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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313932
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
n033.star.cs.uiowa.edu
space
CiME_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
7.06568 seconds
cpu usage
15.5478
user time
14.3279
system time
1.21991
max virtual memory
1.91376E7
max residence set size
3338992.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
15.30/6.32 WORST_CASE(Omega(n^1), O(n^1)) 15.47/6.33 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 15.47/6.33 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 15.47/6.33 15.47/6.33 15.47/6.33 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 15.47/6.33 15.47/6.33 (0) CpxTRS 15.47/6.33 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 15.47/6.33 (2) CpxWeightedTrs 15.47/6.33 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 15.47/6.33 (4) CpxTypedWeightedTrs 15.47/6.33 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 15.47/6.33 (6) CpxTypedWeightedCompleteTrs 15.47/6.33 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 1 ms] 15.47/6.33 (8) CpxRNTS 15.47/6.33 (9) CompleteCoflocoProof [FINISHED, 188 ms] 15.47/6.33 (10) BOUNDS(1, n^1) 15.47/6.33 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 15.47/6.33 (12) TRS for Loop Detection 15.47/6.33 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 15.47/6.33 (14) BEST 15.47/6.33 (15) proven lower bound 15.47/6.33 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 15.47/6.33 (17) BOUNDS(n^1, INF) 15.47/6.33 (18) TRS for Loop Detection 15.47/6.33 15.47/6.33 15.47/6.33 ---------------------------------------- 15.47/6.33 15.47/6.33 (0) 15.47/6.33 Obligation: 15.47/6.33 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 15.47/6.33 15.47/6.33 15.47/6.33 The TRS R consists of the following rules: 15.47/6.33 15.47/6.33 is_empty(nil) -> true 15.47/6.33 is_empty(cons(x, l)) -> false 15.47/6.33 hd(cons(x, l)) -> x 15.47/6.33 tl(cons(x, l)) -> l 15.47/6.33 append(l1, l2) -> ifappend(l1, l2, l1) 15.47/6.33 ifappend(l1, l2, nil) -> l2 15.47/6.33 ifappend(l1, l2, cons(x, l)) -> cons(x, append(l, l2)) 15.47/6.33 15.47/6.33 S is empty. 15.47/6.33 Rewrite Strategy: INNERMOST 15.47/6.33 ---------------------------------------- 15.47/6.33 15.47/6.33 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 15.47/6.33 Transformed relative TRS to weighted TRS 15.47/6.33 ---------------------------------------- 15.47/6.33 15.47/6.33 (2) 15.47/6.33 Obligation: 15.47/6.33 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). 15.47/6.33 15.47/6.33 15.47/6.33 The TRS R consists of the following rules: 15.47/6.33 15.47/6.33 is_empty(nil) -> true [1] 15.47/6.33 is_empty(cons(x, l)) -> false [1] 15.47/6.33 hd(cons(x, l)) -> x [1] 15.47/6.33 tl(cons(x, l)) -> l [1] 15.47/6.33 append(l1, l2) -> ifappend(l1, l2, l1) [1] 15.47/6.33 ifappend(l1, l2, nil) -> l2 [1] 15.47/6.33 ifappend(l1, l2, cons(x, l)) -> cons(x, append(l, l2)) [1] 15.47/6.33 15.47/6.33 Rewrite Strategy: INNERMOST 15.47/6.33 ---------------------------------------- 15.47/6.33 15.47/6.33 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 15.47/6.33 Infered types. 15.47/6.33 ---------------------------------------- 15.47/6.33 15.47/6.33 (4) 15.47/6.33 Obligation: 15.47/6.33 Runtime Complexity Weighted TRS with Types. 15.47/6.33 The TRS R consists of the following rules: 15.47/6.33 15.47/6.33 is_empty(nil) -> true [1] 15.47/6.33 is_empty(cons(x, l)) -> false [1] 15.47/6.33 hd(cons(x, l)) -> x [1] 15.47/6.33 tl(cons(x, l)) -> l [1] 15.47/6.33 append(l1, l2) -> ifappend(l1, l2, l1) [1] 15.47/6.33 ifappend(l1, l2, nil) -> l2 [1] 15.47/6.33 ifappend(l1, l2, cons(x, l)) -> cons(x, append(l, l2)) [1] 15.47/6.33 15.47/6.33 The TRS has the following type information: 15.47/6.33 is_empty :: nil:cons -> true:false 15.47/6.33 nil :: nil:cons 15.47/6.33 true :: true:false 15.47/6.33 cons :: hd -> nil:cons -> nil:cons 15.47/6.33 false :: true:false 15.47/6.33 hd :: nil:cons -> hd 15.47/6.33 tl :: nil:cons -> nil:cons 15.47/6.33 append :: nil:cons -> nil:cons -> nil:cons 15.47/6.33 ifappend :: nil:cons -> nil:cons -> nil:cons -> nil:cons 15.47/6.33 15.47/6.33 Rewrite Strategy: INNERMOST
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