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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308299
details
property
value
status
complete
benchmark
Ex18_Luc06_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n160.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
8.17194 seconds
cpu usage
9.51362
user time
9.00251
system time
0.511107
max virtual memory
1.8279384E7
max residence set size
1600924.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
9.03/3.01 WORST_CASE(Omega(n^1), O(n^1)) 9.11/3.02 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 9.11/3.02 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.11/3.02 9.11/3.02 9.11/3.02 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 9.11/3.02 9.11/3.02 (0) CpxTRS 9.11/3.02 (1) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] 9.11/3.02 (2) CpxTRS 9.11/3.02 (3) CpxTrsMatchBoundsProof [FINISHED, 0 ms] 9.11/3.02 (4) BOUNDS(1, n^1) 9.11/3.02 (5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 9.11/3.02 (6) CpxTRS 9.11/3.02 (7) SlicingProof [LOWER BOUND(ID), 0 ms] 9.11/3.02 (8) CpxTRS 9.11/3.02 (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 9.11/3.02 (10) typed CpxTrs 9.11/3.02 (11) OrderProof [LOWER BOUND(ID), 0 ms] 9.11/3.02 (12) typed CpxTrs 9.11/3.02 (13) RewriteLemmaProof [LOWER BOUND(ID), 729 ms] 9.11/3.02 (14) proven lower bound 9.11/3.02 (15) LowerBoundPropagationProof [FINISHED, 0 ms] 9.11/3.02 (16) BOUNDS(n^1, INF) 9.11/3.02 9.11/3.02 9.11/3.02 ---------------------------------------- 9.11/3.02 9.11/3.02 (0) 9.11/3.02 Obligation: 9.11/3.02 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 9.11/3.02 9.11/3.02 9.11/3.02 The TRS R consists of the following rules: 9.11/3.02 9.11/3.02 a__f(f(a)) -> a__f(g(f(a))) 9.11/3.02 mark(f(X)) -> a__f(mark(X)) 9.11/3.02 mark(a) -> a 9.11/3.02 mark(g(X)) -> g(X) 9.11/3.02 a__f(X) -> f(X) 9.11/3.02 9.11/3.02 S is empty. 9.11/3.02 Rewrite Strategy: FULL 9.11/3.02 ---------------------------------------- 9.11/3.02 9.11/3.02 (1) RelTrsToTrsProof (UPPER BOUND(ID)) 9.11/3.02 transformed relative TRS to TRS 9.11/3.02 ---------------------------------------- 9.11/3.02 9.11/3.02 (2) 9.11/3.02 Obligation: 9.11/3.02 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 9.11/3.02 9.11/3.02 9.11/3.02 The TRS R consists of the following rules: 9.11/3.02 9.11/3.02 a__f(f(a)) -> a__f(g(f(a))) 9.11/3.02 mark(f(X)) -> a__f(mark(X)) 9.11/3.02 mark(a) -> a 9.11/3.02 mark(g(X)) -> g(X) 9.11/3.02 a__f(X) -> f(X) 9.11/3.02 9.11/3.02 S is empty. 9.11/3.02 Rewrite Strategy: FULL 9.11/3.02 ---------------------------------------- 9.11/3.02 9.11/3.02 (3) CpxTrsMatchBoundsProof (FINISHED) 9.11/3.02 A linear upper bound on the runtime complexity of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 3. 9.11/3.02 The certificate found is represented by the following graph. 9.11/3.02 9.11/3.02 "[1, 2, 3, 4, 5, 6, 7, 8, 9] 9.11/3.02 {(1,2,[a__f_1|0, mark_1|0, f_1|1, a|1, g_1|1]), (1,3,[a__f_1|1, f_1|2]), (1,6,[a__f_1|1, f_1|2]), (1,7,[a__f_1|2, f_1|3]), (2,2,[f_1|0, a|0, g_1|0]), (3,4,[g_1|1]), (4,5,[f_1|1]), (5,2,[a|1]), (6,2,[mark_1|1, a|1, g_1|1]), (6,6,[a__f_1|1, f_1|2]), (6,7,[a__f_1|2, f_1|3]), (7,8,[g_1|2]), (8,9,[f_1|2]), (9,2,[a|2])}" 9.11/3.02 ---------------------------------------- 9.11/3.02 9.11/3.02 (4) 9.11/3.02 BOUNDS(1, n^1) 9.11/3.02 9.11/3.02 ---------------------------------------- 9.11/3.02 9.11/3.02 (5) RenamingProof (BOTH BOUNDS(ID, ID)) 9.11/3.02 Renamed function symbols to avoid clashes with predefined symbol. 9.11/3.02 ---------------------------------------- 9.11/3.02 9.11/3.02 (6) 9.11/3.02 Obligation: 9.11/3.02 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 9.11/3.02 9.11/3.02 9.11/3.02 The TRS R consists of the following rules: 9.11/3.02 9.11/3.02 a__f(f(a)) -> a__f(g(f(a))) 9.11/3.02 mark(f(X)) -> a__f(mark(X)) 9.11/3.02 mark(a) -> a 9.11/3.02 mark(g(X)) -> g(X) 9.11/3.02 a__f(X) -> f(X) 9.11/3.02 9.11/3.02 S is empty. 9.11/3.02 Rewrite Strategy: FULL 9.11/3.02 ---------------------------------------- 9.11/3.02
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