n) -> Com_1(eval_srch_bb6_in(nondef_2, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n)) :|: nondef_2 > 0 44.76/35.67 eval_srch_bb5_in(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n) -> Com_1(eval_srch_bb9_in(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n)) :|: nondef_2 <= 0 44.76/35.67 eval_srch_bb6_in(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n) -> Com_1(eval_srch_bb7_in(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n)) :|: v_11 <= v_j_1 + 1 44.76/35.67 eval_srch_bb6_in(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n) -> Com_1(eval_srch_bb8_in(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n)) :|: v_11 > v_j_1 + 1 44.76/35.67 eval_srch_bb7_in(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n) -> Com_1(eval_srch_bb3_in(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1 - v_11, v_m, v_n)) :|: TRUE 44.76/35.67 eval_srch_bb8_in(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n) -> Com_1(eval_srch_24(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n)) :|: TRUE 44.76/35.67 eval_srch_24(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n) -> Com_1(eval_srch_25(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n)) :|: TRUE 44.76/35.67 eval_srch_25(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n) -> Com_1(eval_srch_stop(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n)) :|: TRUE 44.76/35.67 eval_srch_bb9_in(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n) -> Com_1(eval_srch_26(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n)) :|: TRUE 44.76/35.67 eval_srch_26(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n) -> Com_1(eval_srch_27(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n)) :|: TRUE 44.76/35.67 eval_srch_27(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n) -> Com_1(eval_srch_stop(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n)) :|: TRUE 44.76/35.67 eval_srch__critedge_in(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n) -> Com_1(eval_srch_29(v_11, v_i_0 + 1, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n)) :|: TRUE 44.76/35.67 eval_srch_29(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n) -> Com_1(eval_srch_30(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n)) :|: TRUE 44.76/35.67 eval_srch_30(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n) -> Com_1(eval_srch_31(v_11, v_22, v_j_1 + 1, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n)) :|: TRUE 44.76/35.67 eval_srch_31(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n) -> Com_1(eval_srch_32(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n)) :|: TRUE 44.76/35.67 eval_srch_32(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n) -> Com_1(eval_srch_bb10_in(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n)) :|: v_23 >= v_m && v_23 <= v_m 44.76/35.67 eval_srch_32(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n) -> Com_1(eval_srch_bb1_in(v_11, v_22, v_23, v_3, v_22, v_23, v_j_1, v_m, v_n)) :|: v_23 < v_m 44.76/35.67 eval_srch_32(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n) -> Com_1(eval_srch_bb1_in(v_11, v_22, v_23, v_3, v_22, v_23, v_j_1, v_m, v_n)) :|: v_23 > v_m 44.76/35.67 eval_srch_bb10_in(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n) -> Com_1(eval_srch_stop(v_11, v_22, v_23, v_3, v_i_0, v_j_0, v_j_1, v_m, v_n)) :|: TRUE 44.76/35.67 44.76/35.67 The start-symbols are:[eval_srch_start_9] 44.76/35.67 44.76/35.67 44.76/35.67 ---------------------------------------- 44.76/35.67 44.76/35.67 (1) Koat2 Proof (FINISHED) 44.76/35.67 YES( ?, 15+max([0, 7*Arg_2])+max([0, 1+7*Arg_2])+max([0, Arg_2])+max([0, 10*Arg_2])+max([0, Arg_2])+max([0, 1+Arg_2])+max([0, 10*Arg_2])+max([0, 5*Arg_2])+max([0, 9*Arg_2])+max([0, 1+Arg_2])+max([0, 9*Arg_2])+max([0, 2*Arg_2])+max([0, 10*Arg_2])+max([0, Arg_2])+max([0, 5*Arg_2])+max([9, 9+Arg_2]) {O(n)}) 44.76/35.67 44.76/35.67 44.76/35.67 44.76/35.67 Initial Complexity