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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313555
details
property
value
status
complete
benchmark
#4.33.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n013.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.646 seconds
cpu usage
1072.2
user time
1062.52
system time
9.67672
max virtual memory
3.7639888E7
max residence set size
1.0607216E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
1071.81/291.57 WORST_CASE(Omega(n^2), ?) 1072.04/291.58 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1072.04/291.58 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1072.04/291.58 1072.04/291.58 1072.04/291.58 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1072.04/291.58 1072.04/291.58 (0) CpxTRS 1072.04/291.58 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1072.04/291.58 (2) CpxTRS 1072.04/291.58 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1072.04/291.58 (4) typed CpxTrs 1072.04/291.58 (5) OrderProof [LOWER BOUND(ID), 0 ms] 1072.04/291.58 (6) typed CpxTrs 1072.04/291.58 (7) RewriteLemmaProof [LOWER BOUND(ID), 247 ms] 1072.04/291.58 (8) BEST 1072.04/291.58 (9) proven lower bound 1072.04/291.58 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 1072.04/291.58 (11) BOUNDS(n^1, INF) 1072.04/291.58 (12) typed CpxTrs 1072.04/291.58 (13) RewriteLemmaProof [LOWER BOUND(ID), 67 ms] 1072.04/291.58 (14) proven lower bound 1072.04/291.58 (15) LowerBoundPropagationProof [FINISHED, 0 ms] 1072.04/291.58 (16) BOUNDS(n^2, INF) 1072.04/291.58 1072.04/291.58 1072.04/291.58 ---------------------------------------- 1072.04/291.58 1072.04/291.58 (0) 1072.04/291.58 Obligation: 1072.04/291.58 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1072.04/291.58 1072.04/291.58 1072.04/291.58 The TRS R consists of the following rules: 1072.04/291.58 1072.04/291.58 sum(cons(s(n), x), cons(m, y)) -> sum(cons(n, x), cons(s(m), y)) 1072.04/291.58 sum(cons(0, x), y) -> sum(x, y) 1072.04/291.58 sum(nil, y) -> y 1072.04/291.58 weight(cons(n, cons(m, x))) -> weight(sum(cons(n, cons(m, x)), cons(0, x))) 1072.04/291.58 weight(cons(n, nil)) -> n 1072.04/291.58 1072.04/291.58 S is empty. 1072.04/291.58 Rewrite Strategy: INNERMOST 1072.04/291.58 ---------------------------------------- 1072.04/291.58 1072.04/291.58 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 1072.04/291.58 Renamed function symbols to avoid clashes with predefined symbol. 1072.04/291.58 ---------------------------------------- 1072.04/291.58 1072.04/291.58 (2) 1072.04/291.58 Obligation: 1072.04/291.58 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1072.04/291.58 1072.04/291.58 1072.04/291.58 The TRS R consists of the following rules: 1072.04/291.58 1072.04/291.58 sum(cons(s(n), x), cons(m, y)) -> sum(cons(n, x), cons(s(m), y)) 1072.04/291.58 sum(cons(0', x), y) -> sum(x, y) 1072.04/291.58 sum(nil, y) -> y 1072.04/291.58 weight(cons(n, cons(m, x))) -> weight(sum(cons(n, cons(m, x)), cons(0', x))) 1072.04/291.58 weight(cons(n, nil)) -> n 1072.04/291.58 1072.04/291.58 S is empty. 1072.04/291.58 Rewrite Strategy: INNERMOST 1072.04/291.58 ---------------------------------------- 1072.04/291.58 1072.04/291.58 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1072.04/291.58 Infered types. 1072.04/291.58 ---------------------------------------- 1072.04/291.58 1072.04/291.58 (4) 1072.04/291.58 Obligation: 1072.04/291.58 Innermost TRS: 1072.04/291.58 Rules: 1072.04/291.58 sum(cons(s(n), x), cons(m, y)) -> sum(cons(n, x), cons(s(m), y)) 1072.04/291.58 sum(cons(0', x), y) -> sum(x, y) 1072.04/291.58 sum(nil, y) -> y 1072.04/291.58 weight(cons(n, cons(m, x))) -> weight(sum(cons(n, cons(m, x)), cons(0', x))) 1072.04/291.58 weight(cons(n, nil)) -> n 1072.04/291.58 1072.04/291.58 Types: 1072.04/291.58 sum :: cons:nil -> cons:nil -> cons:nil 1072.04/291.58 cons :: s:0' -> cons:nil -> cons:nil 1072.04/291.58 s :: s:0' -> s:0' 1072.04/291.58 0' :: s:0' 1072.04/291.58 nil :: cons:nil 1072.04/291.58 weight :: cons:nil -> s:0' 1072.04/291.58 hole_cons:nil1_0 :: cons:nil 1072.04/291.58 hole_s:0'2_0 :: s:0' 1072.04/291.58 gen_cons:nil3_0 :: Nat -> cons:nil 1072.04/291.58 gen_s:0'4_0 :: Nat -> s:0' 1072.04/291.58 1072.04/291.58 ---------------------------------------- 1072.04/291.58 1072.04/291.58 (5) OrderProof (LOWER BOUND(ID)) 1072.04/291.58 Heuristically decided to analyse the following defined symbols: 1072.04/291.58 sum, weight 1072.04/291.58 1072.04/291.58 They will be analysed ascendingly in the following order: 1072.04/291.58 sum < weight
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