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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308536
details
property
value
status
complete
benchmark
#4.2.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n100.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
5.15713 seconds
cpu usage
15.5798
user time
14.3875
system time
1.19227
max virtual memory
1.8576668E7
max residence set size
3819648.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
15.44/5.11 WORST_CASE(Omega(n^1), O(n^1)) 15.44/5.12 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 15.44/5.12 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 15.44/5.12 15.44/5.12 15.44/5.12 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 15.44/5.12 15.44/5.12 (0) CpxTRS 15.44/5.12 (1) DependencyGraphProof [UPPER BOUND(ID), 0 ms] 15.44/5.12 (2) CpxTRS 15.44/5.12 (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] 15.44/5.12 (4) CpxTRS 15.44/5.12 (5) CpxTrsMatchBoundsProof [FINISHED, 0 ms] 15.44/5.12 (6) BOUNDS(1, n^1) 15.44/5.12 (7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 15.44/5.12 (8) CpxTRS 15.44/5.12 (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 15.44/5.12 (10) typed CpxTrs 15.44/5.12 (11) OrderProof [LOWER BOUND(ID), 0 ms] 15.44/5.12 (12) typed CpxTrs 15.44/5.12 (13) RewriteLemmaProof [LOWER BOUND(ID), 271 ms] 15.44/5.12 (14) BEST 15.44/5.12 (15) proven lower bound 15.44/5.12 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 15.44/5.12 (17) BOUNDS(n^1, INF) 15.44/5.12 (18) typed CpxTrs 15.44/5.12 15.44/5.12 15.44/5.12 ---------------------------------------- 15.44/5.12 15.44/5.12 (0) 15.44/5.12 Obligation: 15.44/5.12 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 15.44/5.12 15.44/5.12 15.44/5.12 The TRS R consists of the following rules: 15.44/5.12 15.44/5.12 f(g(x), s(0), y) -> f(y, y, g(x)) 15.44/5.12 g(s(x)) -> s(g(x)) 15.44/5.12 g(0) -> 0 15.44/5.12 15.44/5.12 S is empty. 15.44/5.12 Rewrite Strategy: FULL 15.44/5.12 ---------------------------------------- 15.44/5.12 15.44/5.12 (1) DependencyGraphProof (UPPER BOUND(ID)) 15.44/5.12 The following rules are not reachable from basic terms in the dependency graph and can be removed: 15.44/5.12 15.44/5.12 f(g(x), s(0), y) -> f(y, y, g(x)) 15.44/5.12 15.44/5.12 ---------------------------------------- 15.44/5.12 15.44/5.12 (2) 15.44/5.12 Obligation: 15.44/5.12 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 15.44/5.12 15.44/5.12 15.44/5.12 The TRS R consists of the following rules: 15.44/5.12 15.44/5.12 g(s(x)) -> s(g(x)) 15.44/5.12 g(0) -> 0 15.44/5.12 15.44/5.12 S is empty. 15.44/5.12 Rewrite Strategy: FULL 15.44/5.12 ---------------------------------------- 15.44/5.12 15.44/5.12 (3) RelTrsToTrsProof (UPPER BOUND(ID)) 15.44/5.12 transformed relative TRS to TRS 15.44/5.12 ---------------------------------------- 15.44/5.12 15.44/5.12 (4) 15.44/5.12 Obligation: 15.44/5.12 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 15.44/5.12 15.44/5.12 15.44/5.12 The TRS R consists of the following rules: 15.44/5.12 15.44/5.12 g(s(x)) -> s(g(x)) 15.44/5.12 g(0) -> 0 15.44/5.12 15.44/5.12 S is empty. 15.44/5.12 Rewrite Strategy: FULL 15.44/5.12 ---------------------------------------- 15.44/5.12 15.44/5.12 (5) CpxTrsMatchBoundsProof (FINISHED) 15.44/5.12 A linear upper bound on the runtime complexity of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. 15.44/5.12 The certificate found is represented by the following graph. 15.44/5.12 15.44/5.12 "[5, 6, 7] 15.44/5.12 {(5,6,[g_1|0, 0|1]), (5,7,[s_1|1]), (6,6,[s_1|0, 0|0]), (7,6,[g_1|1, 0|1]), (7,7,[s_1|1])}" 15.44/5.12 ---------------------------------------- 15.44/5.12 15.44/5.12 (6) 15.44/5.12 BOUNDS(1, n^1) 15.44/5.12 15.44/5.12 ---------------------------------------- 15.44/5.12 15.44/5.12 (7) RenamingProof (BOTH BOUNDS(ID, ID)) 15.44/5.12 Renamed function symbols to avoid clashes with predefined symbol. 15.44/5.12 ----------------------------------------
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