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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307848
details
property
value
status
complete
benchmark
Ex1_Luc04b_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n179.star.cs.uiowa.edu
space
Mixed_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.597 seconds
cpu usage
1075.58
user time
1061.02
system time
14.5531
max virtual memory
3.757414E7
max residence set size
1.5149584E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1075.13/291.52 WORST_CASE(Omega(n^1), ?) 1075.13/291.53 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1075.13/291.53 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1075.13/291.53 1075.13/291.53 1075.13/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1075.13/291.53 1075.13/291.53 (0) CpxTRS 1075.13/291.53 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1075.13/291.53 (2) TRS for Loop Detection 1075.13/291.53 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1075.13/291.53 (4) BEST 1075.13/291.53 (5) proven lower bound 1075.13/291.53 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1075.13/291.53 (7) BOUNDS(n^1, INF) 1075.13/291.53 (8) TRS for Loop Detection 1075.13/291.53 1075.13/291.53 1075.13/291.53 ---------------------------------------- 1075.13/291.53 1075.13/291.53 (0) 1075.13/291.53 Obligation: 1075.13/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1075.13/291.53 1075.13/291.53 1075.13/291.53 The TRS R consists of the following rules: 1075.13/291.53 1075.13/291.53 a__nats -> cons(0, incr(nats)) 1075.13/291.53 a__pairs -> cons(0, incr(odds)) 1075.13/291.53 a__odds -> a__incr(a__pairs) 1075.13/291.53 a__incr(cons(X, XS)) -> cons(s(mark(X)), incr(XS)) 1075.13/291.53 a__head(cons(X, XS)) -> mark(X) 1075.13/291.53 a__tail(cons(X, XS)) -> mark(XS) 1075.13/291.53 mark(nats) -> a__nats 1075.13/291.53 mark(pairs) -> a__pairs 1075.13/291.53 mark(odds) -> a__odds 1075.13/291.53 mark(incr(X)) -> a__incr(mark(X)) 1075.13/291.53 mark(head(X)) -> a__head(mark(X)) 1075.13/291.53 mark(tail(X)) -> a__tail(mark(X)) 1075.13/291.53 mark(0) -> 0 1075.13/291.53 mark(s(X)) -> s(mark(X)) 1075.13/291.53 mark(nil) -> nil 1075.13/291.53 mark(cons(X1, X2)) -> cons(mark(X1), X2) 1075.13/291.53 a__nats -> nats 1075.13/291.53 a__pairs -> pairs 1075.13/291.53 a__odds -> odds 1075.13/291.53 a__incr(X) -> incr(X) 1075.13/291.53 a__head(X) -> head(X) 1075.13/291.53 a__tail(X) -> tail(X) 1075.13/291.53 1075.13/291.53 S is empty. 1075.13/291.53 Rewrite Strategy: FULL 1075.13/291.53 ---------------------------------------- 1075.13/291.53 1075.13/291.53 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1075.13/291.53 Transformed a relative TRS into a decreasing-loop problem. 1075.13/291.53 ---------------------------------------- 1075.13/291.53 1075.13/291.53 (2) 1075.13/291.53 Obligation: 1075.13/291.53 Analyzing the following TRS for decreasing loops: 1075.13/291.53 1075.13/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1075.13/291.53 1075.13/291.53 1075.13/291.53 The TRS R consists of the following rules: 1075.13/291.53 1075.13/291.53 a__nats -> cons(0, incr(nats)) 1075.13/291.53 a__pairs -> cons(0, incr(odds)) 1075.13/291.53 a__odds -> a__incr(a__pairs) 1075.13/291.53 a__incr(cons(X, XS)) -> cons(s(mark(X)), incr(XS)) 1075.13/291.53 a__head(cons(X, XS)) -> mark(X) 1075.13/291.53 a__tail(cons(X, XS)) -> mark(XS) 1075.13/291.53 mark(nats) -> a__nats 1075.13/291.53 mark(pairs) -> a__pairs 1075.13/291.53 mark(odds) -> a__odds 1075.13/291.53 mark(incr(X)) -> a__incr(mark(X)) 1075.13/291.53 mark(head(X)) -> a__head(mark(X)) 1075.13/291.53 mark(tail(X)) -> a__tail(mark(X)) 1075.13/291.53 mark(0) -> 0 1075.13/291.53 mark(s(X)) -> s(mark(X)) 1075.13/291.53 mark(nil) -> nil 1075.13/291.53 mark(cons(X1, X2)) -> cons(mark(X1), X2) 1075.13/291.53 a__nats -> nats 1075.13/291.53 a__pairs -> pairs 1075.13/291.53 a__odds -> odds 1075.13/291.53 a__incr(X) -> incr(X) 1075.13/291.53 a__head(X) -> head(X) 1075.13/291.53 a__tail(X) -> tail(X) 1075.13/291.53 1075.13/291.53 S is empty. 1075.13/291.53 Rewrite Strategy: FULL 1075.13/291.53 ---------------------------------------- 1075.13/291.53 1075.13/291.53 (3) DecreasingLoopProof (LOWER BOUND(ID)) 1075.13/291.53 The following loop(s) give(s) rise to the lower bound Omega(n^1): 1075.13/291.53 1075.13/291.53 The rewrite sequence 1075.13/291.53 1075.13/291.53 mark(incr(X)) ->^+ a__incr(mark(X))
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