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Derivational Complexity: TRS Innermost pair #487105580
details
property
value
status
complete
benchmark
2.54.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n148.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
291.507 seconds
cpu usage
313.171
user time
310.491
system time
2.67999
max virtual memory
1.9058596E7
max residence set size
5269880.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
WORST_CASE(Omega(n^1), O(n^2)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^2). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 193 ms] (4) CpxRelTRS (5) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxWeightedTrs (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedTrs (9) CompletionProof [UPPER BOUND(ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTypedWeightedCompleteTrs (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 15 ms] (14) CpxRNTS (15) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CpxRNTS (17) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CpxRNTS (19) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (20) CpxRNTS (21) IntTrsBoundProof [UPPER BOUND(ID), 94 ms] (22) CpxRNTS (23) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] (24) CpxRNTS (25) ResultPropagationProof [UPPER BOUND(ID), 3 ms] (26) CpxRNTS (27) IntTrsBoundProof [UPPER BOUND(ID), 264 ms] (28) CpxRNTS (29) IntTrsBoundProof [UPPER BOUND(ID), 83 ms] (30) CpxRNTS (31) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (32) CpxRNTS (33) IntTrsBoundProof [UPPER BOUND(ID), 1894 ms] (34) CpxRNTS (35) IntTrsBoundProof [UPPER BOUND(ID), 1298 ms] (36) CpxRNTS (37) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (38) CpxRNTS (39) IntTrsBoundProof [UPPER BOUND(ID), 1639 ms] (40) CpxRNTS (41) IntTrsBoundProof [UPPER BOUND(ID), 667 ms] (42) CpxRNTS (43) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (44) CpxRNTS (45) IntTrsBoundProof [UPPER BOUND(ID), 138 ms] (46) CpxRNTS (47) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] (48) CpxRNTS (49) FinalProof [FINISHED, 0 ms] (50) BOUNDS(1, n^2) (51) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (52) CpxRelTRS (53) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (54) typed CpxTrs (55) OrderProof [LOWER BOUND(ID), 0 ms] (56) typed CpxTrs (57) RewriteLemmaProof [LOWER BOUND(ID), 280 ms] (58) BEST (59) proven lower bound (60) LowerBoundPropagationProof [FINISHED, 0 ms] (61) BOUNDS(n^1, INF) (62) typed CpxTrs (63) RewriteLemmaProof [LOWER BOUND(ID), 42 ms] (64) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: f(x, a) -> x f(x, g(y)) -> f(g(x), y) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(a) -> a encArg(g(x_1)) -> g(encArg(x_1)) encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) encode_a -> a encode_g(x_1) -> g(encArg(x_1))
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