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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313545
details
property
value
status
complete
benchmark
jwno1.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n173.star.cs.uiowa.edu
space
Waldmann_06
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.509 seconds
cpu usage
607.004
user time
603.973
system time
3.03153
max virtual memory
1.8653688E7
max residence set size
5817236.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
606.82/291.47 WORST_CASE(Omega(n^1), ?) 606.94/291.47 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 606.94/291.47 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 606.94/291.47 606.94/291.47 606.94/291.47 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 606.94/291.47 606.94/291.47 (0) CpxTRS 606.94/291.47 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 606.94/291.47 (2) TRS for Loop Detection 606.94/291.47 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 606.94/291.47 (4) BEST 606.94/291.47 (5) proven lower bound 606.94/291.47 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 606.94/291.47 (7) BOUNDS(n^1, INF) 606.94/291.47 (8) TRS for Loop Detection 606.94/291.47 606.94/291.47 606.94/291.47 ---------------------------------------- 606.94/291.47 606.94/291.47 (0) 606.94/291.47 Obligation: 606.94/291.47 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 606.94/291.47 606.94/291.47 606.94/291.47 The TRS R consists of the following rules: 606.94/291.47 606.94/291.47 f(h(x), y) -> h(f(y, f(x, h(f(a, a))))) 606.94/291.47 606.94/291.47 S is empty. 606.94/291.47 Rewrite Strategy: INNERMOST 606.94/291.47 ---------------------------------------- 606.94/291.47 606.94/291.47 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 606.94/291.47 Transformed a relative TRS into a decreasing-loop problem. 606.94/291.47 ---------------------------------------- 606.94/291.47 606.94/291.47 (2) 606.94/291.47 Obligation: 606.94/291.47 Analyzing the following TRS for decreasing loops: 606.94/291.47 606.94/291.47 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 606.94/291.47 606.94/291.47 606.94/291.47 The TRS R consists of the following rules: 606.94/291.47 606.94/291.47 f(h(x), y) -> h(f(y, f(x, h(f(a, a))))) 606.94/291.47 606.94/291.47 S is empty. 606.94/291.47 Rewrite Strategy: INNERMOST 606.94/291.47 ---------------------------------------- 606.94/291.47 606.94/291.47 (3) DecreasingLoopProof (LOWER BOUND(ID)) 606.94/291.47 The following loop(s) give(s) rise to the lower bound Omega(n^1): 606.94/291.47 606.94/291.47 The rewrite sequence 606.94/291.47 606.94/291.47 f(h(x), y) ->^+ h(f(y, f(x, h(f(a, a))))) 606.94/291.47 606.94/291.47 gives rise to a decreasing loop by considering the right hand sides subterm at position [0,1]. 606.94/291.47 606.94/291.47 The pumping substitution is [x / h(x)]. 606.94/291.47 606.94/291.47 The result substitution is [y / h(f(a, a))]. 606.94/291.47 606.94/291.47 606.94/291.47 606.94/291.47 606.94/291.47 ---------------------------------------- 606.94/291.47 606.94/291.47 (4) 606.94/291.47 Complex Obligation (BEST) 606.94/291.47 606.94/291.47 ---------------------------------------- 606.94/291.47 606.94/291.47 (5) 606.94/291.47 Obligation: 606.94/291.47 Proved the lower bound n^1 for the following obligation: 606.94/291.47 606.94/291.47 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 606.94/291.47 606.94/291.47 606.94/291.47 The TRS R consists of the following rules: 606.94/291.47 606.94/291.47 f(h(x), y) -> h(f(y, f(x, h(f(a, a))))) 606.94/291.47 606.94/291.47 S is empty. 606.94/291.47 Rewrite Strategy: INNERMOST 606.94/291.47 ---------------------------------------- 606.94/291.47 606.94/291.47 (6) LowerBoundPropagationProof (FINISHED) 606.94/291.47 Propagated lower bound. 606.94/291.47 ---------------------------------------- 606.94/291.47 606.94/291.47 (7) 606.94/291.47 BOUNDS(n^1, INF) 606.94/291.47 606.94/291.47 ---------------------------------------- 606.94/291.47 606.94/291.47 (8)
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