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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307703
details
property
value
status
complete
benchmark
#3.57.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n159.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.521 seconds
cpu usage
888.653
user time
878.244
system time
10.4088
max virtual memory
3.8253924E7
max residence set size
1.1147E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
888.34/291.46 WORST_CASE(Omega(n^1), ?) 888.54/291.47 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 888.54/291.47 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 888.54/291.47 888.54/291.47 888.54/291.47 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 888.54/291.47 888.54/291.47 (0) CpxTRS 888.54/291.47 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 888.54/291.47 (2) TRS for Loop Detection 888.54/291.47 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 888.54/291.47 (4) BEST 888.54/291.47 (5) proven lower bound 888.54/291.47 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 888.54/291.47 (7) BOUNDS(n^1, INF) 888.54/291.47 (8) TRS for Loop Detection 888.54/291.47 888.54/291.47 888.54/291.47 ---------------------------------------- 888.54/291.47 888.54/291.47 (0) 888.54/291.47 Obligation: 888.54/291.47 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 888.54/291.47 888.54/291.47 888.54/291.47 The TRS R consists of the following rules: 888.54/291.47 888.54/291.47 minus(x, 0) -> x 888.54/291.47 minus(s(x), s(y)) -> minus(x, y) 888.54/291.47 quot(0, s(y)) -> 0 888.54/291.47 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) 888.54/291.47 plus(0, y) -> y 888.54/291.47 plus(s(x), y) -> s(plus(x, y)) 888.54/291.47 minus(minus(x, y), z) -> minus(x, plus(y, z)) 888.54/291.47 app(nil, k) -> k 888.54/291.47 app(l, nil) -> l 888.54/291.47 app(cons(x, l), k) -> cons(x, app(l, k)) 888.54/291.47 sum(cons(x, nil)) -> cons(x, nil) 888.54/291.47 sum(cons(x, cons(y, l))) -> sum(cons(plus(x, y), l)) 888.54/291.47 sum(app(l, cons(x, cons(y, k)))) -> sum(app(l, sum(cons(x, cons(y, k))))) 888.54/291.47 888.54/291.47 S is empty. 888.54/291.47 Rewrite Strategy: FULL 888.54/291.47 ---------------------------------------- 888.54/291.47 888.54/291.47 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 888.54/291.47 Transformed a relative TRS into a decreasing-loop problem. 888.54/291.47 ---------------------------------------- 888.54/291.47 888.54/291.47 (2) 888.54/291.47 Obligation: 888.54/291.47 Analyzing the following TRS for decreasing loops: 888.54/291.47 888.54/291.47 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 888.54/291.47 888.54/291.47 888.54/291.47 The TRS R consists of the following rules: 888.54/291.47 888.54/291.47 minus(x, 0) -> x 888.54/291.47 minus(s(x), s(y)) -> minus(x, y) 888.54/291.47 quot(0, s(y)) -> 0 888.54/291.47 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) 888.54/291.47 plus(0, y) -> y 888.54/291.47 plus(s(x), y) -> s(plus(x, y)) 888.54/291.47 minus(minus(x, y), z) -> minus(x, plus(y, z)) 888.54/291.47 app(nil, k) -> k 888.54/291.47 app(l, nil) -> l 888.54/291.47 app(cons(x, l), k) -> cons(x, app(l, k)) 888.54/291.47 sum(cons(x, nil)) -> cons(x, nil) 888.54/291.47 sum(cons(x, cons(y, l))) -> sum(cons(plus(x, y), l)) 888.54/291.47 sum(app(l, cons(x, cons(y, k)))) -> sum(app(l, sum(cons(x, cons(y, k))))) 888.54/291.47 888.54/291.47 S is empty. 888.54/291.47 Rewrite Strategy: FULL 888.54/291.47 ---------------------------------------- 888.54/291.47 888.54/291.47 (3) DecreasingLoopProof (LOWER BOUND(ID)) 888.54/291.47 The following loop(s) give(s) rise to the lower bound Omega(n^1): 888.54/291.47 888.54/291.47 The rewrite sequence 888.54/291.47 888.54/291.47 app(cons(x, l), k) ->^+ cons(x, app(l, k)) 888.54/291.47 888.54/291.47 gives rise to a decreasing loop by considering the right hand sides subterm at position [1]. 888.54/291.47 888.54/291.47 The pumping substitution is [l / cons(x, l)]. 888.54/291.47 888.54/291.47 The result substitution is [ ]. 888.54/291.47 888.54/291.47 888.54/291.47 888.54/291.47 888.54/291.47 ---------------------------------------- 888.54/291.47 888.54/291.47 (4) 888.54/291.47 Complex Obligation (BEST) 888.54/291.47 888.54/291.47 ---------------------------------------- 888.54/291.47 888.54/291.47 (5)
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