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Complexity_C_Integer 2019-03-21 04.38 pair #429989028
details
property
value
status
complete
benchmark
svcomp_c.01-no-inv.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n086.star.cs.uiowa.edu
space
Adapted_from_Stroeder_15
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.48079 seconds
cpu usage
2.47956
user time
2.27677
system time
0.202787
max virtual memory
1.8273644E7
max residence set size
182288.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^2))
output
2.11/1.45 WORST_CASE(?, O(n^2)) 2.11/1.46 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.11/1.46 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.11/1.46 2.11/1.46 2.11/1.46 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 2.11/1.46 2.11/1.46 (0) CpxIntTrs 2.11/1.46 (1) Koat Proof [FINISHED, 285 ms] 2.11/1.46 (2) BOUNDS(1, n^2) 2.11/1.46 2.11/1.46 2.11/1.46 ---------------------------------------- 2.11/1.46 2.11/1.46 (0) 2.11/1.46 Obligation: 2.11/1.46 Complexity Int TRS consisting of the following rules: 2.11/1.46 eval_foo_start(v_.01, v_.02, v_c, v_x, v_y) -> Com_1(eval_foo_bb0_in(v_.01, v_.02, v_c, v_x, v_y)) :|: TRUE 2.11/1.46 eval_foo_bb0_in(v_.01, v_.02, v_c, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_x, v_.02, v_c, v_x, v_y)) :|: TRUE 2.11/1.46 eval_foo_bb1_in(v_.01, v_.02, v_c, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.01, 1, v_c, v_x, v_y)) :|: v_.01 >= 0 2.11/1.46 eval_foo_bb1_in(v_.01, v_.02, v_c, v_x, v_y) -> Com_1(eval_foo_bb5_in(v_.01, v_.02, v_c, v_x, v_y)) :|: v_.01 < 0 2.11/1.46 eval_foo_bb2_in(v_.01, v_.02, v_c, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.01, v_.02, v_c, v_x, v_y)) :|: v_.01 > v_.02 2.11/1.46 eval_foo_bb2_in(v_.01, v_.02, v_c, v_x, v_y) -> Com_1(eval_foo_bb4_in(v_.01, v_.02, v_c, v_x, v_y)) :|: v_.01 <= v_.02 2.11/1.46 eval_foo_bb3_in(v_.01, v_.02, v_c, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.01, 2 * v_.02, v_c, v_x, v_y)) :|: TRUE 2.11/1.46 eval_foo_bb4_in(v_.01, v_.02, v_c, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.01 - 1, v_.02, v_c, v_x, v_y)) :|: TRUE 2.11/1.46 eval_foo_bb5_in(v_.01, v_.02, v_c, v_x, v_y) -> Com_1(eval_foo_stop(v_.01, v_.02, v_c, v_x, v_y)) :|: TRUE 2.11/1.46 2.11/1.46 The start-symbols are:[eval_foo_start_5] 2.11/1.46 2.11/1.46 2.11/1.46 ---------------------------------------- 2.11/1.46 2.11/1.46 (1) Koat Proof (FINISHED) 2.11/1.46 YES(?, 13*ar_1 + 4*ar_1^2 + 15) 2.11/1.46 2.11/1.46 2.11/1.46 2.11/1.46 Initial complexity problem: 2.11/1.46 2.11/1.46 1: T: 2.11/1.46 2.11/1.46 (Comp: ?, Cost: 1) evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2)) 2.11/1.46 2.11/1.46 (Comp: ?, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2)) 2.11/1.46 2.11/1.46 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 1)) [ ar_0 >= 0 ] 2.11/1.46 2.11/1.46 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ] 2.11/1.46 2.11/1.46 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ] 2.11/1.46 2.11/1.46 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 ] 2.11/1.46 2.11/1.46 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 2*ar_2)) 2.11/1.46 2.11/1.46 (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2)) 2.11/1.46 2.11/1.46 (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2)) 2.11/1.46 2.11/1.46 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ] 2.11/1.46 2.11/1.46 start location: koat_start 2.11/1.46 2.11/1.46 leaf cost: 0 2.11/1.46 2.11/1.46 2.11/1.46 2.11/1.46 Repeatedly propagating knowledge in problem 1 produces the following problem: 2.11/1.46 2.11/1.46 2: T: 2.11/1.46 2.11/1.46 (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2)) 2.11/1.46 2.11/1.46 (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_2)) 2.11/1.46 2.11/1.46 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 1)) [ ar_0 >= 0 ] 2.11/1.46 2.11/1.46 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ] 2.11/1.46 2.11/1.46 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ] 2.11/1.46 2.11/1.46 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 ] 2.11/1.46 2.11/1.46 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, 2*ar_2)) 2.11/1.46 2.11/1.46 (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2)) 2.11/1.46 2.11/1.46 (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2)) 2.11/1.46 2.11/1.46 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ] 2.11/1.46 2.11/1.46 start location: koat_start 2.11/1.46 2.11/1.46 leaf cost: 0 2.11/1.46 2.11/1.46 2.11/1.46 2.11/1.46 A polynomial rank function with 2.11/1.46 2.11/1.46 Pol(evalfoostart) = 2
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