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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313838
details
property
value
status
complete
benchmark
cade12t.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n063.star.cs.uiowa.edu
space
GTSSK07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.61 seconds
cpu usage
1115.05
user time
1109.19
system time
5.8557
max virtual memory
5.730154E7
max residence set size
6138460.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
1114.76/291.56 WORST_CASE(Omega(n^1), O(n^2)) 1114.76/291.57 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1114.76/291.57 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1114.76/291.57 1114.76/291.57 1114.76/291.57 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1114.76/291.57 1114.76/291.57 (0) CpxTRS 1114.76/291.57 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1114.76/291.57 (2) CpxWeightedTrs 1114.76/291.57 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1114.76/291.57 (4) CpxTypedWeightedTrs 1114.76/291.57 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 1114.76/291.57 (6) CpxTypedWeightedCompleteTrs 1114.76/291.57 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1114.76/291.57 (8) CpxRNTS 1114.76/291.57 (9) CompleteCoflocoProof [FINISHED, 522 ms] 1114.76/291.57 (10) BOUNDS(1, n^2) 1114.76/291.57 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1114.76/291.57 (12) TRS for Loop Detection 1114.76/291.57 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1114.76/291.57 (14) BEST 1114.76/291.57 (15) proven lower bound 1114.76/291.57 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 1114.76/291.57 (17) BOUNDS(n^1, INF) 1114.76/291.57 (18) TRS for Loop Detection 1114.76/291.57 1114.76/291.57 1114.76/291.57 ---------------------------------------- 1114.76/291.57 1114.76/291.57 (0) 1114.76/291.57 Obligation: 1114.76/291.57 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1114.76/291.57 1114.76/291.57 1114.76/291.57 The TRS R consists of the following rules: 1114.76/291.57 1114.76/291.57 f(true, x, y) -> f(and(gt(x, y), gt(y, s(s(0)))), plus(s(0), x), double(y)) 1114.76/291.57 gt(0, v) -> false 1114.76/291.57 gt(s(u), 0) -> true 1114.76/291.57 gt(s(u), s(v)) -> gt(u, v) 1114.76/291.57 and(x, true) -> x 1114.76/291.57 and(x, false) -> false 1114.76/291.57 plus(n, 0) -> n 1114.76/291.57 plus(n, s(m)) -> s(plus(n, m)) 1114.76/291.57 double(0) -> 0 1114.76/291.57 double(s(x)) -> s(s(double(x))) 1114.76/291.57 1114.76/291.57 S is empty. 1114.76/291.57 Rewrite Strategy: INNERMOST 1114.76/291.57 ---------------------------------------- 1114.76/291.57 1114.76/291.57 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1114.76/291.57 Transformed relative TRS to weighted TRS 1114.76/291.57 ---------------------------------------- 1114.76/291.57 1114.76/291.57 (2) 1114.76/291.57 Obligation: 1114.76/291.57 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 1114.76/291.57 1114.76/291.57 1114.76/291.57 The TRS R consists of the following rules: 1114.76/291.57 1114.76/291.57 f(true, x, y) -> f(and(gt(x, y), gt(y, s(s(0)))), plus(s(0), x), double(y)) [1] 1114.76/291.57 gt(0, v) -> false [1] 1114.76/291.57 gt(s(u), 0) -> true [1] 1114.76/291.57 gt(s(u), s(v)) -> gt(u, v) [1] 1114.76/291.57 and(x, true) -> x [1] 1114.76/291.57 and(x, false) -> false [1] 1114.76/291.57 plus(n, 0) -> n [1] 1114.76/291.57 plus(n, s(m)) -> s(plus(n, m)) [1] 1114.76/291.57 double(0) -> 0 [1] 1114.76/291.57 double(s(x)) -> s(s(double(x))) [1] 1114.76/291.57 1114.76/291.57 Rewrite Strategy: INNERMOST 1114.76/291.57 ---------------------------------------- 1114.76/291.57 1114.76/291.57 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1114.76/291.57 Infered types. 1114.76/291.57 ---------------------------------------- 1114.76/291.57 1114.76/291.57 (4) 1114.76/291.57 Obligation: 1114.76/291.57 Runtime Complexity Weighted TRS with Types. 1114.76/291.57 The TRS R consists of the following rules: 1114.76/291.57 1114.76/291.57 f(true, x, y) -> f(and(gt(x, y), gt(y, s(s(0)))), plus(s(0), x), double(y)) [1] 1114.76/291.57 gt(0, v) -> false [1] 1114.76/291.57 gt(s(u), 0) -> true [1] 1114.76/291.57 gt(s(u), s(v)) -> gt(u, v) [1] 1114.76/291.57 and(x, true) -> x [1] 1114.76/291.57 and(x, false) -> false [1] 1114.76/291.57 plus(n, 0) -> n [1] 1114.76/291.57 plus(n, s(m)) -> s(plus(n, m)) [1] 1114.76/291.57 double(0) -> 0 [1] 1114.76/291.57 double(s(x)) -> s(s(double(x))) [1] 1114.76/291.57 1114.76/291.57 The TRS has the following type information: 1114.76/291.57 f :: true:false -> 0:s -> 0:s -> f 1114.76/291.57 true :: true:false
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