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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313868
details
property
value
status
complete
benchmark
div2.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n053.star.cs.uiowa.edu
space
Frederiksen_Others
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
1.8351 seconds
cpu usage
4.13906
user time
3.96498
system time
0.174077
max virtual memory
1.8410936E7
max residence set size
313748.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
4.03/1.80 WORST_CASE(Omega(n^1), O(n^1)) 4.03/1.81 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 4.03/1.81 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.03/1.81 4.03/1.81 4.03/1.81 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). 4.03/1.81 4.03/1.81 (0) CpxRelTRS 4.03/1.81 (1) STerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 152 ms] 4.03/1.81 (2) CpxRelTRS 4.03/1.81 (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] 4.03/1.81 (4) CpxTRS 4.03/1.81 (5) CpxTrsMatchBoundsTAProof [FINISHED, 38 ms] 4.03/1.81 (6) BOUNDS(1, n^1) 4.03/1.81 (7) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 4.03/1.81 (8) TRS for Loop Detection 4.03/1.81 (9) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 4.03/1.81 (10) BEST 4.03/1.81 (11) proven lower bound 4.03/1.81 (12) LowerBoundPropagationProof [FINISHED, 0 ms] 4.03/1.81 (13) BOUNDS(n^1, INF) 4.03/1.81 (14) TRS for Loop Detection 4.03/1.81 4.03/1.81 4.03/1.81 ---------------------------------------- 4.03/1.81 4.03/1.81 (0) 4.03/1.81 Obligation: 4.03/1.81 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). 4.03/1.81 4.03/1.81 4.03/1.81 The TRS R consists of the following rules: 4.03/1.81 4.03/1.81 div2(S(S(x))) -> +(S(0), div2(x)) 4.03/1.81 div2(S(0)) -> 0 4.03/1.81 div2(0) -> 0 4.03/1.81 4.03/1.81 The (relative) TRS S consists of the following rules: 4.03/1.81 4.03/1.81 +(x, S(0)) -> S(x) 4.03/1.81 +(S(0), y) -> S(y) 4.03/1.81 4.03/1.81 Rewrite Strategy: INNERMOST 4.03/1.81 ---------------------------------------- 4.03/1.81 4.03/1.81 (1) STerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) 4.03/1.81 proved termination of relative rules 4.03/1.81 ---------------------------------------- 4.03/1.81 4.03/1.81 (2) 4.03/1.81 Obligation: 4.03/1.81 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). 4.03/1.81 4.03/1.81 4.03/1.81 The TRS R consists of the following rules: 4.03/1.81 4.03/1.81 div2(S(S(x))) -> +(S(0), div2(x)) 4.03/1.81 div2(S(0)) -> 0 4.03/1.81 div2(0) -> 0 4.03/1.81 4.03/1.81 The (relative) TRS S consists of the following rules: 4.03/1.81 4.03/1.81 +(x, S(0)) -> S(x) 4.03/1.81 +(S(0), y) -> S(y) 4.03/1.81 4.03/1.81 Rewrite Strategy: INNERMOST 4.03/1.81 ---------------------------------------- 4.03/1.81 4.03/1.81 (3) RelTrsToTrsProof (UPPER BOUND(ID)) 4.03/1.81 transformed relative TRS to TRS 4.03/1.81 ---------------------------------------- 4.03/1.81 4.03/1.81 (4) 4.03/1.81 Obligation: 4.03/1.81 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 4.03/1.81 4.03/1.81 4.03/1.81 The TRS R consists of the following rules: 4.03/1.81 4.03/1.81 div2(S(S(x))) -> +(S(0), div2(x)) 4.03/1.81 div2(S(0)) -> 0 4.03/1.81 div2(0) -> 0 4.03/1.81 +(x, S(0)) -> S(x) 4.03/1.81 +(S(0), y) -> S(y) 4.03/1.81 4.03/1.81 S is empty. 4.03/1.81 Rewrite Strategy: INNERMOST 4.03/1.81 ---------------------------------------- 4.03/1.81 4.03/1.81 (5) CpxTrsMatchBoundsTAProof (FINISHED) 4.03/1.81 A linear upper bound on the runtime complexity of the TRS R could be shown with a Match-Bound[TAB_LEFTLINEAR,TAB_NONLEFTLINEAR] (for contructor-based start-terms) of 2. 4.03/1.81 4.03/1.81 The compatible tree automaton used to show the Match-Boundedness (for constructor-based start-terms) is represented by: 4.03/1.81 final states : [1, 2] 4.03/1.81 transitions: 4.03/1.81 S0(0) -> 0 4.03/1.81 00() -> 0 4.03/1.81 div20(0) -> 1 4.03/1.81 +0(0, 0) -> 2 4.03/1.81 01() -> 4
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