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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307736
details
property
value
status
complete
benchmark
#3.17a.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n109.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.593 seconds
cpu usage
337.033
user time
334.02
system time
3.01239
max virtual memory
1.9212948E7
max residence set size
6074912.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
336.88/291.52 WORST_CASE(Omega(n^1), O(n^2)) 336.88/291.53 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 336.88/291.53 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 336.88/291.53 336.88/291.53 336.88/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 336.88/291.53 336.88/291.53 (0) CpxTRS 336.88/291.53 (1) DependencyGraphProof [UPPER BOUND(ID), 0 ms] 336.88/291.53 (2) CpxTRS 336.88/291.53 (3) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 336.88/291.53 (4) CpxTRS 336.88/291.53 (5) CpxTrsToCdtProof [UPPER BOUND(ID), 3 ms] 336.88/291.53 (6) CdtProblem 336.88/291.53 (7) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 336.88/291.53 (8) CdtProblem 336.88/291.53 (9) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 336.88/291.53 (10) CdtProblem 336.88/291.53 (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 47 ms] 336.88/291.53 (12) CdtProblem 336.88/291.53 (13) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 27 ms] 336.88/291.53 (14) CdtProblem 336.88/291.53 (15) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 336.88/291.53 (16) BOUNDS(1, 1) 336.88/291.53 (17) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 336.88/291.53 (18) CpxTRS 336.88/291.53 (19) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 336.88/291.53 (20) typed CpxTrs 336.88/291.53 (21) OrderProof [LOWER BOUND(ID), 0 ms] 336.88/291.53 (22) typed CpxTrs 336.88/291.53 (23) RewriteLemmaProof [LOWER BOUND(ID), 318 ms] 336.88/291.53 (24) BEST 336.88/291.53 (25) proven lower bound 336.88/291.53 (26) LowerBoundPropagationProof [FINISHED, 0 ms] 336.88/291.53 (27) BOUNDS(n^1, INF) 336.88/291.53 (28) typed CpxTrs 336.88/291.53 336.88/291.53 336.88/291.53 ---------------------------------------- 336.88/291.53 336.88/291.53 (0) 336.88/291.53 Obligation: 336.88/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 336.88/291.53 336.88/291.53 336.88/291.53 The TRS R consists of the following rules: 336.88/291.53 336.88/291.53 app(nil, k) -> k 336.88/291.53 app(l, nil) -> l 336.88/291.53 app(cons(x, l), k) -> cons(x, app(l, k)) 336.88/291.53 sum(cons(x, nil)) -> cons(x, nil) 336.88/291.53 sum(cons(x, cons(y, l))) -> sum(cons(plus(x, y), l)) 336.88/291.53 sum(app(l, cons(x, cons(y, k)))) -> sum(app(l, sum(cons(x, cons(y, k))))) 336.88/291.53 plus(0, y) -> y 336.88/291.53 plus(s(x), y) -> s(plus(x, y)) 336.88/291.53 sum(plus(cons(0, x), cons(y, l))) -> pred(sum(cons(s(x), cons(y, l)))) 336.88/291.53 pred(cons(s(x), nil)) -> cons(x, nil) 336.88/291.53 336.88/291.53 S is empty. 336.88/291.53 Rewrite Strategy: FULL 336.88/291.53 ---------------------------------------- 336.88/291.53 336.88/291.53 (1) DependencyGraphProof (UPPER BOUND(ID)) 336.88/291.53 The following rules are not reachable from basic terms in the dependency graph and can be removed: 336.88/291.53 336.88/291.53 sum(app(l, cons(x, cons(y, k)))) -> sum(app(l, sum(cons(x, cons(y, k))))) 336.88/291.53 sum(plus(cons(0, x), cons(y, l))) -> pred(sum(cons(s(x), cons(y, l)))) 336.88/291.53 336.88/291.53 ---------------------------------------- 336.88/291.53 336.88/291.53 (2) 336.88/291.53 Obligation: 336.88/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^2). 336.88/291.53 336.88/291.53 336.88/291.53 The TRS R consists of the following rules: 336.88/291.53 336.88/291.53 app(nil, k) -> k 336.88/291.53 app(l, nil) -> l 336.88/291.53 app(cons(x, l), k) -> cons(x, app(l, k)) 336.88/291.53 sum(cons(x, nil)) -> cons(x, nil) 336.88/291.53 sum(cons(x, cons(y, l))) -> sum(cons(plus(x, y), l)) 336.88/291.53 plus(0, y) -> y 336.88/291.53 plus(s(x), y) -> s(plus(x, y)) 336.88/291.53 pred(cons(s(x), nil)) -> cons(x, nil) 336.88/291.53 336.88/291.53 S is empty. 336.88/291.53 Rewrite Strategy: FULL 336.88/291.53 ---------------------------------------- 336.88/291.53 336.88/291.53 (3) RcToIrcProof (BOTH BOUNDS(ID, ID)) 336.88/291.53 Converted rc-obligation to irc-obligation. 336.88/291.53 336.88/291.53 As the TRS is a non-duplicating overlay system, we have rc = irc. 336.88/291.53 ---------------------------------------- 336.88/291.53 336.88/291.53 (4) 336.88/291.53 Obligation: 336.88/291.53 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^2). 336.88/291.53
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