details

property	value
status	complete
benchmark	complete4.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n072.star.cs.uiowa.edu
space	VMCAI04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	2.12437 seconds
cpu usage	4.4346
user time	4.12605
system time	0.308549
max virtual memory	1.8685548E7
max residence set size	216336.0

stage attributes

key	value
starexec-result	WORST_CASE(NON_POLY, ?)

output

4.24/2.08 WORST_CASE(NON_POLY, ?) 4.24/2.08 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 4.24/2.08 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.24/2.08 4.24/2.08 4.24/2.08 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF). 4.24/2.08 4.24/2.08 (0) CpxIntTrs 4.24/2.08 (1) Loat Proof [FINISHED, 421 ms] 4.24/2.08 (2) BOUNDS(INF, INF) 4.24/2.08 4.24/2.08 4.24/2.08 ---------------------------------------- 4.24/2.08 4.24/2.08 (0) 4.24/2.08 Obligation: 4.24/2.08 Complexity Int TRS consisting of the following rules: 4.24/2.08 eval(A, B) -> Com_1(eval(A - 1, C)) :|: A >= 0 4.24/2.08 eval(A, B) -> Com_1(eval(A, B - 1)) :|: B >= 0 4.24/2.08 start(A, B) -> Com_1(eval(A, B)) :|: TRUE 4.24/2.08 4.24/2.08 The start-symbols are:[start_2] 4.24/2.08 4.24/2.08 4.24/2.08 ---------------------------------------- 4.24/2.08 4.24/2.08 (1) Loat Proof (FINISHED) 4.24/2.08 4.24/2.08 4.24/2.08 ### Pre-processing the ITS problem ### 4.24/2.08 4.24/2.08 4.24/2.08 4.24/2.08 Initial linear ITS problem 4.24/2.08 4.24/2.08 Start location: start 4.24/2.08 4.24/2.08 0: eval -> eval : A'=-1+A, B'=free, [ A>=0 ], cost: 1 4.24/2.08 4.24/2.08 1: eval -> eval : B'=-1+B, [ B>=0 ], cost: 1 4.24/2.08 4.24/2.08 2: start -> eval : [], cost: 1 4.24/2.08 4.24/2.08 4.24/2.08 4.24/2.08 ### Simplification by acceleration and chaining ### 4.24/2.08 4.24/2.08 4.24/2.08 4.24/2.08 Accelerating simple loops of location 0. 4.24/2.08 4.24/2.08 Accelerating the following rules: 4.24/2.08 4.24/2.08 0: eval -> eval : A'=-1+A, B'=free, [ A>=0 ], cost: 1 4.24/2.08 4.24/2.08 1: eval -> eval : B'=-1+B, [ B>=0 ], cost: 1 4.24/2.08 4.24/2.08 4.24/2.08 4.24/2.08 Accelerated rule 0 with metering function 1+A, yielding the new rule 3. 4.24/2.08 4.24/2.08 Accelerated rule 1 with metering function 1+B, yielding the new rule 4. 4.24/2.08 4.24/2.08 Nested simple loops 0 (outer loop) and 4 (inner loop) with metering function 1+A, resulting in the new rules: 5, 6. 4.24/2.08 4.24/2.08 Removing the simple loops: 0 1. 4.24/2.08 4.24/2.08 4.24/2.08 4.24/2.08 Accelerated all simple loops using metering functions (where possible): 4.24/2.08 4.24/2.08 Start location: start 4.24/2.08 4.24/2.08 3: eval -> eval : A'=-1, B'=free, [ A>=0 ], cost: 1+A 4.24/2.08 4.24/2.08 4: eval -> eval : B'=-1, [ B>=0 ], cost: 1+B 4.24/2.08 4.24/2.08 5: eval -> eval : A'=-1, B'=-1, [ A>=0 && free>=0 ], cost: 2+free*(1+A)+2*A 4.24/2.08 4.24/2.08 6: eval -> eval : A'=-1, B'=-1, [ B>=0 && A>=0 && free>=0 ], cost: 3+free*(1+A)+2*A+B 4.24/2.08 4.24/2.08 2: start -> eval : [], cost: 1 4.24/2.08 4.24/2.08 4.24/2.08 4.24/2.08 Chained accelerated rules (with incoming rules): 4.24/2.08 4.24/2.08 Start location: start 4.24/2.08 4.24/2.08 2: start -> eval : [], cost: 1 4.24/2.08 4.24/2.08 7: start -> eval : A'=-1, B'=free, [ A>=0 ], cost: 2+A 4.24/2.08 4.24/2.08 8: start -> eval : B'=-1, [ B>=0 ], cost: 2+B 4.24/2.08 4.24/2.08 9: start -> eval : A'=-1, B'=-1, [ A>=0 && free>=0 ], cost: 3+free*(1+A)+2*A 4.24/2.08 4.24/2.08 10: start -> eval : A'=-1, B'=-1, [ B>=0 && A>=0 && free>=0 ], cost: 4+free*(1+A)+2*A+B 4.24/2.08 4.24/2.08 popout

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all output return to Complexity_ITS 2019-03-21 04.46