SRS Standard pair #487085712

details

property	value
status	complete
benchmark	07.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n150.star.cs.uiowa.edu
space	Bouchare_06

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	3.74912 seconds
cpu usage	3.70794
user time	3.37802
system time	0.329917
max virtual memory	724232.0
max residence set size	20328.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

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