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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308393
details
property
value
status
complete
benchmark
2.27.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n071.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.547 seconds
cpu usage
316.4
user time
314.24
system time
2.15989
max virtual memory
1.8282052E7
max residence set size
5386436.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
316.28/291.50 WORST_CASE(Omega(n^1), ?) 316.28/291.51 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 316.28/291.51 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 316.28/291.51 316.28/291.51 316.28/291.51 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 316.28/291.51 316.28/291.51 (0) CpxTRS 316.28/291.51 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 316.28/291.51 (2) CpxTRS 316.28/291.51 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 316.28/291.51 (4) typed CpxTrs 316.28/291.51 (5) OrderProof [LOWER BOUND(ID), 0 ms] 316.28/291.51 (6) typed CpxTrs 316.28/291.51 (7) RewriteLemmaProof [LOWER BOUND(ID), 958 ms] 316.28/291.51 (8) BEST 316.28/291.51 (9) proven lower bound 316.28/291.51 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 316.28/291.51 (11) BOUNDS(n^1, INF) 316.28/291.51 (12) typed CpxTrs 316.28/291.51 (13) RewriteLemmaProof [LOWER BOUND(ID), 0 ms] 316.28/291.51 (14) BOUNDS(1, INF) 316.28/291.51 316.28/291.51 316.28/291.51 ---------------------------------------- 316.28/291.51 316.28/291.51 (0) 316.28/291.51 Obligation: 316.28/291.51 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 316.28/291.51 316.28/291.51 316.28/291.51 The TRS R consists of the following rules: 316.28/291.51 316.28/291.51 fib(0) -> 0 316.28/291.51 fib(s(0)) -> s(0) 316.28/291.51 fib(s(s(0))) -> s(0) 316.28/291.51 fib(s(s(x))) -> sp(g(x)) 316.28/291.51 g(0) -> pair(s(0), 0) 316.28/291.51 g(s(0)) -> pair(s(0), s(0)) 316.28/291.51 g(s(x)) -> np(g(x)) 316.28/291.51 sp(pair(x, y)) -> +(x, y) 316.28/291.51 np(pair(x, y)) -> pair(+(x, y), x) 316.28/291.51 +(x, 0) -> x 316.28/291.51 +(x, s(y)) -> s(+(x, y)) 316.28/291.51 316.28/291.51 S is empty. 316.28/291.51 Rewrite Strategy: FULL 316.28/291.51 ---------------------------------------- 316.28/291.51 316.28/291.51 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 316.28/291.51 Renamed function symbols to avoid clashes with predefined symbol. 316.28/291.51 ---------------------------------------- 316.28/291.51 316.28/291.51 (2) 316.28/291.51 Obligation: 316.28/291.51 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 316.28/291.51 316.28/291.51 316.28/291.51 The TRS R consists of the following rules: 316.28/291.51 316.28/291.51 fib(0') -> 0' 316.28/291.51 fib(s(0')) -> s(0') 316.28/291.51 fib(s(s(0'))) -> s(0') 316.28/291.51 fib(s(s(x))) -> sp(g(x)) 316.28/291.51 g(0') -> pair(s(0'), 0') 316.28/291.51 g(s(0')) -> pair(s(0'), s(0')) 316.28/291.51 g(s(x)) -> np(g(x)) 316.28/291.51 sp(pair(x, y)) -> +'(x, y) 316.28/291.51 np(pair(x, y)) -> pair(+'(x, y), x) 316.28/291.51 +'(x, 0') -> x 316.28/291.51 +'(x, s(y)) -> s(+'(x, y)) 316.28/291.51 316.28/291.51 S is empty. 316.28/291.51 Rewrite Strategy: FULL 316.28/291.51 ---------------------------------------- 316.28/291.51 316.28/291.51 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 316.28/291.51 Infered types. 316.28/291.51 ---------------------------------------- 316.28/291.51 316.28/291.51 (4) 316.28/291.51 Obligation: 316.28/291.51 TRS: 316.28/291.51 Rules: 316.28/291.51 fib(0') -> 0' 316.28/291.51 fib(s(0')) -> s(0') 316.28/291.51 fib(s(s(0'))) -> s(0') 316.28/291.51 fib(s(s(x))) -> sp(g(x)) 316.28/291.51 g(0') -> pair(s(0'), 0') 316.28/291.51 g(s(0')) -> pair(s(0'), s(0')) 316.28/291.51 g(s(x)) -> np(g(x)) 316.28/291.51 sp(pair(x, y)) -> +'(x, y) 316.28/291.51 np(pair(x, y)) -> pair(+'(x, y), x) 316.28/291.51 +'(x, 0') -> x 316.28/291.51 +'(x, s(y)) -> s(+'(x, y)) 316.28/291.51 316.28/291.51 Types: 316.28/291.51 fib :: 0':s -> 0':s 316.28/291.51 0' :: 0':s 316.28/291.51 s :: 0':s -> 0':s
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