details

property	value
status	complete
benchmark	complete2.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n014.star.cs.uiowa.edu
space	VMCAI04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	1.81927 seconds
cpu usage	3.94034
user time	3.68657
system time	0.253763
max virtual memory	1.8505492E7
max residence set size	216748.0

stage attributes

key	value
starexec-result	WORST_CASE(?, O(1))

output

3.87/1.78 WORST_CASE(?, O(1)) 3.87/1.79 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 3.87/1.79 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.87/1.79 3.87/1.79 3.87/1.79 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1). 3.87/1.79 3.87/1.79 (0) CpxIntTrs 3.87/1.79 (1) Koat Proof [FINISHED, 84 ms] 3.87/1.79 (2) BOUNDS(1, 1) 3.87/1.79 3.87/1.79 3.87/1.79 ---------------------------------------- 3.87/1.79 3.87/1.79 (0) 3.87/1.79 Obligation: 3.87/1.79 Complexity Int TRS consisting of the following rules: 3.87/1.79 eval(A) -> Com_1(eval(B)) :|: A >= 0 && B + 2 * A >= 10 && 10 >= 2 * A + B 3.87/1.79 start(A) -> Com_1(eval(A)) :|: TRUE 3.87/1.79 3.87/1.79 The start-symbols are:[start_1] 3.87/1.79 3.87/1.79 3.87/1.79 ---------------------------------------- 3.87/1.79 3.87/1.79 (1) Koat Proof (FINISHED) 3.87/1.79 YES(?, 5) 3.87/1.79 3.87/1.79 3.87/1.79 3.87/1.79 Initial complexity problem: 3.87/1.79 3.87/1.79 1: T: 3.87/1.79 3.87/1.79 (Comp: ?, Cost: 1) eval(ar_0) -> Com_1(eval(-2*ar_0 + 10)) [ ar_0 >= 0 ] 3.87/1.79 3.87/1.79 (Comp: ?, Cost: 1) start(ar_0) -> Com_1(eval(ar_0)) 3.87/1.79 3.87/1.79 (Comp: 1, Cost: 0) koat_start(ar_0) -> Com_1(start(ar_0)) [ 0 <= 0 ] 3.87/1.79 3.87/1.79 start location: koat_start 3.87/1.79 3.87/1.79 leaf cost: 0 3.87/1.79 3.87/1.79 3.87/1.79 3.87/1.79 Repeatedly propagating knowledge in problem 1 produces the following problem: 3.87/1.79 3.87/1.79 2: T: 3.87/1.79 3.87/1.79 (Comp: ?, Cost: 1) eval(ar_0) -> Com_1(eval(-2*ar_0 + 10)) [ ar_0 >= 0 ] 3.87/1.79 3.87/1.79 (Comp: 1, Cost: 1) start(ar_0) -> Com_1(eval(ar_0)) 3.87/1.79 3.87/1.79 (Comp: 1, Cost: 0) koat_start(ar_0) -> Com_1(start(ar_0)) [ 0 <= 0 ] 3.87/1.79 3.87/1.79 start location: koat_start 3.87/1.79 3.87/1.79 leaf cost: 0 3.87/1.79 3.87/1.79 3.87/1.79 3.87/1.79 By chaining the transition start(ar_0) -> Com_1(eval(ar_0)) with all transitions in problem 2, the following new transition is obtained: 3.87/1.79 3.87/1.79 start(ar_0) -> Com_1(eval(-2*ar_0 + 10)) [ ar_0 >= 0 ] 3.87/1.79 3.87/1.79 We thus obtain the following problem: 3.87/1.79 3.87/1.79 3: T: 3.87/1.79 3.87/1.79 (Comp: 1, Cost: 2) start(ar_0) -> Com_1(eval(-2*ar_0 + 10)) [ ar_0 >= 0 ] 3.87/1.79 3.87/1.79 (Comp: ?, Cost: 1) eval(ar_0) -> Com_1(eval(-2*ar_0 + 10)) [ ar_0 >= 0 ] 3.87/1.79 3.87/1.79 (Comp: 1, Cost: 0) koat_start(ar_0) -> Com_1(start(ar_0)) [ 0 <= 0 ] 3.87/1.79 3.87/1.79 start location: koat_start 3.87/1.79 3.87/1.79 leaf cost: 0 3.87/1.79 3.87/1.79 3.87/1.79 3.87/1.79 By chaining the transition start(ar_0) -> Com_1(eval(-2*ar_0 + 10)) [ ar_0 >= 0 ] with all transitions in problem 3, the following new transition is obtained: 3.87/1.79 3.87/1.79 start(ar_0) -> Com_1(eval(4*ar_0 - 10)) [ ar_0 >= 0 /\ -2*ar_0 + 10 >= 0 ] 3.87/1.79 3.87/1.79 We thus obtain the following problem: 3.87/1.79 3.87/1.79 4: T: 3.87/1.79 3.87/1.79 (Comp: 1, Cost: 3) start(ar_0) -> Com_1(eval(4*ar_0 - 10)) [ ar_0 >= 0 /\ -2*ar_0 + 10 >= 0 ] 3.87/1.79 3.87/1.79 (Comp: ?, Cost: 1) eval(ar_0) -> Com_1(eval(-2*ar_0 + 10)) [ ar_0 >= 0 ] 3.87/1.79 3.87/1.79 (Comp: 1, Cost: 0) koat_start(ar_0) -> Com_1(start(ar_0)) [ 0 <= 0 ] 3.87/1.79 3.87/1.79 start location: koat_start 3.87/1.79 3.87/1.79 leaf cost: 0 3.87/1.79 popout

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all output return to Complexity_ITS 2019-03-21 04.46