details

property	value
status	complete
benchmark	z18.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n137.star.cs.uiowa.edu
space	Zantema_05

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.601 seconds
cpu usage	1073.96
user time	1052.68
system time	21.2794
max virtual memory	3.7382732E7
max residence set size	1.5130356E7

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), ?)

output

WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (4) typed CpxTrs (5) OrderProof [LOWER BOUND(ID), 0 ms] (6) typed CpxTrs (7) RewriteLemmaProof [LOWER BOUND(ID), 461 ms] (8) proven lower bound (9) LowerBoundPropagationProof [FINISHED, 0 ms] (10) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: f(x, a(b(y))) -> a(f(a(b(x)), y)) f(a(x), y) -> f(x, a(y)) f(b(x), y) -> f(x, b(y)) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: f(x, a(b(y))) -> a(f(a(b(x)), y)) f(a(x), y) -> f(x, a(y)) f(b(x), y) -> f(x, b(y)) S is empty. Rewrite Strategy: FULL ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4) Obligation: TRS: Rules: f(x, a(b(y))) -> a(f(a(b(x)), y)) f(a(x), y) -> f(x, a(y)) f(b(x), y) -> f(x, b(y)) Types: f :: b:a -> b:a -> b:a a :: b:a -> b:a b :: b:a -> b:a hole_b:a1_0 :: b:a gen_b:a2_0 :: Nat -> b:a ---------------------------------------- (5) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: f ---------------------------------------- (6) Obligation: TRS: Rules: f(x, a(b(y))) -> a(f(a(b(x)), y)) f(a(x), y) -> f(x, a(y)) f(b(x), y) -> f(x, b(y)) Types: f :: b:a -> b:a -> b:a a :: b:a -> b:a b :: b:a -> b:a hole_b:a1_0 :: b:a gen_b:a2_0 :: Nat -> b:a Generator Equations: gen_b:a2_0(0) <=> hole_b:a1_0 popout

output may be truncated. 'popout' for the full output.

job log

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actions

all output return to Runtime Complexity: TRS