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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313625
details
property
value
status
complete
benchmark
test76.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n038.star.cs.uiowa.edu
space
Strategy_removed_mixed_05
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
4.91141 seconds
cpu usage
16.3113
user time
14.8173
system time
1.49393
max virtual memory
1.887414E7
max residence set size
4138664.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
15.88/4.83 WORST_CASE(Omega(n^1), O(n^1)) 16.24/4.84 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 16.24/4.84 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 16.24/4.84 16.24/4.84 16.24/4.84 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 16.24/4.84 16.24/4.84 (0) CpxTRS 16.24/4.84 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 16.24/4.84 (2) CpxWeightedTrs 16.24/4.84 (3) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 16.24/4.84 (4) CpxWeightedTrs 16.24/4.84 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 16.24/4.84 (6) CpxTypedWeightedTrs 16.24/4.84 (7) CompletionProof [UPPER BOUND(ID), 0 ms] 16.24/4.84 (8) CpxTypedWeightedCompleteTrs 16.24/4.84 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 16.24/4.84 (10) CpxRNTS 16.24/4.84 (11) CompleteCoflocoProof [FINISHED, 169 ms] 16.24/4.84 (12) BOUNDS(1, n^1) 16.24/4.84 (13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 16.24/4.84 (14) TRS for Loop Detection 16.24/4.84 (15) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 16.24/4.84 (16) BEST 16.24/4.84 (17) proven lower bound 16.24/4.84 (18) LowerBoundPropagationProof [FINISHED, 0 ms] 16.24/4.84 (19) BOUNDS(n^1, INF) 16.24/4.84 (20) TRS for Loop Detection 16.24/4.84 16.24/4.84 16.24/4.84 ---------------------------------------- 16.24/4.84 16.24/4.84 (0) 16.24/4.84 Obligation: 16.24/4.84 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 16.24/4.84 16.24/4.84 16.24/4.84 The TRS R consists of the following rules: 16.24/4.84 16.24/4.84 +(X, 0) -> X 16.24/4.84 +(X, s(Y)) -> s(+(X, Y)) 16.24/4.84 f(0, s(0), X) -> f(X, +(X, X), X) 16.24/4.84 g(X, Y) -> X 16.24/4.84 g(X, Y) -> Y 16.24/4.84 16.24/4.84 S is empty. 16.24/4.84 Rewrite Strategy: INNERMOST 16.24/4.84 ---------------------------------------- 16.24/4.84 16.24/4.84 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 16.24/4.84 Transformed relative TRS to weighted TRS 16.24/4.84 ---------------------------------------- 16.24/4.84 16.24/4.84 (2) 16.24/4.84 Obligation: 16.24/4.84 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). 16.24/4.84 16.24/4.84 16.24/4.84 The TRS R consists of the following rules: 16.24/4.84 16.24/4.84 +(X, 0) -> X [1] 16.24/4.84 +(X, s(Y)) -> s(+(X, Y)) [1] 16.24/4.84 f(0, s(0), X) -> f(X, +(X, X), X) [1] 16.24/4.84 g(X, Y) -> X [1] 16.24/4.84 g(X, Y) -> Y [1] 16.24/4.84 16.24/4.84 Rewrite Strategy: INNERMOST 16.24/4.84 ---------------------------------------- 16.24/4.84 16.24/4.84 (3) CpxWeightedTrsRenamingProof (BOTH BOUNDS(ID, ID)) 16.24/4.84 Renamed defined symbols to avoid conflicts with arithmetic symbols: 16.24/4.84 16.24/4.84 + => plus 16.24/4.84 16.24/4.84 ---------------------------------------- 16.24/4.84 16.24/4.84 (4) 16.24/4.84 Obligation: 16.24/4.84 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). 16.24/4.84 16.24/4.84 16.24/4.84 The TRS R consists of the following rules: 16.24/4.84 16.24/4.84 plus(X, 0) -> X [1] 16.24/4.84 plus(X, s(Y)) -> s(plus(X, Y)) [1] 16.24/4.84 f(0, s(0), X) -> f(X, plus(X, X), X) [1] 16.24/4.84 g(X, Y) -> X [1] 16.24/4.84 g(X, Y) -> Y [1] 16.24/4.84 16.24/4.84 Rewrite Strategy: INNERMOST 16.24/4.84 ---------------------------------------- 16.24/4.84 16.24/4.84 (5) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 16.24/4.84 Infered types. 16.24/4.84 ---------------------------------------- 16.24/4.84 16.24/4.84 (6) 16.24/4.84 Obligation: 16.24/4.84 Runtime Complexity Weighted TRS with Types. 16.24/4.84 The TRS R consists of the following rules:
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