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Complexity_ITS 2019-03-21 04.46 pair #429989974
details
property
value
status
complete
benchmark
ex_paper3.c.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n045.star.cs.uiowa.edu
space
Flores-Montoya_16
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
14.4385 seconds
cpu usage
20.5628
user time
19.3884
system time
1.17437
max virtual memory
1.8854552E7
max residence set size
264584.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
20.48/14.41 WORST_CASE(Omega(n^1), O(n^2)) 20.48/14.42 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 20.48/14.42 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 20.48/14.42 20.48/14.42 20.48/14.42 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, max(10 + Arg_1, 10) + nat(2 + 2 * Arg_1) + nat(2 * Arg_1) + nat(-3 * Arg_1 + 3 * Arg_1 * Arg_7 + 3 * Arg_1^2) + nat(2 * Arg_1 + 2 * Arg_3) + nat(4 * Arg_1 * Arg_7 + Arg_1 * nat(-4 + 4 * Arg_1)) + max(2, 2 + Arg_1 + Arg_3) + nat(9 * Arg_1) + nat(2 + 8 * Arg_1) + nat(-1 * Arg_1 + Arg_1 * Arg_7 + Arg_1 * max(6 * Arg_1, 6)) + nat(6 * Arg_1 + Arg_3) + nat(4 * Arg_1 + 4 * Arg_3)). 20.48/14.42 20.48/14.42 (0) CpxIntTrs 20.48/14.42 (1) Koat2 Proof [FINISHED, 12.7 s] 20.48/14.42 (2) BOUNDS(1, max(10 + Arg_1, 10) + nat(2 + 2 * Arg_1) + nat(2 * Arg_1) + nat(-3 * Arg_1 + 3 * Arg_1 * Arg_7 + 3 * Arg_1^2) + nat(2 * Arg_1 + 2 * Arg_3) + nat(4 * Arg_1 * Arg_7 + Arg_1 * nat(-4 + 4 * Arg_1)) + max(2, 2 + Arg_1 + Arg_3) + nat(9 * Arg_1) + nat(2 + 8 * Arg_1) + nat(-1 * Arg_1 + Arg_1 * Arg_7 + Arg_1 * max(6 * Arg_1, 6)) + nat(6 * Arg_1 + Arg_3) + nat(4 * Arg_1 + 4 * Arg_3)) 20.48/14.42 (3) Loat Proof [FINISHED, 2241 ms] 20.48/14.42 (4) BOUNDS(n^1, INF) 20.48/14.42 20.48/14.42 20.48/14.42 ---------------------------------------- 20.48/14.42 20.48/14.42 (0) 20.48/14.42 Obligation: 20.48/14.42 Complexity Int TRS consisting of the following rules: 20.48/14.42 eval_p3_start(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z) -> Com_1(eval_p3_bb0_in(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z)) :|: TRUE 20.48/14.42 eval_p3_bb0_in(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z) -> Com_1(eval_p3_0(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z)) :|: TRUE 20.48/14.42 eval_p3_0(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z) -> Com_1(eval_p3_1(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z)) :|: TRUE 20.48/14.42 eval_p3_1(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z) -> Com_1(eval_p3_2(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z)) :|: TRUE 20.48/14.42 eval_p3_2(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z) -> Com_1(eval_p3_3(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z)) :|: TRUE 20.48/14.42 eval_p3_3(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z) -> Com_1(eval_p3_4(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z)) :|: TRUE 20.48/14.42 eval_p3_4(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z) -> Com_1(eval_p3_5(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z)) :|: TRUE 20.48/14.42 eval_p3_5(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z) -> Com_1(eval_p3_6(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z)) :|: TRUE 20.48/14.42 eval_p3_6(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z) -> Com_1(eval_p3_7(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z)) :|: TRUE 20.48/14.42 eval_p3_7(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z) -> Com_1(eval_p3_bb1_in(v_x, v_y, v__1, v__3, v_12, v_x, v_y, v_z)) :|: TRUE 20.48/14.42 eval_p3_bb1_in(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z) -> Com_1(eval_p3_bb2_in(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z)) :|: v__0 > 0 20.48/14.42 