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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313413
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
n079.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
6.14905 seconds
cpu usage
18.8144
user time
17.7101
system time
1.10435
max virtual memory
3.7248028E7
max residence set size
3702992.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
18.04/5.54 WORST_CASE(Omega(n^1), O(n^1)) 18.04/5.55 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 18.04/5.55 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 18.04/5.55 18.04/5.55 18.04/5.55 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 18.04/5.55 18.04/5.55 (0) CpxTRS 18.04/5.55 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 18.04/5.55 (2) CpxWeightedTrs 18.04/5.55 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 18.04/5.55 (4) CpxTypedWeightedTrs 18.04/5.55 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 18.04/5.55 (6) CpxTypedWeightedCompleteTrs 18.04/5.55 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 2 ms] 18.04/5.55 (8) CpxRNTS 18.04/5.55 (9) CompleteCoflocoProof [FINISHED, 508 ms] 18.04/5.55 (10) BOUNDS(1, n^1) 18.04/5.55 (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 18.04/5.55 (12) CpxTRS 18.04/5.55 (13) SlicingProof [LOWER BOUND(ID), 0 ms] 18.04/5.55 (14) CpxTRS 18.04/5.55 (15) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 18.04/5.55 (16) typed CpxTrs 18.04/5.55 (17) OrderProof [LOWER BOUND(ID), 0 ms] 18.04/5.55 (18) typed CpxTrs 18.04/5.55 (19) RewriteLemmaProof [LOWER BOUND(ID), 1824 ms] 18.04/5.55 (20) proven lower bound 18.04/5.55 (21) LowerBoundPropagationProof [FINISHED, 0 ms] 18.04/5.55 (22) BOUNDS(n^1, INF) 18.04/5.55 18.04/5.55 18.04/5.55 ---------------------------------------- 18.04/5.55 18.04/5.55 (0) 18.04/5.55 Obligation: 18.04/5.55 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 18.04/5.55 18.04/5.55 18.04/5.55 The TRS R consists of the following rules: 18.04/5.55 18.04/5.55 a__and(true, X) -> mark(X) 18.04/5.55 a__and(false, Y) -> false 18.04/5.55 a__if(true, X, Y) -> mark(X) 18.04/5.55 a__if(false, X, Y) -> mark(Y) 18.04/5.55 a__add(0, X) -> mark(X) 18.04/5.55 a__add(s(X), Y) -> s(add(X, Y)) 18.04/5.55 a__first(0, X) -> nil 18.04/5.55 a__first(s(X), cons(Y, Z)) -> cons(Y, first(X, Z)) 18.04/5.55 a__from(X) -> cons(X, from(s(X))) 18.04/5.55 mark(and(X1, X2)) -> a__and(mark(X1), X2) 18.04/5.55 mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3) 18.04/5.55 mark(add(X1, X2)) -> a__add(mark(X1), X2) 18.04/5.55 mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) 18.04/5.55 mark(from(X)) -> a__from(X) 18.04/5.55 mark(true) -> true 18.04/5.55 mark(false) -> false 18.04/5.55 mark(0) -> 0 18.04/5.55 mark(s(X)) -> s(X) 18.04/5.55 mark(nil) -> nil 18.04/5.55 mark(cons(X1, X2)) -> cons(X1, X2) 18.04/5.55 a__and(X1, X2) -> and(X1, X2) 18.04/5.55 a__if(X1, X2, X3) -> if(X1, X2, X3) 18.04/5.55 a__add(X1, X2) -> add(X1, X2) 18.04/5.55 a__first(X1, X2) -> first(X1, X2) 18.04/5.55 a__from(X) -> from(X) 18.04/5.55 18.04/5.55 S is empty. 18.04/5.55 Rewrite Strategy: INNERMOST 18.04/5.55 ---------------------------------------- 18.04/5.55 18.04/5.55 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 18.04/5.55 Transformed relative TRS to weighted TRS 18.04/5.55 ---------------------------------------- 18.04/5.55 18.04/5.55 (2) 18.04/5.55 Obligation: 18.04/5.55 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). 18.04/5.55 18.04/5.55 18.04/5.55 The TRS R consists of the following rules: 18.04/5.55 18.04/5.55 a__and(true, X) -> mark(X) [1] 18.04/5.55 a__and(false, Y) -> false [1] 18.04/5.55 a__if(true, X, Y) -> mark(X) [1] 18.04/5.55 a__if(false, X, Y) -> mark(Y) [1] 18.04/5.55 a__add(0, X) -> mark(X) [1] 18.04/5.55 a__add(s(X), Y) -> s(add(X, Y)) [1] 18.04/5.55 a__first(0, X) -> nil [1] 18.04/5.55 a__first(s(X), cons(Y, Z)) -> cons(Y, first(X, Z)) [1] 18.04/5.55 a__from(X) -> cons(X, from(s(X))) [1] 18.04/5.55 mark(and(X1, X2)) -> a__and(mark(X1), X2) [1] 18.04/5.55 mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3) [1] 18.04/5.55 mark(add(X1, X2)) -> a__add(mark(X1), X2) [1] 18.04/5.55 mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) [1] 18.04/5.55 mark(from(X)) -> a__from(X) [1] 18.04/5.55 mark(true) -> true [1] 18.04/5.55 mark(false) -> false [1] 18.04/5.55 mark(0) -> 0 [1] 18.04/5.55 mark(s(X)) -> s(X) [1]
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