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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307969
details
property
value
status
complete
benchmark
22.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n005.star.cs.uiowa.edu
space
Various_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
10.4561 seconds
cpu usage
21.6021
user time
20.0704
system time
1.5317
max virtual memory
1.9144292E7
max residence set size
3897816.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
21.36/7.02 WORST_CASE(Omega(n^1), O(n^1)) 21.36/7.03 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 21.36/7.03 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 21.36/7.03 21.36/7.03 21.36/7.03 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 21.36/7.03 21.36/7.03 (0) CpxTRS 21.36/7.03 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 21.36/7.03 (2) CpxTRS 21.36/7.03 (3) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] 21.36/7.03 (4) CdtProblem 21.36/7.03 (5) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 21.36/7.03 (6) CdtProblem 21.36/7.03 (7) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 21.36/7.03 (8) CdtProblem 21.36/7.03 (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 85 ms] 21.36/7.03 (10) CdtProblem 21.36/7.03 (11) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2 ms] 21.36/7.03 (12) CdtProblem 21.36/7.03 (13) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 21.36/7.03 (14) CdtProblem 21.36/7.03 (15) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] 21.36/7.03 (16) CdtProblem 21.36/7.03 (17) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] 21.36/7.03 (18) CdtProblem 21.36/7.03 (19) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 21.36/7.03 (20) CdtProblem 21.36/7.03 (21) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 0 ms] 21.36/7.03 (22) CdtProblem 21.36/7.03 (23) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 21.36/7.03 (24) BOUNDS(1, 1) 21.36/7.03 (25) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 21.36/7.03 (26) TRS for Loop Detection 21.36/7.03 (27) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 21.36/7.03 (28) BEST 21.36/7.03 (29) proven lower bound 21.36/7.03 (30) LowerBoundPropagationProof [FINISHED, 0 ms] 21.36/7.03 (31) BOUNDS(n^1, INF) 21.36/7.03 (32) TRS for Loop Detection 21.36/7.03 21.36/7.03 21.36/7.03 ---------------------------------------- 21.36/7.03 21.36/7.03 (0) 21.36/7.03 Obligation: 21.36/7.03 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 21.36/7.03 21.36/7.03 21.36/7.03 The TRS R consists of the following rules: 21.36/7.03 21.36/7.03 f(x, 0) -> s(0) 21.36/7.03 f(s(x), s(y)) -> s(f(x, y)) 21.36/7.03 g(0, x) -> g(f(x, x), x) 21.36/7.03 21.36/7.03 S is empty. 21.36/7.03 Rewrite Strategy: FULL 21.36/7.03 ---------------------------------------- 21.36/7.03 21.36/7.03 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 21.36/7.03 Converted rc-obligation to irc-obligation. 21.36/7.03 21.36/7.03 The duplicating contexts are: 21.36/7.03 g(0, []) 21.36/7.03 21.36/7.03 21.36/7.03 The defined contexts are: 21.36/7.03 g([], x1) 21.36/7.03 21.36/7.03 21.36/7.03 As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc. 21.36/7.03 ---------------------------------------- 21.36/7.03 21.36/7.03 (2) 21.36/7.03 Obligation: 21.36/7.03 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 21.36/7.03 21.36/7.03 21.36/7.03 The TRS R consists of the following rules: 21.36/7.03 21.36/7.03 f(x, 0) -> s(0) 21.36/7.03 f(s(x), s(y)) -> s(f(x, y)) 21.36/7.03 g(0, x) -> g(f(x, x), x) 21.36/7.03 21.36/7.03 S is empty. 21.36/7.03 Rewrite Strategy: INNERMOST 21.36/7.03 ---------------------------------------- 21.36/7.03 21.36/7.03 (3) CpxTrsToCdtProof (UPPER BOUND(ID)) 21.36/7.03 Converted Cpx (relative) TRS to CDT 21.36/7.03 ---------------------------------------- 21.36/7.03 21.36/7.03 (4) 21.36/7.03 Obligation: 21.36/7.03 Complexity Dependency Tuples Problem 21.36/7.03 21.36/7.03 Rules: 21.36/7.03 f(z0, 0) -> s(0) 21.36/7.03 f(s(z0), s(z1)) -> s(f(z0, z1)) 21.36/7.03 g(0, z0) -> g(f(z0, z0), z0)
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