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Complexity_ITS 2019-03-21 04.46 pair #429989826
details
property
value
status
complete
benchmark
aaron2.c.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n050.star.cs.uiowa.edu
space
Flores-Montoya_16
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
9.38395 seconds
cpu usage
15.4339
user time
14.8611
system time
0.572761
max virtual memory
1.8549816E7
max residence set size
224372.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
15.33/9.33 WORST_CASE(Omega(n^1), O(n^1)) 15.33/9.34 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 15.33/9.34 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 15.33/9.34 15.33/9.34 15.33/9.34 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, nat(2 + 6 * Arg_2 + -6 * Arg_4) + nat(3 + 3 * Arg_2 + -3 * Arg_4) + max(6 + Arg_2 + -1 * Arg_4, 5) + max(4, 5 + 2 * Arg_2 + -2 * Arg_4)). 15.33/9.34 15.33/9.34 (0) CpxIntTrs 15.33/9.34 (1) Koat2 Proof [FINISHED, 3739 ms] 15.33/9.34 (2) BOUNDS(1, nat(2 + 6 * Arg_2 + -6 * Arg_4) + nat(3 + 3 * Arg_2 + -3 * Arg_4) + max(6 + Arg_2 + -1 * Arg_4, 5) + max(4, 5 + 2 * Arg_2 + -2 * Arg_4)) 15.33/9.34 (3) Loat Proof [FINISHED, 7570 ms] 15.33/9.34 (4) BOUNDS(n^1, INF) 15.33/9.34 15.33/9.34 15.33/9.34 ---------------------------------------- 15.33/9.34 15.33/9.34 (0) 15.33/9.34 Obligation: 15.33/9.34 Complexity Int TRS consisting of the following rules: 15.33/9.34 eval_aaron2_start(v__01, v__02, v_3, v_tx, v_x, v_y) -> Com_1(eval_aaron2_bb0_in(v__01, v__02, v_3, v_tx, v_x, v_y)) :|: TRUE 15.33/9.34 eval_aaron2_bb0_in(v__01, v__02, v_3, v_tx, v_x, v_y) -> Com_1(eval_aaron2_0(v__01, v__02, v_3, v_tx, v_x, v_y)) :|: TRUE 15.33/9.34 eval_aaron2_0(v__01, v__02, v_3, v_tx, v_x, v_y) -> Com_1(eval_aaron2_1(v__01, v__02, v_3, v_tx, v_x, v_y)) :|: TRUE 15.33/9.34 eval_aaron2_1(v__01, v__02, v_3, v_tx, v_x, v_y) -> Com_1(eval_aaron2_2(v__01, v__02, v_3, v_tx, v_x, v_y)) :|: TRUE 15.33/9.34 eval_aaron2_2(v__01, v__02, v_3, v_tx, v_x, v_y) -> Com_1(eval_aaron2_3(v__01, v__02, v_3, v_tx, v_x, v_y)) :|: TRUE 15.33/9.34 eval_aaron2_3(v__01, v__02, v_3, v_tx, v_x, v_y) -> Com_1(eval_aaron2_bb1_in(v_x, v_y, v_3, v_tx, v_x, v_y)) :|: v_tx >= 0 15.33/9.34 eval_aaron2_3(v__01, v__02, v_3, v_tx, v_x, v_y) -> Com_1(eval_aaron2_bb5_in(v__01, v__02, v_3, v_tx, v_x, v_y)) :|: v_tx < 0 15.33/9.34 eval_aaron2_bb1_in(v__01, v__02, v_3, v_tx, v_x, v_y) -> Com_1(eval_aaron2_bb5_in(v__01, v__02, v_3, v_tx, v_x, v_y)) :|: v__01 < v__02 15.33/9.34 eval_aaron2_bb1_in(v__01, v__02, v_3, v_tx, v_x, v_y) -> Com_1(eval_aaron2_bb5_in(v__01, v__02, v_3, v_tx, v_x, v_y)) :|: v_tx < 0 15.33/9.34 eval_aaron2_bb1_in(v__01, v__02, v_3, v_tx, v_x, v_y) -> Com_1(eval_aaron2_bb2_in(v__01, v__02, v_3, v_tx, v_x, v_y)) :|: v__01 >= v__02 && v_tx >= 0 15.33/9.34 