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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313380
details
property
value
status
complete
benchmark
while.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n033.star.cs.uiowa.edu
space
Mixed_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.571 seconds
cpu usage
882.337
user time
878.024
system time
4.31282
max virtual memory
3.7904544E7
max residence set size
5336720.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
882.02/291.52 WORST_CASE(Omega(n^1), O(n^2)) 882.23/291.53 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 882.23/291.53 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 882.23/291.53 882.23/291.53 882.23/291.53 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 882.23/291.53 882.23/291.53 (0) CpxTRS 882.23/291.53 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 882.23/291.53 (2) CpxWeightedTrs 882.23/291.53 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 882.23/291.53 (4) CpxTypedWeightedTrs 882.23/291.53 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 882.23/291.53 (6) CpxTypedWeightedCompleteTrs 882.23/291.53 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 3 ms] 882.23/291.53 (8) CpxRNTS 882.23/291.53 (9) CompleteCoflocoProof [FINISHED, 228 ms] 882.23/291.53 (10) BOUNDS(1, n^2) 882.23/291.53 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 882.23/291.53 (12) TRS for Loop Detection 882.23/291.53 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 882.23/291.53 (14) BEST 882.23/291.53 (15) proven lower bound 882.23/291.53 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 882.23/291.53 (17) BOUNDS(n^1, INF) 882.23/291.53 (18) TRS for Loop Detection 882.23/291.53 882.23/291.53 882.23/291.53 ---------------------------------------- 882.23/291.53 882.23/291.53 (0) 882.23/291.53 Obligation: 882.23/291.53 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 882.23/291.53 882.23/291.53 882.23/291.53 The TRS R consists of the following rules: 882.23/291.53 882.23/291.53 f(t, x, y) -> f(g(x, y), x, s(y)) 882.23/291.53 g(s(x), 0) -> t 882.23/291.53 g(s(x), s(y)) -> g(x, y) 882.23/291.53 882.23/291.53 S is empty. 882.23/291.53 Rewrite Strategy: INNERMOST 882.23/291.53 ---------------------------------------- 882.23/291.53 882.23/291.53 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 882.23/291.53 Transformed relative TRS to weighted TRS 882.23/291.53 ---------------------------------------- 882.23/291.53 882.23/291.53 (2) 882.23/291.53 Obligation: 882.23/291.53 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 882.23/291.53 882.23/291.53 882.23/291.53 The TRS R consists of the following rules: 882.23/291.53 882.23/291.53 f(t, x, y) -> f(g(x, y), x, s(y)) [1] 882.23/291.53 g(s(x), 0) -> t [1] 882.23/291.53 g(s(x), s(y)) -> g(x, y) [1] 882.23/291.53 882.23/291.53 Rewrite Strategy: INNERMOST 882.23/291.53 ---------------------------------------- 882.23/291.53 882.23/291.53 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 882.23/291.53 Infered types. 882.23/291.53 ---------------------------------------- 882.23/291.53 882.23/291.53 (4) 882.23/291.53 Obligation: 882.23/291.53 Runtime Complexity Weighted TRS with Types. 882.23/291.53 The TRS R consists of the following rules: 882.23/291.53 882.23/291.53 f(t, x, y) -> f(g(x, y), x, s(y)) [1] 882.23/291.53 g(s(x), 0) -> t [1] 882.23/291.53 g(s(x), s(y)) -> g(x, y) [1] 882.23/291.53 882.23/291.53 The TRS has the following type information: 882.23/291.53 f :: t -> s:0 -> s:0 -> f 882.23/291.53 t :: t 882.23/291.53 g :: s:0 -> s:0 -> t 882.23/291.53 s :: s:0 -> s:0 882.23/291.53 0 :: s:0 882.23/291.53 882.23/291.53 Rewrite Strategy: INNERMOST 882.23/291.53 ---------------------------------------- 882.23/291.53 882.23/291.53 (5) CompletionProof (UPPER BOUND(ID)) 882.23/291.53 The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: 882.23/291.53 882.23/291.53 g(v0, v1) -> null_g [0] 882.23/291.53 f(v0, v1, v2) -> null_f [0] 882.23/291.53 882.23/291.53 And the following fresh constants: null_g, null_f 882.23/291.53 882.23/291.53 ---------------------------------------- 882.23/291.53 882.23/291.53 (6) 882.23/291.53 Obligation: 882.23/291.53 Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is: 882.23/291.53
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