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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308146
details
property
value
status
complete
benchmark
Ex9_Luc06_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n045.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
8.6049 seconds
cpu usage
29.2139
user time
27.7751
system time
1.43882
max virtual memory
3.7576088E7
max residence set size
3852500.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
28.97/8.52 WORST_CASE(Omega(n^1), O(n^1)) 28.97/8.55 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 28.97/8.55 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 28.97/8.55 28.97/8.55 28.97/8.55 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 28.97/8.55 28.97/8.55 (0) CpxTRS 28.97/8.55 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 28.97/8.55 (2) CpxTRS 28.97/8.55 (3) CpxTrsToCdtProof [UPPER BOUND(ID), 3 ms] 28.97/8.55 (4) CdtProblem 28.97/8.55 (5) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 28.97/8.55 (6) CdtProblem 28.97/8.55 (7) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] 28.97/8.55 (8) CdtProblem 28.97/8.55 (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 73 ms] 28.97/8.55 (10) CdtProblem 28.97/8.55 (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 22 ms] 28.97/8.55 (12) CdtProblem 28.97/8.55 (13) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 28.97/8.55 (14) BOUNDS(1, 1) 28.97/8.55 (15) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 28.97/8.55 (16) TRS for Loop Detection 28.97/8.55 (17) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 28.97/8.55 (18) BEST 28.97/8.55 (19) proven lower bound 28.97/8.55 (20) LowerBoundPropagationProof [FINISHED, 0 ms] 28.97/8.55 (21) BOUNDS(n^1, INF) 28.97/8.55 (22) TRS for Loop Detection 28.97/8.55 28.97/8.55 28.97/8.55 ---------------------------------------- 28.97/8.55 28.97/8.55 (0) 28.97/8.55 Obligation: 28.97/8.55 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 28.97/8.55 28.97/8.55 28.97/8.55 The TRS R consists of the following rules: 28.97/8.55 28.97/8.55 a__f(a, X, X) -> a__f(X, a__b, b) 28.97/8.55 a__b -> a 28.97/8.55 mark(f(X1, X2, X3)) -> a__f(X1, mark(X2), X3) 28.97/8.55 mark(b) -> a__b 28.97/8.55 mark(a) -> a 28.97/8.55 a__f(X1, X2, X3) -> f(X1, X2, X3) 28.97/8.55 a__b -> b 28.97/8.55 28.97/8.55 S is empty. 28.97/8.55 Rewrite Strategy: FULL 28.97/8.55 ---------------------------------------- 28.97/8.55 28.97/8.55 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 28.97/8.55 Converted rc-obligation to irc-obligation. 28.97/8.55 28.97/8.55 As the TRS is a non-duplicating overlay system, we have rc = irc. 28.97/8.55 ---------------------------------------- 28.97/8.55 28.97/8.55 (2) 28.97/8.55 Obligation: 28.97/8.55 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 28.97/8.55 28.97/8.55 28.97/8.55 The TRS R consists of the following rules: 28.97/8.55 28.97/8.55 a__f(a, X, X) -> a__f(X, a__b, b) 28.97/8.55 a__b -> a 28.97/8.55 mark(f(X1, X2, X3)) -> a__f(X1, mark(X2), X3) 28.97/8.55 mark(b) -> a__b 28.97/8.55 mark(a) -> a 28.97/8.55 a__f(X1, X2, X3) -> f(X1, X2, X3) 28.97/8.55 a__b -> b 28.97/8.55 28.97/8.55 S is empty. 28.97/8.55 Rewrite Strategy: INNERMOST 28.97/8.55 ---------------------------------------- 28.97/8.55 28.97/8.55 (3) CpxTrsToCdtProof (UPPER BOUND(ID)) 28.97/8.55 Converted Cpx (relative) TRS to CDT 28.97/8.55 ---------------------------------------- 28.97/8.55 28.97/8.55 (4) 28.97/8.55 Obligation: 28.97/8.55 Complexity Dependency Tuples Problem 28.97/8.55 28.97/8.55 Rules: 28.97/8.55 a__f(a, z0, z0) -> a__f(z0, a__b, b) 28.97/8.55 a__f(z0, z1, z2) -> f(z0, z1, z2) 28.97/8.55 a__b -> a 28.97/8.55 a__b -> b 28.97/8.55 mark(f(z0, z1, z2)) -> a__f(z0, mark(z1), z2) 28.97/8.55 mark(b) -> a__b 28.97/8.55 mark(a) -> a 28.97/8.55 Tuples: 28.97/8.55 A__F(a, z0, z0) -> c(A__F(z0, a__b, b), A__B) 28.97/8.55 A__F(z0, z1, z2) -> c1 28.97/8.55 A__B -> c2 28.97/8.55 A__B -> c3 28.97/8.55 MARK(f(z0, z1, z2)) -> c4(A__F(z0, mark(z1), z2), MARK(z1))
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