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Runtime Complexity: TRS Innermost pair #487111754
details
property
value
status
complete
benchmark
thiemann25.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n144.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.696 seconds
cpu usage
942.0
user time
935.726
system time
6.2744
max virtual memory
5.6003832E7
max residence set size
6405680.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).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), 283 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), 30 ms] (14) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: plus(0, y) -> y plus(s(x), y) -> s(plus(x, y)) lt(0, s(y)) -> true lt(x, 0) -> false lt(s(x), s(y)) -> lt(x, y) fib(x) -> fibiter(x, 0, 0, s(0)) fibiter(b, c, x, y) -> if(lt(c, b), b, c, x, y) if(false, b, c, x, y) -> x if(true, b, c, x, y) -> fibiter(b, s(c), y, plus(x, y)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: plus(0', y) -> y plus(s(x), y) -> s(plus(x, y)) lt(0', s(y)) -> true lt(x, 0') -> false lt(s(x), s(y)) -> lt(x, y) fib(x) -> fibiter(x, 0', 0', s(0')) fibiter(b, c, x, y) -> if(lt(c, b), b, c, x, y) if(false, b, c, x, y) -> x if(true, b, c, x, y) -> fibiter(b, s(c), y, plus(x, y)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4) Obligation: Innermost TRS: Rules: plus(0', y) -> y plus(s(x), y) -> s(plus(x, y)) lt(0', s(y)) -> true lt(x, 0') -> false lt(s(x), s(y)) -> lt(x, y) fib(x) -> fibiter(x, 0', 0', s(0')) fibiter(b, c, x, y) -> if(lt(c, b), b, c, x, y) if(false, b, c, x, y) -> x if(true, b, c, x, y) -> fibiter(b, s(c), y, plus(x, y)) Types: plus :: 0':s -> 0':s -> 0':s 0' :: 0':s s :: 0':s -> 0':s lt :: 0':s -> 0':s -> true:false true :: true:false false :: true:false fib :: 0':s -> 0':s fibiter :: 0':s -> 0':s -> 0':s -> 0':s -> 0':s if :: true:false -> 0':s -> 0':s -> 0':s -> 0':s -> 0':s
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