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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313842
details
property
value
status
complete
benchmark
cade03.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n057.star.cs.uiowa.edu
space
GTSSK07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.565 seconds
cpu usage
880.357
user time
876.051
system time
4.30648
max virtual memory
3.804504E7
max residence set size
5387736.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
880.14/291.50 WORST_CASE(Omega(n^1), O(n^2)) 880.14/291.52 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 880.14/291.52 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 880.14/291.52 880.14/291.52 880.14/291.52 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 880.14/291.52 880.14/291.52 (0) CpxTRS 880.14/291.52 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 880.14/291.52 (2) CpxWeightedTrs 880.14/291.52 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 880.14/291.52 (4) CpxTypedWeightedTrs 880.14/291.52 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 880.14/291.52 (6) CpxTypedWeightedCompleteTrs 880.14/291.52 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 2 ms] 880.14/291.52 (8) CpxRNTS 880.14/291.52 (9) CompleteCoflocoProof [FINISHED, 219 ms] 880.14/291.52 (10) BOUNDS(1, n^2) 880.14/291.52 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 880.14/291.52 (12) TRS for Loop Detection 880.14/291.52 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 880.14/291.52 (14) BEST 880.14/291.52 (15) proven lower bound 880.14/291.52 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 880.14/291.52 (17) BOUNDS(n^1, INF) 880.14/291.52 (18) TRS for Loop Detection 880.14/291.52 880.14/291.52 880.14/291.52 ---------------------------------------- 880.14/291.52 880.14/291.52 (0) 880.14/291.52 Obligation: 880.14/291.52 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 880.14/291.52 880.14/291.52 880.14/291.52 The TRS R consists of the following rules: 880.14/291.52 880.14/291.52 minus(x, y) -> cond(ge(x, s(y)), x, y) 880.14/291.52 cond(false, x, y) -> 0 880.14/291.52 cond(true, x, y) -> s(minus(x, s(y))) 880.14/291.52 ge(u, 0) -> true 880.14/291.52 ge(0, s(v)) -> false 880.14/291.52 ge(s(u), s(v)) -> ge(u, v) 880.14/291.52 880.14/291.52 S is empty. 880.14/291.52 Rewrite Strategy: INNERMOST 880.14/291.52 ---------------------------------------- 880.14/291.52 880.14/291.52 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 880.14/291.52 Transformed relative TRS to weighted TRS 880.14/291.52 ---------------------------------------- 880.14/291.52 880.14/291.52 (2) 880.14/291.52 Obligation: 880.14/291.52 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 880.14/291.52 880.14/291.52 880.14/291.52 The TRS R consists of the following rules: 880.14/291.52 880.14/291.52 minus(x, y) -> cond(ge(x, s(y)), x, y) [1] 880.14/291.52 cond(false, x, y) -> 0 [1] 880.14/291.52 cond(true, x, y) -> s(minus(x, s(y))) [1] 880.14/291.52 ge(u, 0) -> true [1] 880.14/291.52 ge(0, s(v)) -> false [1] 880.14/291.52 ge(s(u), s(v)) -> ge(u, v) [1] 880.14/291.52 880.14/291.52 Rewrite Strategy: INNERMOST 880.14/291.52 ---------------------------------------- 880.14/291.52 880.14/291.52 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 880.14/291.52 Infered types. 880.14/291.52 ---------------------------------------- 880.14/291.52 880.14/291.52 (4) 880.14/291.52 Obligation: 880.14/291.52 Runtime Complexity Weighted TRS with Types. 880.14/291.52 The TRS R consists of the following rules: 880.14/291.52 880.14/291.52 minus(x, y) -> cond(ge(x, s(y)), x, y) [1] 880.14/291.52 cond(false, x, y) -> 0 [1] 880.14/291.52 cond(true, x, y) -> s(minus(x, s(y))) [1] 880.14/291.52 ge(u, 0) -> true [1] 880.14/291.52 ge(0, s(v)) -> false [1] 880.14/291.52 ge(s(u), s(v)) -> ge(u, v) [1] 880.14/291.52 880.14/291.52 The TRS has the following type information: 880.14/291.52 minus :: s:0 -> s:0 -> s:0 880.14/291.52 cond :: false:true -> s:0 -> s:0 -> s:0 880.14/291.52 ge :: s:0 -> s:0 -> false:true 880.14/291.52 s :: s:0 -> s:0 880.14/291.52 false :: false:true 880.14/291.52 0 :: s:0 880.14/291.52 true :: false:true 880.14/291.52 880.14/291.52 Rewrite Strategy: INNERMOST 880.14/291.52 ---------------------------------------- 880.14/291.52 880.14/291.52 (5) CompletionProof (UPPER BOUND(ID)) 880.14/291.52 The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: 880.14/291.52 none
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