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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313698
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
n139.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.643 seconds
cpu usage
958.372
user time
952.284
system time
6.08846
max virtual memory
3.7398448E7
max residence set size
5957860.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
958.18/291.58 WORST_CASE(Omega(n^1), ?) 958.18/291.59 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 958.18/291.59 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 958.18/291.59 958.18/291.59 958.18/291.59 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 958.18/291.59 958.18/291.59 (0) CpxTRS 958.18/291.59 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 958.18/291.59 (2) CpxTRS 958.18/291.59 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 958.18/291.59 (4) typed CpxTrs 958.18/291.59 (5) OrderProof [LOWER BOUND(ID), 0 ms] 958.18/291.59 (6) typed CpxTrs 958.18/291.59 (7) RewriteLemmaProof [LOWER BOUND(ID), 301 ms] 958.18/291.59 (8) BEST 958.18/291.59 (9) proven lower bound 958.18/291.59 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 958.18/291.59 (11) BOUNDS(n^1, INF) 958.18/291.59 (12) typed CpxTrs 958.18/291.59 (13) RewriteLemmaProof [LOWER BOUND(ID), 78 ms] 958.18/291.59 (14) typed CpxTrs 958.18/291.59 958.18/291.59 958.18/291.59 ---------------------------------------- 958.18/291.59 958.18/291.59 (0) 958.18/291.59 Obligation: 958.18/291.59 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 958.18/291.59 958.18/291.59 958.18/291.59 The TRS R consists of the following rules: 958.18/291.59 958.18/291.59 plus(0, y) -> y 958.18/291.59 plus(s(x), y) -> s(plus(x, y)) 958.18/291.59 lt(0, s(y)) -> true 958.18/291.59 lt(x, 0) -> false 958.18/291.59 lt(s(x), s(y)) -> lt(x, y) 958.18/291.59 fib(x) -> fibiter(x, 0, 0, s(0)) 958.18/291.59 fibiter(b, c, x, y) -> if(lt(c, b), b, c, x, y) 958.18/291.59 if(false, b, c, x, y) -> x 958.18/291.59 if(true, b, c, x, y) -> fibiter(b, s(c), y, plus(x, y)) 958.18/291.59 958.18/291.59 S is empty. 958.18/291.59 Rewrite Strategy: INNERMOST 958.18/291.59 ---------------------------------------- 958.18/291.59 958.18/291.59 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 958.18/291.59 Renamed function symbols to avoid clashes with predefined symbol. 958.18/291.59 ---------------------------------------- 958.18/291.59 958.18/291.59 (2) 958.18/291.59 Obligation: 958.18/291.59 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 958.18/291.59 958.18/291.59 958.18/291.59 The TRS R consists of the following rules: 958.18/291.59 958.18/291.59 plus(0', y) -> y 958.18/291.59 plus(s(x), y) -> s(plus(x, y)) 958.18/291.59 lt(0', s(y)) -> true 958.18/291.59 lt(x, 0') -> false 958.18/291.59 lt(s(x), s(y)) -> lt(x, y) 958.18/291.59 fib(x) -> fibiter(x, 0', 0', s(0')) 958.18/291.59 fibiter(b, c, x, y) -> if(lt(c, b), b, c, x, y) 958.18/291.59 if(false, b, c, x, y) -> x 958.18/291.59 if(true, b, c, x, y) -> fibiter(b, s(c), y, plus(x, y)) 958.18/291.59 958.18/291.59 S is empty. 958.18/291.59 Rewrite Strategy: INNERMOST 958.18/291.59 ---------------------------------------- 958.18/291.59 958.18/291.59 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 958.18/291.60 Infered types. 958.18/291.60 ---------------------------------------- 958.18/291.60 958.18/291.60 (4) 958.18/291.60 Obligation: 958.18/291.60 Innermost TRS: 958.18/291.60 Rules: 958.18/291.60 plus(0', y) -> y 958.18/291.60 plus(s(x), y) -> s(plus(x, y)) 958.18/291.60 lt(0', s(y)) -> true 958.18/291.60 lt(x, 0') -> false 958.18/291.60 lt(s(x), s(y)) -> lt(x, y) 958.18/291.60 fib(x) -> fibiter(x, 0', 0', s(0')) 958.18/291.60 fibiter(b, c, x, y) -> if(lt(c, b), b, c, x, y) 958.18/291.60 if(false, b, c, x, y) -> x 958.18/291.60 if(true, b, c, x, y) -> fibiter(b, s(c), y, plus(x, y)) 958.18/291.60 958.18/291.60 Types: 958.18/291.60 plus :: 0':s -> 0':s -> 0':s 958.18/291.60 0' :: 0':s 958.18/291.60 s :: 0':s -> 0':s 958.18/291.60 lt :: 0':s -> 0':s -> true:false 958.18/291.60 true :: true:false 958.18/291.60 false :: true:false 958.18/291.60 fib :: 0':s -> 0':s 958.18/291.60 fibiter :: 0':s -> 0':s -> 0':s -> 0':s -> 0':s 958.18/291.60 if :: true:false -> 0':s -> 0':s -> 0':s -> 0':s -> 0':s
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