SRS Standard pair #487510867

details

property	value
status	complete
benchmark	random-436.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n134.star.cs.uiowa.edu
space	Waldmann_19

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	23.9068169594 seconds
cpu usage	23.953743264
max memory	6.46885376E8

stage attributes

key	value
output-size	4775
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


YES

Problem 1: 

(VAR v_NonEmpty:S x1:S)
(RULES
a(a(b(a(x1:S)))) -> a(b(b(a(x1:S))))
a(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
a(b(b(a(x1:S)))) -> a(b(a(b(x1:S))))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 A(a(b(a(x1:S)))) -> A(b(b(a(x1:S))))
 A(a(b(b(x1:S)))) -> A(a(x1:S))
 A(a(b(b(x1:S)))) -> A(x1:S)
 A(b(b(a(x1:S)))) -> A(b(a(b(x1:S))))
 A(b(b(a(x1:S)))) -> A(b(x1:S))
-> Rules:
 a(a(b(a(x1:S)))) -> a(b(b(a(x1:S))))
 a(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
 a(b(b(a(x1:S)))) -> a(b(a(b(x1:S))))

Problem 1: 

SCC Processor:
-> Pairs:
 A(a(b(a(x1:S)))) -> A(b(b(a(x1:S))))
 A(a(b(b(x1:S)))) -> A(a(x1:S))
 A(a(b(b(x1:S)))) -> A(x1:S)
 A(b(b(a(x1:S)))) -> A(b(a(b(x1:S))))
 A(b(b(a(x1:S)))) -> A(b(x1:S))
-> Rules:
 a(a(b(a(x1:S)))) -> a(b(b(a(x1:S))))
 a(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
 a(b(b(a(x1:S)))) -> a(b(a(b(x1:S))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A(b(b(a(x1:S)))) -> A(b(a(b(x1:S))))
 A(b(b(a(x1:S)))) -> A(b(x1:S))
->->-> Rules:
 a(a(b(a(x1:S)))) -> a(b(b(a(x1:S))))
 a(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
 a(b(b(a(x1:S)))) -> a(b(a(b(x1:S))))
->->Cycle:
->->-> Pairs:
 A(a(b(b(x1:S)))) -> A(a(x1:S))
 A(a(b(b(x1:S)))) -> A(x1:S)
->->-> Rules:
 a(a(b(a(x1:S)))) -> a(b(b(a(x1:S))))
 a(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
 a(b(b(a(x1:S)))) -> a(b(a(b(x1:S))))


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Reduction Pair Processor:
-> Pairs:
 A(b(b(a(x1:S)))) -> A(b(a(b(x1:S))))
 A(b(b(a(x1:S)))) -> A(b(x1:S))
-> Rules:
 a(a(b(a(x1:S)))) -> a(b(b(a(x1:S))))
 a(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
 a(b(b(a(x1:S)))) -> a(b(a(b(x1:S))))
-> Usable rules:
 a(a(b(a(x1:S)))) -> a(b(b(a(x1:S))))
 a(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
 a(b(b(a(x1:S)))) -> a(b(a(b(x1:S))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a](X) = 2.X + 1
[b](X) = 2.X + 1
[A](X) = 2.X

Problem 1.1: 

SCC Processor:
-> Pairs:
 A(b(b(a(x1:S)))) -> A(b(a(b(x1:S))))
-> Rules:
 a(a(b(a(x1:S)))) -> a(b(b(a(x1:S))))

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