eval_p3_bb1_in(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z) -> Com_1(eval_p3_bb7_in(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z)) :|: v__0 <= 0 20.48/14.42 eval_p3_bb2_in(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z) -> Com_1(eval_p3_bb3_in(v__0, v__01, v__01, v__3, v_12, v_x, v_y, v_z)) :|: nondef_0 < 0 20.48/14.42 eval_p3_bb2_in(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z) -> Com_1(eval_p3_bb3_in(v__0, v__01, v__01, v__3, v_12, v_x, v_y, v_z)) :|: nondef_0 > 0 20.48/14.42 eval_p3_bb2_in(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z) -> Com_1(eval_p3_bb5_in(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z)) :|: nondef_0 >= 0 && nondef_0 <= 0 20.48/14.42 eval_p3_bb3_in(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z) -> Com_1(eval_p3_bb4_in(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z)) :|: nondef_1 < 0 && v__1 > 0 20.48/14.42 eval_p3_bb3_in(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z) -> Com_1(eval_p3_bb4_in(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z)) :|: nondef_1 > 0 && v__1 > 0 20.48/14.42 eval_p3_bb3_in(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z) -> Com_1(eval_p3_bb6_in(v__0, v__01, v__1, v__1, v_12, v_x, v_y, v_z)) :|: nondef_1 >= 0 && nondef_1 <= 0 20.48/14.42 eval_p3_bb3_in(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z) -> Com_1(eval_p3_bb6_in(v__0, v__01, v__1, v__1, v_12, v_x, v_y, v_z)) :|: v__1 <= 0 20.48/14.42 eval_p3_bb4_in(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z) -> Com_1(eval_p3_15(v__0, v__01, v__1, v__3, v__1 - 1, v_x, v_y, v_z)) :|: TRUE 20.48/14.42 eval_p3_15(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z) -> Com_1(eval_p3_16(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z)) :|: TRUE 20.48/14.42 eval_p3_16(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z) -> Com_1(eval_p3_bb3_in(v__0, v__01, v_12, v__3, v_12, v_x, v_y, v_z)) :|: TRUE 20.48/14.42 eval_p3_bb5_in(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z) -> Com_1(eval_p3_bb6_in(v__0, v__01, v__1, v__01 + 1, v_12, v_x, v_y, v_z)) :|: nondef_2 < 0 20.48/14.42 eval_p3_bb5_in(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z) -> Com_1(eval_p3_bb6_in(v__0, v__01, v__1, v__01 + 1, v_12, v_x, v_y, v_z)) :|: nondef_2 > 0 20.48/14.42 eval_p3_bb5_in(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z) -> Com_1(eval_p3_bb6_in(v__0, v__01, v__1, v_z, v_12, v_x, v_y, v_z)) :|: nondef_2 >= 0 && nondef_2 <= 0 20.48/14.42 eval_p3_bb6_in(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z) -> Com_1(eval_p3_bb1_in(v__0 - 1, v__3, v__1, v__3, v_12, v_x, v_y, v_z)) :|: TRUE 20.48/14.42 eval_p3_bb7_in(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z) -> Com_1(eval_p3_stop(v__0, v__01, v__1, v__3, v_12, v_x, v_y, v_z)) :|: TRUE 20.48/14.42 20.48/14.42 The start-symbols are:[eval_p3_start_8] 20.48/14.42 20.48/14.42 20.48/14.42 ---------------------------------------- 20.48/14.42 20.48/14.42 (1) Koat2 Proof (FINISHED) 20.48/14.42 YES( ?, 10+max([0, Arg_1])+max([0, 1+Arg_1])+max([0, Arg_1])+max([0, Arg_1*(-1+Arg_7+Arg_1)])+max([0, 3*Arg_1])+max([0, 1+4*Arg_1])+max([0, Arg_1])+max([0, Arg_1*(-1+Arg_7+max([6, 6*Arg_1]))])+max([0, Arg_3+6*Arg_1])+max([0, 4*Arg_1+4*Arg_3])+max([0, 3*Arg_1])+max([0, 1+4*Arg_1])+max([0, 3*Arg_1])+max([0, Arg_1*(-1+Arg_7+Arg_1)])+max([0, Arg_1+Arg_3])+max([0, Arg_1*(-1+Arg_7+Arg_1)])+max([0, Arg_1+Arg_3])+max([0, Arg_1*(4*Arg_7+max([0, -4+4*Arg_1]))])+max([0, 1+Arg_1])+max([2, 2+Arg_1+Arg_3]) {O(n^2)}) 20.48/14.42 20.48/14.42 20.48/14.42 20.48/14.42 Initial Complexity Problem: 20.48/14.42 20.48/14.42 Start: evalp3start 20.48/14.42 20.48/14.42 Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5, Arg_6, Arg_7 20.48/14.42 20.48/14.42 Temp_Vars: I 20.48/14.42 20.48/14.42 Locations: