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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308032
details
property
value
status
complete
benchmark
Ex15_Luc98_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n123.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
5.22715 seconds
cpu usage
17.332
user time
16.2822
system time
1.04988
max virtual memory
1.8848248E7
max residence set size
3406124.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
17.01/5.15 WORST_CASE(Omega(n^1), O(n^1)) 17.01/5.17 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 17.01/5.17 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 17.01/5.17 17.01/5.17 17.01/5.17 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 17.01/5.17 17.01/5.17 (0) CpxTRS 17.01/5.17 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 17.01/5.17 (2) CpxTRS 17.01/5.17 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 17.01/5.17 (4) CpxWeightedTrs 17.01/5.17 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 17.01/5.17 (6) CpxTypedWeightedTrs 17.01/5.17 (7) CompletionProof [UPPER BOUND(ID), 0 ms] 17.01/5.17 (8) CpxTypedWeightedCompleteTrs 17.01/5.17 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 3 ms] 17.01/5.17 (10) CpxRNTS 17.01/5.17 (11) CompleteCoflocoProof [FINISHED, 516 ms] 17.01/5.17 (12) BOUNDS(1, n^1) 17.01/5.17 (13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 17.01/5.17 (14) TRS for Loop Detection 17.01/5.17 (15) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 17.01/5.17 (16) BEST 17.01/5.17 (17) proven lower bound 17.01/5.17 (18) LowerBoundPropagationProof [FINISHED, 0 ms] 17.01/5.17 (19) BOUNDS(n^1, INF) 17.01/5.17 (20) TRS for Loop Detection 17.01/5.17 17.01/5.17 17.01/5.17 ---------------------------------------- 17.01/5.17 17.01/5.17 (0) 17.01/5.17 Obligation: 17.01/5.17 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 17.01/5.17 17.01/5.17 17.01/5.17 The TRS R consists of the following rules: 17.01/5.17 17.01/5.17 a__and(true, X) -> mark(X) 17.01/5.17 a__and(false, Y) -> false 17.01/5.17 a__if(true, X, Y) -> mark(X) 17.01/5.17 a__if(false, X, Y) -> mark(Y) 17.01/5.17 a__add(0, X) -> mark(X) 17.01/5.17 a__add(s(X), Y) -> s(add(X, Y)) 17.01/5.17 a__first(0, X) -> nil 17.01/5.17 a__first(s(X), cons(Y, Z)) -> cons(Y, first(X, Z)) 17.01/5.17 a__from(X) -> cons(X, from(s(X))) 17.01/5.17 mark(and(X1, X2)) -> a__and(mark(X1), X2) 17.01/5.17 mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3) 17.01/5.17 mark(add(X1, X2)) -> a__add(mark(X1), X2) 17.01/5.17 mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) 17.01/5.17 mark(from(X)) -> a__from(X) 17.01/5.17 mark(true) -> true 17.01/5.17 mark(false) -> false 17.01/5.17 mark(0) -> 0 17.01/5.17 mark(s(X)) -> s(X) 17.01/5.17 mark(nil) -> nil 17.01/5.17 mark(cons(X1, X2)) -> cons(X1, X2) 17.01/5.17 a__and(X1, X2) -> and(X1, X2) 17.01/5.17 a__if(X1, X2, X3) -> if(X1, X2, X3) 17.01/5.17 a__add(X1, X2) -> add(X1, X2) 17.01/5.17 a__first(X1, X2) -> first(X1, X2) 17.01/5.17 a__from(X) -> from(X) 17.01/5.17 17.01/5.17 S is empty. 17.01/5.17 Rewrite Strategy: FULL 17.01/5.17 ---------------------------------------- 17.01/5.17 17.01/5.17 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 17.01/5.17 Converted rc-obligation to irc-obligation. 17.01/5.17 17.01/5.17 The duplicating contexts are: 17.01/5.17 a__from([]) 17.01/5.17 17.01/5.17 17.01/5.17 The defined contexts are: 17.01/5.17 a__first([], x1) 17.01/5.17 a__first(x0, []) 17.01/5.17 a__add([], x1) 17.01/5.17 a__and([], x1) 17.01/5.17 a__if([], x1, x2) 17.01/5.17 17.01/5.17 17.01/5.17 As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc. 17.01/5.17 ---------------------------------------- 17.01/5.17 17.01/5.17 (2) 17.01/5.17 Obligation: 17.01/5.17 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 17.01/5.17 17.01/5.17 17.01/5.17 The TRS R consists of the following rules: 17.01/5.17 17.01/5.17 a__and(true, X) -> mark(X) 17.01/5.17 a__and(false, Y) -> false 17.01/5.17 a__if(true, X, Y) -> mark(X) 17.01/5.17 a__if(false, X, Y) -> mark(Y) 17.01/5.17 a__add(0, X) -> mark(X) 17.01/5.17 a__add(s(X), Y) -> s(add(X, Y))
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