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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313431
details
property
value
status
complete
benchmark
Ex5_7_Luc97_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n142.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
293.552 seconds
cpu usage
1148.53
user time
1136.55
system time
11.9753
max virtual memory
5.61082E7
max residence set size
1.5222724E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1140.86/291.59 WORST_CASE(Omega(n^1), ?) 1148.39/293.48 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1148.39/293.48 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1148.39/293.48 1148.39/293.48 1148.39/293.48 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1148.39/293.48 1148.39/293.48 (0) CpxTRS 1148.39/293.48 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1148.39/293.48 (2) TRS for Loop Detection 1148.39/293.48 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1148.39/293.48 (4) BEST 1148.39/293.48 (5) proven lower bound 1148.39/293.48 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1148.39/293.48 (7) BOUNDS(n^1, INF) 1148.39/293.48 (8) TRS for Loop Detection 1148.39/293.48 1148.39/293.48 1148.39/293.48 ---------------------------------------- 1148.39/293.48 1148.39/293.48 (0) 1148.39/293.48 Obligation: 1148.39/293.48 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1148.39/293.48 1148.39/293.48 1148.39/293.48 The TRS R consists of the following rules: 1148.39/293.48 1148.39/293.48 a__dbl(0) -> 0 1148.39/293.48 a__dbl(s(X)) -> s(s(dbl(X))) 1148.39/293.48 a__dbls(nil) -> nil 1148.39/293.48 a__dbls(cons(X, Y)) -> cons(dbl(X), dbls(Y)) 1148.39/293.48 a__sel(0, cons(X, Y)) -> mark(X) 1148.39/293.48 a__sel(s(X), cons(Y, Z)) -> a__sel(mark(X), mark(Z)) 1148.39/293.48 a__indx(nil, X) -> nil 1148.39/293.48 a__indx(cons(X, Y), Z) -> cons(sel(X, Z), indx(Y, Z)) 1148.39/293.48 a__from(X) -> cons(X, from(s(X))) 1148.39/293.48 a__dbl1(0) -> 01 1148.39/293.48 a__dbl1(s(X)) -> s1(s1(a__dbl1(mark(X)))) 1148.39/293.48 a__sel1(0, cons(X, Y)) -> mark(X) 1148.39/293.48 a__sel1(s(X), cons(Y, Z)) -> a__sel1(mark(X), mark(Z)) 1148.39/293.48 a__quote(0) -> 01 1148.39/293.48 a__quote(s(X)) -> s1(a__quote(mark(X))) 1148.39/293.48 a__quote(dbl(X)) -> a__dbl1(mark(X)) 1148.39/293.48 a__quote(sel(X, Y)) -> a__sel1(mark(X), mark(Y)) 1148.39/293.48 mark(dbl(X)) -> a__dbl(mark(X)) 1148.39/293.48 mark(dbls(X)) -> a__dbls(mark(X)) 1148.39/293.48 mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) 1148.39/293.48 mark(indx(X1, X2)) -> a__indx(mark(X1), X2) 1148.39/293.48 mark(from(X)) -> a__from(X) 1148.39/293.48 mark(dbl1(X)) -> a__dbl1(mark(X)) 1148.39/293.48 mark(sel1(X1, X2)) -> a__sel1(mark(X1), mark(X2)) 1148.39/293.48 mark(quote(X)) -> a__quote(mark(X)) 1148.39/293.48 mark(0) -> 0 1148.39/293.48 mark(s(X)) -> s(X) 1148.39/293.48 mark(nil) -> nil 1148.39/293.48 mark(cons(X1, X2)) -> cons(X1, X2) 1148.39/293.48 mark(01) -> 01 1148.39/293.48 mark(s1(X)) -> s1(mark(X)) 1148.39/293.48 a__dbl(X) -> dbl(X) 1148.39/293.48 a__dbls(X) -> dbls(X) 1148.39/293.48 a__sel(X1, X2) -> sel(X1, X2) 1148.39/293.48 a__indx(X1, X2) -> indx(X1, X2) 1148.39/293.48 a__from(X) -> from(X) 1148.39/293.48 a__dbl1(X) -> dbl1(X) 1148.39/293.48 a__sel1(X1, X2) -> sel1(X1, X2) 1148.39/293.48 a__quote(X) -> quote(X) 1148.39/293.48 1148.39/293.48 S is empty. 1148.39/293.48 Rewrite Strategy: INNERMOST 1148.39/293.48 ---------------------------------------- 1148.39/293.48 1148.39/293.48 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1148.39/293.48 Transformed a relative TRS into a decreasing-loop problem. 1148.39/293.48 ---------------------------------------- 1148.39/293.48 1148.39/293.48 (2) 1148.39/293.48 Obligation: 1148.39/293.48 Analyzing the following TRS for decreasing loops: 1148.39/293.48 1148.39/293.48 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1148.39/293.48 1148.39/293.48 1148.39/293.48 The TRS R consists of the following rules: 1148.39/293.48 1148.39/293.48 a__dbl(0) -> 0 1148.39/293.48 a__dbl(s(X)) -> s(s(dbl(X))) 1148.39/293.48 a__dbls(nil) -> nil 1148.39/293.48 a__dbls(cons(X, Y)) -> cons(dbl(X), dbls(Y)) 1148.39/293.48 a__sel(0, cons(X, Y)) -> mark(X) 1148.39/293.48 a__sel(s(X), cons(Y, Z)) -> a__sel(mark(X), mark(Z)) 1148.39/293.48 a__indx(nil, X) -> nil 1148.39/293.48 a__indx(cons(X, Y), Z) -> cons(sel(X, Z), indx(Y, Z)) 1148.39/293.48 a__from(X) -> cons(X, from(s(X))) 1148.39/293.48 a__dbl1(0) -> 01 1148.39/293.48 a__dbl1(s(X)) -> s1(s1(a__dbl1(mark(X)))) 1148.39/293.48 a__sel1(0, cons(X, Y)) -> mark(X) 1148.39/293.48 a__sel1(s(X), cons(Y, Z)) -> a__sel1(mark(X), mark(Z)) 1148.39/293.48 a__quote(0) -> 01 1148.39/293.48 a__quote(s(X)) -> s1(a__quote(mark(X))) 1148.39/293.48 a__quote(dbl(X)) -> a__dbl1(mark(X))
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return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40
