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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308164
details
property
value
status
complete
benchmark
Ex4_7_37_Bor03_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n180.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.556 seconds
cpu usage
352.782
user time
349.693
system time
3.08888
max virtual memory
1.8281252E7
max residence set size
6314836.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
352.69/291.51 WORST_CASE(Omega(n^1), ?) 352.69/291.52 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 352.69/291.52 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 352.69/291.52 352.69/291.52 352.69/291.52 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 352.69/291.52 352.69/291.52 (0) CpxTRS 352.69/291.52 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 352.69/291.52 (2) TRS for Loop Detection 352.69/291.52 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 352.69/291.52 (4) BEST 352.69/291.52 (5) proven lower bound 352.69/291.52 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 352.69/291.52 (7) BOUNDS(n^1, INF) 352.69/291.52 (8) TRS for Loop Detection 352.69/291.52 352.69/291.52 352.69/291.52 ---------------------------------------- 352.69/291.52 352.69/291.52 (0) 352.69/291.52 Obligation: 352.69/291.52 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 352.69/291.52 352.69/291.52 352.69/291.52 The TRS R consists of the following rules: 352.69/291.52 352.69/291.52 from(X) -> cons(X, n__from(s(X))) 352.69/291.52 sel(0, cons(X, XS)) -> X 352.69/291.52 sel(s(N), cons(X, XS)) -> sel(N, activate(XS)) 352.69/291.52 minus(X, 0) -> 0 352.69/291.52 minus(s(X), s(Y)) -> minus(X, Y) 352.69/291.52 quot(0, s(Y)) -> 0 352.69/291.52 quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y))) 352.69/291.52 zWquot(XS, nil) -> nil 352.69/291.52 zWquot(nil, XS) -> nil 352.69/291.52 zWquot(cons(X, XS), cons(Y, YS)) -> cons(quot(X, Y), n__zWquot(activate(XS), activate(YS))) 352.69/291.52 from(X) -> n__from(X) 352.69/291.52 zWquot(X1, X2) -> n__zWquot(X1, X2) 352.69/291.52 activate(n__from(X)) -> from(X) 352.69/291.52 activate(n__zWquot(X1, X2)) -> zWquot(X1, X2) 352.69/291.52 activate(X) -> X 352.69/291.52 352.69/291.52 S is empty. 352.69/291.52 Rewrite Strategy: FULL 352.69/291.52 ---------------------------------------- 352.69/291.52 352.69/291.52 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 352.69/291.52 Transformed a relative TRS into a decreasing-loop problem. 352.69/291.52 ---------------------------------------- 352.69/291.52 352.69/291.52 (2) 352.69/291.52 Obligation: 352.69/291.52 Analyzing the following TRS for decreasing loops: 352.69/291.52 352.69/291.52 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 352.69/291.52 352.69/291.52 352.69/291.52 The TRS R consists of the following rules: 352.69/291.52 352.69/291.52 from(X) -> cons(X, n__from(s(X))) 352.69/291.52 sel(0, cons(X, XS)) -> X 352.69/291.52 sel(s(N), cons(X, XS)) -> sel(N, activate(XS)) 352.69/291.52 minus(X, 0) -> 0 352.69/291.52 minus(s(X), s(Y)) -> minus(X, Y) 352.69/291.52 quot(0, s(Y)) -> 0 352.69/291.52 quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y))) 352.69/291.52 zWquot(XS, nil) -> nil 352.69/291.52 zWquot(nil, XS) -> nil 352.69/291.52 zWquot(cons(X, XS), cons(Y, YS)) -> cons(quot(X, Y), n__zWquot(activate(XS), activate(YS))) 352.69/291.52 from(X) -> n__from(X) 352.69/291.52 zWquot(X1, X2) -> n__zWquot(X1, X2) 352.69/291.52 activate(n__from(X)) -> from(X) 352.69/291.52 activate(n__zWquot(X1, X2)) -> zWquot(X1, X2) 352.69/291.52 activate(X) -> X 352.69/291.52 352.69/291.52 S is empty. 352.69/291.52 Rewrite Strategy: FULL 352.69/291.52 ---------------------------------------- 352.69/291.52 352.69/291.52 (3) DecreasingLoopProof (LOWER BOUND(ID)) 352.69/291.52 The following loop(s) give(s) rise to the lower bound Omega(n^1): 352.69/291.52 352.69/291.52 The rewrite sequence 352.69/291.52 352.69/291.52 minus(s(X), s(Y)) ->^+ minus(X, Y) 352.69/291.52 352.69/291.52 gives rise to a decreasing loop by considering the right hand sides subterm at position []. 352.69/291.52 352.69/291.52 The pumping substitution is [X / s(X), Y / s(Y)]. 352.69/291.52 352.69/291.52 The result substitution is [ ]. 352.69/291.52 352.69/291.52 352.69/291.52 352.69/291.52 352.69/291.52 ---------------------------------------- 352.69/291.52 352.69/291.52 (4) 352.69/291.52 Complex Obligation (BEST)
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