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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313531
details
property
value
status
complete
benchmark
Ex4_7_56_Bor03_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n121.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
8.59555 seconds
cpu usage
18.105
user time
16.7268
system time
1.37815
max virtual memory
1.8911488E7
max residence set size
3448168.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
17.76/6.27 WORST_CASE(Omega(n^1), O(n^1)) 18.04/6.29 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 18.04/6.29 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 18.04/6.29 18.04/6.29 18.04/6.29 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 18.04/6.29 18.04/6.29 (0) CpxTRS 18.04/6.29 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 18.04/6.29 (2) CpxWeightedTrs 18.04/6.29 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 18.04/6.29 (4) CpxTypedWeightedTrs 18.04/6.29 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 18.04/6.29 (6) CpxTypedWeightedCompleteTrs 18.04/6.29 (7) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 18.04/6.29 (8) CpxTypedWeightedCompleteTrs 18.04/6.29 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 18.04/6.29 (10) CpxRNTS 18.04/6.29 (11) InliningProof [UPPER BOUND(ID), 78 ms] 18.04/6.29 (12) CpxRNTS 18.04/6.29 (13) SimplificationProof [BOTH BOUNDS(ID, ID), 1 ms] 18.04/6.29 (14) CpxRNTS 18.04/6.29 (15) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] 18.04/6.29 (16) CpxRNTS 18.04/6.29 (17) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 18.04/6.29 (18) CpxRNTS 18.04/6.29 (19) IntTrsBoundProof [UPPER BOUND(ID), 149 ms] 18.04/6.29 (20) CpxRNTS 18.04/6.29 (21) IntTrsBoundProof [UPPER BOUND(ID), 5 ms] 18.04/6.29 (22) CpxRNTS 18.04/6.29 (23) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 18.04/6.29 (24) CpxRNTS 18.04/6.29 (25) IntTrsBoundProof [UPPER BOUND(ID), 189 ms] 18.04/6.29 (26) CpxRNTS 18.04/6.29 (27) IntTrsBoundProof [UPPER BOUND(ID), 42 ms] 18.04/6.29 (28) CpxRNTS 18.04/6.29 (29) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 18.04/6.29 (30) CpxRNTS 18.04/6.29 (31) IntTrsBoundProof [UPPER BOUND(ID), 310 ms] 18.04/6.29 (32) CpxRNTS 18.04/6.29 (33) IntTrsBoundProof [UPPER BOUND(ID), 158 ms] 18.04/6.29 (34) CpxRNTS 18.04/6.29 (35) FinalProof [FINISHED, 0 ms] 18.04/6.29 (36) BOUNDS(1, n^1) 18.04/6.29 (37) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 18.04/6.29 (38) CpxTRS 18.04/6.29 (39) SlicingProof [LOWER BOUND(ID), 0 ms] 18.04/6.29 (40) CpxTRS 18.04/6.29 (41) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 18.04/6.29 (42) typed CpxTrs 18.04/6.29 (43) OrderProof [LOWER BOUND(ID), 0 ms] 18.04/6.29 (44) typed CpxTrs 18.04/6.29 (45) RewriteLemmaProof [LOWER BOUND(ID), 237 ms] 18.04/6.29 (46) proven lower bound 18.04/6.29 (47) LowerBoundPropagationProof [FINISHED, 0 ms] 18.04/6.29 (48) BOUNDS(n^1, INF) 18.04/6.29 18.04/6.29 18.04/6.29 ---------------------------------------- 18.04/6.29 18.04/6.29 (0) 18.04/6.29 Obligation: 18.04/6.29 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 18.04/6.29 18.04/6.29 18.04/6.29 The TRS R consists of the following rules: 18.04/6.29 18.04/6.29 from(X) -> cons(X, n__from(s(X))) 18.04/6.29 after(0, XS) -> XS 18.04/6.29 after(s(N), cons(X, XS)) -> after(N, activate(XS)) 18.04/6.29 from(X) -> n__from(X) 18.04/6.29 activate(n__from(X)) -> from(X) 18.04/6.29 activate(X) -> X 18.04/6.29 18.04/6.29 S is empty. 18.04/6.29 Rewrite Strategy: INNERMOST 18.04/6.29 ---------------------------------------- 18.04/6.29 18.04/6.29 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 18.04/6.29 Transformed relative TRS to weighted TRS 18.04/6.29 ---------------------------------------- 18.04/6.29 18.04/6.29 (2) 18.04/6.29 Obligation: 18.04/6.29 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). 18.04/6.29 18.04/6.29 18.04/6.29 The TRS R consists of the following rules: 18.04/6.29 18.04/6.29 from(X) -> cons(X, n__from(s(X))) [1] 18.04/6.29 after(0, XS) -> XS [1] 18.04/6.29 after(s(N), cons(X, XS)) -> after(N, activate(XS)) [1] 18.04/6.29 from(X) -> n__from(X) [1] 18.04/6.29 activate(n__from(X)) -> from(X) [1] 18.04/6.29 activate(X) -> X [1] 18.04/6.29 18.04/6.29 Rewrite Strategy: INNERMOST 18.04/6.29 ---------------------------------------- 18.04/6.29 18.04/6.29 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID))
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