eval_aaron2_bb2_in(v__01, v__02, v_3, v_tx, v_x, v_y) -> Com_1(eval_aaron2_4(v__01, v__02, v_3, v_tx, v_x, v_y)) :|: TRUE 15.33/9.34 eval_aaron2_4(v__01, v__02, v_3, v_tx, v_x, v_y) -> Com_1(eval_aaron2_5(v__01, v__02, nondef_0, v_tx, v_x, v_y)) :|: TRUE 15.33/9.34 eval_aaron2_5(v__01, v__02, v_3, v_tx, v_x, v_y) -> Com_1(eval_aaron2_bb3_in(v__01, v__02, v_3, v_tx, v_x, v_y)) :|: v_3 > 0 15.33/9.34 eval_aaron2_5(v__01, v__02, v_3, v_tx, v_x, v_y) -> Com_1(eval_aaron2_bb4_in(v__01, v__02, v_3, v_tx, v_x, v_y)) :|: v_3 <= 0 15.33/9.34 eval_aaron2_bb3_in(v__01, v__02, v_3, v_tx, v_x, v_y) -> Com_1(eval_aaron2_bb1_in(v__01 - v_tx - 1, v__02, v_3, v_tx, v_x, v_y)) :|: TRUE 15.33/9.34 eval_aaron2_bb4_in(v__01, v__02, v_3, v_tx, v_x, v_y) -> Com_1(eval_aaron2_bb1_in(v__01, v__02 + v_tx + 1, v_3, v_tx, v_x, v_y)) :|: TRUE 15.33/9.34 eval_aaron2_bb5_in(v__01, v__02, v_3, v_tx, v_x, v_y) -> Com_1(eval_aaron2_stop(v__01, v__02, v_3, v_tx, v_x, v_y)) :|: TRUE 15.33/9.34 15.33/9.34 The start-symbols are:[eval_aaron2_start_6] 15.33/9.34 15.33/9.34 15.33/9.34 ---------------------------------------- 15.33/9.34 15.33/9.34 (1) Koat2 Proof (FINISHED) 15.33/9.34 YES( ?, 4+max([0, 1+2*Arg_2+-2*Arg_4])+max([0, 1+3*Arg_2+-3*Arg_4])+max([0, 1+3*Arg_2+-3*Arg_4])+max([0, 1+Arg_2-Arg_4])+max([0, 1+Arg_2-Arg_4])+max([5, 6+Arg_2-Arg_4])+max([0, 1+Arg_2-Arg_4]) {O(n)}) 15.33/9.34 15.33/9.34 15.33/9.34 15.33/9.34 Initial Complexity Problem: 15.33/9.34 15.33/9.34 Start: evalaaron2start 15.33/9.34 15.33/9.34 Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5 15.33/9.34 15.33/9.34 Temp_Vars: G 15.33/9.34 15.33/9.34 Locations: evalaaron20, evalaaron21, evalaaron22, evalaaron23, evalaaron24, evalaaron25, evalaaron2bb0in, evalaaron2bb1in, evalaaron2bb2in, evalaaron2bb3in, evalaaron2bb4in, evalaaron2bb5in, evalaaron2start, evalaaron2stop 15.33/9.34 15.33/9.34 Transitions: 15.33/9.34 15.33/9.34 evalaaron20(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalaaron21(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|: 15.33/9.34 15.33/9.34 evalaaron21(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalaaron22(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|: 15.33/9.34 15.33/9.34 evalaaron22(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalaaron23(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|: 15.33/9.34 15.33/9.34 evalaaron23(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalaaron2bb1in(Arg_0,Arg_2,Arg_2,Arg_4,Arg_4,Arg_5):|:0 <= Arg_0 15.33/9.34 15.33/9.34 evalaaron23(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalaaron2bb5in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_0+1 <= 0 15.33/9.34 15.33/9.34 evalaaron24(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalaaron25(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,G):|:Arg_4 <= Arg_3 && Arg_4 <= Arg_2 && Arg_4 <= Arg_1 && Arg_3 <= Arg_2 && Arg_3 <= Arg_1 && Arg_1 <= Arg_2 && 0 <= Arg_0 15.33/9.34 15.33/9.34 evalaaron25(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalaaron2bb3in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_4 <= Arg_3 && Arg_4 <= Arg_2 && Arg_4 <= Arg_1 && Arg_3 <= Arg_2 && Arg_3 <= Arg_1 && Arg_1 <= Arg_2 && 0 <= Arg_0 && 1 <= Arg_5 15.33/9.34 15.33/9.34 evalaaron25(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalaaron2bb4in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_4 <= Arg_3 && Arg_4 <= Arg_2 && Arg_4 <= Arg_1 && Arg_3 <= Arg_2 && Arg_3 <= Arg_1 && Arg_1 <= Arg_2 && 0 <= Arg_0 && Arg_5 <= 0 15.33/9.34 15.33/9.34 evalaaron2bb0in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalaaron20(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|: 15.33/9.34 15.33/9.34 evalaaron2bb1in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalaaron2bb2in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_4 <= Arg_3 && Arg_1 <= Arg_2 && 0 <= Arg_0 && Arg_3 <= Arg_1 && 0 <= Arg_0 15.33/9.34 15.33/9.34 evalaaron2bb1in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalaaron2bb5in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_4 <= Arg_3 && Arg_1 <= Arg_2 && 0 <= Arg_0 && Arg_1+1 <= Arg_3 15.33/9.34 15.33/9.34 evalaaron2bb2in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalaaron24(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_4 <= Arg_3 && Arg_4 <= Arg_2 && Arg_4 <= Arg_1 && Arg_3 <= Arg_2 && Arg_3 <= Arg_1 && Arg_1 <= Arg_2 && 0 <= Arg_0 15.33/9.34 15.33/9.34 evalaaron2bb3in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalaaron2bb1in(Arg_0,Arg_1-Arg_0-1,Arg_2,Arg_3,Arg_4,Arg_5):|:1 <= Arg_5 && 1 <= Arg_0+Arg_5 && Arg_4 <= Arg_3 && Arg_4 <= Arg_2 && Arg_4 <= Arg_1 && Arg_3 <= Arg_2 && Arg_3 <= Arg_1 && Arg_1 <= Arg_2 && 0 <= Arg_0 15.33/9.34 15.33/9.34 evalaaron2bb4in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalaaron2bb1in(Arg_0,Arg_1,Arg_2,Arg_3+Arg_0+1,Arg_4,Arg_5):|:Arg_5 <= 0 && Arg_5 <= Arg_0 && Arg_4 <= Arg_3 && Arg_4 <= Arg_2 && Arg_4 <= Arg_1 && Arg_3 <= Arg_2 && Arg_3 <= Arg_1 && Arg_1 <= Arg_2 && 0 <= Arg_0 15.33/9.34 15.33/9.34 evalaaron2bb5in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalaaron2stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|: 15.33/9.34 15.33/9.34 evalaaron2start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> evalaaron2bb0in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|: 15.33/9.34 15.33/9.34 15.33/9.34 15.33/9.34 Timebounds: 15.33/9.34 15.33/9.34 Overall timebound: 4+max([0, 1+2*Arg_2+-2*Arg_4])+max([0, 1+3*Arg_2+-3*Arg_4])+max([0, 1+3*Arg_2+-3*Arg_4])+max([0, 1+Arg_2-Arg_4])+max([0, 1+Arg_2-Arg_4])+max([5, 6+Arg_2-Arg_4])+max([0, 1+Arg_2-Arg_4]) {O(n)} 15.33/9.34 15.33/9.34 2: evalaaron20->evalaaron21: 1 {O(1)} 15.33/9.34 15.33/9.34 3: evalaaron21->evalaaron22: 1 {O(1)}
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