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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307892
details
property
value
status
complete
benchmark
aprove5.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n157.star.cs.uiowa.edu
space
Secret_05_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.665 seconds
cpu usage
1107.97
user time
1097.15
system time
10.8151
max virtual memory
3.7580444E7
max residence set size
1.18204E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^3))
output
1107.65/291.57 WORST_CASE(Omega(n^1), O(n^3)) 1107.65/291.59 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1107.65/291.59 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1107.65/291.59 1107.65/291.59 1107.65/291.59 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^3). 1107.65/291.59 1107.65/291.59 (0) CpxTRS 1107.65/291.59 (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] 1107.65/291.59 (2) CpxTRS 1107.65/291.59 (3) RcToIrcProof [BOTH BOUNDS(ID, ID), 9 ms] 1107.65/291.59 (4) CpxTRS 1107.65/291.59 (5) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1107.65/291.59 (6) CpxWeightedTrs 1107.65/291.59 (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1107.65/291.59 (8) CpxTypedWeightedTrs 1107.65/291.59 (9) CompletionProof [UPPER BOUND(ID), 0 ms] 1107.65/291.59 (10) CpxTypedWeightedCompleteTrs 1107.65/291.59 (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 3 ms] 1107.65/291.59 (12) CpxRNTS 1107.65/291.59 (13) CompleteCoflocoProof [FINISHED, 550 ms] 1107.65/291.59 (14) BOUNDS(1, n^3) 1107.65/291.59 (15) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1107.65/291.59 (16) TRS for Loop Detection 1107.65/291.59 (17) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1107.65/291.59 (18) BEST 1107.65/291.59 (19) proven lower bound 1107.65/291.59 (20) LowerBoundPropagationProof [FINISHED, 0 ms] 1107.65/291.59 (21) BOUNDS(n^1, INF) 1107.65/291.59 (22) TRS for Loop Detection 1107.65/291.59 1107.65/291.59 1107.65/291.59 ---------------------------------------- 1107.65/291.59 1107.65/291.59 (0) 1107.65/291.59 Obligation: 1107.65/291.59 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^3). 1107.65/291.59 1107.65/291.59 1107.65/291.59 The TRS R consists of the following rules: 1107.65/291.59 1107.65/291.59 minus(x, 0) -> x 1107.65/291.59 minus(0, y) -> 0 1107.65/291.59 minus(s(x), s(y)) -> minus(p(s(x)), p(s(y))) 1107.65/291.59 minus(x, plus(y, z)) -> minus(minus(x, y), z) 1107.65/291.59 p(s(s(x))) -> s(p(s(x))) 1107.65/291.59 p(0) -> s(s(0)) 1107.65/291.59 div(s(x), s(y)) -> s(div(minus(x, y), s(y))) 1107.65/291.59 div(plus(x, y), z) -> plus(div(x, z), div(y, z)) 1107.65/291.59 plus(0, y) -> y 1107.65/291.59 plus(s(x), y) -> s(plus(y, minus(s(x), s(0)))) 1107.65/291.59 1107.65/291.59 S is empty. 1107.65/291.59 Rewrite Strategy: FULL 1107.65/291.59 ---------------------------------------- 1107.65/291.59 1107.65/291.59 (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) 1107.65/291.59 The following defined symbols can occur below the 0th argument of minus: p, minus 1107.65/291.59 The following defined symbols can occur below the 1th argument of minus: p 1107.65/291.59 The following defined symbols can occur below the 0th argument of p: p 1107.65/291.59 The following defined symbols can occur below the 0th argument of plus: p, minus 1107.65/291.59 The following defined symbols can occur below the 1th argument of plus: p, minus 1107.65/291.59 The following defined symbols can occur below the 0th argument of div: p, minus 1107.65/291.59 1107.65/291.59 Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: 1107.65/291.59 minus(x, plus(y, z)) -> minus(minus(x, y), z) 1107.65/291.59 div(plus(x, y), z) -> plus(div(x, z), div(y, z)) 1107.65/291.59 1107.65/291.59 ---------------------------------------- 1107.65/291.59 1107.65/291.59 (2) 1107.65/291.59 Obligation: 1107.65/291.59 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^3). 1107.65/291.59 1107.65/291.59 1107.65/291.59 The TRS R consists of the following rules: 1107.65/291.59 1107.65/291.59 minus(x, 0) -> x 1107.65/291.59 minus(0, y) -> 0 1107.65/291.59 minus(s(x), s(y)) -> minus(p(s(x)), p(s(y))) 1107.65/291.59 p(s(s(x))) -> s(p(s(x))) 1107.65/291.59 p(0) -> s(s(0)) 1107.65/291.59 div(s(x), s(y)) -> s(div(minus(x, y), s(y))) 1107.65/291.59 plus(0, y) -> y 1107.65/291.59 plus(s(x), y) -> s(plus(y, minus(s(x), s(0)))) 1107.65/291.59 1107.65/291.59 S is empty. 1107.65/291.59 Rewrite Strategy: FULL 1107.65/291.59 ---------------------------------------- 1107.65/291.59 1107.65/291.59 (3) RcToIrcProof (BOTH BOUNDS(ID, ID)) 1107.65/291.59 Converted rc-obligation to irc-obligation. 1107.65/291.59 1107.65/291.59 The duplicating contexts are: 1107.65/291.59 div(s(x), s([])) 1107.65/291.59 1107.65/291.59 1107.65/291.59 The defined contexts are: 1107.65/291.59 minus([], x1) 1107.65/291.59 minus(x0, [])
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