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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313430
details
property
value
status
complete
benchmark
Ex2_Luc02a_L.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n123.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
10.9892 seconds
cpu usage
37.4922
user time
35.4008
system time
2.09145
max virtual memory
3.7509272E7
max residence set size
4645240.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^3), O(n^3))
output
37.31/10.92 WORST_CASE(Omega(n^3), O(n^3)) 37.31/10.94 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 37.31/10.94 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 37.31/10.94 37.31/10.94 37.31/10.94 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^3, n^3). 37.31/10.94 37.31/10.94 (0) CpxTRS 37.31/10.94 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 37.31/10.94 (2) CpxWeightedTrs 37.31/10.94 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 37.31/10.94 (4) CpxTypedWeightedTrs 37.31/10.94 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 37.31/10.94 (6) CpxTypedWeightedCompleteTrs 37.31/10.94 (7) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 37.31/10.94 (8) CpxTypedWeightedCompleteTrs 37.31/10.94 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 37.31/10.94 (10) CpxRNTS 37.31/10.94 (11) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 37.31/10.94 (12) CpxRNTS 37.31/10.94 (13) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] 37.31/10.94 (14) CpxRNTS 37.31/10.94 (15) ResultPropagationProof [UPPER BOUND(ID), 1 ms] 37.31/10.94 (16) CpxRNTS 37.31/10.94 (17) IntTrsBoundProof [UPPER BOUND(ID), 213 ms] 37.31/10.94 (18) CpxRNTS 37.31/10.94 (19) IntTrsBoundProof [UPPER BOUND(ID), 15 ms] 37.31/10.94 (20) CpxRNTS 37.31/10.94 (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 37.31/10.94 (22) CpxRNTS 37.31/10.94 (23) IntTrsBoundProof [UPPER BOUND(ID), 178 ms] 37.31/10.94 (24) CpxRNTS 37.31/10.94 (25) IntTrsBoundProof [UPPER BOUND(ID), 94 ms] 37.31/10.94 (26) CpxRNTS 37.31/10.94 (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 37.31/10.94 (28) CpxRNTS 37.31/10.94 (29) IntTrsBoundProof [UPPER BOUND(ID), 330 ms] 37.31/10.94 (30) CpxRNTS 37.31/10.94 (31) IntTrsBoundProof [UPPER BOUND(ID), 115 ms] 37.31/10.94 (32) CpxRNTS 37.31/10.94 (33) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 37.31/10.94 (34) CpxRNTS 37.31/10.94 (35) IntTrsBoundProof [UPPER BOUND(ID), 493 ms] 37.31/10.94 (36) CpxRNTS 37.31/10.94 (37) IntTrsBoundProof [UPPER BOUND(ID), 54 ms] 37.31/10.94 (38) CpxRNTS 37.31/10.94 (39) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 37.31/10.94 (40) CpxRNTS 37.31/10.94 (41) IntTrsBoundProof [UPPER BOUND(ID), 597 ms] 37.31/10.94 (42) CpxRNTS 37.31/10.94 (43) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] 37.31/10.94 (44) CpxRNTS 37.31/10.94 (45) FinalProof [FINISHED, 0 ms] 37.31/10.94 (46) BOUNDS(1, n^3) 37.31/10.94 (47) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 37.31/10.94 (48) CpxTRS 37.31/10.94 (49) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 37.31/10.94 (50) typed CpxTrs 37.31/10.94 (51) OrderProof [LOWER BOUND(ID), 0 ms] 37.31/10.94 (52) typed CpxTrs 37.31/10.94 (53) RewriteLemmaProof [LOWER BOUND(ID), 320 ms] 37.31/10.94 (54) BEST 37.31/10.94 (55) proven lower bound 37.31/10.94 (56) LowerBoundPropagationProof [FINISHED, 0 ms] 37.31/10.94 (57) BOUNDS(n^1, INF) 37.31/10.94 (58) typed CpxTrs 37.31/10.94 (59) RewriteLemmaProof [LOWER BOUND(ID), 69 ms] 37.31/10.94 (60) typed CpxTrs 37.31/10.94 (61) RewriteLemmaProof [LOWER BOUND(ID), 115 ms] 37.31/10.94 (62) proven lower bound 37.31/10.94 (63) LowerBoundPropagationProof [FINISHED, 0 ms] 37.31/10.94 (64) BOUNDS(n^3, INF) 37.31/10.94 37.31/10.94 37.31/10.94 ---------------------------------------- 37.31/10.94 37.31/10.94 (0) 37.31/10.94 Obligation: 37.31/10.94 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^3, n^3). 37.31/10.94 37.31/10.94 37.31/10.94 The TRS R consists of the following rules: 37.31/10.94 37.31/10.94 terms(N) -> cons(recip(sqr(N))) 37.31/10.94 sqr(0) -> 0 37.31/10.94 sqr(s(X)) -> s(add(sqr(X), dbl(X))) 37.31/10.94 dbl(0) -> 0 37.31/10.94 dbl(s(X)) -> s(s(dbl(X))) 37.31/10.94 add(0, X) -> X 37.31/10.94 add(s(X), Y) -> s(add(X, Y)) 37.31/10.94 first(0, X) -> nil 37.31/10.94 first(s(X), cons(Y)) -> cons(Y) 37.31/10.94 37.31/10.94 S is empty. 37.31/10.94 Rewrite Strategy: INNERMOST 37.31/10.94 ---------------------------------------- 37.31/10.94 37.31/10.94 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 37.31/10.94 Transformed relative TRS to weighted TRS 37.31/10.94 ----------------------------------------
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