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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313746
details
property
value
status
complete
benchmark
#3.18.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n123.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
9.62043 seconds
cpu usage
33.9243
user time
32.149
system time
1.77528
max virtual memory
3.7976984E7
max residence set size
3911044.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
33.62/9.55 WORST_CASE(Omega(n^1), O(n^1)) 33.62/9.56 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 33.62/9.56 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 33.62/9.56 33.62/9.56 33.62/9.56 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 33.62/9.56 33.62/9.56 (0) CpxTRS 33.62/9.56 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 33.62/9.56 (2) CpxWeightedTrs 33.62/9.56 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 33.62/9.56 (4) CpxTypedWeightedTrs 33.62/9.56 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 33.62/9.56 (6) CpxTypedWeightedCompleteTrs 33.62/9.56 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 33.62/9.56 (8) CpxRNTS 33.62/9.56 (9) CompleteCoflocoProof [FINISHED, 740 ms] 33.62/9.56 (10) BOUNDS(1, n^1) 33.62/9.56 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 33.62/9.56 (12) TRS for Loop Detection 33.62/9.56 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 33.62/9.56 (14) BEST 33.62/9.56 (15) proven lower bound 33.62/9.56 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 33.62/9.56 (17) BOUNDS(n^1, INF) 33.62/9.56 (18) TRS for Loop Detection 33.62/9.56 33.62/9.56 33.62/9.56 ---------------------------------------- 33.62/9.56 33.62/9.56 (0) 33.62/9.56 Obligation: 33.62/9.56 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 33.62/9.56 33.62/9.56 33.62/9.56 The TRS R consists of the following rules: 33.62/9.56 33.62/9.56 minus(x, 0) -> x 33.62/9.56 minus(s(x), s(y)) -> minus(x, y) 33.62/9.56 double(0) -> 0 33.62/9.56 double(s(x)) -> s(s(double(x))) 33.62/9.56 plus(0, y) -> y 33.62/9.56 plus(s(x), y) -> s(plus(x, y)) 33.62/9.56 plus(s(x), y) -> plus(x, s(y)) 33.62/9.56 plus(s(x), y) -> s(plus(minus(x, y), double(y))) 33.62/9.56 33.62/9.56 S is empty. 33.62/9.56 Rewrite Strategy: INNERMOST 33.62/9.56 ---------------------------------------- 33.62/9.56 33.62/9.56 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 33.62/9.56 Transformed relative TRS to weighted TRS 33.62/9.56 ---------------------------------------- 33.62/9.56 33.62/9.56 (2) 33.62/9.56 Obligation: 33.62/9.56 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). 33.62/9.56 33.62/9.56 33.62/9.56 The TRS R consists of the following rules: 33.62/9.56 33.62/9.56 minus(x, 0) -> x [1] 33.62/9.56 minus(s(x), s(y)) -> minus(x, y) [1] 33.62/9.56 double(0) -> 0 [1] 33.62/9.56 double(s(x)) -> s(s(double(x))) [1] 33.62/9.56 plus(0, y) -> y [1] 33.62/9.56 plus(s(x), y) -> s(plus(x, y)) [1] 33.62/9.56 plus(s(x), y) -> plus(x, s(y)) [1] 33.62/9.56 plus(s(x), y) -> s(plus(minus(x, y), double(y))) [1] 33.62/9.56 33.62/9.56 Rewrite Strategy: INNERMOST 33.62/9.56 ---------------------------------------- 33.62/9.56 33.62/9.56 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 33.62/9.56 Infered types. 33.62/9.56 ---------------------------------------- 33.62/9.56 33.62/9.56 (4) 33.62/9.56 Obligation: 33.62/9.56 Runtime Complexity Weighted TRS with Types. 33.62/9.56 The TRS R consists of the following rules: 33.62/9.56 33.62/9.56 minus(x, 0) -> x [1] 33.62/9.56 minus(s(x), s(y)) -> minus(x, y) [1] 33.62/9.56 double(0) -> 0 [1] 33.62/9.56 double(s(x)) -> s(s(double(x))) [1] 33.62/9.56 plus(0, y) -> y [1] 33.62/9.56 plus(s(x), y) -> s(plus(x, y)) [1] 33.62/9.56 plus(s(x), y) -> plus(x, s(y)) [1] 33.62/9.56 plus(s(x), y) -> s(plus(minus(x, y), double(y))) [1] 33.62/9.56 33.62/9.56 The TRS has the following type information: 33.62/9.56 minus :: 0:s -> 0:s -> 0:s 33.62/9.56 0 :: 0:s 33.62/9.56 s :: 0:s -> 0:s 33.62/9.56 double :: 0:s -> 0:s 33.62/9.56 plus :: 0:s -> 0:s -> 0:s 33.62/9.56 33.62/9.56 Rewrite Strategy: INNERMOST 33.62/9.56 ----------------------------------------
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