Problem: 44.76/35.67 44.76/35.67 Start: evalsrchstart 44.76/35.67 44.76/35.67 Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5, Arg_6, Arg_7, Arg_8 44.76/35.67 44.76/35.67 Temp_Vars: J 44.76/35.67 44.76/35.67 Locations: evalsrch0, evalsrch1, evalsrch10, evalsrch2, evalsrch24, evalsrch25, evalsrch26, evalsrch27, evalsrch29, evalsrch3, evalsrch30, evalsrch31, evalsrch32, evalsrch4, evalsrch5, evalsrch6, evalsrch7, evalsrch8, evalsrch9, evalsrchbb0in, evalsrchbb10in, evalsrchbb1in, evalsrchbb2in, evalsrchbb3in, evalsrchbb4in, evalsrchbb5in, evalsrchbb6in, evalsrchbb7in, evalsrchbb8in, evalsrchbb9in, evalsrchcritedgein, evalsrchstart, evalsrchstop 44.76/35.67 44.76/35.67 Transitions: 44.76/35.67 44.76/35.67 evalsrch0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8) -> evalsrch1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8):|: 44.76/35.67 44.76/35.67 evalsrch1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8) -> evalsrch2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8):|: 44.76/35.67 44.76/35.67 evalsrch10(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8) -> evalsrchbb1in(0,0,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8):|: 44.76/35.67 44.76/35.67 evalsrch2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8) -> evalsrch3(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8):|: 44.76/35.67 44.76/35.67 evalsrch24(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8) -> evalsrch25(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8):|:2 <= Arg_5 && 2 <= Arg_4+Arg_5 && 2+Arg_4 <= Arg_5 && 3 <= Arg_2+Arg_5 && 2 <= Arg_1+Arg_5 && 2 <= Arg_0+Arg_5 && 1+Arg_4 <= Arg_2 && Arg_4 <= Arg_1 && Arg_4 <= Arg_0 && 0 <= Arg_4 && 1 <= Arg_2+Arg_4 && 0 <= Arg_1+Arg_4 && 0 <= Arg_0+Arg_4 && 1 <= Arg_2 && 1 <= Arg_1+Arg_2 && 1+Arg_1 <= Arg_2 && 1 <= Arg_0+Arg_2 && 1+Arg_0 <= Arg_2 && Arg_1 <= Arg_0 && 0 <= Arg_1 && 0 <= Arg_0+Arg_1 && 0 <= Arg_0 44.76/35.67 44.76/35.67 evalsrch25(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8) -> evalsrchstop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8):|:2 <= Arg_5 && 2 <= Arg_4+Arg_5 && 2+Arg_4 <= Arg_5 && 3 <= Arg_2+Arg_5 && 2 <= Arg_1+Arg_5 && 2 <= Arg_0+Arg_5 && 1+Arg_4 <= Arg_2 && Arg_4 <= Arg_1 && Arg_4 <= Arg_0 && 0 <= Arg_4 && 1 <= Arg_2+Arg_4 && 0 <= Arg_1+Arg_4 && 0 <= Arg_0+Arg_4 && 1 <= Arg_2 && 1 <= Arg_1+Arg_2 && 1+Arg_1 <= Arg_2 && 1 <= Arg_0+Arg_2 && 1+Arg_0 <= Arg_2 && Arg_1 <= Arg_0 && 0 <= Arg_1 && 0 <= Arg_0+Arg_1 && 0 <= Arg_0 44.76/35.67 44.76/35.67 evalsrch26(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8) -> evalsrch27(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8):|:1+Arg_4 <= Arg_2 && Arg_4 <= Arg_1 && Arg_4 <= Arg_0 && 0 <= Arg_4 && 1 <= Arg_2+Arg_4 && 0 <= Arg_1+Arg_4 && 0 <= Arg_0+Arg_4 && 1 <= Arg_2 && 1 <= Arg_1+Arg_2 && 1+Arg_1 <= Arg_2 && 1 <= Arg_0+Arg_2 && 1+Arg_0 <= Arg_2 && Arg_1 <= Arg_0 && 0 <= Arg_1 && 0 <= Arg_0+Arg_1 && 0 <= Arg_0 44.76/35.67 44.76/35.67 evalsrch27(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8) -> evalsrchstop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8):|:1+Arg_4 <= Arg_2 && Arg_4 <= Arg_1 && Arg_4 <= Arg_0 && 0 <= Arg_4 && 1 <= Arg_2+Arg_4 && 0 <= Arg_1+Arg_4 && 0 <= Arg_0+Arg_4 && 1 <= Arg_2 && 1 <= Arg_1+Arg_2 && 1+Arg_1 <= Arg_2 && 1 <= Arg_0+Arg_2 && 1+Arg_0 <= Arg_2 && Arg_1 <= Arg_0 && 0 <= Arg_1 && 0 <= Arg_0+Arg_1 && 0 <= Arg_0 44.76/35.67 44.76/35.67 evalsrch29(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8) -> evalsrch30(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8):|:Arg_6 <= Arg_2 && Arg_6 <= 1+Arg_0 && 1 <= Arg_6 && 1+Arg_4 <= Arg_6 && 2 <= Arg_2+Arg_6 && 1+Arg_1 <= Arg_6 && 1 <= Arg_0+Arg_6 && 1+Arg_0 <= Arg_6 && 1+Arg_4 <= Arg_2 && Arg_4 <= Arg_1 && Arg_4 <= Arg_0 && 1 <= Arg_2 && 1+Arg_1 <= Arg_2 && 1 <= Arg_0+Arg_2 && 1+Arg_0 <= Arg_2 && Arg_1 <= Arg_0 && 0 <= Arg_0 44.76/35.67
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