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Runti Compl Inner Rewri 22807 pair #381903996
details
property
value
status
complete
benchmark
match.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n033.star.cs.uiowa.edu
space
Frederiksen_Others
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.639788866 seconds
cpu usage
344.323101809
max memory
5.924196352E9
stage attributes
key
value
output-size
46461
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^2)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). (0) CpxRelTRS (1) STerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 260 ms] (2) CpxRelTRS (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxWeightedTrs (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxTypedWeightedTrs (7) CompletionProof [UPPER BOUND(ID), 0 ms] (8) CpxTypedWeightedCompleteTrs (9) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (12) CpxRNTS (13) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CpxRNTS (15) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CpxRNTS (17) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (18) CpxRNTS (19) IntTrsBoundProof [UPPER BOUND(ID), 563 ms] (20) CpxRNTS (21) IntTrsBoundProof [UPPER BOUND(ID), 68 ms] (22) CpxRNTS (23) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (24) CpxRNTS (25) IntTrsBoundProof [UPPER BOUND(ID), 9481 ms] (26) CpxRNTS (27) IntTrsBoundProof [UPPER BOUND(ID), 4625 ms] (28) CpxRNTS (29) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (30) CpxRNTS (31) IntTrsBoundProof [UPPER BOUND(ID), 177 ms] (32) CpxRNTS (33) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] (34) CpxRNTS (35) FinalProof [FINISHED, 0 ms] (36) BOUNDS(1, n^2) (37) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (38) CpxRelTRS (39) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (40) typed CpxTrs (41) OrderProof [LOWER BOUND(ID), 0 ms] (42) typed CpxTrs (43) RewriteLemmaProof [LOWER BOUND(ID), 307 ms] (44) typed CpxTrs (45) RewriteLemmaProof [LOWER BOUND(ID), 31 ms] (46) proven lower bound (47) LowerBoundPropagationProof [FINISHED, 0 ms] (48) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: loop(Cons(x, xs), Nil, pp, ss) -> False loop(Cons(x', xs'), Cons(x, xs), pp, ss) -> loop[Ite](!EQ(x', x), Cons(x', xs'), Cons(x, xs), pp, ss) loop(Nil, s, pp, ss) -> True match1(p, s) -> loop(p, s, p, s) The (relative) TRS S consists of the following rules: !EQ(S(x), S(y)) -> !EQ(x, y) !EQ(0, S(y)) -> False !EQ(S(x), 0) -> False !EQ(0, 0) -> True loop[Ite](False, p, s, pp, Cons(x, xs)) -> loop(pp, xs, pp, xs) loop[Ite](True, Cons(x', xs'), Cons(x, xs), pp, ss) -> loop(xs', xs, pp, ss) Rewrite Strategy: INNERMOST ---------------------------------------- (1) STerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved termination of relative rules ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules:
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