details

property	value
status	complete
benchmark	thiemann05.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n148.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.6 seconds
cpu usage	317.958
user time	315.876
system time	2.08208
max virtual memory	1.8281392E7
max residence set size	5461072.0

stage attributes

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

output

WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).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), 258 ms] (8) BEST (9) proven lower bound (10) LowerBoundPropagationProof [FINISHED, 0 ms] (11) BOUNDS(n^1, INF) (12) typed CpxTrs (13) RewriteLemmaProof [LOWER BOUND(ID), 145 ms] (14) BOUNDS(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: isLeaf(leaf) -> true isLeaf(cons(u, v)) -> false left(cons(u, v)) -> u right(cons(u, v)) -> v concat(leaf, y) -> y concat(cons(u, v), y) -> cons(u, concat(v, y)) less_leaves(u, v) -> if1(isLeaf(u), isLeaf(v), u, v) if1(b, true, u, v) -> false if1(b, false, u, v) -> if2(b, u, v) if2(true, u, v) -> true if2(false, u, v) -> less_leaves(concat(left(u), right(u)), concat(left(v), right(v))) 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: isLeaf(leaf) -> true isLeaf(cons(u, v)) -> false left(cons(u, v)) -> u right(cons(u, v)) -> v concat(leaf, y) -> y concat(cons(u, v), y) -> cons(u, concat(v, y)) less_leaves(u, v) -> if1(isLeaf(u), isLeaf(v), u, v) if1(b, true, u, v) -> false if1(b, false, u, v) -> if2(b, u, v) if2(true, u, v) -> true if2(false, u, v) -> less_leaves(concat(left(u), right(u)), concat(left(v), right(v))) S is empty. Rewrite Strategy: FULL ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4) Obligation: TRS: Rules: isLeaf(leaf) -> true isLeaf(cons(u, v)) -> false left(cons(u, v)) -> u right(cons(u, v)) -> v concat(leaf, y) -> y concat(cons(u, v), y) -> cons(u, concat(v, y)) less_leaves(u, v) -> if1(isLeaf(u), isLeaf(v), u, v) if1(b, true, u, v) -> false if1(b, false, u, v) -> if2(b, u, v) if2(true, u, v) -> true if2(false, u, v) -> less_leaves(concat(left(u), right(u)), concat(left(v), right(v))) Types: isLeaf :: leaf:cons -> true:false leaf :: leaf:cons true :: true:false popout

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all output return to Runtime Complexity: TRS