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Runtime Complexity: TRS pair #487109800
details
property
value
status
complete
benchmark
Ex15_Luc06_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)
1.54032 seconds
cpu usage
3.25168
user time
3.13057
system time
0.121107
max virtual memory
1.8275312E7
max residence set size
214984.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(1))
output
WORST_CASE(?, O(1)) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1). (0) CpxTRS (1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms] (2) BOUNDS(1, 1) ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1). The TRS R consists of the following rules: f(n__f(n__a)) -> f(n__g(f(n__a))) f(X) -> n__f(X) a -> n__a g(X) -> n__g(X) activate(n__f(X)) -> f(X) activate(n__a) -> a activate(n__g(X)) -> g(X) activate(X) -> X S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) NarrowingOnBasicTermsTerminatesProof (FINISHED) Constant runtime complexity proven by termination of constructor-based narrowing. The maximal most general narrowing sequences give rise to the following rewrite sequences: activate(n__g(x0)) ->^* n__g(x0) activate(n__a) ->^* n__a activate(n__f(x0)) ->^* n__f(x0) activate(n__f(n__f(n__a))) ->^* n__f(n__g(n__f(n__a))) g(x0) ->^* n__g(x0) a ->^* n__a f(x0) ->^* n__f(x0) f(n__f(n__a)) ->^* n__f(n__g(n__f(n__a))) ---------------------------------------- (2) BOUNDS(1, 1)
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