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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313553
details
property
value
status
complete
benchmark
#4.37.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n086.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
4.38688 seconds
cpu usage
13.1206
user time
12.0427
system time
1.07785
max virtual memory
1.9208424E7
max residence set size
3570868.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
12.76/4.33 WORST_CASE(Omega(n^1), O(n^1)) 12.76/4.33 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 12.76/4.33 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 12.76/4.33 12.76/4.33 12.76/4.33 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 12.76/4.33 12.76/4.33 (0) CpxTRS 12.76/4.33 (1) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] 12.76/4.33 (2) CpxTRS 12.76/4.33 (3) CpxTrsMatchBoundsTAProof [FINISHED, 0 ms] 12.76/4.33 (4) BOUNDS(1, n^1) 12.76/4.33 (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 12.76/4.33 (6) TRS for Loop Detection 12.76/4.33 (7) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 12.76/4.33 (8) BEST 12.76/4.33 (9) proven lower bound 12.76/4.33 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 12.76/4.33 (11) BOUNDS(n^1, INF) 12.76/4.33 (12) TRS for Loop Detection 12.76/4.33 12.76/4.33 12.76/4.33 ---------------------------------------- 12.76/4.33 12.76/4.33 (0) 12.76/4.33 Obligation: 12.76/4.33 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 12.76/4.33 12.76/4.33 12.76/4.33 The TRS R consists of the following rules: 12.76/4.33 12.76/4.33 f(c(s(x), y)) -> f(c(x, s(y))) 12.76/4.33 g(c(x, s(y))) -> g(c(s(x), y)) 12.76/4.33 12.76/4.33 S is empty. 12.76/4.33 Rewrite Strategy: INNERMOST 12.76/4.33 ---------------------------------------- 12.76/4.33 12.76/4.33 (1) RelTrsToTrsProof (UPPER BOUND(ID)) 12.76/4.33 transformed relative TRS to TRS 12.76/4.33 ---------------------------------------- 12.76/4.33 12.76/4.33 (2) 12.76/4.33 Obligation: 12.76/4.33 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 12.76/4.33 12.76/4.33 12.76/4.33 The TRS R consists of the following rules: 12.76/4.33 12.76/4.33 f(c(s(x), y)) -> f(c(x, s(y))) 12.76/4.33 g(c(x, s(y))) -> g(c(s(x), y)) 12.76/4.33 12.76/4.33 S is empty. 12.76/4.33 Rewrite Strategy: INNERMOST 12.76/4.33 ---------------------------------------- 12.76/4.33 12.76/4.33 (3) CpxTrsMatchBoundsTAProof (FINISHED) 12.76/4.33 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. 12.76/4.33 12.76/4.33 The compatible tree automaton used to show the Match-Boundedness (for constructor-based start-terms) is represented by: 12.76/4.33 final states : [1, 2] 12.76/4.33 transitions: 12.76/4.33 c0(0, 0) -> 0 12.76/4.33 s0(0) -> 0 12.76/4.33 f0(0) -> 1 12.76/4.33 g0(0) -> 2 12.76/4.33 s1(0) -> 4 12.76/4.33 c1(0, 4) -> 3 12.76/4.33 f1(3) -> 1 12.76/4.33 s1(0) -> 6 12.76/4.33 c1(6, 0) -> 5 12.76/4.33 g1(5) -> 2 12.76/4.33 s1(4) -> 4 12.76/4.33 s1(6) -> 6 12.76/4.33 12.76/4.33 ---------------------------------------- 12.76/4.33 12.76/4.33 (4) 12.76/4.33 BOUNDS(1, n^1) 12.76/4.33 12.76/4.33 ---------------------------------------- 12.76/4.33 12.76/4.33 (5) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 12.76/4.33 Transformed a relative TRS into a decreasing-loop problem. 12.76/4.33 ---------------------------------------- 12.76/4.33 12.76/4.33 (6) 12.76/4.33 Obligation: 12.76/4.33 Analyzing the following TRS for decreasing loops: 12.76/4.33 12.76/4.33 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 12.76/4.33 12.76/4.33 12.76/4.33 The TRS R consists of the following rules: 12.76/4.33 12.76/4.33 f(c(s(x), y)) -> f(c(x, s(y))) 12.76/4.33 g(c(x, s(y))) -> g(c(s(x), y)) 12.76/4.33 12.76/4.33 S is empty. 12.76/4.33 Rewrite Strategy: INNERMOST
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