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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308530
details
property
value
status
complete
benchmark
#4.30a.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n126.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
11.0624 seconds
cpu usage
27.3602
user time
25.5512
system time
1.80902
max virtual memory
1.92087E7
max residence set size
4010348.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
27.19/8.42 WORST_CASE(Omega(n^1), O(n^1)) 27.19/8.43 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 27.19/8.43 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 27.19/8.43 27.19/8.43 27.19/8.43 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 27.19/8.43 27.19/8.43 (0) CpxTRS 27.19/8.43 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 27.19/8.43 (2) CpxTRS 27.19/8.43 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 27.19/8.43 (4) CpxWeightedTrs 27.19/8.43 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 1 ms] 27.19/8.43 (6) CpxTypedWeightedTrs 27.19/8.43 (7) CompletionProof [UPPER BOUND(ID), 0 ms] 27.19/8.43 (8) CpxTypedWeightedCompleteTrs 27.19/8.43 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 3 ms] 27.19/8.43 (10) CpxRNTS 27.19/8.43 (11) CompleteCoflocoProof [FINISHED, 270 ms] 27.19/8.43 (12) BOUNDS(1, n^1) 27.19/8.43 (13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 27.19/8.43 (14) TRS for Loop Detection 27.19/8.43 (15) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 27.19/8.43 (16) BEST 27.19/8.43 (17) proven lower bound 27.19/8.43 (18) LowerBoundPropagationProof [FINISHED, 0 ms] 27.19/8.43 (19) BOUNDS(n^1, INF) 27.19/8.43 (20) TRS for Loop Detection 27.19/8.43 27.19/8.43 27.19/8.43 ---------------------------------------- 27.19/8.43 27.19/8.43 (0) 27.19/8.43 Obligation: 27.19/8.43 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 27.19/8.43 27.19/8.43 27.19/8.43 The TRS R consists of the following rules: 27.19/8.43 27.19/8.43 minus(x, 0) -> x 27.19/8.43 minus(s(x), s(y)) -> minus(x, y) 27.19/8.43 le(0, y) -> true 27.19/8.43 le(s(x), 0) -> false 27.19/8.43 le(s(x), s(y)) -> le(x, y) 27.19/8.43 quot(0, s(y)) -> 0 27.19/8.43 quot(s(x), s(y)) -> s(quot(minus(s(x), s(y)), s(y))) 27.19/8.43 27.19/8.43 S is empty. 27.19/8.43 Rewrite Strategy: FULL 27.19/8.43 ---------------------------------------- 27.19/8.43 27.19/8.43 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 27.19/8.43 Converted rc-obligation to irc-obligation. 27.19/8.43 27.19/8.43 The duplicating contexts are: 27.19/8.43 quot(s(x), s([])) 27.19/8.43 27.19/8.43 27.19/8.43 The defined contexts are: 27.19/8.43 quot([], s(x1)) 27.19/8.43 minus(s([]), s(x1)) 27.19/8.43 minus([], x1) 27.19/8.43 27.19/8.43 27.19/8.43 [] just represents basic- or constructor-terms in the following defined contexts: 27.19/8.43 quot([], s(x1)) 27.19/8.43 27.19/8.43 27.19/8.43 As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc. 27.19/8.43 ---------------------------------------- 27.19/8.43 27.19/8.43 (2) 27.19/8.43 Obligation: 27.19/8.43 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 27.19/8.43 27.19/8.43 27.19/8.43 The TRS R consists of the following rules: 27.19/8.43 27.19/8.43 minus(x, 0) -> x 27.19/8.43 minus(s(x), s(y)) -> minus(x, y) 27.19/8.43 le(0, y) -> true 27.19/8.43 le(s(x), 0) -> false 27.19/8.43 le(s(x), s(y)) -> le(x, y) 27.19/8.43 quot(0, s(y)) -> 0 27.19/8.43 quot(s(x), s(y)) -> s(quot(minus(s(x), s(y)), s(y))) 27.19/8.43 27.19/8.43 S is empty. 27.19/8.43 Rewrite Strategy: INNERMOST 27.19/8.43 ---------------------------------------- 27.19/8.43 27.19/8.43 (3) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 27.19/8.43 Transformed relative TRS to weighted TRS 27.19/8.43 ---------------------------------------- 27.19/8.43 27.19/8.43 (4) 27.19/8.43 Obligation: 27.19/8.43 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). 27.19/8.43 27.19/8.43 27.19/8.43 The TRS R consists of the following rules:
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