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Derivational Complexity: TRS pair #487100864
details
property
value
status
complete
benchmark
27.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n145.star.cs.uiowa.edu
space
Der95
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
291.633 seconds
cpu usage
325.5
user time
323.005
system time
2.49498
max virtual memory
3.7514588E7
max residence set size
5201128.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^2).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), 183 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), 0 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), 295 ms] (24) CpxRNTS (25) IntTrsBoundProof [UPPER BOUND(ID), 164 ms] (26) CpxRNTS (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (28) CpxRNTS (29) IntTrsBoundProof [UPPER BOUND(ID), 2679 ms] (30) CpxRNTS (31) IntTrsBoundProof [UPPER BOUND(ID), 5396 ms] (32) CpxRNTS (33) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (34) CpxRNTS (35) IntTrsBoundProof [UPPER BOUND(ID), 159 ms] (36) CpxRNTS (37) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] (38) CpxRNTS (39) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (40) CpxRNTS (41) IntTrsBoundProof [UPPER BOUND(ID), 1176 ms] (42) CpxRNTS (43) IntTrsBoundProof [UPPER BOUND(ID), 798 ms] (44) CpxRNTS (45) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (46) CpxRNTS (47) IntTrsBoundProof [UPPER BOUND(ID), 1182 ms] (48) CpxRNTS (49) IntTrsBoundProof [UPPER BOUND(ID), 837 ms] (50) CpxRNTS (51) FinalProof [FINISHED, 0 ms] (52) BOUNDS(1, n^2) (53) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (54) TRS for Loop Detection (55) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (56) BEST (57) proven lower bound (58) LowerBoundPropagationProof [FINISHED, 0 ms] (59) BOUNDS(n^1, INF) (60) TRS for Loop Detection ---------------------------------------- (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: h(f(x), y) -> f(g(x, y)) g(x, y) -> h(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(f(x_1)) -> f(encArg(x_1)) encArg(cons_h(x_1, x_2)) -> h(encArg(x_1), encArg(x_2)) encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2)) encode_h(x_1, x_2) -> h(encArg(x_1), encArg(x_2)) encode_f(x_1) -> f(encArg(x_1)) encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2)) ---------------------------------------- (2)
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