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Runti Compl Inner Rewri 22807 pair #381904612
details
property
value
status
complete
benchmark
#4.34.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n052.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.465495825 seconds
cpu usage
461.762922621
max memory
7.864717312E9
stage attributes
key
value
output-size
28903
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
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^2)) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). (0) CpxTRS (1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (2) CdtProblem (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CdtProblem (5) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CdtProblem (7) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 105 ms] (8) CdtProblem (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 18 ms] (10) CdtProblem (11) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CdtProblem (13) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CdtProblem (15) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CdtProblem (17) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CdtProblem (19) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (20) CdtProblem (21) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (22) CdtProblem (23) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (24) CdtProblem (25) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (26) CdtProblem (27) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (28) CdtProblem (29) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (30) CdtProblem (31) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (32) CdtProblem (33) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 1872 ms] (34) CdtProblem (35) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (36) BOUNDS(1, 1) (37) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (38) CpxTRS (39) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (40) typed CpxTrs (41) OrderProof [LOWER BOUND(ID), 0 ms] (42) typed CpxTrs (43) RewriteLemmaProof [LOWER BOUND(ID), 184 ms] (44) BEST (45) proven lower bound (46) LowerBoundPropagationProof [FINISHED, 0 ms] (47) BOUNDS(n^1, INF) (48) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: f(0) -> true f(1) -> false f(s(x)) -> f(x) if(true, x, y) -> x if(false, x, y) -> y g(s(x), s(y)) -> if(f(x), s(x), s(y)) g(x, c(y)) -> g(x, g(s(c(y)), y)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (2) Obligation: Complexity Dependency Tuples Problem Rules: f(0) -> true f(1) -> false f(s(z0)) -> f(z0) if(true, z0, z1) -> z0 if(false, z0, z1) -> z1 g(s(z0), s(z1)) -> if(f(z0), s(z0), s(z1))
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