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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307903
details
property
value
status
complete
benchmark
11.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n129.star.cs.uiowa.edu
space
Der95
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
10.7163 seconds
cpu usage
30.1569
user time
28.4825
system time
1.6745
max virtual memory
1.9307044E7
max residence set size
4078640.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
29.90/10.65 WORST_CASE(Omega(n^1), O(n^1)) 29.90/10.66 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 29.90/10.66 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 29.90/10.66 29.90/10.66 29.90/10.66 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 29.90/10.66 29.90/10.66 (0) CpxTRS 29.90/10.66 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 29.90/10.66 (2) CpxTRS 29.90/10.66 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 29.90/10.66 (4) CpxWeightedTrs 29.90/10.66 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 29.90/10.66 (6) CpxTypedWeightedTrs 29.90/10.66 (7) CompletionProof [UPPER BOUND(ID), 0 ms] 29.90/10.66 (8) CpxTypedWeightedCompleteTrs 29.90/10.66 (9) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 29.90/10.66 (10) CpxTypedWeightedCompleteTrs 29.90/10.66 (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 29.90/10.66 (12) CpxRNTS 29.90/10.66 (13) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 29.90/10.66 (14) CpxRNTS 29.90/10.66 (15) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] 29.90/10.66 (16) CpxRNTS 29.90/10.66 (17) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 29.90/10.66 (18) CpxRNTS 29.90/10.66 (19) IntTrsBoundProof [UPPER BOUND(ID), 5067 ms] 29.90/10.66 (20) CpxRNTS 29.90/10.66 (21) IntTrsBoundProof [UPPER BOUND(ID), 149 ms] 29.90/10.66 (22) CpxRNTS 29.90/10.66 (23) FinalProof [FINISHED, 0 ms] 29.90/10.66 (24) BOUNDS(1, n^1) 29.90/10.66 (25) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 29.90/10.66 (26) TRS for Loop Detection 29.90/10.66 (27) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 29.90/10.66 (28) BEST 29.90/10.66 (29) proven lower bound 29.90/10.66 (30) LowerBoundPropagationProof [FINISHED, 0 ms] 29.90/10.66 (31) BOUNDS(n^1, INF) 29.90/10.66 (32) TRS for Loop Detection 29.90/10.66 29.90/10.66 29.90/10.66 ---------------------------------------- 29.90/10.66 29.90/10.66 (0) 29.90/10.66 Obligation: 29.90/10.66 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 29.90/10.66 29.90/10.66 29.90/10.66 The TRS R consists of the following rules: 29.90/10.66 29.90/10.66 D(t) -> 1 29.90/10.66 D(constant) -> 0 29.90/10.66 D(+(x, y)) -> +(D(x), D(y)) 29.90/10.66 D(*(x, y)) -> +(*(y, D(x)), *(x, D(y))) 29.90/10.66 D(-(x, y)) -> -(D(x), D(y)) 29.90/10.66 D(minus(x)) -> minus(D(x)) 29.90/10.66 D(div(x, y)) -> -(div(D(x), y), div(*(x, D(y)), pow(y, 2))) 29.90/10.66 D(ln(x)) -> div(D(x), x) 29.90/10.66 D(pow(x, y)) -> +(*(*(y, pow(x, -(y, 1))), D(x)), *(*(pow(x, y), ln(x)), D(y))) 29.90/10.66 29.90/10.66 S is empty. 29.90/10.66 Rewrite Strategy: FULL 29.90/10.66 ---------------------------------------- 29.90/10.66 29.90/10.66 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 29.90/10.66 Converted rc-obligation to irc-obligation. 29.90/10.66 29.90/10.66 As the TRS does not nest defined symbols, we have rc = irc. 29.90/10.66 ---------------------------------------- 29.90/10.66 29.90/10.66 (2) 29.90/10.66 Obligation: 29.90/10.66 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 29.90/10.66 29.90/10.66 29.90/10.66 The TRS R consists of the following rules: 29.90/10.66 29.90/10.66 D(t) -> 1 29.90/10.66 D(constant) -> 0 29.90/10.66 D(+(x, y)) -> +(D(x), D(y)) 29.90/10.66 D(*(x, y)) -> +(*(y, D(x)), *(x, D(y))) 29.90/10.66 D(-(x, y)) -> -(D(x), D(y)) 29.90/10.66 D(minus(x)) -> minus(D(x)) 29.90/10.66 D(div(x, y)) -> -(div(D(x), y), div(*(x, D(y)), pow(y, 2))) 29.90/10.66 D(ln(x)) -> div(D(x), x) 29.90/10.66 D(pow(x, y)) -> +(*(*(y, pow(x, -(y, 1))), D(x)), *(*(pow(x, y), ln(x)), D(y))) 29.90/10.66 29.90/10.66 S is empty. 29.90/10.66 Rewrite Strategy: INNERMOST 29.90/10.66 ---------------------------------------- 29.90/10.66 29.90/10.66 (3) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 29.90/10.66 Transformed relative TRS to weighted TRS 29.90/10.66 ---------------------------------------- 29.90/10.66 29.90/10.66 (4) 29.90/10.66 Obligation: 29.90/10.66 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). 29.90/10.66
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