evalp30, evalp31, evalp315, evalp316, evalp32, evalp33, evalp34, evalp35, evalp36, evalp37, evalp3bb0in, evalp3bb1in, evalp3bb2in, evalp3bb3in, evalp3bb4in, evalp3bb5in, evalp3bb6in, evalp3bb7in, evalp3start, evalp3stop 20.48/14.42 20.48/14.42 Transitions: 20.48/14.42 20.48/14.42 evalp30(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> evalp31(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|: 20.48/14.42 20.48/14.42 evalp31(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> evalp32(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|: 20.48/14.42 20.48/14.42 evalp315(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> evalp316(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:1+Arg_6 <= Arg_4 && 1+Arg_6 <= Arg_2 && 0 <= Arg_6 && 1 <= Arg_4+Arg_6 && Arg_4 <= 1+Arg_6 && 1 <= Arg_2+Arg_6 && 1 <= Arg_1+Arg_6 && 1 <= Arg_0+Arg_6 && Arg_4 <= Arg_2 && 1 <= Arg_4 && 2 <= Arg_2+Arg_4 && 2 <= Arg_1+Arg_4 && 2 <= Arg_0+Arg_4 && 1 <= Arg_2 && 2 <= Arg_1+Arg_2 && 2 <= Arg_0+Arg_2 && 1 <= Arg_1 && 2 <= Arg_0+Arg_1 && Arg_0 <= Arg_1 && 1 <= Arg_0 20.48/14.42 20.48/14.42 evalp316(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> evalp3bb3in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_6,Arg_5,Arg_6,Arg_7):|:1+Arg_6 <= Arg_4 && 1+Arg_6 <= Arg_2 && 0 <= Arg_6 && 1 <= Arg_4+Arg_6 && Arg_4 <= 1+Arg_6 && 1 <= Arg_2+Arg_6 && 1 <= Arg_1+Arg_6 && 1 <= Arg_0+Arg_6 && Arg_4 <= Arg_2 && 1 <= Arg_4 && 2 <= Arg_2+Arg_4 && 2 <= Arg_1+Arg_4 && 2 <= Arg_0+Arg_4 && 1 <= Arg_2 && 2 <= Arg_1+Arg_2 && 2 <= Arg_0+Arg_2 && 1 <= Arg_1 && 2 <= Arg_0+Arg_1 && Arg_0 <= Arg_1 && 1 <= Arg_0 20.48/14.42 20.48/14.42 evalp32(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> evalp33(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|: 20.48/14.42 20.48/14.42 evalp33(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> evalp34(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|: 20.48/14.42 20.48/14.42 evalp34(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> evalp35(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|: 20.48/14.42 20.48/14.42 evalp35(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> evalp36(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|: 20.48/14.42 20.48/14.42 evalp36(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> evalp37(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|: 20.48/14.42 20.48/14.42 evalp37(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> evalp3bb1in(Arg_1,Arg_1,Arg_3,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|: 20.48/14.42 20.48/14.42 evalp3bb0in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> evalp30(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|: 20.48/14.42 20.48/14.42 evalp3bb1in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> evalp3bb2in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:Arg_0 <= Arg_1 && 1 <= Arg_0 20.48/14.42 20.48/14.42 evalp3bb1in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> evalp3bb7in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:Arg_0 <= Arg_1 && Arg_0 <= 0 20.48/14.42 20.48/14.42 evalp3bb2in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> evalp3bb3in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_2,Arg_5,Arg_6,Arg_7):|:1 <= Arg_1 && 2 <= Arg_0+Arg_1 && Arg_0 <= Arg_1 && 1 <= Arg_0 && I+1 <= 0 20.48/14.42 20.48/14.42 evalp3bb2in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> evalp3bb3in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_2,Arg_5,Arg_6,Arg_7):|:1 <= Arg_1 && 2 <= Arg_0+Arg_1 && Arg_0 <= Arg_1 && 1 <= Arg_0 && 1 <= I 20.48/14.42 20.48/14.42 evalp3bb2in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> evalp3bb5in(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:1 <= Arg_1 && 2 <= Arg_0+Arg_1 && Arg_0 <= Arg_1 && 1 <= Arg_0
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