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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313527
details
property
value
status
complete
benchmark
Ex6_15_AEL02_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n002.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
292.641 seconds
cpu usage
1143.31
user time
1131.93
system time
11.3833
max virtual memory
3.7373192E7
max residence set size
1.5174376E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1139.03/291.54 WORST_CASE(Omega(n^1), ?) 1143.06/292.57 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1143.06/292.57 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1143.06/292.57 1143.06/292.57 1143.06/292.57 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1143.06/292.57 1143.06/292.57 (0) CpxTRS 1143.06/292.57 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1143.06/292.57 (2) TRS for Loop Detection 1143.06/292.57 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1143.06/292.57 (4) BEST 1143.06/292.57 (5) proven lower bound 1143.06/292.57 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1143.06/292.57 (7) BOUNDS(n^1, INF) 1143.06/292.57 (8) TRS for Loop Detection 1143.06/292.57 1143.06/292.57 1143.06/292.57 ---------------------------------------- 1143.06/292.57 1143.06/292.57 (0) 1143.06/292.57 Obligation: 1143.06/292.57 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1143.06/292.57 1143.06/292.57 1143.06/292.57 The TRS R consists of the following rules: 1143.06/292.57 1143.06/292.57 a__sel(s(X), cons(Y, Z)) -> a__sel(mark(X), mark(Z)) 1143.06/292.57 a__sel(0, cons(X, Z)) -> mark(X) 1143.06/292.57 a__first(0, Z) -> nil 1143.06/292.57 a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) 1143.06/292.57 a__from(X) -> cons(mark(X), from(s(X))) 1143.06/292.57 a__sel1(s(X), cons(Y, Z)) -> a__sel1(mark(X), mark(Z)) 1143.06/292.57 a__sel1(0, cons(X, Z)) -> a__quote(X) 1143.06/292.57 a__first1(0, Z) -> nil1 1143.06/292.57 a__first1(s(X), cons(Y, Z)) -> cons1(a__quote(Y), a__first1(mark(X), mark(Z))) 1143.06/292.57 a__quote(0) -> 01 1143.06/292.57 a__quote1(cons(X, Z)) -> cons1(a__quote(X), a__quote1(Z)) 1143.06/292.57 a__quote1(nil) -> nil1 1143.06/292.57 a__quote(s(X)) -> s1(a__quote(X)) 1143.06/292.57 a__quote(sel(X, Z)) -> a__sel1(mark(X), mark(Z)) 1143.06/292.57 a__quote1(first(X, Z)) -> a__first1(mark(X), mark(Z)) 1143.06/292.57 a__unquote(01) -> 0 1143.06/292.57 a__unquote(s1(X)) -> s(a__unquote(mark(X))) 1143.06/292.57 a__unquote1(nil1) -> nil 1143.06/292.57 a__unquote1(cons1(X, Z)) -> a__fcons(a__unquote(mark(X)), a__unquote1(mark(Z))) 1143.06/292.57 a__fcons(X, Z) -> cons(mark(X), Z) 1143.06/292.57 mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) 1143.06/292.57 mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) 1143.06/292.57 mark(from(X)) -> a__from(mark(X)) 1143.06/292.57 mark(sel1(X1, X2)) -> a__sel1(mark(X1), mark(X2)) 1143.06/292.57 mark(quote(X)) -> a__quote(X) 1143.06/292.57 mark(first1(X1, X2)) -> a__first1(mark(X1), mark(X2)) 1143.06/292.57 mark(quote1(X)) -> a__quote1(X) 1143.06/292.57 mark(unquote(X)) -> a__unquote(mark(X)) 1143.06/292.57 mark(unquote1(X)) -> a__unquote1(mark(X)) 1143.06/292.57 mark(fcons(X1, X2)) -> a__fcons(mark(X1), mark(X2)) 1143.06/292.57 mark(s(X)) -> s(mark(X)) 1143.06/292.57 mark(cons(X1, X2)) -> cons(mark(X1), X2) 1143.06/292.57 mark(0) -> 0 1143.06/292.57 mark(nil) -> nil 1143.06/292.57 mark(nil1) -> nil1 1143.06/292.57 mark(cons1(X1, X2)) -> cons1(mark(X1), mark(X2)) 1143.06/292.57 mark(01) -> 01 1143.06/292.57 mark(s1(X)) -> s1(mark(X)) 1143.06/292.57 a__sel(X1, X2) -> sel(X1, X2) 1143.06/292.57 a__first(X1, X2) -> first(X1, X2) 1143.06/292.57 a__from(X) -> from(X) 1143.06/292.57 a__sel1(X1, X2) -> sel1(X1, X2) 1143.06/292.57 a__quote(X) -> quote(X) 1143.06/292.57 a__first1(X1, X2) -> first1(X1, X2) 1143.06/292.57 a__quote1(X) -> quote1(X) 1143.06/292.57 a__unquote(X) -> unquote(X) 1143.06/292.57 a__unquote1(X) -> unquote1(X) 1143.06/292.57 a__fcons(X1, X2) -> fcons(X1, X2) 1143.06/292.57 1143.06/292.57 S is empty. 1143.06/292.57 Rewrite Strategy: INNERMOST 1143.06/292.57 ---------------------------------------- 1143.06/292.57 1143.06/292.57 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1143.06/292.57 Transformed a relative TRS into a decreasing-loop problem. 1143.06/292.57 ---------------------------------------- 1143.06/292.57 1143.06/292.57 (2) 1143.06/292.57 Obligation: 1143.06/292.57 Analyzing the following TRS for decreasing loops: 1143.06/292.57 1143.06/292.57 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1143.06/292.57 1143.06/292.57 1143.06/292.57 The TRS R consists of the following rules: 1143.06/292.57 1143.06/292.57 a__sel(s(X), cons(Y, Z)) -> a__sel(mark(X), mark(Z)) 1143.06/292.57 a__sel(0, cons(X, Z)) -> mark(X) 1143.06/292.57 a__first(0, Z) -> nil 1143.06/292.57 a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) 1143.06/292.57 a__from(X) -> cons(mark(X), from(s(X))) 1143.06/292.57 a__sel1(s(X), cons(Y, Z)) -> a__sel1(mark(X), mark(Z)) 1143.06/292.57 a__sel1(0, cons(X, Z)) -> a__quote(X)
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