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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308534
details
property
value
status
complete
benchmark
#4.37a.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n001.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
11.8361 seconds
cpu usage
21.4504
user time
19.9842
system time
1.46621
max virtual memory
3.8047488E7
max residence set size
3967788.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
21.30/7.33 WORST_CASE(Omega(n^1), O(n^1)) 21.30/7.33 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 21.30/7.33 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 21.30/7.33 21.30/7.33 21.30/7.33 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 21.30/7.33 21.30/7.33 (0) CpxTRS 21.30/7.33 (1) DependencyGraphProof [UPPER BOUND(ID), 0 ms] 21.30/7.33 (2) CpxTRS 21.30/7.33 (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] 21.30/7.33 (4) CpxTRS 21.30/7.33 (5) CpxTrsMatchBoundsTAProof [FINISHED, 0 ms] 21.30/7.33 (6) BOUNDS(1, n^1) 21.30/7.33 (7) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 21.30/7.33 (8) TRS for Loop Detection 21.30/7.33 (9) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 21.30/7.33 (10) BEST 21.30/7.33 (11) proven lower bound 21.30/7.33 (12) LowerBoundPropagationProof [FINISHED, 0 ms] 21.30/7.33 (13) BOUNDS(n^1, INF) 21.30/7.33 (14) TRS for Loop Detection 21.30/7.33 21.30/7.33 21.30/7.33 ---------------------------------------- 21.30/7.33 21.30/7.33 (0) 21.30/7.33 Obligation: 21.30/7.33 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 21.30/7.33 21.30/7.33 21.30/7.33 The TRS R consists of the following rules: 21.30/7.33 21.30/7.33 f(c(s(x), y)) -> f(c(x, s(y))) 21.30/7.33 g(c(x, s(y))) -> g(c(s(x), y)) 21.30/7.33 g(s(f(x))) -> g(f(x)) 21.30/7.33 21.30/7.33 S is empty. 21.30/7.33 Rewrite Strategy: FULL 21.30/7.33 ---------------------------------------- 21.30/7.33 21.30/7.33 (1) DependencyGraphProof (UPPER BOUND(ID)) 21.30/7.33 The following rules are not reachable from basic terms in the dependency graph and can be removed: 21.30/7.33 21.30/7.33 g(s(f(x))) -> g(f(x)) 21.30/7.33 21.30/7.33 ---------------------------------------- 21.30/7.33 21.30/7.33 (2) 21.30/7.33 Obligation: 21.30/7.33 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 21.30/7.33 21.30/7.33 21.30/7.33 The TRS R consists of the following rules: 21.30/7.33 21.30/7.33 f(c(s(x), y)) -> f(c(x, s(y))) 21.30/7.33 g(c(x, s(y))) -> g(c(s(x), y)) 21.30/7.33 21.30/7.33 S is empty. 21.30/7.33 Rewrite Strategy: FULL 21.30/7.33 ---------------------------------------- 21.30/7.33 21.30/7.33 (3) RelTrsToTrsProof (UPPER BOUND(ID)) 21.30/7.33 transformed relative TRS to TRS 21.30/7.33 ---------------------------------------- 21.30/7.33 21.30/7.33 (4) 21.30/7.33 Obligation: 21.30/7.33 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 21.30/7.33 21.30/7.33 21.30/7.33 The TRS R consists of the following rules: 21.30/7.33 21.30/7.33 f(c(s(x), y)) -> f(c(x, s(y))) 21.30/7.33 g(c(x, s(y))) -> g(c(s(x), y)) 21.30/7.33 21.30/7.33 S is empty. 21.30/7.33 Rewrite Strategy: FULL 21.30/7.33 ---------------------------------------- 21.30/7.33 21.30/7.33 (5) CpxTrsMatchBoundsTAProof (FINISHED) 21.30/7.33 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. 21.30/7.33 21.30/7.33 The compatible tree automaton used to show the Match-Boundedness (for constructor-based start-terms) is represented by: 21.30/7.33 final states : [1, 2] 21.30/7.33 transitions: 21.30/7.33 c0(0, 0) -> 0 21.30/7.33 s0(0) -> 0 21.30/7.33 f0(0) -> 1 21.30/7.33 g0(0) -> 2 21.30/7.33 s1(0) -> 4 21.30/7.33 c1(0, 4) -> 3 21.30/7.33 f1(3) -> 1 21.30/7.33 s1(0) -> 6 21.30/7.33 c1(6, 0) -> 5 21.30/7.33 g1(5) -> 2 21.30/7.33 s1(4) -> 4 21.30/7.33 s1(6) -> 6 21.30/7.33 21.30/7.33 ----------------------------------------
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