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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307713
details
property
value
status
complete
benchmark
#3.17.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n058.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.513 seconds
cpu usage
319.34
user time
316.31
system time
3.03
max virtual memory
1.8946436E7
max residence set size
6271372.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
319.34/291.46 WORST_CASE(Omega(n^1), O(n^2)) 319.34/291.48 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 319.34/291.48 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 319.34/291.48 319.34/291.48 319.34/291.48 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 319.34/291.48 319.34/291.48 (0) CpxTRS 319.34/291.48 (1) DependencyGraphProof [UPPER BOUND(ID), 0 ms] 319.34/291.48 (2) CpxTRS 319.34/291.48 (3) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 319.34/291.48 (4) CpxTRS 319.34/291.48 (5) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 1 ms] 319.34/291.48 (6) CpxWeightedTrs 319.34/291.48 (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 319.34/291.48 (8) CpxTypedWeightedTrs 319.34/291.48 (9) CompletionProof [UPPER BOUND(ID), 0 ms] 319.34/291.48 (10) CpxTypedWeightedCompleteTrs 319.34/291.48 (11) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 319.34/291.48 (12) CpxTypedWeightedCompleteTrs 319.34/291.48 (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 319.34/291.48 (14) CpxRNTS 319.34/291.48 (15) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 319.34/291.48 (16) CpxRNTS 319.34/291.48 (17) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 1 ms] 319.34/291.48 (18) CpxRNTS 319.34/291.48 (19) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 319.34/291.48 (20) CpxRNTS 319.34/291.48 (21) IntTrsBoundProof [UPPER BOUND(ID), 521 ms] 319.34/291.48 (22) CpxRNTS 319.34/291.48 (23) IntTrsBoundProof [UPPER BOUND(ID), 108 ms] 319.34/291.48 (24) CpxRNTS 319.34/291.48 (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 319.34/291.48 (26) CpxRNTS 319.34/291.48 (27) IntTrsBoundProof [UPPER BOUND(ID), 289 ms] 319.34/291.48 (28) CpxRNTS 319.34/291.48 (29) IntTrsBoundProof [UPPER BOUND(ID), 115 ms] 319.34/291.48 (30) CpxRNTS 319.34/291.48 (31) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 319.34/291.48 (32) CpxRNTS 319.34/291.48 (33) IntTrsBoundProof [UPPER BOUND(ID), 384 ms] 319.34/291.48 (34) CpxRNTS 319.34/291.48 (35) IntTrsBoundProof [UPPER BOUND(ID), 167 ms] 319.34/291.48 (36) CpxRNTS 319.34/291.48 (37) FinalProof [FINISHED, 0 ms] 319.34/291.48 (38) BOUNDS(1, n^2) 319.34/291.48 (39) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 319.34/291.48 (40) TRS for Loop Detection 319.34/291.48 (41) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 319.34/291.48 (42) BEST 319.34/291.48 (43) proven lower bound 319.34/291.48 (44) LowerBoundPropagationProof [FINISHED, 0 ms] 319.34/291.48 (45) BOUNDS(n^1, INF) 319.34/291.48 (46) TRS for Loop Detection 319.34/291.48 319.34/291.48 319.34/291.48 ---------------------------------------- 319.34/291.48 319.34/291.48 (0) 319.34/291.48 Obligation: 319.34/291.48 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 319.34/291.48 319.34/291.48 319.34/291.48 The TRS R consists of the following rules: 319.34/291.48 319.34/291.48 app(nil, k) -> k 319.34/291.48 app(l, nil) -> l 319.34/291.48 app(cons(x, l), k) -> cons(x, app(l, k)) 319.34/291.48 sum(cons(x, nil)) -> cons(x, nil) 319.34/291.48 sum(cons(x, cons(y, l))) -> sum(cons(plus(x, y), l)) 319.34/291.48 sum(app(l, cons(x, cons(y, k)))) -> sum(app(l, sum(cons(x, cons(y, k))))) 319.34/291.48 plus(0, y) -> y 319.34/291.48 plus(s(x), y) -> s(plus(x, y)) 319.34/291.48 319.34/291.48 S is empty. 319.34/291.48 Rewrite Strategy: FULL 319.34/291.48 ---------------------------------------- 319.34/291.48 319.34/291.48 (1) DependencyGraphProof (UPPER BOUND(ID)) 319.34/291.48 The following rules are not reachable from basic terms in the dependency graph and can be removed: 319.34/291.48 319.34/291.48 sum(app(l, cons(x, cons(y, k)))) -> sum(app(l, sum(cons(x, cons(y, k))))) 319.34/291.48 319.34/291.48 ---------------------------------------- 319.34/291.48 319.34/291.48 (2) 319.34/291.48 Obligation: 319.34/291.48 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^2). 319.34/291.48 319.34/291.48 319.34/291.48 The TRS R consists of the following rules: 319.34/291.48 319.34/291.48 app(nil, k) -> k 319.34/291.48 app(l, nil) -> l 319.34/291.48 app(cons(x, l), k) -> cons(x, app(l, k)) 319.34/291.48 sum(cons(x, nil)) -> cons(x, nil) 319.34/291.48 sum(cons(x, cons(y, l))) -> sum(cons(plus(x, y), l)) 319.34/291.48 plus(0, y) -> y 319.34/291.48 plus(s(x), y) -> s(plus(x, y)) 319.34/291.48
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