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Complexity_ITS 2019-03-21 04.46 pair #429989938
details
property
value
status
complete
benchmark
Loopus2015_ex1.c.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n103.star.cs.uiowa.edu
space
Flores-Montoya_16
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
9.50479 seconds
cpu usage
12.9196
user time
12.3067
system time
0.61292
max virtual memory
1.8659764E7
max residence set size
224044.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
12.74/9.47 WORST_CASE(Omega(n^1), O(n^2)) 12.74/9.48 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 12.74/9.48 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 12.74/9.48 12.74/9.48 12.74/9.48 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, max(10 + 2 * Arg_2, 10) + nat(Arg_2^2) + nat(4 * Arg_2) + max(2, 2 + Arg_2) + nat(1 + 4 * Arg_2) + nat(Arg_2^2) * nat(Arg_2) + nat(Arg_2)^2). 12.74/9.48 12.74/9.48 (0) CpxIntTrs 12.74/9.48 (1) Loat Proof [FINISHED, 1117 ms] 12.74/9.48 (2) BOUNDS(n^1, INF) 12.74/9.48 12.74/9.48 12.74/9.48 ---------------------------------------- 12.74/9.48 12.74/9.48 (0) 12.74/9.48 Obligation: 12.74/9.48 Complexity Int TRS consisting of the following rules: 12.74/9.48 eval_foo_start(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0) -> Com_1(eval_foo_bb0_in(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0)) :|: TRUE 12.74/9.48 eval_foo_bb0_in(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0) -> Com_1(eval_foo_0(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0)) :|: TRUE 12.74/9.48 eval_foo_0(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0) -> Com_1(eval_foo_1(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0)) :|: TRUE 12.74/9.48 eval_foo_1(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0) -> Com_1(eval_foo_2(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0)) :|: TRUE 12.74/9.48 eval_foo_2(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0) -> Com_1(eval_foo_3(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0)) :|: TRUE 12.74/9.48 eval_foo_3(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0) -> Com_1(eval_foo_4(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0)) :|: TRUE 12.74/9.48 eval_foo_4(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0) -> Com_1(eval_foo_5(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0)) :|: TRUE 12.74/9.48 eval_foo_5(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0) -> Com_1(eval_foo_6(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0)) :|: TRUE 12.74/9.48 eval_foo_6(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0) -> Com_1(eval_foo_7(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0)) :|: TRUE 12.74/9.48 eval_foo_7(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0) -> Com_1(eval_foo_bb1_in(v_1, v_2, v_3, v_n, v_p_0, 0, v_n)) :|: TRUE 12.74/9.48 eval_foo_bb1_in(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0) -> Com_1(eval_foo_bb2_in(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0)) :|: v_x_0 > 0 12.74/9.48 eval_foo_bb1_in(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0) -> Com_1(eval_foo_bb5_in(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0)) :|: v_x_0 <= 0 12.74/9.48 eval_foo_bb2_in(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0) -> Com_1(eval_foo_10(v_x_0 - 1, v_r_0 + 1, v_3, v_n, v_p_0, v_r_0, v_x_0)) :|: TRUE 12.74/9.48 eval_foo_10(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0) -> Com_1(eval_foo_11(v_1, v_2, nondef_0, v_n, v_p_0, v_r_0, v_x_0)) :|: TRUE 12.74/9.48 eval_foo_11(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0) -> Com_1(eval_foo_bb3_in(v_1, v_2, v_3, v_n, v_2, v_r_0, v_x_0)) :|: v_3 > 0 12.74/9.48 eval_foo_11(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0) -> Com_1(eval_foo_bb1_in(v_1, v_2, v_3, v_n, v_p_0, v_2, v_1)) :|: v_3 <= 0 12.74/9.48 eval_foo_bb3_in(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0) -> Com_1(eval_foo_bb4_in(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0)) :|: v_p_0 > 0 12.74/9.48 eval_foo_bb3_in(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0) -> Com_1(eval_foo_bb1_in(v_1, v_2, v_3, v_n, v_p_0, 0, v_1)) :|: v_p_0 <= 0 12.74/9.48 eval_foo_bb4_in(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0) -> Com_1(eval_foo_bb3_in(v_1, v_2, v_3, v_n, v_p_0 - 1, v_r_0, v_x_0)) :|: TRUE 12.74/9.48 eval_foo_bb5_in(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0) -> Com_1(eval_foo_stop(v_1, v_2, v_3, v_n, v_p_0, v_r_0, v_x_0)) :|: TRUE 12.74/9.48 12.74/9.48 The start-symbols are:[eval_foo_start_7] 12.74/9.48 12.74/9.48 12.74/9.48 ---------------------------------------- 12.74/9.48 12.74/9.48 (1) Loat Proof (FINISHED) 12.74/9.48 12.74/9.48 12.74/9.48 ### Pre-processing the ITS problem ### 12.74/9.48 12.74/9.48 12.74/9.48 12.74/9.48 Initial linear ITS problem 12.74/9.48 12.74/9.48 Start location: evalfoostart 12.74/9.48 12.74/9.48 0: evalfoostart -> evalfoobb0in : [], cost: 1 12.74/9.48 12.74/9.48 1: evalfoobb0in -> evalfoo0 : [], cost: 1 12.74/9.48 12.74/9.48 2: evalfoo0 -> evalfoo1 : [], cost: 1 12.74/9.48 12.74/9.48 3: evalfoo1 -> evalfoo2 : [], cost: 1 12.74/9.48 12.74/9.48 4: evalfoo2 -> evalfoo3 : [], cost: 1 12.74/9.48 12.74/9.48 5: evalfoo3 -> evalfoo4 : [], cost: 1 12.74/9.48 12.74/9.48 6: evalfoo4 -> evalfoo5 : [], cost: 1 12.74/9.48 12.74/9.48 7: evalfoo5 -> evalfoo6 : [], cost: 1 12.74/9.48 12.74/9.48 8: evalfoo6 -> evalfoo7 : [], cost: 1 12.74/9.48 12.74/9.48 9: evalfoo7 -> evalfoobb1in : A'=0, B'=C, [], cost: 1 12.74/9.48 12.74/9.48 10: evalfoobb1in -> evalfoobb2in : [ B>=1 ], cost: 1 12.74/9.48 12.74/9.48 11: evalfoobb1in -> evalfoobb5in : [ 0>=B ], cost: 1 12.74/9.48 12.74/9.48 12: evalfoobb2in -> evalfoo10 : D'=-1+B, E'=1+A, [], cost: 1 12.74/9.48 12.74/9.48 13: evalfoo10 -> evalfoo11 : F'=free, [], cost: 1 12.74/9.48 12.74/9.48 14: evalfoo11 -> evalfoobb3in : G'=E, [ F>=1 ], cost: 1 12.74/9.48 12.74/9.48 15: evalfoo11 -> evalfoobb1in : A'=E, B'=D, [ 0>=F ], cost: 1 12.74/9.48 12.74/9.48 16: evalfoobb3in -> evalfoobb4in : [ G>=1 ], cost: 1 12.74/9.48 12.74/9.48 17: evalfoobb3in -> evalfoobb1in : A'=0, B'=D, [ 0>=G ], cost: 1 12.74/9.48 12.74/9.48 18: evalfoobb4in -> evalfoobb3in : G'=-1+G, [], cost: 1 12.74/9.48 12.74/9.48 19: evalfoobb5in -> evalfoostop : [], cost: 1 12.74/9.48 12.74/9.48 12.74/9.48 12.74/9.48 Removed unreachable and leaf rules: 12.74/9.48 12.74/9.48 Start location: evalfoostart 12.74/9.48
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