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Runti Compl Full Rewri 10127 pair #381902456
details
property
value
status
complete
benchmark
hydra-Zantema06.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n035.star.cs.uiowa.edu
space
Mixed_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
9.84615516663 seconds
cpu usage
26.233726377
max memory
4.283056128E9
stage attributes
key
value
output-size
10242
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
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^1)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] (2) CpxTRS (3) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxTRS (5) CpxTrsToCdtProof [UPPER BOUND(ID), 8 ms] (6) CdtProblem (7) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CdtProblem (9) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CdtProblem (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 45 ms] (12) CdtProblem (13) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (14) BOUNDS(1, 1) (15) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CpxTRS (17) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (18) typed CpxTrs (19) OrderProof [LOWER BOUND(ID), 0 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 548 ms] (22) BEST (23) proven lower bound (24) LowerBoundPropagationProof [FINISHED, 0 ms] (25) BOUNDS(n^1, INF) (26) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: h(e(x), y) -> h(d(x, y), s(y)) d(g(g(0, x), y), s(z)) -> g(e(x), d(g(g(0, x), y), z)) d(g(g(0, x), y), 0) -> e(y) d(g(0, x), y) -> e(x) d(g(x, y), z) -> g(d(x, z), e(y)) g(e(x), e(y)) -> e(g(x, y)) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) The following defined symbols can occur below the 0th argument of h: d The following defined symbols can occur below the 0th argument of d: d Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: d(g(g(0, x), y), s(z)) -> g(e(x), d(g(g(0, x), y), z)) d(g(g(0, x), y), 0) -> e(y) d(g(0, x), y) -> e(x) d(g(x, y), z) -> g(d(x, z), e(y)) ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: h(e(x), y) -> h(d(x, y), s(y)) g(e(x), e(y)) -> e(g(x, y)) S is empty. Rewrite Strategy: FULL ---------------------------------------- (3) RcToIrcProof (BOTH BOUNDS(ID, ID)) Converted rc-obligation to irc-obligation. As the TRS does not nest defined symbols, we have rc = irc. ---------------------------------------- (4) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules:
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