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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307907
details
property
value
status
complete
benchmark
31.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n063.star.cs.uiowa.edu
space
Der95
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
42.9651 seconds
cpu usage
103.023
user time
99.7979
system time
3.2252
max virtual memory
1.9076388E7
max residence set size
5895488.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
102.80/42.92 WORST_CASE(Omega(n^1), O(n^1)) 102.80/42.93 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 102.80/42.93 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 102.80/42.93 102.80/42.93 102.80/42.93 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 102.80/42.93 102.80/42.93 (0) CpxTRS 102.80/42.93 (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] 102.80/42.93 (2) CpxTRS 102.80/42.93 (3) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 102.80/42.93 (4) CpxTRS 102.80/42.93 (5) CpxTrsToCdtProof [UPPER BOUND(ID), 5 ms] 102.80/42.93 (6) CdtProblem 102.80/42.93 (7) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 102.80/42.93 (8) CdtProblem 102.80/42.93 (9) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 102.80/42.93 (10) CdtProblem 102.80/42.93 (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 18 ms] 102.80/42.93 (12) CdtProblem 102.80/42.93 (13) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 102.80/42.93 (14) BOUNDS(1, 1) 102.80/42.93 (15) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 102.80/42.93 (16) TRS for Loop Detection 102.80/42.93 (17) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 102.80/42.93 (18) BEST 102.80/42.93 (19) proven lower bound 102.80/42.93 (20) LowerBoundPropagationProof [FINISHED, 0 ms] 102.80/42.93 (21) BOUNDS(n^1, INF) 102.80/42.93 (22) TRS for Loop Detection 102.80/42.93 102.80/42.93 102.80/42.93 ---------------------------------------- 102.80/42.93 102.80/42.93 (0) 102.80/42.93 Obligation: 102.80/42.93 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 102.80/42.93 102.80/42.93 102.80/42.93 The TRS R consists of the following rules: 102.80/42.93 102.80/42.93 :(:(x, y), z) -> :(x, :(y, z)) 102.80/42.93 :(+(x, y), z) -> +(:(x, z), :(y, z)) 102.80/42.93 :(z, +(x, f(y))) -> :(g(z, y), +(x, a)) 102.80/42.93 102.80/42.93 S is empty. 102.80/42.93 Rewrite Strategy: FULL 102.80/42.93 ---------------------------------------- 102.80/42.93 102.80/42.93 (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) 102.80/42.93 The TRS does not nest defined symbols. 102.80/42.93 Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: 102.80/42.93 :(:(x, y), z) -> :(x, :(y, z)) 102.80/42.93 102.80/42.93 ---------------------------------------- 102.80/42.93 102.80/42.93 (2) 102.80/42.93 Obligation: 102.80/42.93 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 102.80/42.93 102.80/42.93 102.80/42.93 The TRS R consists of the following rules: 102.80/42.93 102.80/42.93 :(+(x, y), z) -> +(:(x, z), :(y, z)) 102.80/42.93 :(z, +(x, f(y))) -> :(g(z, y), +(x, a)) 102.80/42.93 102.80/42.93 S is empty. 102.80/42.93 Rewrite Strategy: FULL 102.80/42.93 ---------------------------------------- 102.80/42.93 102.80/42.93 (3) RcToIrcProof (BOTH BOUNDS(ID, ID)) 102.80/42.93 Converted rc-obligation to irc-obligation. 102.80/42.93 102.80/42.93 As the TRS does not nest defined symbols, we have rc = irc. 102.80/42.93 ---------------------------------------- 102.80/42.93 102.80/42.93 (4) 102.80/42.93 Obligation: 102.80/42.93 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 102.80/42.93 102.80/42.93 102.80/42.93 The TRS R consists of the following rules: 102.80/42.93 102.80/42.93 :(+(x, y), z) -> +(:(x, z), :(y, z)) 102.80/42.93 :(z, +(x, f(y))) -> :(g(z, y), +(x, a)) 102.80/42.93 102.80/42.93 S is empty. 102.80/42.93 Rewrite Strategy: INNERMOST 102.80/42.93 ---------------------------------------- 102.80/42.93 102.80/42.93 (5) CpxTrsToCdtProof (UPPER BOUND(ID)) 102.80/42.93 Converted Cpx (relative) TRS to CDT 102.80/42.93 ---------------------------------------- 102.80/42.93 102.80/42.93 (6) 102.80/42.93 Obligation: 102.80/42.93 Complexity Dependency Tuples Problem 102.80/42.93 102.80/42.93 Rules: 102.80/42.93 :(+(z0, z1), z2) -> +(:(z0, z2), :(z1, z2))
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