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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313835
details
property
value
status
complete
benchmark
cade11.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n058.star.cs.uiowa.edu
space
GTSSK07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.571 seconds
cpu usage
878.416
user time
873.542
system time
4.87468
max virtual memory
5.759968E7
max residence set size
5650940.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
878.01/291.50 WORST_CASE(Omega(n^1), O(n^2)) 878.01/291.51 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 878.01/291.51 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 878.01/291.51 878.01/291.51 878.01/291.51 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 878.01/291.51 878.01/291.51 (0) CpxTRS 878.01/291.51 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 878.01/291.51 (2) CpxWeightedTrs 878.01/291.51 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 878.01/291.51 (4) CpxTypedWeightedTrs 878.01/291.51 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 878.01/291.51 (6) CpxTypedWeightedCompleteTrs 878.01/291.51 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 878.01/291.51 (8) CpxRNTS 878.01/291.51 (9) CompleteCoflocoProof [FINISHED, 277 ms] 878.01/291.51 (10) BOUNDS(1, n^2) 878.01/291.51 (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 878.01/291.51 (12) CpxTRS 878.01/291.51 (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 878.01/291.51 (14) typed CpxTrs 878.01/291.51 (15) OrderProof [LOWER BOUND(ID), 0 ms] 878.01/291.51 (16) typed CpxTrs 878.01/291.51 (17) RewriteLemmaProof [LOWER BOUND(ID), 308 ms] 878.01/291.51 (18) BEST 878.01/291.51 (19) proven lower bound 878.01/291.51 (20) LowerBoundPropagationProof [FINISHED, 0 ms] 878.01/291.51 (21) BOUNDS(n^1, INF) 878.01/291.51 (22) typed CpxTrs 878.01/291.51 878.01/291.51 878.01/291.51 ---------------------------------------- 878.01/291.51 878.01/291.51 (0) 878.01/291.51 Obligation: 878.01/291.51 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 878.01/291.51 878.01/291.51 878.01/291.51 The TRS R consists of the following rules: 878.01/291.51 878.01/291.51 f(true, x, y) -> f(gt(x, y), s(x), s(s(y))) 878.01/291.51 gt(0, v) -> false 878.01/291.51 gt(s(u), 0) -> true 878.01/291.51 gt(s(u), s(v)) -> gt(u, v) 878.01/291.51 878.01/291.51 S is empty. 878.01/291.51 Rewrite Strategy: INNERMOST 878.01/291.51 ---------------------------------------- 878.01/291.51 878.01/291.51 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 878.01/291.51 Transformed relative TRS to weighted TRS 878.01/291.51 ---------------------------------------- 878.01/291.51 878.01/291.51 (2) 878.01/291.51 Obligation: 878.01/291.51 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 878.01/291.51 878.01/291.51 878.01/291.51 The TRS R consists of the following rules: 878.01/291.51 878.01/291.51 f(true, x, y) -> f(gt(x, y), s(x), s(s(y))) [1] 878.01/291.51 gt(0, v) -> false [1] 878.01/291.51 gt(s(u), 0) -> true [1] 878.01/291.51 gt(s(u), s(v)) -> gt(u, v) [1] 878.01/291.51 878.01/291.51 Rewrite Strategy: INNERMOST 878.01/291.51 ---------------------------------------- 878.01/291.51 878.01/291.51 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 878.01/291.51 Infered types. 878.01/291.51 ---------------------------------------- 878.01/291.51 878.01/291.51 (4) 878.01/291.51 Obligation: 878.01/291.51 Runtime Complexity Weighted TRS with Types. 878.01/291.51 The TRS R consists of the following rules: 878.01/291.51 878.01/291.51 f(true, x, y) -> f(gt(x, y), s(x), s(s(y))) [1] 878.01/291.51 gt(0, v) -> false [1] 878.01/291.51 gt(s(u), 0) -> true [1] 878.01/291.51 gt(s(u), s(v)) -> gt(u, v) [1] 878.01/291.51 878.01/291.51 The TRS has the following type information: 878.01/291.51 f :: true:false -> s:0 -> s:0 -> f 878.01/291.51 true :: true:false 878.01/291.51 gt :: s:0 -> s:0 -> true:false 878.01/291.51 s :: s:0 -> s:0 878.01/291.51 0 :: s:0 878.01/291.51 false :: true:false 878.01/291.51 878.01/291.51 Rewrite Strategy: INNERMOST 878.01/291.51 ---------------------------------------- 878.01/291.51 878.01/291.51 (5) CompletionProof (UPPER BOUND(ID)) 878.01/291.51 The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: 878.01/291.51 878.01/291.51 f(v0, v1, v2) -> null_f [0] 878.01/291.51 878.01/291.51 And the following fresh constants: null_f
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