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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308181
details
property
value
status
complete
benchmark
Ex1_Luc02b_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n142.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.585 seconds
cpu usage
319.963
user time
317.362
system time
2.60057
max virtual memory
1.828162E7
max residence set size
6064052.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
319.88/291.54 WORST_CASE(Omega(n^1), ?) 319.88/291.54 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 319.88/291.54 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 319.88/291.54 319.88/291.54 319.88/291.54 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 319.88/291.54 319.88/291.54 (0) CpxTRS 319.88/291.54 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 319.88/291.54 (2) TRS for Loop Detection 319.88/291.54 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 319.88/291.54 (4) BEST 319.88/291.54 (5) proven lower bound 319.88/291.54 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 319.88/291.54 (7) BOUNDS(n^1, INF) 319.88/291.54 (8) TRS for Loop Detection 319.88/291.54 319.88/291.54 319.88/291.54 ---------------------------------------- 319.88/291.54 319.88/291.54 (0) 319.88/291.54 Obligation: 319.88/291.54 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 319.88/291.54 319.88/291.54 319.88/291.54 The TRS R consists of the following rules: 319.88/291.54 319.88/291.54 from(X) -> cons(X, n__from(s(X))) 319.88/291.54 first(0, Z) -> nil 319.88/291.54 first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z))) 319.88/291.54 sel(0, cons(X, Z)) -> X 319.88/291.54 sel(s(X), cons(Y, Z)) -> sel(X, activate(Z)) 319.88/291.54 from(X) -> n__from(X) 319.88/291.54 first(X1, X2) -> n__first(X1, X2) 319.88/291.54 activate(n__from(X)) -> from(X) 319.88/291.54 activate(n__first(X1, X2)) -> first(X1, X2) 319.88/291.54 activate(X) -> X 319.88/291.54 319.88/291.54 S is empty. 319.88/291.54 Rewrite Strategy: FULL 319.88/291.54 ---------------------------------------- 319.88/291.54 319.88/291.54 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 319.88/291.54 Transformed a relative TRS into a decreasing-loop problem. 319.88/291.54 ---------------------------------------- 319.88/291.54 319.88/291.54 (2) 319.88/291.54 Obligation: 319.88/291.54 Analyzing the following TRS for decreasing loops: 319.88/291.54 319.88/291.54 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 319.88/291.54 319.88/291.54 319.88/291.54 The TRS R consists of the following rules: 319.88/291.54 319.88/291.54 from(X) -> cons(X, n__from(s(X))) 319.88/291.54 first(0, Z) -> nil 319.88/291.54 first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z))) 319.88/291.54 sel(0, cons(X, Z)) -> X 319.88/291.54 sel(s(X), cons(Y, Z)) -> sel(X, activate(Z)) 319.88/291.54 from(X) -> n__from(X) 319.88/291.54 first(X1, X2) -> n__first(X1, X2) 319.88/291.54 activate(n__from(X)) -> from(X) 319.88/291.54 activate(n__first(X1, X2)) -> first(X1, X2) 319.88/291.54 activate(X) -> X 319.88/291.54 319.88/291.54 S is empty. 319.88/291.54 Rewrite Strategy: FULL 319.88/291.54 ---------------------------------------- 319.88/291.54 319.88/291.54 (3) DecreasingLoopProof (LOWER BOUND(ID)) 319.88/291.54 The following loop(s) give(s) rise to the lower bound Omega(n^1): 319.88/291.54 319.88/291.54 The rewrite sequence 319.88/291.54 319.88/291.54 sel(s(X), cons(Y, Z)) ->^+ sel(X, Z) 319.88/291.54 319.88/291.54 gives rise to a decreasing loop by considering the right hand sides subterm at position []. 319.88/291.54 319.88/291.54 The pumping substitution is [X / s(X), Z / cons(Y, Z)]. 319.88/291.54 319.88/291.54 The result substitution is [ ]. 319.88/291.54 319.88/291.54 319.88/291.54 319.88/291.54 319.88/291.54 ---------------------------------------- 319.88/291.54 319.88/291.54 (4) 319.88/291.54 Complex Obligation (BEST) 319.88/291.54 319.88/291.54 ---------------------------------------- 319.88/291.54 319.88/291.54 (5) 319.88/291.54 Obligation: 319.88/291.54 Proved the lower bound n^1 for the following obligation: 319.88/291.54 319.88/291.54 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 319.88/291.54 319.88/291.54
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