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Runtime Complexity: TRS pair #487110006
details
property
value
status
complete
benchmark
Ex6_15_AEL02_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n147.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
2.92989 seconds
cpu usage
8.73013
user time
8.31741
system time
0.412726
max virtual memory
1.8279408E7
max residence set size
1234172.0
stage attributes
key
value
starexec-result
WORST_CASE(NON_POLY, ?)
output
WORST_CASE(NON_POLY, ?) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF). (0) CpxTRS (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (2) TRS for Loop Detection (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (4) BEST (5) proven lower bound (6) LowerBoundPropagationProof [FINISHED, 0 ms] (7) BOUNDS(n^1, INF) (8) TRS for Loop Detection (9) InfiniteLowerBoundProof [FINISHED, 858 ms] (10) BOUNDS(INF, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF). The TRS R consists of the following rules: sel(s(X), cons(Y, Z)) -> sel(X, activate(Z)) sel(0, cons(X, Z)) -> X first(0, Z) -> nil first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z))) from(X) -> cons(X, n__from(s(X))) sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z)) sel1(0, cons(X, Z)) -> quote(X) first1(0, Z) -> nil1 first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z))) quote(n__0) -> 01 quote1(n__cons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z))) quote1(n__nil) -> nil1 quote(n__s(X)) -> s1(quote(activate(X))) quote(n__sel(X, Z)) -> sel1(activate(X), activate(Z)) quote1(n__first(X, Z)) -> first1(activate(X), activate(Z)) unquote(01) -> 0 unquote(s1(X)) -> s(unquote(X)) unquote1(nil1) -> nil unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z)) fcons(X, Z) -> cons(X, Z) first(X1, X2) -> n__first(X1, X2) from(X) -> n__from(X) 0 -> n__0 cons(X1, X2) -> n__cons(X1, X2) nil -> n__nil s(X) -> n__s(X) sel(X1, X2) -> n__sel(X1, X2) activate(n__first(X1, X2)) -> first(X1, X2) activate(n__from(X)) -> from(X) activate(n__0) -> 0 activate(n__cons(X1, X2)) -> cons(X1, X2) activate(n__nil) -> nil activate(n__s(X)) -> s(X) activate(n__sel(X1, X2)) -> sel(X1, X2) activate(X) -> X S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (2) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF). The TRS R consists of the following rules: sel(s(X), cons(Y, Z)) -> sel(X, activate(Z)) sel(0, cons(X, Z)) -> X first(0, Z) -> nil first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z))) from(X) -> cons(X, n__from(s(X))) sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z)) sel1(0, cons(X, Z)) -> quote(X) first1(0, Z) -> nil1 first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z))) quote(n__0) -> 01 quote1(n__cons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z))) quote1(n__nil) -> nil1 quote(n__s(X)) -> s1(quote(activate(X))) quote(n__sel(X, Z)) -> sel1(activate(X), activate(Z)) quote1(n__first(X, Z)) -> first1(activate(X), activate(Z)) unquote(01) -> 0 unquote(s1(X)) -> s(unquote(X)) unquote1(nil1) -> nil
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