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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313410
details
property
value
status
complete
benchmark
Ex9_BLR02_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n003.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.591 seconds
cpu usage
1123.91
user time
1111.25
system time
12.6536
max virtual memory
3.7269376E7
max residence set size
1.4786084E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1123.54/291.51 WORST_CASE(Omega(n^1), ?) 1123.54/291.52 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1123.54/291.52 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1123.54/291.52 1123.54/291.52 1123.54/291.52 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1123.54/291.52 1123.54/291.52 (0) CpxTRS 1123.54/291.52 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1123.54/291.52 (2) TRS for Loop Detection 1123.54/291.52 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1123.54/291.52 (4) BEST 1123.54/291.52 (5) proven lower bound 1123.54/291.52 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1123.54/291.52 (7) BOUNDS(n^1, INF) 1123.54/291.52 (8) TRS for Loop Detection 1123.54/291.52 1123.54/291.52 1123.54/291.52 ---------------------------------------- 1123.54/291.52 1123.54/291.52 (0) 1123.54/291.52 Obligation: 1123.54/291.52 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1123.54/291.52 1123.54/291.52 1123.54/291.52 The TRS R consists of the following rules: 1123.54/291.52 1123.54/291.52 a__filter(cons(X, Y), 0, M) -> cons(0, filter(Y, M, M)) 1123.54/291.52 a__filter(cons(X, Y), s(N), M) -> cons(mark(X), filter(Y, N, M)) 1123.54/291.52 a__sieve(cons(0, Y)) -> cons(0, sieve(Y)) 1123.54/291.52 a__sieve(cons(s(N), Y)) -> cons(s(mark(N)), sieve(filter(Y, N, N))) 1123.54/291.52 a__nats(N) -> cons(mark(N), nats(s(N))) 1123.54/291.52 a__zprimes -> a__sieve(a__nats(s(s(0)))) 1123.54/291.52 mark(filter(X1, X2, X3)) -> a__filter(mark(X1), mark(X2), mark(X3)) 1123.54/291.52 mark(sieve(X)) -> a__sieve(mark(X)) 1123.54/291.52 mark(nats(X)) -> a__nats(mark(X)) 1123.54/291.52 mark(zprimes) -> a__zprimes 1123.54/291.52 mark(cons(X1, X2)) -> cons(mark(X1), X2) 1123.54/291.52 mark(0) -> 0 1123.54/291.52 mark(s(X)) -> s(mark(X)) 1123.54/291.52 a__filter(X1, X2, X3) -> filter(X1, X2, X3) 1123.54/291.52 a__sieve(X) -> sieve(X) 1123.54/291.52 a__nats(X) -> nats(X) 1123.54/291.52 a__zprimes -> zprimes 1123.54/291.52 1123.54/291.52 S is empty. 1123.54/291.52 Rewrite Strategy: INNERMOST 1123.54/291.52 ---------------------------------------- 1123.54/291.52 1123.54/291.52 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1123.54/291.52 Transformed a relative TRS into a decreasing-loop problem. 1123.54/291.52 ---------------------------------------- 1123.54/291.52 1123.54/291.52 (2) 1123.54/291.52 Obligation: 1123.54/291.52 Analyzing the following TRS for decreasing loops: 1123.54/291.52 1123.54/291.52 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1123.54/291.52 1123.54/291.52 1123.54/291.52 The TRS R consists of the following rules: 1123.54/291.52 1123.54/291.52 a__filter(cons(X, Y), 0, M) -> cons(0, filter(Y, M, M)) 1123.54/291.52 a__filter(cons(X, Y), s(N), M) -> cons(mark(X), filter(Y, N, M)) 1123.54/291.52 a__sieve(cons(0, Y)) -> cons(0, sieve(Y)) 1123.54/291.52 a__sieve(cons(s(N), Y)) -> cons(s(mark(N)), sieve(filter(Y, N, N))) 1123.54/291.52 a__nats(N) -> cons(mark(N), nats(s(N))) 1123.54/291.52 a__zprimes -> a__sieve(a__nats(s(s(0)))) 1123.54/291.52 mark(filter(X1, X2, X3)) -> a__filter(mark(X1), mark(X2), mark(X3)) 1123.54/291.52 mark(sieve(X)) -> a__sieve(mark(X)) 1123.54/291.52 mark(nats(X)) -> a__nats(mark(X)) 1123.54/291.52 mark(zprimes) -> a__zprimes 1123.54/291.52 mark(cons(X1, X2)) -> cons(mark(X1), X2) 1123.54/291.52 mark(0) -> 0 1123.54/291.52 mark(s(X)) -> s(mark(X)) 1123.54/291.52 a__filter(X1, X2, X3) -> filter(X1, X2, X3) 1123.54/291.52 a__sieve(X) -> sieve(X) 1123.54/291.52 a__nats(X) -> nats(X) 1123.54/291.52 a__zprimes -> zprimes 1123.54/291.52 1123.54/291.52 S is empty. 1123.54/291.52 Rewrite Strategy: INNERMOST 1123.54/291.52 ---------------------------------------- 1123.54/291.52 1123.54/291.52 (3) DecreasingLoopProof (LOWER BOUND(ID)) 1123.54/291.52 The following loop(s) give(s) rise to the lower bound Omega(n^1): 1123.54/291.52 1123.54/291.52 The rewrite sequence 1123.54/291.52 1123.54/291.52 mark(nats(X)) ->^+ a__nats(mark(X)) 1123.54/291.52 1123.54/291.52 gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. 1123.54/291.52 1123.54/291.52 The pumping substitution is [X / nats(X)]. 1123.54/291.52 1123.54/291.52 The result substitution is [ ]. 1123.54/291.52 1123.54/291.52 1123.54/291.52 1123.54/291.52
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