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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307741
details
property
value
status
complete
benchmark
thiemann31.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n058.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.551 seconds
cpu usage
1153.03
user time
1139.58
system time
13.4493
max virtual memory
3.7783328E7
max residence set size
1.3019276E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
1152.81/291.46 WORST_CASE(Omega(n^1), O(n^2)) 1152.81/291.48 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1152.81/291.48 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1152.81/291.48 1152.81/291.48 1152.81/291.48 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1152.81/291.48 1152.81/291.48 (0) CpxTRS 1152.81/291.48 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 1152.81/291.48 (2) CpxTRS 1152.81/291.48 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1152.81/291.48 (4) CpxWeightedTrs 1152.81/291.48 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1152.81/291.48 (6) CpxTypedWeightedTrs 1152.81/291.48 (7) CompletionProof [UPPER BOUND(ID), 7 ms] 1152.81/291.48 (8) CpxTypedWeightedCompleteTrs 1152.81/291.48 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1152.81/291.48 (10) CpxRNTS 1152.81/291.48 (11) CompleteCoflocoProof [FINISHED, 1187 ms] 1152.81/291.48 (12) BOUNDS(1, n^2) 1152.81/291.48 (13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1152.81/291.48 (14) TRS for Loop Detection 1152.81/291.48 (15) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1152.81/291.48 (16) BEST 1152.81/291.48 (17) proven lower bound 1152.81/291.48 (18) LowerBoundPropagationProof [FINISHED, 0 ms] 1152.81/291.48 (19) BOUNDS(n^1, INF) 1152.81/291.48 (20) TRS for Loop Detection 1152.81/291.48 1152.81/291.48 1152.81/291.48 ---------------------------------------- 1152.81/291.48 1152.81/291.48 (0) 1152.81/291.48 Obligation: 1152.81/291.48 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1152.81/291.48 1152.81/291.48 1152.81/291.48 The TRS R consists of the following rules: 1152.81/291.48 1152.81/291.48 le(0, y) -> true 1152.81/291.48 le(s(x), 0) -> false 1152.81/291.48 le(s(x), s(y)) -> le(x, y) 1152.81/291.48 mod(x, 0) -> modZeroErro 1152.81/291.48 mod(x, s(y)) -> modIter(x, s(y), 0, 0) 1152.81/291.48 modIter(x, s(y), z, u) -> if(le(x, z), x, s(y), z, u) 1152.81/291.48 if(true, x, y, z, u) -> u 1152.81/291.48 if(false, x, y, z, u) -> if2(le(y, s(u)), x, y, s(z), s(u)) 1152.81/291.48 if2(false, x, y, z, u) -> modIter(x, y, z, u) 1152.81/291.48 if2(true, x, y, z, u) -> modIter(x, y, z, 0) 1152.81/291.48 1152.81/291.48 S is empty. 1152.81/291.48 Rewrite Strategy: FULL 1152.81/291.48 ---------------------------------------- 1152.81/291.48 1152.81/291.48 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 1152.81/291.48 Converted rc-obligation to irc-obligation. 1152.81/291.48 1152.81/291.48 The duplicating contexts are: 1152.81/291.48 modIter([], s(y), z, u) 1152.81/291.48 modIter(x, s(y), [], u) 1152.81/291.48 if(false, x, [], z, u) 1152.81/291.48 if(false, x, y, z, []) 1152.81/291.48 1152.81/291.48 1152.81/291.48 The defined contexts are: 1152.81/291.48 if2([], x1, x2, s(x3), s(x4)) 1152.81/291.48 if([], x1, s(x2), x3, x4) 1152.81/291.48 1152.81/291.48 1152.81/291.48 [] just represents basic- or constructor-terms in the following defined contexts: 1152.81/291.48 if2([], x1, x2, s(x3), s(x4)) 1152.81/291.48 if([], x1, s(x2), x3, x4) 1152.81/291.48 1152.81/291.48 1152.81/291.48 As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc. 1152.81/291.48 ---------------------------------------- 1152.81/291.48 1152.81/291.48 (2) 1152.81/291.48 Obligation: 1152.81/291.48 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^2). 1152.81/291.48 1152.81/291.48 1152.81/291.48 The TRS R consists of the following rules: 1152.81/291.48 1152.81/291.48 le(0, y) -> true 1152.81/291.48 le(s(x), 0) -> false 1152.81/291.48 le(s(x), s(y)) -> le(x, y) 1152.81/291.48 mod(x, 0) -> modZeroErro 1152.81/291.48 mod(x, s(y)) -> modIter(x, s(y), 0, 0) 1152.81/291.48 modIter(x, s(y), z, u) -> if(le(x, z), x, s(y), z, u) 1152.81/291.48 if(true, x, y, z, u) -> u 1152.81/291.48 if(false, x, y, z, u) -> if2(le(y, s(u)), x, y, s(z), s(u)) 1152.81/291.48 if2(false, x, y, z, u) -> modIter(x, y, z, u) 1152.81/291.48 if2(true, x, y, z, u) -> modIter(x, y, z, 0) 1152.81/291.48 1152.81/291.48 S is empty. 1152.81/291.48 Rewrite Strategy: INNERMOST 1152.81/291.48 ---------------------------------------- 1152.81/291.48 1152.81/291.48 (3) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
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