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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313575
details
property
value
status
complete
benchmark
2.52.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n117.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.943 seconds
cpu usage
1110.42
user time
1098.89
system time
11.5339
max virtual memory
3.7249384E7
max residence set size
1.5111832E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1110.20/291.86 WORST_CASE(Omega(n^1), ?) 1110.20/291.87 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1110.20/291.87 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1110.20/291.87 1110.20/291.87 1110.20/291.87 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1110.20/291.87 1110.20/291.87 (0) CpxTRS 1110.20/291.87 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1110.20/291.87 (2) TRS for Loop Detection 1110.20/291.87 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1110.20/291.87 (4) BEST 1110.20/291.87 (5) proven lower bound 1110.20/291.87 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1110.20/291.87 (7) BOUNDS(n^1, INF) 1110.20/291.87 (8) TRS for Loop Detection 1110.20/291.87 1110.20/291.87 1110.20/291.87 ---------------------------------------- 1110.20/291.87 1110.20/291.87 (0) 1110.20/291.87 Obligation: 1110.20/291.87 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1110.20/291.87 1110.20/291.87 1110.20/291.87 The TRS R consists of the following rules: 1110.20/291.87 1110.20/291.87 f(x, 0, 0) -> s(x) 1110.20/291.87 f(0, y, 0) -> s(y) 1110.20/291.87 f(0, 0, z) -> s(z) 1110.20/291.87 f(s(0), y, z) -> f(0, s(y), s(z)) 1110.20/291.87 f(s(x), s(y), 0) -> f(x, y, s(0)) 1110.20/291.87 f(s(x), 0, s(z)) -> f(x, s(0), z) 1110.20/291.87 f(0, s(0), s(0)) -> s(s(0)) 1110.20/291.87 f(s(x), s(y), s(z)) -> f(x, y, f(s(x), s(y), z)) 1110.20/291.87 f(0, s(s(y)), s(0)) -> f(0, y, s(0)) 1110.20/291.87 f(0, s(0), s(s(z))) -> f(0, s(0), z) 1110.20/291.87 f(0, s(s(y)), s(s(z))) -> f(0, y, f(0, s(s(y)), s(z))) 1110.20/291.87 1110.20/291.87 S is empty. 1110.20/291.87 Rewrite Strategy: INNERMOST 1110.20/291.87 ---------------------------------------- 1110.20/291.87 1110.20/291.87 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1110.20/291.87 Transformed a relative TRS into a decreasing-loop problem. 1110.20/291.87 ---------------------------------------- 1110.20/291.87 1110.20/291.87 (2) 1110.20/291.87 Obligation: 1110.20/291.87 Analyzing the following TRS for decreasing loops: 1110.20/291.87 1110.20/291.87 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1110.20/291.87 1110.20/291.87 1110.20/291.87 The TRS R consists of the following rules: 1110.20/291.87 1110.20/291.87 f(x, 0, 0) -> s(x) 1110.20/291.87 f(0, y, 0) -> s(y) 1110.20/291.87 f(0, 0, z) -> s(z) 1110.20/291.87 f(s(0), y, z) -> f(0, s(y), s(z)) 1110.20/291.87 f(s(x), s(y), 0) -> f(x, y, s(0)) 1110.20/291.87 f(s(x), 0, s(z)) -> f(x, s(0), z) 1110.20/291.87 f(0, s(0), s(0)) -> s(s(0)) 1110.20/291.87 f(s(x), s(y), s(z)) -> f(x, y, f(s(x), s(y), z)) 1110.20/291.87 f(0, s(s(y)), s(0)) -> f(0, y, s(0)) 1110.20/291.87 f(0, s(0), s(s(z))) -> f(0, s(0), z) 1110.20/291.87 f(0, s(s(y)), s(s(z))) -> f(0, y, f(0, s(s(y)), s(z))) 1110.20/291.87 1110.20/291.87 S is empty. 1110.20/291.87 Rewrite Strategy: INNERMOST 1110.20/291.87 ---------------------------------------- 1110.20/291.87 1110.20/291.87 (3) DecreasingLoopProof (LOWER BOUND(ID)) 1110.20/291.87 The following loop(s) give(s) rise to the lower bound Omega(n^1): 1110.20/291.87 1110.20/291.87 The rewrite sequence 1110.20/291.87 1110.20/291.87 f(s(x), s(y), s(z)) ->^+ f(x, y, f(s(x), s(y), z)) 1110.20/291.87 1110.20/291.87 gives rise to a decreasing loop by considering the right hand sides subterm at position [2]. 1110.20/291.87 1110.20/291.87 The pumping substitution is [z / s(z)]. 1110.20/291.87 1110.20/291.87 The result substitution is [ ]. 1110.20/291.87 1110.20/291.87 1110.20/291.87 1110.20/291.87 1110.20/291.87 ---------------------------------------- 1110.20/291.87 1110.20/291.87 (4) 1110.20/291.87 Complex Obligation (BEST) 1110.20/291.87 1110.20/291.87 ---------------------------------------- 1110.20/291.87 1110.20/291.87 (5) 1110.20/291.87 Obligation: 1110.20/291.87 Proved the lower bound n^1 for the following obligation: 1110.20/291.87 1110.20/291.87 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
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