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Runti Compl Inner Rewri 22807 pair #381904279
details
property
value
status
complete
benchmark
prov.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n078.star.cs.uiowa.edu
space
Rubio_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
4.8153898716 seconds
cpu usage
13.044576662
max memory
2.817040384E9
stage attributes
key
value
output-size
11641
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxWeightedTrs (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxTypedWeightedTrs (5) CompletionProof [UPPER BOUND(ID), 0 ms] (6) CpxTypedWeightedCompleteTrs (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (8) CpxRNTS (9) CompleteCoflocoProof [FINISHED, 136 ms] (10) BOUNDS(1, n^1) (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTRS (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (14) typed CpxTrs (15) OrderProof [LOWER BOUND(ID), 0 ms] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 504 ms] (18) BEST (19) proven lower bound (20) LowerBoundPropagationProof [FINISHED, 0 ms] (21) BOUNDS(n^1, INF) (22) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: ackin(s(X), s(Y)) -> u21(ackin(s(X), Y), X) u21(ackout(X), Y) -> u22(ackin(Y, X)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: ackin(s(X), s(Y)) -> u21(ackin(s(X), Y), X) [1] u21(ackout(X), Y) -> u22(ackin(Y, X)) [1] Rewrite Strategy: INNERMOST ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: ackin(s(X), s(Y)) -> u21(ackin(s(X), Y), X) [1] u21(ackout(X), Y) -> u22(ackin(Y, X)) [1] The TRS has the following type information: ackin :: s -> s -> ackout:u22 s :: s -> s u21 :: ackout:u22 -> s -> ackout:u22 ackout :: s -> ackout:u22 u22 :: ackout:u22 -> ackout:u22 Rewrite Strategy: INNERMOST ---------------------------------------- (5) CompletionProof (UPPER BOUND(ID)) The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: ackin(v0, v1) -> null_ackin [0] u21(v0, v1) -> null_u21 [0] And the following fresh constants: null_ackin, null_u21, const
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