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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313604
details
property
value
status
complete
benchmark
2.16.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n099.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
8.93618 seconds
cpu usage
26.8713
user time
24.9162
system time
1.95511
max virtual memory
1.9263716E7
max residence set size
4126788.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), O(n^2))
output
26.44/8.27 WORST_CASE(Omega(n^2), O(n^2)) 26.44/8.28 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 26.44/8.28 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 26.44/8.28 26.44/8.28 26.44/8.28 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2). 26.44/8.28 26.44/8.28 (0) CpxTRS 26.44/8.28 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 26.44/8.28 (2) CpxWeightedTrs 26.44/8.28 (3) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 26.44/8.28 (4) CpxWeightedTrs 26.44/8.28 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 26.44/8.28 (6) CpxTypedWeightedTrs 26.44/8.28 (7) CompletionProof [UPPER BOUND(ID), 0 ms] 26.44/8.28 (8) CpxTypedWeightedCompleteTrs 26.44/8.28 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 26.44/8.28 (10) CpxRNTS 26.44/8.28 (11) CompleteCoflocoProof [FINISHED, 277 ms] 26.44/8.28 (12) BOUNDS(1, n^2) 26.44/8.28 (13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 26.44/8.28 (14) CpxTRS 26.44/8.28 (15) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 26.44/8.28 (16) typed CpxTrs 26.44/8.28 (17) OrderProof [LOWER BOUND(ID), 0 ms] 26.44/8.28 (18) typed CpxTrs 26.44/8.28 (19) RewriteLemmaProof [LOWER BOUND(ID), 293 ms] 26.44/8.28 (20) BEST 26.44/8.28 (21) proven lower bound 26.44/8.28 (22) LowerBoundPropagationProof [FINISHED, 0 ms] 26.44/8.28 (23) BOUNDS(n^1, INF) 26.44/8.28 (24) typed CpxTrs 26.44/8.28 (25) RewriteLemmaProof [LOWER BOUND(ID), 802 ms] 26.44/8.28 (26) proven lower bound 26.44/8.28 (27) LowerBoundPropagationProof [FINISHED, 0 ms] 26.44/8.28 (28) BOUNDS(n^2, INF) 26.44/8.28 26.44/8.28 26.44/8.28 ---------------------------------------- 26.44/8.28 26.44/8.28 (0) 26.44/8.28 Obligation: 26.44/8.28 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2). 26.44/8.28 26.44/8.28 26.44/8.28 The TRS R consists of the following rules: 26.44/8.28 26.44/8.28 f(0) -> 1 26.44/8.28 f(s(x)) -> g(x, s(x)) 26.44/8.28 g(0, y) -> y 26.44/8.28 g(s(x), y) -> g(x, +(y, s(x))) 26.44/8.28 +(x, 0) -> x 26.44/8.28 +(x, s(y)) -> s(+(x, y)) 26.44/8.28 g(s(x), y) -> g(x, s(+(y, x))) 26.44/8.28 26.44/8.28 S is empty. 26.44/8.28 Rewrite Strategy: INNERMOST 26.44/8.28 ---------------------------------------- 26.44/8.28 26.44/8.28 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 26.44/8.28 Transformed relative TRS to weighted TRS 26.44/8.28 ---------------------------------------- 26.44/8.28 26.44/8.28 (2) 26.44/8.28 Obligation: 26.44/8.28 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 26.44/8.28 26.44/8.28 26.44/8.28 The TRS R consists of the following rules: 26.44/8.28 26.44/8.28 f(0) -> 1 [1] 26.44/8.28 f(s(x)) -> g(x, s(x)) [1] 26.44/8.28 g(0, y) -> y [1] 26.44/8.28 g(s(x), y) -> g(x, +(y, s(x))) [1] 26.44/8.28 +(x, 0) -> x [1] 26.44/8.28 +(x, s(y)) -> s(+(x, y)) [1] 26.44/8.28 g(s(x), y) -> g(x, s(+(y, x))) [1] 26.44/8.28 26.44/8.28 Rewrite Strategy: INNERMOST 26.44/8.28 ---------------------------------------- 26.44/8.28 26.44/8.28 (3) CpxWeightedTrsRenamingProof (BOTH BOUNDS(ID, ID)) 26.44/8.28 Renamed defined symbols to avoid conflicts with arithmetic symbols: 26.44/8.28 26.44/8.28 + => plus 26.44/8.28 26.44/8.28 ---------------------------------------- 26.44/8.28 26.44/8.28 (4) 26.44/8.28 Obligation: 26.44/8.28 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 26.44/8.28 26.44/8.28 26.44/8.28 The TRS R consists of the following rules: 26.44/8.28 26.44/8.28 f(0) -> 1 [1] 26.44/8.28 f(s(x)) -> g(x, s(x)) [1] 26.44/8.28 g(0, y) -> y [1] 26.44/8.28 g(s(x), y) -> g(x, plus(y, s(x))) [1] 26.44/8.28 plus(x, 0) -> x [1]
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