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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313438
details
property
value
status
complete
benchmark
Ex4_7_56_Bor03_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n177.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
296.655 seconds
cpu usage
1137.71
user time
1125.58
system time
12.1295
max virtual memory
3.7245348E7
max residence set size
1.4947248E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1117.37/291.51 WORST_CASE(Omega(n^1), ?) 1137.59/296.58 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1137.59/296.58 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1137.59/296.58 1137.59/296.58 1137.59/296.58 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1137.59/296.58 1137.59/296.58 (0) CpxTRS 1137.59/296.58 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1137.59/296.58 (2) TRS for Loop Detection 1137.59/296.58 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1137.59/296.58 (4) BEST 1137.59/296.58 (5) proven lower bound 1137.59/296.58 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1137.59/296.58 (7) BOUNDS(n^1, INF) 1137.59/296.58 (8) TRS for Loop Detection 1137.59/296.58 1137.59/296.58 1137.59/296.58 ---------------------------------------- 1137.59/296.58 1137.59/296.58 (0) 1137.59/296.58 Obligation: 1137.59/296.58 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1137.59/296.58 1137.59/296.58 1137.59/296.58 The TRS R consists of the following rules: 1137.59/296.58 1137.59/296.58 a__from(X) -> cons(mark(X), from(s(X))) 1137.59/296.58 a__after(0, XS) -> mark(XS) 1137.59/296.58 a__after(s(N), cons(X, XS)) -> a__after(mark(N), mark(XS)) 1137.59/296.58 mark(from(X)) -> a__from(mark(X)) 1137.59/296.58 mark(after(X1, X2)) -> a__after(mark(X1), mark(X2)) 1137.59/296.58 mark(cons(X1, X2)) -> cons(mark(X1), X2) 1137.59/296.59 mark(s(X)) -> s(mark(X)) 1137.59/296.59 mark(0) -> 0 1137.59/296.59 a__from(X) -> from(X) 1137.59/296.59 a__after(X1, X2) -> after(X1, X2) 1137.59/296.59 1137.59/296.59 S is empty. 1137.59/296.59 Rewrite Strategy: INNERMOST 1137.59/296.59 ---------------------------------------- 1137.59/296.59 1137.59/296.59 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1137.59/296.59 Transformed a relative TRS into a decreasing-loop problem. 1137.59/296.59 ---------------------------------------- 1137.59/296.59 1137.59/296.59 (2) 1137.59/296.59 Obligation: 1137.59/296.59 Analyzing the following TRS for decreasing loops: 1137.59/296.59 1137.59/296.59 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1137.59/296.59 1137.59/296.59 1137.59/296.59 The TRS R consists of the following rules: 1137.59/296.59 1137.59/296.59 a__from(X) -> cons(mark(X), from(s(X))) 1137.59/296.59 a__after(0, XS) -> mark(XS) 1137.59/296.59 a__after(s(N), cons(X, XS)) -> a__after(mark(N), mark(XS)) 1137.59/296.59 mark(from(X)) -> a__from(mark(X)) 1137.59/296.59 mark(after(X1, X2)) -> a__after(mark(X1), mark(X2)) 1137.59/296.59 mark(cons(X1, X2)) -> cons(mark(X1), X2) 1137.59/296.59 mark(s(X)) -> s(mark(X)) 1137.59/296.59 mark(0) -> 0 1137.59/296.59 a__from(X) -> from(X) 1137.59/296.59 a__after(X1, X2) -> after(X1, X2) 1137.59/296.59 1137.59/296.59 S is empty. 1137.59/296.59 Rewrite Strategy: INNERMOST 1137.59/296.59 ---------------------------------------- 1137.59/296.59 1137.59/296.59 (3) DecreasingLoopProof (LOWER BOUND(ID)) 1137.59/296.59 The following loop(s) give(s) rise to the lower bound Omega(n^1): 1137.59/296.59 1137.59/296.59 The rewrite sequence 1137.59/296.59 1137.59/296.59 mark(from(X)) ->^+ a__from(mark(X)) 1137.59/296.59 1137.59/296.59 gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. 1137.59/296.59 1137.59/296.59 The pumping substitution is [X / from(X)]. 1137.59/296.59 1137.59/296.59 The result substitution is [ ]. 1137.59/296.59 1137.59/296.59 1137.59/296.59 1137.59/296.59 1137.59/296.59 ---------------------------------------- 1137.59/296.59 1137.59/296.59 (4) 1137.59/296.59 Complex Obligation (BEST) 1137.59/296.59 1137.59/296.59 ---------------------------------------- 1137.59/296.59 1137.59/296.59 (5) 1137.59/296.59 Obligation: 1137.59/296.59 Proved the lower bound n^1 for the following obligation: 1137.59/296.59 1137.59/296.59 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1137.59/296.59 1137.59/296.59
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