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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313303
details
property
value
status
complete
benchmark
secret3.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n172.star.cs.uiowa.edu
space
Secret_07_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.712 seconds
cpu usage
991.809
user time
980.755
system time
11.0536
max virtual memory
3.73814E7
max residence set size
1.37298E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
991.50/291.63 WORST_CASE(Omega(n^1), ?) 991.50/291.63 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 991.50/291.63 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 991.50/291.63 991.50/291.63 991.50/291.63 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 991.50/291.63 991.50/291.63 (0) CpxTRS 991.50/291.63 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 991.50/291.63 (2) TRS for Loop Detection 991.50/291.63 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 991.50/291.63 (4) BEST 991.50/291.63 (5) proven lower bound 991.50/291.63 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 991.50/291.63 (7) BOUNDS(n^1, INF) 991.50/291.63 (8) TRS for Loop Detection 991.50/291.63 991.50/291.63 991.50/291.63 ---------------------------------------- 991.50/291.63 991.50/291.63 (0) 991.50/291.63 Obligation: 991.50/291.63 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 991.50/291.63 991.50/291.63 991.50/291.63 The TRS R consists of the following rules: 991.50/291.63 991.50/291.63 app(nil, k) -> k 991.50/291.63 app(l, nil) -> l 991.50/291.63 app(cons(x, l), k) -> cons(x, app(l, k)) 991.50/291.63 sum(cons(x, nil)) -> cons(x, nil) 991.50/291.63 sum(cons(x, cons(y, l))) -> sum(cons(a(x, y, h), l)) 991.50/291.63 a(h, h, x) -> s(x) 991.50/291.63 a(x, s(y), h) -> a(x, y, s(h)) 991.50/291.63 a(x, s(y), s(z)) -> a(x, y, a(x, s(y), z)) 991.50/291.63 a(s(x), h, z) -> a(x, z, z) 991.50/291.63 991.50/291.63 S is empty. 991.50/291.63 Rewrite Strategy: INNERMOST 991.50/291.63 ---------------------------------------- 991.50/291.63 991.50/291.63 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 991.50/291.63 Transformed a relative TRS into a decreasing-loop problem. 991.50/291.63 ---------------------------------------- 991.50/291.63 991.50/291.63 (2) 991.50/291.63 Obligation: 991.50/291.63 Analyzing the following TRS for decreasing loops: 991.50/291.63 991.50/291.63 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 991.50/291.63 991.50/291.63 991.50/291.63 The TRS R consists of the following rules: 991.50/291.63 991.50/291.63 app(nil, k) -> k 991.50/291.63 app(l, nil) -> l 991.50/291.63 app(cons(x, l), k) -> cons(x, app(l, k)) 991.50/291.63 sum(cons(x, nil)) -> cons(x, nil) 991.50/291.63 sum(cons(x, cons(y, l))) -> sum(cons(a(x, y, h), l)) 991.50/291.63 a(h, h, x) -> s(x) 991.50/291.63 a(x, s(y), h) -> a(x, y, s(h)) 991.50/291.63 a(x, s(y), s(z)) -> a(x, y, a(x, s(y), z)) 991.50/291.63 a(s(x), h, z) -> a(x, z, z) 991.50/291.63 991.50/291.63 S is empty. 991.50/291.63 Rewrite Strategy: INNERMOST 991.50/291.63 ---------------------------------------- 991.50/291.63 991.50/291.63 (3) DecreasingLoopProof (LOWER BOUND(ID)) 991.50/291.63 The following loop(s) give(s) rise to the lower bound Omega(n^1): 991.50/291.63 991.50/291.63 The rewrite sequence 991.50/291.63 991.50/291.63 app(cons(x, l), k) ->^+ cons(x, app(l, k)) 991.50/291.63 991.50/291.63 gives rise to a decreasing loop by considering the right hand sides subterm at position [1]. 991.50/291.63 991.50/291.63 The pumping substitution is [l / cons(x, l)]. 991.50/291.63 991.50/291.63 The result substitution is [ ]. 991.50/291.63 991.50/291.63 991.50/291.63 991.50/291.63 991.50/291.63 ---------------------------------------- 991.50/291.63 991.50/291.63 (4) 991.50/291.63 Complex Obligation (BEST) 991.50/291.63 991.50/291.63 ---------------------------------------- 991.50/291.63 991.50/291.63 (5) 991.50/291.63 Obligation: 991.50/291.63 Proved the lower bound n^1 for the following obligation: 991.50/291.63 991.50/291.63 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 991.50/291.63 991.50/291.63 991.50/291.63 The TRS R consists of the following rules: 991.50/291.63
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