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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313696
details
property
value
status
complete
benchmark
thiemann31.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n175.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.653 seconds
cpu usage
1144.54
user time
1130.45
system time
14.0886
max virtual memory
3.7860256E7
max residence set size
1.23247E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
1144.14/291.57 WORST_CASE(Omega(n^1), O(n^2)) 1144.40/291.58 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1144.40/291.58 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1144.40/291.58 1144.40/291.58 1144.40/291.58 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1144.40/291.58 1144.40/291.58 (0) CpxTRS 1144.40/291.58 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1144.40/291.58 (2) CpxWeightedTrs 1144.40/291.58 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1144.40/291.58 (4) CpxTypedWeightedTrs 1144.40/291.58 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 1144.40/291.58 (6) CpxTypedWeightedCompleteTrs 1144.40/291.58 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1144.40/291.58 (8) CpxRNTS 1144.40/291.58 (9) CompleteCoflocoProof [FINISHED, 1203 ms] 1144.40/291.58 (10) BOUNDS(1, n^2) 1144.40/291.58 (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1144.40/291.58 (12) CpxTRS 1144.40/291.58 (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1144.40/291.58 (14) typed CpxTrs 1144.40/291.58 (15) OrderProof [LOWER BOUND(ID), 0 ms] 1144.40/291.58 (16) typed CpxTrs 1144.40/291.58 (17) RewriteLemmaProof [LOWER BOUND(ID), 276 ms] 1144.40/291.58 (18) BEST 1144.40/291.58 (19) proven lower bound 1144.40/291.58 (20) LowerBoundPropagationProof [FINISHED, 0 ms] 1144.40/291.58 (21) BOUNDS(n^1, INF) 1144.40/291.58 (22) typed CpxTrs 1144.40/291.58 1144.40/291.58 1144.40/291.58 ---------------------------------------- 1144.40/291.58 1144.40/291.58 (0) 1144.40/291.58 Obligation: 1144.40/291.58 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1144.40/291.58 1144.40/291.58 1144.40/291.58 The TRS R consists of the following rules: 1144.40/291.58 1144.40/291.58 le(0, y) -> true 1144.40/291.58 le(s(x), 0) -> false 1144.40/291.58 le(s(x), s(y)) -> le(x, y) 1144.40/291.58 mod(x, 0) -> modZeroErro 1144.40/291.58 mod(x, s(y)) -> modIter(x, s(y), 0, 0) 1144.40/291.58 modIter(x, s(y), z, u) -> if(le(x, z), x, s(y), z, u) 1144.40/291.58 if(true, x, y, z, u) -> u 1144.40/291.58 if(false, x, y, z, u) -> if2(le(y, s(u)), x, y, s(z), s(u)) 1144.40/291.58 if2(false, x, y, z, u) -> modIter(x, y, z, u) 1144.40/291.58 if2(true, x, y, z, u) -> modIter(x, y, z, 0) 1144.40/291.58 1144.40/291.58 S is empty. 1144.40/291.58 Rewrite Strategy: INNERMOST 1144.40/291.58 ---------------------------------------- 1144.40/291.58 1144.40/291.58 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1144.40/291.58 Transformed relative TRS to weighted TRS 1144.40/291.58 ---------------------------------------- 1144.40/291.58 1144.40/291.58 (2) 1144.40/291.58 Obligation: 1144.40/291.58 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 1144.40/291.58 1144.40/291.58 1144.40/291.58 The TRS R consists of the following rules: 1144.40/291.58 1144.40/291.58 le(0, y) -> true [1] 1144.40/291.58 le(s(x), 0) -> false [1] 1144.40/291.58 le(s(x), s(y)) -> le(x, y) [1] 1144.40/291.58 mod(x, 0) -> modZeroErro [1] 1144.40/291.58 mod(x, s(y)) -> modIter(x, s(y), 0, 0) [1] 1144.40/291.58 modIter(x, s(y), z, u) -> if(le(x, z), x, s(y), z, u) [1] 1144.40/291.58 if(true, x, y, z, u) -> u [1] 1144.40/291.58 if(false, x, y, z, u) -> if2(le(y, s(u)), x, y, s(z), s(u)) [1] 1144.40/291.58 if2(false, x, y, z, u) -> modIter(x, y, z, u) [1] 1144.40/291.58 if2(true, x, y, z, u) -> modIter(x, y, z, 0) [1] 1144.40/291.58 1144.40/291.58 Rewrite Strategy: INNERMOST 1144.40/291.58 ---------------------------------------- 1144.40/291.58 1144.40/291.58 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1144.40/291.58 Infered types. 1144.40/291.58 ---------------------------------------- 1144.40/291.58 1144.40/291.58 (4) 1144.40/291.58 Obligation: 1144.40/291.58 Runtime Complexity Weighted TRS with Types. 1144.40/291.58 The TRS R consists of the following rules: 1144.40/291.58 1144.40/291.58 le(0, y) -> true [1] 1144.40/291.58 le(s(x), 0) -> false [1] 1144.40/291.58 le(s(x), s(y)) -> le(x, y) [1] 1144.40/291.58 mod(x, 0) -> modZeroErro [1] 1144.40/291.58 mod(x, s(y)) -> modIter(x, s(y), 0, 0) [1] 1144.40/291.58 modIter(x, s(y), z, u) -> if(le(x, z), x, s(y), z, u) [1] 1144.40/291.58 if(true, x, y, z, u) -> u [1] 1144.40/291.58 if(false, x, y, z, u) -> if2(le(y, s(u)), x, y, s(z), s(u)) [1] 1144.40/291.58 if2(false, x, y, z, u) -> modIter(x, y, z, u) [1] 1144.40/291.58 if2(true, x, y, z, u) -> modIter(x, y, z, 0) [1]
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