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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313878
details
property
value
status
complete
benchmark
strmatch.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n124.star.cs.uiowa.edu
space
Frederiksen_Others
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.631 seconds
cpu usage
570.025
user time
563.149
system time
6.87601
max virtual memory
3.8715748E7
max residence set size
7490128.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
569.82/291.54 WORST_CASE(Omega(n^1), O(n^2)) 569.82/291.55 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 569.82/291.55 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 569.82/291.55 569.82/291.55 569.82/291.55 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). 569.82/291.55 569.82/291.55 (0) CpxRelTRS 569.82/291.55 (1) STerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 292 ms] 569.82/291.55 (2) CpxRelTRS 569.82/291.55 (3) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] 569.82/291.55 (4) CdtProblem 569.82/291.55 (5) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] 569.82/291.55 (6) CdtProblem 569.82/291.55 (7) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] 569.82/291.55 (8) CdtProblem 569.82/291.55 (9) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 569.82/291.55 (10) CdtProblem 569.82/291.55 (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 62 ms] 569.82/291.55 (12) CdtProblem 569.82/291.55 (13) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 28 ms] 569.82/291.55 (14) CdtProblem 569.82/291.55 (15) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 22 ms] 569.82/291.55 (16) CdtProblem 569.82/291.55 (17) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 25 ms] 569.82/291.55 (18) CdtProblem 569.82/291.55 (19) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 23 ms] 569.82/291.55 (20) CdtProblem 569.82/291.55 (21) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 218 ms] 569.82/291.55 (22) CdtProblem 569.82/291.55 (23) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 569.82/291.55 (24) BOUNDS(1, 1) 569.82/291.55 (25) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 569.82/291.55 (26) TRS for Loop Detection 569.82/291.55 (27) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 569.82/291.55 (28) BEST 569.82/291.55 (29) proven lower bound 569.82/291.55 (30) LowerBoundPropagationProof [FINISHED, 0 ms] 569.82/291.55 (31) BOUNDS(n^1, INF) 569.82/291.55 (32) TRS for Loop Detection 569.82/291.55 569.82/291.55 569.82/291.55 ---------------------------------------- 569.82/291.55 569.82/291.55 (0) 569.82/291.55 Obligation: 569.82/291.55 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). 569.82/291.55 569.82/291.55 569.82/291.55 The TRS R consists of the following rules: 569.82/291.55 569.82/291.55 prefix(Cons(x', xs'), Cons(x, xs)) -> and(!EQ(x', x), prefix(xs', xs)) 569.82/291.55 domatch(Cons(x, xs), Nil, n) -> Nil 569.82/291.55 domatch(Nil, Nil, n) -> Cons(n, Nil) 569.82/291.55 prefix(Cons(x, xs), Nil) -> False 569.82/291.55 prefix(Nil, cs) -> True 569.82/291.55 domatch(patcs, Cons(x, xs), n) -> domatch[Ite](prefix(patcs, Cons(x, xs)), patcs, Cons(x, xs), n) 569.82/291.56 eqNatList(Cons(x, xs), Cons(y, ys)) -> eqNatList[Ite](!EQ(x, y), y, ys, x, xs) 569.82/291.56 eqNatList(Cons(x, xs), Nil) -> False 569.82/291.56 eqNatList(Nil, Cons(y, ys)) -> False 569.82/291.56 eqNatList(Nil, Nil) -> True 569.82/291.56 notEmpty(Cons(x, xs)) -> True 569.82/291.56 notEmpty(Nil) -> False 569.82/291.56 strmatch(patstr, str) -> domatch(patstr, str, Nil) 569.82/291.56 569.82/291.56 The (relative) TRS S consists of the following rules: 569.82/291.56 569.82/291.56 and(False, False) -> False 569.82/291.56 and(True, False) -> False 569.82/291.56 and(False, True) -> False 569.82/291.56 and(True, True) -> True 569.82/291.56 !EQ(S(x), S(y)) -> !EQ(x, y) 569.82/291.56 !EQ(0, S(y)) -> False 569.82/291.56 !EQ(S(x), 0) -> False 569.82/291.56 !EQ(0, 0) -> True 569.82/291.56 domatch[Ite](False, patcs, Cons(x, xs), n) -> domatch(patcs, xs, Cons(n, Cons(Nil, Nil))) 569.82/291.56 domatch[Ite](True, patcs, Cons(x, xs), n) -> Cons(n, domatch(patcs, xs, Cons(n, Cons(Nil, Nil)))) 569.82/291.56 eqNatList[Ite](False, y, ys, x, xs) -> False 569.82/291.56 eqNatList[Ite](True, y, ys, x, xs) -> eqNatList(xs, ys) 569.82/291.56 569.82/291.56 Rewrite Strategy: INNERMOST 569.82/291.56 ---------------------------------------- 569.82/291.56 569.82/291.56 (1) STerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) 569.82/291.56 proved termination of relative rules 569.82/291.56 ---------------------------------------- 569.82/291.56 569.82/291.56 (2) 569.82/291.56 Obligation: 569.82/291.56 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). 569.82/291.56 569.82/291.56 569.82/291.56 The TRS R consists of the following rules: 569.82/291.56 569.82/291.56 prefix(Cons(x', xs'), Cons(x, xs)) -> and(!EQ(x', x), prefix(xs', xs)) 569.82/291.56 domatch(Cons(x, xs), Nil, n) -> Nil 569.82/291.56 domatch(Nil, Nil, n) -> Cons(n, Nil) 569.82/291.56 prefix(Cons(x, xs), Nil) -> False 569.82/291.56 prefix(Nil, cs) -> True 569.82/291.56 domatch(patcs, Cons(x, xs), n) -> domatch[Ite](prefix(patcs, Cons(x, xs)), patcs, Cons(x, xs), n)
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return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40
