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Runti Compl Full Rewri 10127 pair #381902741
details
property
value
status
complete
benchmark
lse.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
CiME_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
23.7587640285 seconds
cpu usage
58.428741501
max memory
4.879028224E9
stage attributes
key
value
output-size
83859
starexec-result
WORST_CASE(Omega(n^2), 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^2), O(n^2)) 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2). (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), 0 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)), 117 ms] (12) CdtProblem (13) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CdtProblem (15) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 74 ms] (16) CdtProblem (17) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 82 ms] (18) CdtProblem (19) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 46 ms] (20) CdtProblem (21) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 48 ms] (22) CdtProblem (23) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (24) BOUNDS(1, 1) (25) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (26) CpxTRS (27) SlicingProof [LOWER BOUND(ID), 0 ms] (28) CpxTRS (29) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (30) typed CpxTrs (31) OrderProof [LOWER BOUND(ID), 0 ms] (32) typed CpxTrs (33) RewriteLemmaProof [LOWER BOUND(ID), 194 ms] (34) BEST (35) proven lower bound (36) LowerBoundPropagationProof [FINISHED, 0 ms] (37) BOUNDS(n^1, INF) (38) typed CpxTrs (39) RewriteLemmaProof [LOWER BOUND(ID), 695 ms] (40) typed CpxTrs (41) RewriteLemmaProof [LOWER BOUND(ID), 693 ms] (42) typed CpxTrs (43) RewriteLemmaProof [LOWER BOUND(ID), 19 ms] (44) proven lower bound (45) LowerBoundPropagationProof [FINISHED, 0 ms] (46) BOUNDS(n^2, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2). The TRS R consists of the following rules: Term_sub(Case(m, xi, n), s) -> Frozen(m, Sum_sub(xi, s), n, s) Frozen(m, Sum_constant(Left), n, s) -> Term_sub(m, s) Frozen(m, Sum_constant(Right), n, s) -> Term_sub(n, s) Frozen(m, Sum_term_var(xi), n, s) -> Case(Term_sub(m, s), xi, Term_sub(n, s)) Term_sub(Term_app(m, n), s) -> Term_app(Term_sub(m, s), Term_sub(n, s)) Term_sub(Term_pair(m, n), s) -> Term_pair(Term_sub(m, s), Term_sub(n, s)) Term_sub(Term_inl(m), s) -> Term_inl(Term_sub(m, s)) Term_sub(Term_inr(m), s) -> Term_inr(Term_sub(m, s)) Term_sub(Term_var(x), Id) -> Term_var(x) Term_sub(Term_var(x), Cons_usual(y, m, s)) -> m Term_sub(Term_var(x), Cons_usual(y, m, s)) -> Term_sub(Term_var(x), s) Term_sub(Term_var(x), Cons_sum(xi, k, s)) -> Term_sub(Term_var(x), s) Term_sub(Term_sub(m, s), t) -> Term_sub(m, Concat(s, t)) Sum_sub(xi, Id) -> Sum_term_var(xi) Sum_sub(xi, Cons_sum(psi, k, s)) -> Sum_constant(k) Sum_sub(xi, Cons_sum(psi, k, s)) -> Sum_sub(xi, s) Sum_sub(xi, Cons_usual(y, m, s)) -> Sum_sub(xi, s) Concat(Concat(s, t), u) -> Concat(s, Concat(t, u)) Concat(Cons_usual(x, m, s), t) -> Cons_usual(x, Term_sub(m, t), Concat(s, t)) Concat(Cons_sum(xi, k, s), t) -> Cons_sum(xi, k, Concat(s, t)) Concat(Id, s) -> s S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) The following defined symbols can occur below the 1th argument of Frozen: Sum_sub
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