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Runtime Complexity: TRS Innermost pair #487112222
details
property
value
status
complete
benchmark
Ex4_7_56_Bor03_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)
4.26842 seconds
cpu usage
13.0571
user time
12.0259
system time
1.03119
max virtual memory
1.8976144E7
max residence set size
3585968.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxWeightedTrs (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxTypedWeightedTrs (5) CompletionProof [UPPER BOUND(ID), 0 ms] (6) CpxTypedWeightedCompleteTrs (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (8) CpxRNTS (9) CompleteCoflocoProof [FINISHED, 102 ms] (10) BOUNDS(1, n^1) (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTRS (13) SlicingProof [LOWER BOUND(ID), 0 ms] (14) CpxTRS (15) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (16) typed CpxTrs (17) OrderProof [LOWER BOUND(ID), 0 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 198 ms] (20) proven lower bound (21) LowerBoundPropagationProof [FINISHED, 0 ms] (22) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: from(X) -> cons(X, n__from(s(X))) after(0, XS) -> XS after(s(N), cons(X, XS)) -> after(N, activate(XS)) from(X) -> n__from(X) activate(n__from(X)) -> from(X) activate(X) -> X S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: from(X) -> cons(X, n__from(s(X))) [1] after(0, XS) -> XS [1] after(s(N), cons(X, XS)) -> after(N, activate(XS)) [1] from(X) -> n__from(X) [1] activate(n__from(X)) -> from(X) [1] activate(X) -> X [1] Rewrite Strategy: INNERMOST ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: from(X) -> cons(X, n__from(s(X))) [1] after(0, XS) -> XS [1] after(s(N), cons(X, XS)) -> after(N, activate(XS)) [1] from(X) -> n__from(X) [1] activate(n__from(X)) -> from(X) [1] activate(X) -> X [1] The TRS has the following type information: from :: s:0 -> n__from:cons cons :: s:0 -> n__from:cons -> n__from:cons n__from :: s:0 -> n__from:cons s :: s:0 -> s:0 after :: s:0 -> n__from:cons -> n__from:cons 0 :: s:0 activate :: n__from:cons -> n__from:cons Rewrite Strategy: INNERMOST ----------------------------------------
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