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Runtime Complexity: TRS Innermost pair #487112660
details
property
value
status
complete
benchmark
add.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n140.star.cs.uiowa.edu
space
Frederiksen_Glenstrup
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
1.60371 seconds
cpu usage
3.47891
user time
3.33365
system time
0.14526
max virtual memory
1.827736E7
max residence set size
222648.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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, 0 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: add0(x', Cons(x, xs)) -> add0(Cons(Cons(Nil, Nil), x'), xs) notEmpty(Cons(x, xs)) -> True notEmpty(Nil) -> False add0(x, Nil) -> x goal(x, y) -> add0(x, y) 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: add0(x', Cons(x, xs)) -> add0(Cons(Cons(Nil, Nil), x'), xs) notEmpty(Cons(x, xs)) -> True notEmpty(Nil) -> False add0(x, Nil) -> x goal(x, y) -> add0(x, y) 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 1. The compatible tree automaton used to show the Match-Boundedness (for constructor-based start-terms) is represented by: final states : [1, 2, 3] transitions: Cons0(0, 0) -> 0 Nil0() -> 0 True0() -> 0 False0() -> 0 add00(0, 0) -> 1 notEmpty0(0) -> 2 goal0(0, 0) -> 3 Nil1() -> 6 Nil1() -> 7 Cons1(6, 7) -> 5 Cons1(5, 0) -> 4 add01(4, 0) -> 1 True1() -> 2 False1() -> 2 add01(0, 0) -> 3 Cons1(5, 4) -> 4 add01(4, 0) -> 3 0 -> 1 0 -> 3 4 -> 1 4 -> 3 ---------------------------------------- (4) BOUNDS(1, n^1) ---------------------------------------- (5) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ----------------------------------------
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