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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307670
details
property
value
status
complete
benchmark
IJCAR_1.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n013.star.cs.uiowa.edu
space
AProVE_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
7.24743 seconds
cpu usage
21.7424
user time
20.3594
system time
1.38291
max virtual memory
1.9208244E7
max residence set size
3412964.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
21.48/6.95 WORST_CASE(Omega(n^1), O(n^1)) 21.48/6.96 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 21.48/6.96 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 21.48/6.96 21.48/6.96 21.48/6.96 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 21.48/6.96 21.48/6.96 (0) CpxTRS 21.48/6.96 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 21.48/6.96 (2) CpxTRS 21.48/6.96 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 21.48/6.96 (4) CpxWeightedTrs 21.48/6.96 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 21.48/6.96 (6) CpxTypedWeightedTrs 21.48/6.96 (7) CompletionProof [UPPER BOUND(ID), 0 ms] 21.48/6.96 (8) CpxTypedWeightedCompleteTrs 21.48/6.96 (9) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 21.48/6.96 (10) CpxTypedWeightedCompleteTrs 21.48/6.96 (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 21.48/6.96 (12) CpxRNTS 21.48/6.96 (13) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 21.48/6.96 (14) CpxRNTS 21.48/6.96 (15) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] 21.48/6.96 (16) CpxRNTS 21.48/6.96 (17) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 21.48/6.96 (18) CpxRNTS 21.48/6.96 (19) IntTrsBoundProof [UPPER BOUND(ID), 1198 ms] 21.48/6.96 (20) CpxRNTS 21.48/6.96 (21) IntTrsBoundProof [UPPER BOUND(ID), 481 ms] 21.48/6.96 (22) CpxRNTS 21.48/6.96 (23) FinalProof [FINISHED, 0 ms] 21.48/6.96 (24) BOUNDS(1, n^1) 21.48/6.96 (25) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 21.48/6.96 (26) TRS for Loop Detection 21.48/6.96 (27) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 21.48/6.96 (28) BEST 21.48/6.96 (29) proven lower bound 21.48/6.96 (30) LowerBoundPropagationProof [FINISHED, 0 ms] 21.48/6.96 (31) BOUNDS(n^1, INF) 21.48/6.96 (32) TRS for Loop Detection 21.48/6.96 21.48/6.96 21.48/6.96 ---------------------------------------- 21.48/6.96 21.48/6.96 (0) 21.48/6.96 Obligation: 21.48/6.96 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 21.48/6.96 21.48/6.96 21.48/6.96 The TRS R consists of the following rules: 21.48/6.96 21.48/6.96 div(0, y) -> 0 21.48/6.96 div(x, y) -> quot(x, y, y) 21.48/6.96 quot(0, s(y), z) -> 0 21.48/6.96 quot(s(x), s(y), z) -> quot(x, y, z) 21.48/6.96 quot(x, 0, s(z)) -> s(div(x, s(z))) 21.48/6.96 21.48/6.96 S is empty. 21.48/6.96 Rewrite Strategy: FULL 21.48/6.96 ---------------------------------------- 21.48/6.96 21.48/6.96 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 21.48/6.96 Converted rc-obligation to irc-obligation. 21.48/6.96 21.48/6.96 As the TRS does not nest defined symbols, we have rc = irc. 21.48/6.96 ---------------------------------------- 21.48/6.96 21.48/6.96 (2) 21.48/6.96 Obligation: 21.48/6.96 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 21.48/6.96 21.48/6.96 21.48/6.96 The TRS R consists of the following rules: 21.48/6.96 21.48/6.96 div(0, y) -> 0 21.48/6.96 div(x, y) -> quot(x, y, y) 21.48/6.96 quot(0, s(y), z) -> 0 21.48/6.96 quot(s(x), s(y), z) -> quot(x, y, z) 21.48/6.96 quot(x, 0, s(z)) -> s(div(x, s(z))) 21.48/6.96 21.48/6.96 S is empty. 21.48/6.96 Rewrite Strategy: INNERMOST 21.48/6.96 ---------------------------------------- 21.48/6.96 21.48/6.96 (3) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 21.48/6.96 Transformed relative TRS to weighted TRS 21.48/6.96 ---------------------------------------- 21.48/6.96 21.48/6.96 (4) 21.48/6.96 Obligation: 21.48/6.96 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). 21.48/6.96 21.48/6.96 21.48/6.96 The TRS R consists of the following rules: 21.48/6.96 21.48/6.96 div(0, y) -> 0 [1] 21.48/6.96 div(x, y) -> quot(x, y, y) [1] 21.48/6.96 quot(0, s(y), z) -> 0 [1] 21.48/6.96 quot(s(x), s(y), z) -> quot(x, y, z) [1] 21.48/6.96 quot(x, 0, s(z)) -> s(div(x, s(z))) [1]
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