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Runtime Complexity: TRS Innermost pair #487112606
details
property
value
status
complete
benchmark
dfs-flatten.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n143.star.cs.uiowa.edu
space
hoca
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
1.64178 seconds
cpu usage
3.9065
user time
3.75661
system time
0.149889
max virtual memory
1.827736E7
max residence set size
251260.0
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/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (2) CpxTRS (3) CpxTrsMatchBoundsTAProof [FINISHED, 42 ms] (4) BOUNDS(1, n^1) (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (6) TRS for Loop Detection (7) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (8) BEST (9) proven lower bound (10) LowerBoundPropagationProof [FINISHED, 0 ms] (11) BOUNDS(n^1, INF) (12) TRS for Loop Detection ---------------------------------------- (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: revApp#2(Nil, x16) -> x16 revApp#2(Cons(x6, x4), x2) -> revApp#2(x4, Cons(x6, x2)) dfsAcc#3(Leaf(x8), x16) -> Cons(x8, x16) dfsAcc#3(Node(x6, x4), x2) -> dfsAcc#3(x4, dfsAcc#3(x6, x2)) main(x1) -> revApp#2(dfsAcc#3(x1, Nil), Nil) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: revApp#2(Nil, x16) -> x16 revApp#2(Cons(x6, x4), x2) -> revApp#2(x4, Cons(x6, x2)) dfsAcc#3(Leaf(x8), x16) -> Cons(x8, x16) dfsAcc#3(Node(x6, x4), x2) -> dfsAcc#3(x4, dfsAcc#3(x6, x2)) main(x1) -> revApp#2(dfsAcc#3(x1, Nil), Nil) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (3) CpxTrsMatchBoundsTAProof (FINISHED) A linear upper bound on the runtime complexity of the TRS R could be shown with a Match-Bound[TAB_LEFTLINEAR,TAB_NONLEFTLINEAR] (for contructor-based start-terms) of 2. The compatible tree automaton used to show the Match-Boundedness (for constructor-based start-terms) is represented by: final states : [1, 2, 3] transitions: Nil0() -> 0 Cons0(0, 0) -> 0 Leaf0(0) -> 0 Node0(0, 0) -> 0 revApp#20(0, 0) -> 1 dfsAcc#30(0, 0) -> 2 main0(0) -> 3 Cons1(0, 0) -> 4 revApp#21(0, 4) -> 1 Cons1(0, 0) -> 2 dfsAcc#31(0, 0) -> 5 dfsAcc#31(0, 5) -> 2 Nil1() -> 7 dfsAcc#31(0, 7) -> 6 Nil1() -> 8 revApp#21(6, 8) -> 3 Cons1(0, 4) -> 4 Cons1(0, 5) -> 2 Cons1(0, 0) -> 5 Cons1(0, 7) -> 6 dfsAcc#31(0, 5) -> 5 dfsAcc#31(0, 7) -> 5 dfsAcc#31(0, 5) -> 6 Cons2(0, 8) -> 9 revApp#22(7, 9) -> 3 Cons1(0, 5) -> 5 Cons1(0, 7) -> 5 Cons1(0, 5) -> 6 revApp#22(5, 9) -> 3 Cons2(0, 9) -> 9 revApp#22(0, 9) -> 3 Cons1(0, 9) -> 4
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