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Derivational Complexity: TRS pair #487100760
details
property
value
status
complete
benchmark
4.45.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n139.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
291.594 seconds
cpu usage
334.996
user time
330.958
system time
4.03772
max virtual memory
1.8948648E7
max residence set size
7191996.0
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/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^2).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), 160 ms] (4) CpxRelTRS (5) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxRelTRS (7) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxWeightedTrs (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CpxTypedWeightedTrs (11) CompletionProof [UPPER BOUND(ID), 0 ms] (12) CpxTypedWeightedCompleteTrs (13) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CpxTypedWeightedCompleteTrs (15) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 3 ms] (16) CpxRNTS (17) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CpxRNTS (19) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (20) CpxRNTS (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (22) CpxRNTS (23) IntTrsBoundProof [UPPER BOUND(ID), 25 ms] (24) CpxRNTS (25) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] (26) CpxRNTS (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (28) CpxRNTS (29) IntTrsBoundProof [UPPER BOUND(ID), 192 ms] (30) CpxRNTS (31) IntTrsBoundProof [UPPER BOUND(ID), 93 ms] (32) CpxRNTS (33) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (34) CpxRNTS (35) IntTrsBoundProof [UPPER BOUND(ID), 531 ms] (36) CpxRNTS (37) IntTrsBoundProof [UPPER BOUND(ID), 1190 ms] (38) CpxRNTS (39) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (40) CpxRNTS (41) IntTrsBoundProof [UPPER BOUND(ID), 880 ms] (42) CpxRNTS (43) IntTrsBoundProof [UPPER BOUND(ID), 326 ms] (44) CpxRNTS (45) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (46) CpxRNTS (47) IntTrsBoundProof [UPPER BOUND(ID), 148 ms] (48) CpxRNTS (49) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] (50) CpxRNTS (51) FinalProof [FINISHED, 0 ms] (52) BOUNDS(1, n^2) (53) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (54) CpxRelTRS (55) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (56) typed CpxTrs (57) OrderProof [LOWER BOUND(ID), 0 ms] (58) typed CpxTrs (59) RewriteLemmaProof [LOWER BOUND(ID), 373 ms] (60) BEST (61) proven lower bound (62) LowerBoundPropagationProof [FINISHED, 0 ms] (63) BOUNDS(n^1, INF) (64) typed CpxTrs (65) RewriteLemmaProof [LOWER BOUND(ID), 10 ms] (66) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: f(x, x) -> a f(g(x), y) -> f(x, y) S is empty. Rewrite Strategy: FULL ---------------------------------------- (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
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