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Runti Compl Full Rewri 10127 pair #381902644
details
property
value
status
complete
benchmark
secret4.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n054.star.cs.uiowa.edu
space
Secret_07_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.489284992 seconds
cpu usage
332.917097019
max memory
6.087348224E9
stage attributes
key
value
output-size
19820
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
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^2)) proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). (0) CpxTRS (1) DependencyGraphProof [UPPER BOUND(ID), 0 ms] (2) CpxTRS (3) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms] (6) CpxRelTRS (7) RcToIrcProof [BOTH BOUNDS(ID, ID), 4 ms] (8) CpxRelTRS (9) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (10) CdtProblem (11) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CdtProblem (13) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CdtProblem (15) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 87 ms] (16) CdtProblem (17) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 2 ms] (18) CdtProblem (19) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 145 ms] (20) CdtProblem (21) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (22) BOUNDS(1, 1) (23) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (24) TRS for Loop Detection (25) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (26) BEST (27) proven lower bound (28) LowerBoundPropagationProof [FINISHED, 0 ms] (29) BOUNDS(n^1, INF) (30) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: a(h, h, h, x) -> s(x) a(l, x, s(y), h) -> a(l, x, y, s(h)) a(l, x, s(y), s(z)) -> a(l, x, y, a(l, x, s(y), z)) a(l, s(x), h, z) -> a(l, x, z, z) a(s(l), h, h, z) -> a(l, z, h, z) +(x, h) -> x +(h, x) -> x +(s(x), s(y)) -> s(s(+(x, y))) +(+(x, y), z) -> +(x, +(y, z)) s(h) -> 1 app(nil, k) -> k app(l, nil) -> l app(cons(x, l), k) -> cons(x, app(l, k)) sum(cons(x, nil)) -> cons(x, nil) sum(cons(x, cons(y, l))) -> sum(cons(a(x, y, h, h), l)) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) DependencyGraphProof (UPPER BOUND(ID)) The following rules are not reachable from basic terms in the dependency graph and can be removed: +(s(x), s(y)) -> s(s(+(x, y))) +(+(x, y), z) -> +(x, +(y, z)) ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^2). The TRS R consists of the following rules: a(h, h, h, x) -> s(x) a(l, x, s(y), h) -> a(l, x, y, s(h)) a(l, x, s(y), s(z)) -> a(l, x, y, a(l, x, s(y), z)) a(l, s(x), h, z) -> a(l, x, z, z) a(s(l), h, h, z) -> a(l, z, h, z) +(x, h) -> x +(h, x) -> x s(h) -> 1 app(nil, k) -> k app(l, nil) -> l
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