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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313776
details
property
value
status
complete
benchmark
#3.24.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n136.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
2.10946 seconds
cpu usage
5.33034
user time
5.08112
system time
0.24922
max virtual memory
1.8277336E7
max residence set size
584468.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
5.19/2.07 WORST_CASE(Omega(n^1), O(n^1)) 5.19/2.07 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 5.19/2.07 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 5.19/2.07 5.19/2.07 5.19/2.07 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 5.19/2.07 5.19/2.07 (0) CpxTRS 5.19/2.07 (1) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] 5.19/2.07 (2) CpxTRS 5.19/2.07 (3) CpxTrsMatchBoundsProof [FINISHED, 0 ms] 5.19/2.07 (4) BOUNDS(1, n^1) 5.19/2.07 (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 5.19/2.07 (6) TRS for Loop Detection 5.19/2.07 (7) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 5.19/2.07 (8) BEST 5.19/2.07 (9) proven lower bound 5.19/2.07 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 5.19/2.07 (11) BOUNDS(n^1, INF) 5.19/2.07 (12) TRS for Loop Detection 5.19/2.07 5.19/2.07 5.19/2.07 ---------------------------------------- 5.19/2.07 5.19/2.07 (0) 5.19/2.07 Obligation: 5.19/2.07 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 5.19/2.07 5.19/2.07 5.19/2.07 The TRS R consists of the following rules: 5.19/2.07 5.19/2.07 f(0) -> s(0) 5.19/2.07 f(s(0)) -> s(0) 5.19/2.07 f(s(s(x))) -> f(f(s(x))) 5.19/2.07 5.19/2.07 S is empty. 5.19/2.07 Rewrite Strategy: INNERMOST 5.19/2.07 ---------------------------------------- 5.19/2.07 5.19/2.07 (1) RelTrsToTrsProof (UPPER BOUND(ID)) 5.19/2.07 transformed relative TRS to TRS 5.19/2.07 ---------------------------------------- 5.19/2.07 5.19/2.07 (2) 5.19/2.07 Obligation: 5.19/2.07 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 5.19/2.07 5.19/2.07 5.19/2.07 The TRS R consists of the following rules: 5.19/2.07 5.19/2.07 f(0) -> s(0) 5.19/2.07 f(s(0)) -> s(0) 5.19/2.07 f(s(s(x))) -> f(f(s(x))) 5.19/2.07 5.19/2.07 S is empty. 5.19/2.07 Rewrite Strategy: INNERMOST 5.19/2.07 ---------------------------------------- 5.19/2.07 5.19/2.07 (3) CpxTrsMatchBoundsProof (FINISHED) 5.19/2.07 A linear upper bound on the runtime complexity of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. 5.19/2.07 The certificate found is represented by the following graph. 5.19/2.07 5.19/2.07 "[1, 2, 3, 4, 5, 6, 7] 5.19/2.07 {(1,2,[f_1|0]), (1,3,[s_1|1]), (1,4,[f_1|1]), (1,7,[s_1|2]), (2,2,[0|0, s_1|0]), (3,2,[0|1]), (4,5,[f_1|1]), (4,6,[s_1|1]), (4,4,[f_1|1]), (4,7,[s_1|2]), (5,2,[s_1|1]), (6,2,[0|1]), (7,2,[0|2])}" 5.19/2.07 ---------------------------------------- 5.19/2.07 5.19/2.07 (4) 5.19/2.07 BOUNDS(1, n^1) 5.19/2.07 5.19/2.07 ---------------------------------------- 5.19/2.07 5.19/2.07 (5) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 5.19/2.07 Transformed a relative TRS into a decreasing-loop problem. 5.19/2.07 ---------------------------------------- 5.19/2.07 5.19/2.07 (6) 5.19/2.07 Obligation: 5.19/2.07 Analyzing the following TRS for decreasing loops: 5.19/2.07 5.19/2.07 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 5.19/2.07 5.19/2.07 5.19/2.07 The TRS R consists of the following rules: 5.19/2.07 5.19/2.07 f(0) -> s(0) 5.19/2.07 f(s(0)) -> s(0) 5.19/2.07 f(s(s(x))) -> f(f(s(x))) 5.19/2.07 5.19/2.07 S is empty. 5.19/2.07 Rewrite Strategy: INNERMOST 5.19/2.07 ---------------------------------------- 5.19/2.07 5.19/2.07 (7) DecreasingLoopProof (LOWER BOUND(ID)) 5.19/2.07 The following loop(s) give(s) rise to the lower bound Omega(n^1): 5.19/2.07 5.19/2.07 The rewrite sequence 5.19/2.07 5.19/2.07 f(s(s(x))) ->^+ f(f(s(x))) 5.19/2.07 5.19/2.07 gives rise to a decreasing loop by considering the right hand sides subterm at position [0].
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