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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313834
details
property
value
status
complete
benchmark
cade01.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n174.star.cs.uiowa.edu
space
GTSSK07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.642 seconds
cpu usage
883.582
user time
879.208
system time
4.37413
max virtual memory
1.9235916E7
max residence set size
5496796.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
883.24/291.57 WORST_CASE(Omega(n^1), O(n^2)) 883.50/291.59 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 883.50/291.59 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 883.50/291.59 883.50/291.59 883.50/291.59 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 883.50/291.59 883.50/291.59 (0) CpxTRS 883.50/291.59 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 883.50/291.59 (2) CpxWeightedTrs 883.50/291.59 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 883.50/291.59 (4) CpxTypedWeightedTrs 883.50/291.59 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 883.50/291.59 (6) CpxTypedWeightedCompleteTrs 883.50/291.59 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 883.50/291.59 (8) CpxRNTS 883.50/291.59 (9) CompleteCoflocoProof [FINISHED, 243 ms] 883.50/291.59 (10) BOUNDS(1, n^2) 883.50/291.59 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 883.50/291.59 (12) TRS for Loop Detection 883.50/291.59 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 883.50/291.59 (14) BEST 883.50/291.59 (15) proven lower bound 883.50/291.59 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 883.50/291.59 (17) BOUNDS(n^1, INF) 883.50/291.59 (18) TRS for Loop Detection 883.50/291.59 883.50/291.59 883.50/291.59 ---------------------------------------- 883.50/291.59 883.50/291.59 (0) 883.50/291.59 Obligation: 883.50/291.59 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 883.50/291.59 883.50/291.59 883.50/291.59 The TRS R consists of the following rules: 883.50/291.59 883.50/291.59 minus(x, y) -> cond(gt(x, y), x, y) 883.50/291.59 cond(false, x, y) -> 0 883.50/291.59 cond(true, x, y) -> s(minus(x, s(y))) 883.50/291.59 gt(0, v) -> false 883.50/291.59 gt(s(u), 0) -> true 883.50/291.59 gt(s(u), s(v)) -> gt(u, v) 883.50/291.59 883.50/291.59 S is empty. 883.50/291.59 Rewrite Strategy: INNERMOST 883.50/291.59 ---------------------------------------- 883.50/291.59 883.50/291.59 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 883.50/291.59 Transformed relative TRS to weighted TRS 883.50/291.59 ---------------------------------------- 883.50/291.59 883.50/291.59 (2) 883.50/291.59 Obligation: 883.50/291.59 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 883.50/291.59 883.50/291.59 883.50/291.59 The TRS R consists of the following rules: 883.50/291.59 883.50/291.59 minus(x, y) -> cond(gt(x, y), x, y) [1] 883.50/291.59 cond(false, x, y) -> 0 [1] 883.50/291.59 cond(true, x, y) -> s(minus(x, s(y))) [1] 883.50/291.59 gt(0, v) -> false [1] 883.50/291.59 gt(s(u), 0) -> true [1] 883.50/291.59 gt(s(u), s(v)) -> gt(u, v) [1] 883.50/291.59 883.50/291.59 Rewrite Strategy: INNERMOST 883.50/291.59 ---------------------------------------- 883.50/291.59 883.50/291.59 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 883.50/291.59 Infered types. 883.50/291.59 ---------------------------------------- 883.50/291.59 883.50/291.59 (4) 883.50/291.59 Obligation: 883.50/291.59 Runtime Complexity Weighted TRS with Types. 883.50/291.59 The TRS R consists of the following rules: 883.50/291.59 883.50/291.59 minus(x, y) -> cond(gt(x, y), x, y) [1] 883.50/291.59 cond(false, x, y) -> 0 [1] 883.50/291.59 cond(true, x, y) -> s(minus(x, s(y))) [1] 883.50/291.59 gt(0, v) -> false [1] 883.50/291.59 gt(s(u), 0) -> true [1] 883.50/291.59 gt(s(u), s(v)) -> gt(u, v) [1] 883.50/291.59 883.50/291.59 The TRS has the following type information: 883.50/291.59 minus :: 0:s -> 0:s -> 0:s 883.50/291.59 cond :: false:true -> 0:s -> 0:s -> 0:s 883.50/291.59 gt :: 0:s -> 0:s -> false:true 883.50/291.59 false :: false:true 883.50/291.59 0 :: 0:s 883.50/291.59 true :: false:true 883.50/291.59 s :: 0:s -> 0:s 883.50/291.59 883.50/291.59 Rewrite Strategy: INNERMOST 883.50/291.59 ---------------------------------------- 883.50/291.59 883.50/291.59 (5) CompletionProof (UPPER BOUND(ID)) 883.50/291.59 The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: 883.50/291.59 none
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