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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308521
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
n107.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.648 seconds
cpu usage
1072.11
user time
1062.85
system time
9.26166
max virtual memory
3.7912368E7
max residence set size
1.0614932E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
1071.75/291.52 WORST_CASE(Omega(n^2), ?) 1071.90/291.57 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1071.90/291.57 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1071.90/291.57 1071.90/291.57 1071.90/291.57 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1071.90/291.57 1071.90/291.57 (0) CpxTRS 1071.90/291.57 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1071.90/291.57 (2) CpxTRS 1071.90/291.57 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1071.90/291.57 (4) typed CpxTrs 1071.90/291.57 (5) OrderProof [LOWER BOUND(ID), 0 ms] 1071.90/291.57 (6) typed CpxTrs 1071.90/291.57 (7) RewriteLemmaProof [LOWER BOUND(ID), 243 ms] 1071.90/291.57 (8) BEST 1071.90/291.57 (9) proven lower bound 1071.90/291.57 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 1071.90/291.57 (11) BOUNDS(n^1, INF) 1071.90/291.57 (12) typed CpxTrs 1071.90/291.57 (13) RewriteLemmaProof [LOWER BOUND(ID), 36 ms] 1071.90/291.57 (14) proven lower bound 1071.90/291.57 (15) LowerBoundPropagationProof [FINISHED, 0 ms] 1071.90/291.57 (16) BOUNDS(n^2, INF) 1071.90/291.57 1071.90/291.57 1071.90/291.57 ---------------------------------------- 1071.90/291.57 1071.90/291.57 (0) 1071.90/291.57 Obligation: 1071.90/291.57 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1071.90/291.57 1071.90/291.57 1071.90/291.57 The TRS R consists of the following rules: 1071.90/291.57 1071.90/291.57 sum(cons(s(n), x), cons(m, y)) -> sum(cons(n, x), cons(s(m), y)) 1071.90/291.57 sum(cons(0, x), y) -> sum(x, y) 1071.90/291.57 sum(nil, y) -> y 1071.90/291.57 weight(cons(n, cons(m, x))) -> weight(sum(cons(n, cons(m, x)), cons(0, x))) 1071.90/291.57 weight(cons(n, nil)) -> n 1071.90/291.57 1071.90/291.57 S is empty. 1071.90/291.57 Rewrite Strategy: FULL 1071.90/291.57 ---------------------------------------- 1071.90/291.57 1071.90/291.57 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 1071.90/291.57 Renamed function symbols to avoid clashes with predefined symbol. 1071.90/291.57 ---------------------------------------- 1071.90/291.57 1071.90/291.57 (2) 1071.90/291.57 Obligation: 1071.90/291.57 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1071.90/291.57 1071.90/291.57 1071.90/291.57 The TRS R consists of the following rules: 1071.90/291.57 1071.90/291.57 sum(cons(s(n), x), cons(m, y)) -> sum(cons(n, x), cons(s(m), y)) 1071.90/291.57 sum(cons(0', x), y) -> sum(x, y) 1071.90/291.57 sum(nil, y) -> y 1071.90/291.57 weight(cons(n, cons(m, x))) -> weight(sum(cons(n, cons(m, x)), cons(0', x))) 1071.90/291.57 weight(cons(n, nil)) -> n 1071.90/291.57 1071.90/291.57 S is empty. 1071.90/291.57 Rewrite Strategy: FULL 1071.90/291.57 ---------------------------------------- 1071.90/291.57 1071.90/291.57 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1071.90/291.57 Infered types. 1071.90/291.57 ---------------------------------------- 1071.90/291.57 1071.90/291.57 (4) 1071.90/291.57 Obligation: 1071.90/291.57 TRS: 1071.90/291.57 Rules: 1071.90/291.57 sum(cons(s(n), x), cons(m, y)) -> sum(cons(n, x), cons(s(m), y)) 1071.90/291.57 sum(cons(0', x), y) -> sum(x, y) 1071.90/291.57 sum(nil, y) -> y 1071.90/291.57 weight(cons(n, cons(m, x))) -> weight(sum(cons(n, cons(m, x)), cons(0', x))) 1071.90/291.57 weight(cons(n, nil)) -> n 1071.90/291.57 1071.90/291.57 Types: 1071.90/291.57 sum :: cons:nil -> cons:nil -> cons:nil 1071.90/291.57 cons :: s:0' -> cons:nil -> cons:nil 1071.90/291.57 s :: s:0' -> s:0' 1071.90/291.57 0' :: s:0' 1071.90/291.57 nil :: cons:nil 1071.90/291.57 weight :: cons:nil -> s:0' 1071.90/291.57 hole_cons:nil1_0 :: cons:nil 1071.90/291.57 hole_s:0'2_0 :: s:0' 1071.90/291.57 gen_cons:nil3_0 :: Nat -> cons:nil 1071.90/291.57 gen_s:0'4_0 :: Nat -> s:0' 1071.90/291.57 1071.90/291.57 ---------------------------------------- 1071.90/291.57 1071.90/291.57 (5) OrderProof (LOWER BOUND(ID)) 1071.90/291.57 Heuristically decided to analyse the following defined symbols: 1071.90/291.57 sum, weight 1071.90/291.57 1071.90/291.57 They will be analysed ascendingly in the following order: 1071.90/291.57 sum < weight
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