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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307983
details
property
value
status
complete
benchmark
Ex2_Luc02a_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n074.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.645 seconds
cpu usage
1093.94
user time
1078.52
system time
15.4134
max virtual memory
2.0344944E7
max residence set size
1.5176148E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^3), O(n^3))
output
1093.40/291.50 WORST_CASE(Omega(n^3), O(n^3)) 1093.61/291.52 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1093.61/291.52 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1093.61/291.52 1093.61/291.52 1093.61/291.52 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^3, n^3). 1093.61/291.52 1093.61/291.52 (0) CpxTRS 1093.61/291.52 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 1093.61/291.52 (2) CpxTRS 1093.61/291.52 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1093.61/291.52 (4) CpxWeightedTrs 1093.61/291.52 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1093.61/291.52 (6) CpxTypedWeightedTrs 1093.61/291.52 (7) CompletionProof [UPPER BOUND(ID), 0 ms] 1093.61/291.52 (8) CpxTypedWeightedCompleteTrs 1093.61/291.52 (9) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 1093.61/291.52 (10) CpxTypedWeightedCompleteTrs 1093.61/291.52 (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1093.61/291.52 (12) CpxRNTS 1093.61/291.52 (13) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 1093.61/291.52 (14) CpxRNTS 1093.61/291.52 (15) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] 1093.61/291.52 (16) CpxRNTS 1093.61/291.52 (17) ResultPropagationProof [UPPER BOUND(ID), 2 ms] 1093.61/291.52 (18) CpxRNTS 1093.61/291.52 (19) IntTrsBoundProof [UPPER BOUND(ID), 179 ms] 1093.61/291.52 (20) CpxRNTS 1093.61/291.52 (21) IntTrsBoundProof [UPPER BOUND(ID), 15 ms] 1093.61/291.52 (22) CpxRNTS 1093.61/291.52 (23) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1093.61/291.52 (24) CpxRNTS 1093.61/291.52 (25) IntTrsBoundProof [UPPER BOUND(ID), 372 ms] 1093.61/291.52 (26) CpxRNTS 1093.61/291.52 (27) IntTrsBoundProof [UPPER BOUND(ID), 115 ms] 1093.61/291.52 (28) CpxRNTS 1093.61/291.52 (29) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1093.61/291.52 (30) CpxRNTS 1093.61/291.52 (31) IntTrsBoundProof [UPPER BOUND(ID), 524 ms] 1093.61/291.52 (32) CpxRNTS 1093.61/291.52 (33) IntTrsBoundProof [UPPER BOUND(ID), 64 ms] 1093.61/291.52 (34) CpxRNTS 1093.61/291.52 (35) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1093.61/291.52 (36) CpxRNTS 1093.61/291.52 (37) IntTrsBoundProof [UPPER BOUND(ID), 699 ms] 1093.61/291.52 (38) CpxRNTS 1093.61/291.52 (39) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] 1093.61/291.52 (40) CpxRNTS 1093.61/291.52 (41) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1093.61/291.52 (42) CpxRNTS 1093.61/291.52 (43) IntTrsBoundProof [UPPER BOUND(ID), 2697 ms] 1093.61/291.52 (44) CpxRNTS 1093.61/291.52 (45) IntTrsBoundProof [UPPER BOUND(ID), 49 ms] 1093.61/291.52 (46) CpxRNTS 1093.61/291.52 (47) FinalProof [FINISHED, 0 ms] 1093.61/291.52 (48) BOUNDS(1, n^3) 1093.61/291.52 (49) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1093.61/291.52 (50) CpxTRS 1093.61/291.52 (51) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1093.61/291.52 (52) typed CpxTrs 1093.61/291.52 (53) OrderProof [LOWER BOUND(ID), 0 ms] 1093.61/291.52 (54) typed CpxTrs 1093.61/291.52 (55) RewriteLemmaProof [LOWER BOUND(ID), 270 ms] 1093.61/291.52 (56) BEST 1093.61/291.52 (57) proven lower bound 1093.61/291.52 (58) LowerBoundPropagationProof [FINISHED, 0 ms] 1093.61/291.52 (59) BOUNDS(n^1, INF) 1093.61/291.52 (60) typed CpxTrs 1093.61/291.52 (61) RewriteLemmaProof [LOWER BOUND(ID), 47 ms] 1093.61/291.52 (62) typed CpxTrs 1093.61/291.52 (63) RewriteLemmaProof [LOWER BOUND(ID), 101 ms] 1093.61/291.52 (64) BEST 1093.61/291.52 (65) proven lower bound 1093.61/291.52 (66) LowerBoundPropagationProof [FINISHED, 0 ms] 1093.61/291.52 (67) BOUNDS(n^3, INF) 1093.61/291.52 (68) typed CpxTrs 1093.61/291.52 1093.61/291.52 1093.61/291.52 ---------------------------------------- 1093.61/291.52 1093.61/291.52 (0) 1093.61/291.52 Obligation: 1093.61/291.52 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^3, n^3). 1093.61/291.52 1093.61/291.52 1093.61/291.52 The TRS R consists of the following rules: 1093.61/291.52 1093.61/291.52 terms(N) -> cons(recip(sqr(N)), n__terms(s(N))) 1093.61/291.52 sqr(0) -> 0 1093.61/291.52 sqr(s(X)) -> s(add(sqr(X), dbl(X))) 1093.61/291.52 dbl(0) -> 0 1093.61/291.52 dbl(s(X)) -> s(s(dbl(X))) 1093.61/291.52 add(0, X) -> X 1093.61/291.52 add(s(X), Y) -> s(add(X, Y)) 1093.61/291.52 first(0, X) -> nil 1093.61/291.52 first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z))) 1093.61/291.52 terms(X) -> n__terms(X) 1093.61/291.52 first(X1, X2) -> n__first(X1, X2) 1093.61/291.52 activate(n__terms(X)) -> terms(X) 1093.61/291.52 activate(n__first(X1, X2)) -> first(X1, X2)
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