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Runtime Complexity: TRS Innermost pair #487111628
details
property
value
status
complete
benchmark
append.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n140.star.cs.uiowa.edu
space
CiME_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
4.13998 seconds
cpu usage
11.4914
user time
10.5787
system time
0.91268
max virtual memory
3.7159468E7
max residence set size
3234936.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxWeightedTrs (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxTypedWeightedTrs (5) CompletionProof [UPPER BOUND(ID), 0 ms] (6) CpxTypedWeightedCompleteTrs (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 2 ms] (8) CpxRNTS (9) CompleteCoflocoProof [FINISHED, 108 ms] (10) BOUNDS(1, n^1) (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTRS (13) SlicingProof [LOWER BOUND(ID), 0 ms] (14) CpxTRS (15) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (16) typed CpxTrs (17) OrderProof [LOWER BOUND(ID), 0 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 209 ms] (20) BEST (21) proven lower bound (22) LowerBoundPropagationProof [FINISHED, 0 ms] (23) BOUNDS(n^1, INF) (24) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: is_empty(nil) -> true is_empty(cons(x, l)) -> false hd(cons(x, l)) -> x tl(cons(x, l)) -> l append(l1, l2) -> ifappend(l1, l2, l1) ifappend(l1, l2, nil) -> l2 ifappend(l1, l2, cons(x, l)) -> cons(x, append(l, l2)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: is_empty(nil) -> true [1] is_empty(cons(x, l)) -> false [1] hd(cons(x, l)) -> x [1] tl(cons(x, l)) -> l [1] append(l1, l2) -> ifappend(l1, l2, l1) [1] ifappend(l1, l2, nil) -> l2 [1] ifappend(l1, l2, cons(x, l)) -> cons(x, append(l, l2)) [1] Rewrite Strategy: INNERMOST ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: is_empty(nil) -> true [1] is_empty(cons(x, l)) -> false [1] hd(cons(x, l)) -> x [1] tl(cons(x, l)) -> l [1] append(l1, l2) -> ifappend(l1, l2, l1) [1] ifappend(l1, l2, nil) -> l2 [1] ifappend(l1, l2, cons(x, l)) -> cons(x, append(l, l2)) [1] The TRS has the following type information: is_empty :: nil:cons -> true:false nil :: nil:cons true :: true:false cons :: hd -> nil:cons -> nil:cons false :: true:false
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