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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308515
details
property
value
status
complete
benchmark
#4.17.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n166.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
4.88234 seconds
cpu usage
15.3354
user time
14.106
system time
1.22948
max virtual memory
1.861188E7
max residence set size
3876684.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
15.23/4.84 WORST_CASE(Omega(n^1), O(n^1)) 15.23/4.84 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 15.23/4.84 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 15.23/4.84 15.23/4.84 15.23/4.84 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 15.23/4.84 15.23/4.84 (0) CpxTRS 15.23/4.84 (1) DependencyGraphProof [UPPER BOUND(ID), 0 ms] 15.23/4.84 (2) CpxTRS 15.23/4.84 (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] 15.23/4.84 (4) CpxTRS 15.23/4.84 (5) CpxTrsMatchBoundsProof [FINISHED, 0 ms] 15.23/4.84 (6) BOUNDS(1, n^1) 15.23/4.84 (7) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 15.23/4.84 (8) TRS for Loop Detection 15.23/4.84 (9) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 15.23/4.84 (10) BEST 15.23/4.84 (11) proven lower bound 15.23/4.84 (12) LowerBoundPropagationProof [FINISHED, 0 ms] 15.23/4.84 (13) BOUNDS(n^1, INF) 15.23/4.84 (14) TRS for Loop Detection 15.23/4.84 15.23/4.84 15.23/4.84 ---------------------------------------- 15.23/4.84 15.23/4.84 (0) 15.23/4.84 Obligation: 15.23/4.84 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 15.23/4.84 15.23/4.84 15.23/4.84 The TRS R consists of the following rules: 15.23/4.84 15.23/4.84 f(g(x), s(0), y) -> f(g(s(0)), y, g(x)) 15.23/4.84 g(s(x)) -> s(g(x)) 15.23/4.84 g(0) -> 0 15.23/4.84 15.23/4.84 S is empty. 15.23/4.84 Rewrite Strategy: FULL 15.23/4.84 ---------------------------------------- 15.23/4.84 15.23/4.84 (1) DependencyGraphProof (UPPER BOUND(ID)) 15.23/4.84 The following rules are not reachable from basic terms in the dependency graph and can be removed: 15.23/4.84 15.23/4.84 f(g(x), s(0), y) -> f(g(s(0)), y, g(x)) 15.23/4.84 15.23/4.84 ---------------------------------------- 15.23/4.84 15.23/4.84 (2) 15.23/4.84 Obligation: 15.23/4.84 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 15.23/4.84 15.23/4.84 15.23/4.84 The TRS R consists of the following rules: 15.23/4.84 15.23/4.84 g(s(x)) -> s(g(x)) 15.23/4.84 g(0) -> 0 15.23/4.84 15.23/4.84 S is empty. 15.23/4.84 Rewrite Strategy: FULL 15.23/4.84 ---------------------------------------- 15.23/4.84 15.23/4.84 (3) RelTrsToTrsProof (UPPER BOUND(ID)) 15.23/4.84 transformed relative TRS to TRS 15.23/4.84 ---------------------------------------- 15.23/4.84 15.23/4.84 (4) 15.23/4.84 Obligation: 15.23/4.84 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 15.23/4.84 15.23/4.84 15.23/4.84 The TRS R consists of the following rules: 15.23/4.84 15.23/4.84 g(s(x)) -> s(g(x)) 15.23/4.84 g(0) -> 0 15.23/4.84 15.23/4.84 S is empty. 15.23/4.84 Rewrite Strategy: FULL 15.23/4.84 ---------------------------------------- 15.23/4.84 15.23/4.84 (5) CpxTrsMatchBoundsProof (FINISHED) 15.23/4.84 A linear upper bound on the runtime complexity of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. 15.23/4.84 The certificate found is represented by the following graph. 15.23/4.84 15.23/4.84 "[3, 4, 5] 15.23/4.84 {(3,4,[g_1|0, 0|1]), (3,5,[s_1|1]), (4,4,[s_1|0, 0|0]), (5,4,[g_1|1, 0|1]), (5,5,[s_1|1])}" 15.23/4.84 ---------------------------------------- 15.23/4.84 15.23/4.84 (6) 15.23/4.84 BOUNDS(1, n^1) 15.23/4.84 15.23/4.84 ---------------------------------------- 15.23/4.84 15.23/4.84 (7) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 15.23/4.84 Transformed a relative TRS into a decreasing-loop problem. 15.23/4.84 ---------------------------------------- 15.23/4.84 15.23/4.84 (8) 15.23/4.84 Obligation: 15.23/4.84 Analyzing the following TRS for decreasing loops:
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