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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313762
details
property
value
status
complete
benchmark
#3.8a.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n080.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
7.38703 seconds
cpu usage
25.7626
user time
24.3228
system time
1.43984
max virtual memory
1.9175344E7
max residence set size
3759620.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
25.63/7.31 WORST_CASE(Omega(n^1), O(n^1)) 25.63/7.31 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 25.63/7.31 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 25.63/7.31 25.63/7.31 25.63/7.31 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 25.63/7.31 25.63/7.31 (0) CpxTRS 25.63/7.31 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 25.63/7.31 (2) CpxWeightedTrs 25.63/7.31 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 25.63/7.31 (4) CpxTypedWeightedTrs 25.63/7.31 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 25.63/7.31 (6) CpxTypedWeightedCompleteTrs 25.63/7.31 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 25.63/7.31 (8) CpxRNTS 25.63/7.31 (9) CompleteCoflocoProof [FINISHED, 477 ms] 25.63/7.31 (10) BOUNDS(1, n^1) 25.63/7.31 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 25.63/7.31 (12) TRS for Loop Detection 25.63/7.31 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 25.63/7.31 (14) BEST 25.63/7.31 (15) proven lower bound 25.63/7.31 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 25.63/7.31 (17) BOUNDS(n^1, INF) 25.63/7.31 (18) TRS for Loop Detection 25.63/7.31 25.63/7.31 25.63/7.31 ---------------------------------------- 25.63/7.31 25.63/7.31 (0) 25.63/7.31 Obligation: 25.63/7.31 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 25.63/7.31 25.63/7.31 25.63/7.31 The TRS R consists of the following rules: 25.63/7.31 25.63/7.31 pred(s(x)) -> x 25.63/7.31 minus(x, 0) -> x 25.63/7.31 minus(x, s(y)) -> pred(minus(x, y)) 25.63/7.31 quot(0, s(y)) -> 0 25.63/7.31 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) 25.63/7.31 log(s(0)) -> 0 25.63/7.31 log(s(s(x))) -> s(log(s(quot(x, s(s(0)))))) 25.63/7.31 25.63/7.31 S is empty. 25.63/7.31 Rewrite Strategy: INNERMOST 25.63/7.31 ---------------------------------------- 25.63/7.31 25.63/7.31 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 25.63/7.31 Transformed relative TRS to weighted TRS 25.63/7.31 ---------------------------------------- 25.63/7.31 25.63/7.31 (2) 25.63/7.31 Obligation: 25.63/7.31 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). 25.63/7.31 25.63/7.31 25.63/7.31 The TRS R consists of the following rules: 25.63/7.31 25.63/7.31 pred(s(x)) -> x [1] 25.63/7.31 minus(x, 0) -> x [1] 25.63/7.31 minus(x, s(y)) -> pred(minus(x, y)) [1] 25.63/7.31 quot(0, s(y)) -> 0 [1] 25.63/7.31 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) [1] 25.63/7.31 log(s(0)) -> 0 [1] 25.63/7.31 log(s(s(x))) -> s(log(s(quot(x, s(s(0)))))) [1] 25.63/7.31 25.63/7.31 Rewrite Strategy: INNERMOST 25.63/7.31 ---------------------------------------- 25.63/7.31 25.63/7.31 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 25.63/7.31 Infered types. 25.63/7.31 ---------------------------------------- 25.63/7.31 25.63/7.31 (4) 25.63/7.31 Obligation: 25.63/7.31 Runtime Complexity Weighted TRS with Types. 25.63/7.31 The TRS R consists of the following rules: 25.63/7.31 25.63/7.31 pred(s(x)) -> x [1] 25.63/7.31 minus(x, 0) -> x [1] 25.63/7.31 minus(x, s(y)) -> pred(minus(x, y)) [1] 25.63/7.31 quot(0, s(y)) -> 0 [1] 25.63/7.31 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) [1] 25.63/7.31 log(s(0)) -> 0 [1] 25.63/7.31 log(s(s(x))) -> s(log(s(quot(x, s(s(0)))))) [1] 25.63/7.31 25.63/7.31 The TRS has the following type information: 25.63/7.31 pred :: s:0 -> s:0 25.63/7.31 s :: s:0 -> s:0 25.63/7.31 minus :: s:0 -> s:0 -> s:0 25.63/7.31 0 :: s:0 25.63/7.31 quot :: s:0 -> s:0 -> s:0 25.63/7.31 log :: s:0 -> s:0 25.63/7.31 25.63/7.31 Rewrite Strategy: INNERMOST 25.63/7.31 ---------------------------------------- 25.63/7.31 25.63/7.31 (5) CompletionProof (UPPER BOUND(ID))
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