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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313731
details
property
value
status
complete
benchmark
thiemann20.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n032.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.568 seconds
cpu usage
1111.16
user time
1096.6
system time
14.5563
max virtual memory
3.7977716E7
max residence set size
1.5067744E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
1110.88/291.48 WORST_CASE(Omega(n^1), O(n^2)) 1110.88/291.50 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1110.88/291.50 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1110.88/291.50 1110.88/291.50 1110.88/291.50 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1110.88/291.50 1110.88/291.50 (0) CpxTRS 1110.88/291.50 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1110.88/291.50 (2) CpxWeightedTrs 1110.88/291.50 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1110.88/291.50 (4) CpxTypedWeightedTrs 1110.88/291.50 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 1110.88/291.50 (6) CpxTypedWeightedCompleteTrs 1110.88/291.50 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1110.88/291.50 (8) CpxRNTS 1110.88/291.50 (9) CompleteCoflocoProof [FINISHED, 414 ms] 1110.88/291.50 (10) BOUNDS(1, n^2) 1110.88/291.50 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1110.88/291.50 (12) TRS for Loop Detection 1110.88/291.50 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1110.88/291.50 (14) BEST 1110.88/291.50 (15) proven lower bound 1110.88/291.50 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 1110.88/291.50 (17) BOUNDS(n^1, INF) 1110.88/291.50 (18) TRS for Loop Detection 1110.88/291.50 1110.88/291.50 1110.88/291.50 ---------------------------------------- 1110.88/291.50 1110.88/291.50 (0) 1110.88/291.50 Obligation: 1110.88/291.50 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1110.88/291.50 1110.88/291.50 1110.88/291.50 The TRS R consists of the following rules: 1110.88/291.50 1110.88/291.50 gt(0, y) -> false 1110.88/291.50 gt(s(x), 0) -> true 1110.88/291.50 gt(s(x), s(y)) -> gt(x, y) 1110.88/291.50 plus(0, y) -> y 1110.88/291.50 plus(s(x), y) -> s(plus(x, y)) 1110.88/291.50 double(0) -> 0 1110.88/291.50 double(s(x)) -> s(s(double(x))) 1110.88/291.50 average(x, y) -> aver(plus(x, y), 0) 1110.88/291.50 aver(sum, z) -> if(gt(sum, double(z)), sum, z) 1110.88/291.50 if(true, sum, z) -> aver(sum, s(z)) 1110.88/291.50 if(false, sum, z) -> z 1110.88/291.50 1110.88/291.50 S is empty. 1110.88/291.50 Rewrite Strategy: INNERMOST 1110.88/291.50 ---------------------------------------- 1110.88/291.50 1110.88/291.50 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1110.88/291.50 Transformed relative TRS to weighted TRS 1110.88/291.50 ---------------------------------------- 1110.88/291.50 1110.88/291.50 (2) 1110.88/291.50 Obligation: 1110.88/291.50 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 1110.88/291.50 1110.88/291.50 1110.88/291.50 The TRS R consists of the following rules: 1110.88/291.50 1110.88/291.50 gt(0, y) -> false [1] 1110.88/291.50 gt(s(x), 0) -> true [1] 1110.88/291.50 gt(s(x), s(y)) -> gt(x, y) [1] 1110.88/291.50 plus(0, y) -> y [1] 1110.88/291.50 plus(s(x), y) -> s(plus(x, y)) [1] 1110.88/291.50 double(0) -> 0 [1] 1110.88/291.50 double(s(x)) -> s(s(double(x))) [1] 1110.88/291.50 average(x, y) -> aver(plus(x, y), 0) [1] 1110.88/291.50 aver(sum, z) -> if(gt(sum, double(z)), sum, z) [1] 1110.88/291.50 if(true, sum, z) -> aver(sum, s(z)) [1] 1110.88/291.50 if(false, sum, z) -> z [1] 1110.88/291.50 1110.88/291.50 Rewrite Strategy: INNERMOST 1110.88/291.50 ---------------------------------------- 1110.88/291.50 1110.88/291.50 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1110.88/291.50 Infered types. 1110.88/291.50 ---------------------------------------- 1110.88/291.50 1110.88/291.50 (4) 1110.88/291.50 Obligation: 1110.88/291.50 Runtime Complexity Weighted TRS with Types. 1110.88/291.50 The TRS R consists of the following rules: 1110.88/291.50 1110.88/291.50 gt(0, y) -> false [1] 1110.88/291.50 gt(s(x), 0) -> true [1] 1110.88/291.50 gt(s(x), s(y)) -> gt(x, y) [1] 1110.88/291.50 plus(0, y) -> y [1] 1110.88/291.50 plus(s(x), y) -> s(plus(x, y)) [1] 1110.88/291.50 double(0) -> 0 [1] 1110.88/291.50 double(s(x)) -> s(s(double(x))) [1] 1110.88/291.50 average(x, y) -> aver(plus(x, y), 0) [1] 1110.88/291.50 aver(sum, z) -> if(gt(sum, double(z)), sum, z) [1] 1110.88/291.50 if(true, sum, z) -> aver(sum, s(z)) [1] 1110.88/291.50 if(false, sum, z) -> z [1] 1110.88/291.50
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