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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308475
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
n167.star.cs.uiowa.edu
space
Secret_07_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.642 seconds
cpu usage
343.233
user time
339.356
system time
3.87754
max virtual memory
1.9164004E7
max residence set size
6029756.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
343.01/291.57 WORST_CASE(Omega(n^1), O(n^2)) 343.11/291.59 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 343.11/291.59 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 343.11/291.59 343.11/291.59 343.11/291.59 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 343.11/291.59 343.11/291.59 (0) CpxTRS 343.11/291.59 (1) DependencyGraphProof [UPPER BOUND(ID), 0 ms] 343.11/291.59 (2) CpxTRS 343.11/291.59 (3) NestedDefinedSymbolProof [UPPER BOUND(ID), 11 ms] 343.11/291.59 (4) CpxTRS 343.11/291.59 (5) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms] 343.11/291.59 (6) CpxRelTRS 343.11/291.59 (7) RcToIrcProof [BOTH BOUNDS(ID, ID), 8 ms] 343.11/291.59 (8) CpxRelTRS 343.11/291.59 (9) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] 343.11/291.59 (10) CdtProblem 343.11/291.59 (11) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 343.11/291.59 (12) CdtProblem 343.11/291.59 (13) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 343.11/291.59 (14) CdtProblem 343.11/291.59 (15) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 201 ms] 343.11/291.59 (16) CdtProblem 343.11/291.59 (17) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 15 ms] 343.11/291.59 (18) CdtProblem 343.11/291.59 (19) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 11 ms] 343.11/291.59 (20) CdtProblem 343.11/291.59 (21) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 69 ms] 343.11/291.59 (22) CdtProblem 343.11/291.59 (23) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 343.11/291.59 (24) BOUNDS(1, 1) 343.11/291.59 (25) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 343.11/291.59 (26) TRS for Loop Detection 343.11/291.59 (27) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 343.11/291.59 (28) BEST 343.11/291.59 (29) proven lower bound 343.11/291.59 (30) LowerBoundPropagationProof [FINISHED, 0 ms] 343.11/291.59 (31) BOUNDS(n^1, INF) 343.11/291.59 (32) TRS for Loop Detection 343.11/291.59 343.11/291.59 343.11/291.59 ---------------------------------------- 343.11/291.59 343.11/291.59 (0) 343.11/291.59 Obligation: 343.11/291.59 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 343.11/291.59 343.11/291.59 343.11/291.59 The TRS R consists of the following rules: 343.11/291.59 343.11/291.59 a(h, h, h, x) -> s(x) 343.11/291.59 a(l, x, s(y), h) -> a(l, x, y, s(h)) 343.11/291.59 a(l, x, s(y), s(z)) -> a(l, x, y, a(l, x, s(y), z)) 343.11/291.59 a(l, s(x), h, z) -> a(l, x, z, z) 343.11/291.59 a(s(l), h, h, z) -> a(l, z, h, z) 343.11/291.59 +(x, h) -> x 343.11/291.59 +(h, x) -> x 343.11/291.59 +(s(x), s(y)) -> s(s(+(x, y))) 343.11/291.59 +(+(x, y), z) -> +(x, +(y, z)) 343.11/291.59 s(h) -> 1 343.11/291.59 app(nil, k) -> k 343.11/291.59 app(l, nil) -> l 343.11/291.59 app(cons(x, l), k) -> cons(x, app(l, k)) 343.11/291.59 sum(cons(x, nil)) -> cons(x, nil) 343.11/291.59 sum(cons(x, cons(y, l))) -> sum(cons(a(x, y, h, h), l)) 343.11/291.59 343.11/291.59 S is empty. 343.11/291.59 Rewrite Strategy: FULL 343.11/291.59 ---------------------------------------- 343.11/291.59 343.11/291.59 (1) DependencyGraphProof (UPPER BOUND(ID)) 343.11/291.59 The following rules are not reachable from basic terms in the dependency graph and can be removed: 343.11/291.59 343.11/291.59 +(s(x), s(y)) -> s(s(+(x, y))) 343.11/291.59 +(+(x, y), z) -> +(x, +(y, z)) 343.11/291.59 343.11/291.59 ---------------------------------------- 343.11/291.59 343.11/291.59 (2) 343.11/291.59 Obligation: 343.11/291.59 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^2). 343.11/291.59 343.11/291.59 343.11/291.59 The TRS R consists of the following rules: 343.11/291.59 343.11/291.59 a(h, h, h, x) -> s(x) 343.11/291.59 a(l, x, s(y), h) -> a(l, x, y, s(h)) 343.11/291.59 a(l, x, s(y), s(z)) -> a(l, x, y, a(l, x, s(y), z)) 343.11/291.59 a(l, s(x), h, z) -> a(l, x, z, z) 343.11/291.59 a(s(l), h, h, z) -> a(l, z, h, z) 343.11/291.59 +(x, h) -> x 343.11/291.59 +(h, x) -> x 343.11/291.59 s(h) -> 1 343.11/291.59 app(nil, k) -> k 343.11/291.59 app(l, nil) -> l 343.11/291.59 app(cons(x, l), k) -> cons(x, app(l, k)) 343.11/291.59 sum(cons(x, nil)) -> cons(x, nil) 343.11/291.59 sum(cons(x, cons(y, l))) -> sum(cons(a(x, y, h, h), l)) 343.11/291.59
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