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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313712
details
property
value
status
complete
benchmark
thiemann36.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n106.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.594 seconds
cpu usage
1142.45
user time
1127.65
system time
14.8026
max virtual memory
7.51666E7
max residence set size
1.3730484E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
1142.10/291.50 WORST_CASE(Omega(n^1), O(n^2)) 1142.10/291.51 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1142.10/291.51 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1142.10/291.51 1142.10/291.51 1142.10/291.51 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1142.10/291.51 1142.10/291.51 (0) CpxTRS 1142.10/291.51 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1142.10/291.51 (2) CpxWeightedTrs 1142.10/291.51 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1142.10/291.51 (4) CpxTypedWeightedTrs 1142.10/291.51 (5) CompletionProof [UPPER BOUND(ID), 49 ms] 1142.10/291.51 (6) CpxTypedWeightedCompleteTrs 1142.10/291.51 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1142.10/291.51 (8) CpxRNTS 1142.10/291.51 (9) CompleteCoflocoProof [FINISHED, 1305 ms] 1142.10/291.51 (10) BOUNDS(1, n^2) 1142.10/291.51 (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1142.10/291.51 (12) CpxTRS 1142.10/291.51 (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1142.10/291.51 (14) typed CpxTrs 1142.10/291.51 (15) OrderProof [LOWER BOUND(ID), 0 ms] 1142.10/291.51 (16) typed CpxTrs 1142.10/291.51 (17) RewriteLemmaProof [LOWER BOUND(ID), 268 ms] 1142.10/291.51 (18) BEST 1142.10/291.51 (19) proven lower bound 1142.10/291.51 (20) LowerBoundPropagationProof [FINISHED, 0 ms] 1142.10/291.51 (21) BOUNDS(n^1, INF) 1142.10/291.51 (22) typed CpxTrs 1142.10/291.51 1142.10/291.51 1142.10/291.51 ---------------------------------------- 1142.10/291.51 1142.10/291.51 (0) 1142.10/291.51 Obligation: 1142.10/291.51 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1142.10/291.51 1142.10/291.51 1142.10/291.51 The TRS R consists of the following rules: 1142.10/291.51 1142.10/291.51 le(0, y) -> true 1142.10/291.51 le(s(x), 0) -> false 1142.10/291.51 le(s(x), s(y)) -> le(x, y) 1142.10/291.51 quot(x, 0) -> quotZeroErro 1142.10/291.51 quot(x, s(y)) -> quotIter(x, s(y), 0, 0, 0) 1142.10/291.51 quotIter(x, s(y), z, u, v) -> if(le(x, z), x, s(y), z, u, v) 1142.10/291.51 if(true, x, y, z, u, v) -> v 1142.10/291.51 if(false, x, y, z, u, v) -> if2(le(y, s(u)), x, y, s(z), s(u), v) 1142.10/291.51 if2(false, x, y, z, u, v) -> quotIter(x, y, z, u, v) 1142.10/291.51 if2(true, x, y, z, u, v) -> quotIter(x, y, z, 0, s(v)) 1142.10/291.51 1142.10/291.51 S is empty. 1142.10/291.51 Rewrite Strategy: INNERMOST 1142.10/291.51 ---------------------------------------- 1142.10/291.51 1142.10/291.51 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1142.10/291.51 Transformed relative TRS to weighted TRS 1142.10/291.51 ---------------------------------------- 1142.10/291.51 1142.10/291.51 (2) 1142.10/291.51 Obligation: 1142.10/291.51 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 1142.10/291.51 1142.10/291.51 1142.10/291.51 The TRS R consists of the following rules: 1142.10/291.51 1142.10/291.51 le(0, y) -> true [1] 1142.10/291.51 le(s(x), 0) -> false [1] 1142.10/291.51 le(s(x), s(y)) -> le(x, y) [1] 1142.10/291.51 quot(x, 0) -> quotZeroErro [1] 1142.10/291.51 quot(x, s(y)) -> quotIter(x, s(y), 0, 0, 0) [1] 1142.10/291.51 quotIter(x, s(y), z, u, v) -> if(le(x, z), x, s(y), z, u, v) [1] 1142.10/291.51 if(true, x, y, z, u, v) -> v [1] 1142.10/291.51 if(false, x, y, z, u, v) -> if2(le(y, s(u)), x, y, s(z), s(u), v) [1] 1142.10/291.51 if2(false, x, y, z, u, v) -> quotIter(x, y, z, u, v) [1] 1142.10/291.51 if2(true, x, y, z, u, v) -> quotIter(x, y, z, 0, s(v)) [1] 1142.10/291.51 1142.10/291.51 Rewrite Strategy: INNERMOST 1142.10/291.51 ---------------------------------------- 1142.10/291.51 1142.10/291.51 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1142.10/291.51 Infered types. 1142.10/291.51 ---------------------------------------- 1142.10/291.51 1142.10/291.51 (4) 1142.10/291.51 Obligation: 1142.10/291.51 Runtime Complexity Weighted TRS with Types. 1142.10/291.51 The TRS R consists of the following rules: 1142.10/291.51 1142.10/291.51 le(0, y) -> true [1] 1142.10/291.51 le(s(x), 0) -> false [1] 1142.10/291.51 le(s(x), s(y)) -> le(x, y) [1] 1142.10/291.51 quot(x, 0) -> quotZeroErro [1] 1142.10/291.51 quot(x, s(y)) -> quotIter(x, s(y), 0, 0, 0) [1] 1142.10/291.51 quotIter(x, s(y), z, u, v) -> if(le(x, z), x, s(y), z, u, v) [1] 1142.10/291.51 if(true, x, y, z, u, v) -> v [1] 1142.10/291.51 if(false, x, y, z, u, v) -> if2(le(y, s(u)), x, y, s(z), s(u), v) [1] 1142.10/291.51 if2(false, x, y, z, u, v) -> quotIter(x, y, z, u, v) [1] 1142.10/291.51 if2(true, x, y, z, u, v) -> quotIter(x, y, z, 0, s(v)) [1]
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