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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307958
details
property
value
status
complete
benchmark
12.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n181.star.cs.uiowa.edu
space
Various_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.698 seconds
cpu usage
1091.01
user time
1081.16
system time
9.84732
max virtual memory
5.630548E7
max residence set size
1.463254E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
1090.44/291.55 WORST_CASE(Omega(n^1), O(n^2)) 1090.44/291.58 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1090.44/291.58 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1090.44/291.58 1090.44/291.58 1090.44/291.58 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1090.44/291.58 1090.44/291.58 (0) CpxTRS 1090.44/291.58 (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] 1090.44/291.58 (2) CpxTRS 1090.44/291.58 (3) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms] 1090.44/291.58 (4) CpxRelTRS 1090.44/291.58 (5) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 1090.44/291.58 (6) CpxRelTRS 1090.44/291.58 (7) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1090.44/291.58 (8) CpxWeightedTrs 1090.44/291.58 (9) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1090.44/291.58 (10) CpxWeightedTrs 1090.44/291.58 (11) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1090.44/291.58 (12) CpxTypedWeightedTrs 1090.44/291.58 (13) CompletionProof [UPPER BOUND(ID), 0 ms] 1090.44/291.58 (14) CpxTypedWeightedCompleteTrs 1090.44/291.58 (15) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1090.44/291.58 (16) CpxRNTS 1090.44/291.58 (17) CompleteCoflocoProof [FINISHED, 305 ms] 1090.44/291.58 (18) BOUNDS(1, n^2) 1090.44/291.58 (19) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1090.44/291.58 (20) CpxTRS 1090.44/291.58 (21) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1090.44/291.58 (22) typed CpxTrs 1090.44/291.58 (23) OrderProof [LOWER BOUND(ID), 0 ms] 1090.44/291.58 (24) typed CpxTrs 1090.44/291.58 (25) RewriteLemmaProof [LOWER BOUND(ID), 1048 ms] 1090.44/291.58 (26) BEST 1090.44/291.58 (27) proven lower bound 1090.44/291.58 (28) LowerBoundPropagationProof [FINISHED, 0 ms] 1090.44/291.58 (29) BOUNDS(n^1, INF) 1090.44/291.58 (30) typed CpxTrs 1090.44/291.58 (31) RewriteLemmaProof [LOWER BOUND(ID), 25 ms] 1090.44/291.58 (32) BOUNDS(1, INF) 1090.44/291.58 1090.44/291.58 1090.44/291.58 ---------------------------------------- 1090.44/291.58 1090.44/291.58 (0) 1090.44/291.58 Obligation: 1090.44/291.58 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1090.44/291.58 1090.44/291.58 1090.44/291.58 The TRS R consists of the following rules: 1090.44/291.58 1090.44/291.58 O(0) -> 0 1090.44/291.58 +(0, x) -> x 1090.44/291.58 +(x, 0) -> x 1090.44/291.58 +(O(x), O(y)) -> O(+(x, y)) 1090.44/291.58 +(O(x), I(y)) -> I(+(x, y)) 1090.44/291.58 +(I(x), O(y)) -> I(+(x, y)) 1090.44/291.58 +(I(x), I(y)) -> O(+(+(x, y), I(0))) 1090.44/291.58 *(0, x) -> 0 1090.44/291.58 *(x, 0) -> 0 1090.44/291.58 *(O(x), y) -> O(*(x, y)) 1090.44/291.58 *(I(x), y) -> +(O(*(x, y)), y) 1090.44/291.58 1090.44/291.58 S is empty. 1090.44/291.58 Rewrite Strategy: FULL 1090.44/291.58 ---------------------------------------- 1090.44/291.58 1090.44/291.58 (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) 1090.44/291.58 The following defined symbols can occur below the 0th argument of +: O, +, * 1090.44/291.58 The following defined symbols can occur below the 0th argument of O: O, +, * 1090.44/291.58 1090.44/291.58 Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: 1090.44/291.58 +(O(x), O(y)) -> O(+(x, y)) 1090.44/291.58 +(I(x), O(y)) -> I(+(x, y)) 1090.44/291.58 *(O(x), y) -> O(*(x, y)) 1090.44/291.58 1090.44/291.58 ---------------------------------------- 1090.44/291.58 1090.44/291.58 (2) 1090.44/291.58 Obligation: 1090.44/291.58 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^2). 1090.44/291.58 1090.44/291.58 1090.44/291.58 The TRS R consists of the following rules: 1090.44/291.58 1090.44/291.58 O(0) -> 0 1090.44/291.58 +(0, x) -> x 1090.44/291.58 +(x, 0) -> x 1090.44/291.58 +(O(x), I(y)) -> I(+(x, y)) 1090.44/291.58 +(I(x), I(y)) -> O(+(+(x, y), I(0))) 1090.44/291.58 *(0, x) -> 0 1090.44/291.58 *(x, 0) -> 0 1090.44/291.58 *(I(x), y) -> +(O(*(x, y)), y) 1090.44/291.58 1090.44/291.58 S is empty. 1090.44/291.58 Rewrite Strategy: FULL 1090.44/291.58 ---------------------------------------- 1090.44/291.58 1090.44/291.58 (3) NonCtorToCtorProof (UPPER BOUND(ID)) 1090.44/291.58 transformed non-ctor to ctor-system
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