details

property	value
status	complete
benchmark	a.02.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n069.star.cs.uiowa.edu
space	pasta

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	11.1270279884 seconds
cpu usage	11.095288661
max memory	2.83332608E8

stage attributes

key	value
output-size	3989
starexec-result	MAYBE

output

/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- MAYBE proof of /export/starexec/sandbox/benchmark/theBenchmark.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, INF). (0) CpxIntTrs (1) Loat Proof [FINISHED, 445 ms] (2) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval(A, B) -> Com_1(eval(D, B)) :|: A >= 0 && B >= 0 && B >= A + 1 && A + B >= 2 * C && 3 * C >= A + B + 1 && D >= C + 1 && A + B >= 2 * E && 3 * E >= A + B + 1 && E + 1 >= D eval(A, B) -> Com_1(eval(A, D)) :|: A >= 0 && B >= 0 && B >= A + 1 && A + B >= 2 * C && 3 * C >= A + B + 1 && D >= C && A + B >= 2 * E && 3 * E >= A + B + 1 && E >= D start(A, B) -> Com_1(eval(A, B)) :|: TRUE The start-symbols are:[start_2] ---------------------------------------- (1) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: start 0: eval -> eval : A'=free_1, [ A>=0 && B>=0 && B>=1+A && A+B>=2*free && 3*free>=1+A+B && free_1>=1+free && A+B>=2*free_2 && 3*free_2>=1+A+B && 1+free_2>=free_1 ], cost: 1 1: eval -> eval : B'=free_4, [ A>=0 && B>=0 && B>=1+A && A+B>=2*free_3 && 3*free_3>=1+A+B && free_4>=free_3 && A+B>=2*free_5 && 3*free_5>=1+A+B && free_5>=free_4 ], cost: 1 2: start -> eval : [], cost: 1 Simplified all rules, resulting in: Start location: start 0: eval -> eval : A'=free_1, [ A>=0 && B>=1+A && 3*free>=1+A+B && free_1>=1+free && A+B>=2*free_2 && 3*free_2>=1+A+B && 1+free_2>=free_1 ], cost: 1 1: eval -> eval : B'=free_4, [ A>=0 && B>=1+A && 3*free_3>=1+A+B && free_4>=free_3 && A+B>=2*free_5 && 3*free_5>=1+A+B && free_5>=free_4 ], cost: 1 2: start -> eval : [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 0. Accelerating the following rules: 0: eval -> eval : A'=free_1, [ A>=0 && B>=1+A && 3*free>=1+A+B && free_1>=1+free && A+B>=2*free_2 && 3*free_2>=1+A+B && 1+free_2>=free_1 ], cost: 1 1: eval -> eval : B'=free_4, [ A>=0 && B>=1+A && 3*free_3>=1+A+B && free_4>=free_3 && A+B>=2*free_5 && 3*free_5>=1+A+B && free_5>=free_4 ], cost: 1 During metering: Instantiating temporary variables by {free==-1+free_1,free_1==1+free_2,free_2==-1+free_1} Accelerated rule 0 with metering function -1+free_1-free_2, yielding the new rule 3. During metering: Instantiating temporary variables by {free_3==free_4,free_4==free_3,free_5==free_4} Accelerated rule 1 with metering function free_3-free_4, yielding the new rule 4. Removing the simple loops: 0 1. Accelerated all simple loops using metering functions (where possible): Start location: start 3: eval -> eval : A'=1+free_2, [ A>=0 && B>=1+A && -3+3*free_1>=1+A+B && 1+free_2>=free_1 && A+B>=-2+2*free_1 && -1+free_1-free_2>=1 ], cost: -1+free_1-free_2 4: eval -> eval : B'=free_3, [ A>=0 && B>=1+A && 3*free_4>=1+A+B && A+B>=2*free_4 && free_4>=free_3 && free_3-free_4>=1 ], cost: free_3-free_4 2: start -> eval : [], cost: 1 popout

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all output return to Compl Integ Trans Syste 26843