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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308130
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
n124.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.653 seconds
cpu usage
1089.38
user time
1073.77
system time
15.6129
max virtual memory
3.74384E7
max residence set size
1.4980088E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1088.82/291.55 WORST_CASE(Omega(n^1), ?) 1088.82/291.57 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1088.82/291.57 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1088.82/291.57 1088.82/291.57 1088.82/291.57 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1088.82/291.57 1088.82/291.57 (0) CpxTRS 1088.82/291.57 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1088.82/291.57 (2) TRS for Loop Detection 1088.82/291.57 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1088.82/291.57 (4) BEST 1088.82/291.57 (5) proven lower bound 1088.82/291.57 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1088.82/291.57 (7) BOUNDS(n^1, INF) 1088.82/291.57 (8) TRS for Loop Detection 1088.82/291.57 1088.82/291.57 1088.82/291.57 ---------------------------------------- 1088.82/291.57 1088.82/291.57 (0) 1088.82/291.57 Obligation: 1088.82/291.57 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1088.82/291.57 1088.82/291.57 1088.82/291.57 The TRS R consists of the following rules: 1088.82/291.57 1088.82/291.57 a__nats -> cons(0, incr(nats)) 1088.82/291.57 a__pairs -> cons(0, incr(odds)) 1088.82/291.57 a__odds -> a__incr(a__pairs) 1088.82/291.57 a__incr(cons(X, XS)) -> cons(s(mark(X)), incr(XS)) 1088.82/291.57 a__head(cons(X, XS)) -> mark(X) 1088.82/291.57 a__tail(cons(X, XS)) -> mark(XS) 1088.82/291.57 mark(nats) -> a__nats 1088.82/291.57 mark(incr(X)) -> a__incr(mark(X)) 1088.82/291.57 mark(pairs) -> a__pairs 1088.82/291.57 mark(odds) -> a__odds 1088.82/291.57 mark(head(X)) -> a__head(mark(X)) 1088.82/291.57 mark(tail(X)) -> a__tail(mark(X)) 1088.82/291.57 mark(cons(X1, X2)) -> cons(mark(X1), X2) 1088.82/291.57 mark(0) -> 0 1088.82/291.57 mark(s(X)) -> s(mark(X)) 1088.82/291.57 a__nats -> nats 1088.82/291.57 a__incr(X) -> incr(X) 1088.82/291.57 a__pairs -> pairs 1088.82/291.57 a__odds -> odds 1088.82/291.57 a__head(X) -> head(X) 1088.82/291.57 a__tail(X) -> tail(X) 1088.82/291.57 1088.82/291.57 S is empty. 1088.82/291.57 Rewrite Strategy: FULL 1088.82/291.57 ---------------------------------------- 1088.82/291.57 1088.82/291.57 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1088.82/291.57 Transformed a relative TRS into a decreasing-loop problem. 1088.82/291.57 ---------------------------------------- 1088.82/291.57 1088.82/291.57 (2) 1088.82/291.57 Obligation: 1088.82/291.57 Analyzing the following TRS for decreasing loops: 1088.82/291.57 1088.82/291.57 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1088.82/291.57 1088.82/291.57 1088.82/291.57 The TRS R consists of the following rules: 1088.82/291.57 1088.82/291.57 a__nats -> cons(0, incr(nats)) 1088.82/291.57 a__pairs -> cons(0, incr(odds)) 1088.82/291.57 a__odds -> a__incr(a__pairs) 1088.82/291.57 a__incr(cons(X, XS)) -> cons(s(mark(X)), incr(XS)) 1088.82/291.57 a__head(cons(X, XS)) -> mark(X) 1088.82/291.57 a__tail(cons(X, XS)) -> mark(XS) 1088.82/291.57 mark(nats) -> a__nats 1088.82/291.57 mark(incr(X)) -> a__incr(mark(X)) 1088.82/291.57 mark(pairs) -> a__pairs 1088.82/291.57 mark(odds) -> a__odds 1088.82/291.57 mark(head(X)) -> a__head(mark(X)) 1088.82/291.57 mark(tail(X)) -> a__tail(mark(X)) 1088.82/291.57 mark(cons(X1, X2)) -> cons(mark(X1), X2) 1088.82/291.57 mark(0) -> 0 1088.82/291.57 mark(s(X)) -> s(mark(X)) 1088.82/291.57 a__nats -> nats 1088.82/291.57 a__incr(X) -> incr(X) 1088.82/291.57 a__pairs -> pairs 1088.82/291.57 a__odds -> odds 1088.82/291.57 a__head(X) -> head(X) 1088.82/291.57 a__tail(X) -> tail(X) 1088.82/291.57 1088.82/291.57 S is empty. 1088.82/291.57 Rewrite Strategy: FULL 1088.82/291.57 ---------------------------------------- 1088.82/291.57 1088.82/291.57 (3) DecreasingLoopProof (LOWER BOUND(ID)) 1088.82/291.57 The following loop(s) give(s) rise to the lower bound Omega(n^1): 1088.82/291.57 1088.82/291.57 The rewrite sequence 1088.82/291.57 1088.82/291.57 mark(incr(X)) ->^+ a__incr(mark(X)) 1088.82/291.57 1088.82/291.57 gives rise to a decreasing loop by considering the right hand sides subterm at position [0].
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