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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308269
details
property
value
status
complete
benchmark
PALINDROME_nokinds-noand_Z.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
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.594 seconds
cpu usage
632.734
user time
629.459
system time
3.27496
max virtual memory
3.7250632E7
max residence set size
6309948.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
632.46/291.52 WORST_CASE(Omega(n^1), O(n^2)) 632.62/291.53 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 632.62/291.53 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 632.62/291.53 632.62/291.53 632.62/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 632.62/291.53 632.62/291.53 (0) CpxTRS 632.62/291.53 (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 5 ms] 632.62/291.53 (2) CpxTRS 632.62/291.53 (3) NonCtorToCtorProof [UPPER BOUND(ID), 4 ms] 632.62/291.53 (4) CpxRelTRS 632.62/291.53 (5) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 632.62/291.53 (6) CpxRelTRS 632.62/291.53 (7) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] 632.62/291.53 (8) CdtProblem 632.62/291.53 (9) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 632.62/291.53 (10) CdtProblem 632.62/291.53 (11) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] 632.62/291.53 (12) CdtProblem 632.62/291.53 (13) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 2 ms] 632.62/291.53 (14) CdtProblem 632.62/291.53 (15) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 1442 ms] 632.62/291.53 (16) CdtProblem 632.62/291.53 (17) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] 632.62/291.53 (18) CdtProblem 632.62/291.53 (19) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 90 ms] 632.62/291.53 (20) CdtProblem 632.62/291.53 (21) CdtKnowledgeProof [FINISHED, 0 ms] 632.62/291.53 (22) BOUNDS(1, 1) 632.62/291.53 (23) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 632.62/291.53 (24) TRS for Loop Detection 632.62/291.53 (25) DecreasingLoopProof [LOWER BOUND(ID), 50 ms] 632.62/291.53 (26) BEST 632.62/291.53 (27) proven lower bound 632.62/291.53 (28) LowerBoundPropagationProof [FINISHED, 0 ms] 632.62/291.53 (29) BOUNDS(n^1, INF) 632.62/291.53 (30) TRS for Loop Detection 632.62/291.53 632.62/291.53 632.62/291.53 ---------------------------------------- 632.62/291.53 632.62/291.53 (0) 632.62/291.53 Obligation: 632.62/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 632.62/291.53 632.62/291.53 632.62/291.53 The TRS R consists of the following rules: 632.62/291.53 632.62/291.53 __(__(X, Y), Z) -> __(X, __(Y, Z)) 632.62/291.53 __(X, nil) -> X 632.62/291.53 __(nil, X) -> X 632.62/291.53 U11(tt) -> tt 632.62/291.53 U21(tt, V2) -> U22(isList(activate(V2))) 632.62/291.53 U22(tt) -> tt 632.62/291.53 U31(tt) -> tt 632.62/291.53 U41(tt, V2) -> U42(isNeList(activate(V2))) 632.62/291.53 U42(tt) -> tt 632.62/291.53 U51(tt, V2) -> U52(isList(activate(V2))) 632.62/291.53 U52(tt) -> tt 632.62/291.53 U61(tt) -> tt 632.62/291.53 U71(tt, P) -> U72(isPal(activate(P))) 632.62/291.53 U72(tt) -> tt 632.62/291.53 U81(tt) -> tt 632.62/291.53 isList(V) -> U11(isNeList(activate(V))) 632.62/291.53 isList(n__nil) -> tt 632.62/291.53 isList(n____(V1, V2)) -> U21(isList(activate(V1)), activate(V2)) 632.62/291.53 isNeList(V) -> U31(isQid(activate(V))) 632.62/291.53 isNeList(n____(V1, V2)) -> U41(isList(activate(V1)), activate(V2)) 632.62/291.53 isNeList(n____(V1, V2)) -> U51(isNeList(activate(V1)), activate(V2)) 632.62/291.53 isNePal(V) -> U61(isQid(activate(V))) 632.62/291.53 isNePal(n____(I, __(P, I))) -> U71(isQid(activate(I)), activate(P)) 632.62/291.53 isPal(V) -> U81(isNePal(activate(V))) 632.62/291.53 isPal(n__nil) -> tt 632.62/291.53 isQid(n__a) -> tt 632.62/291.53 isQid(n__e) -> tt 632.62/291.53 isQid(n__i) -> tt 632.62/291.53 isQid(n__o) -> tt 632.62/291.53 isQid(n__u) -> tt 632.62/291.53 nil -> n__nil 632.62/291.53 __(X1, X2) -> n____(X1, X2) 632.62/291.53 a -> n__a 632.62/291.53 e -> n__e 632.62/291.53 i -> n__i 632.62/291.53 o -> n__o 632.62/291.53 u -> n__u 632.62/291.53 activate(n__nil) -> nil 632.62/291.53 activate(n____(X1, X2)) -> __(X1, X2) 632.62/291.53 activate(n__a) -> a 632.62/291.53 activate(n__e) -> e 632.62/291.53 activate(n__i) -> i 632.62/291.53 activate(n__o) -> o 632.62/291.53 activate(n__u) -> u 632.62/291.53 activate(X) -> X 632.62/291.53 632.62/291.53 S is empty. 632.62/291.53 Rewrite Strategy: FULL 632.62/291.53 ---------------------------------------- 632.62/291.53 632.62/291.53 (1) NestedDefinedSymbolProof (UPPER BOUND(ID))
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