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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308547
details
property
value
status
complete
benchmark
z15.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n068.star.cs.uiowa.edu
space
Zantema_05
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.644 seconds
cpu usage
1095.56
user time
1074.61
system time
20.9506
max virtual memory
3.7772716E7
max residence set size
1.5027944E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1095.01/291.50 WORST_CASE(Omega(n^1), ?) 1095.26/291.54 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1095.26/291.54 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1095.26/291.54 1095.26/291.54 1095.26/291.54 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1095.26/291.54 1095.26/291.54 (0) CpxTRS 1095.26/291.54 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1095.26/291.54 (2) CpxTRS 1095.26/291.54 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1095.26/291.54 (4) typed CpxTrs 1095.26/291.54 (5) OrderProof [LOWER BOUND(ID), 0 ms] 1095.26/291.54 (6) typed CpxTrs 1095.26/291.54 (7) RewriteLemmaProof [LOWER BOUND(ID), 561 ms] 1095.26/291.54 (8) proven lower bound 1095.26/291.54 (9) LowerBoundPropagationProof [FINISHED, 0 ms] 1095.26/291.54 (10) BOUNDS(n^1, INF) 1095.26/291.54 1095.26/291.54 1095.26/291.54 ---------------------------------------- 1095.26/291.54 1095.26/291.54 (0) 1095.26/291.54 Obligation: 1095.26/291.54 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1095.26/291.54 1095.26/291.54 1095.26/291.54 The TRS R consists of the following rules: 1095.26/291.54 1095.26/291.54 f(x, a(b(y))) -> f(a(b(x)), y) 1095.26/291.54 f(a(x), y) -> f(x, a(y)) 1095.26/291.54 f(b(x), y) -> f(x, b(y)) 1095.26/291.54 1095.26/291.54 S is empty. 1095.26/291.54 Rewrite Strategy: FULL 1095.26/291.54 ---------------------------------------- 1095.26/291.54 1095.26/291.54 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 1095.26/291.54 Renamed function symbols to avoid clashes with predefined symbol. 1095.26/291.54 ---------------------------------------- 1095.26/291.54 1095.26/291.54 (2) 1095.26/291.54 Obligation: 1095.26/291.54 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1095.26/291.54 1095.26/291.54 1095.26/291.54 The TRS R consists of the following rules: 1095.26/291.54 1095.26/291.54 f(x, a(b(y))) -> f(a(b(x)), y) 1095.26/291.54 f(a(x), y) -> f(x, a(y)) 1095.26/291.54 f(b(x), y) -> f(x, b(y)) 1095.26/291.54 1095.26/291.54 S is empty. 1095.26/291.54 Rewrite Strategy: FULL 1095.26/291.54 ---------------------------------------- 1095.26/291.54 1095.26/291.54 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1095.26/291.54 Infered types. 1095.26/291.54 ---------------------------------------- 1095.26/291.54 1095.26/291.54 (4) 1095.26/291.54 Obligation: 1095.26/291.54 TRS: 1095.26/291.54 Rules: 1095.26/291.54 f(x, a(b(y))) -> f(a(b(x)), y) 1095.26/291.54 f(a(x), y) -> f(x, a(y)) 1095.26/291.54 f(b(x), y) -> f(x, b(y)) 1095.26/291.54 1095.26/291.54 Types: 1095.26/291.54 f :: b:a -> b:a -> f 1095.26/291.54 a :: b:a -> b:a 1095.26/291.54 b :: b:a -> b:a 1095.26/291.54 hole_f1_0 :: f 1095.26/291.54 hole_b:a2_0 :: b:a 1095.26/291.54 gen_b:a3_0 :: Nat -> b:a 1095.26/291.54 1095.26/291.54 ---------------------------------------- 1095.26/291.54 1095.26/291.54 (5) OrderProof (LOWER BOUND(ID)) 1095.26/291.54 Heuristically decided to analyse the following defined symbols: 1095.26/291.54 f 1095.26/291.54 ---------------------------------------- 1095.26/291.54 1095.26/291.54 (6) 1095.26/291.54 Obligation: 1095.26/291.54 TRS: 1095.26/291.54 Rules: 1095.26/291.54 f(x, a(b(y))) -> f(a(b(x)), y) 1095.26/291.54 f(a(x), y) -> f(x, a(y)) 1095.26/291.54 f(b(x), y) -> f(x, b(y)) 1095.26/291.54 1095.26/291.54 Types: 1095.26/291.54 f :: b:a -> b:a -> f 1095.26/291.55 a :: b:a -> b:a 1095.26/291.55 b :: b:a -> b:a 1095.26/291.55 hole_f1_0 :: f 1095.26/291.55 hole_b:a2_0 :: b:a 1095.26/291.55 gen_b:a3_0 :: Nat -> b:a 1095.26/291.55 1095.26/291.55
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