SRS Standard pair #487091292

details

property	value
status	complete
benchmark	z085.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n151.star.cs.uiowa.edu
space	Zantema_04

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.0534959 seconds
cpu usage	0.035759
user time	0.019579
system time	0.01618
max virtual memory	113188.0
max residence set size	4772.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

Subterm Processor:
-> Pairs:
 A(x1:S) -> B(x1:S)
 B(b(b(x1:S))) -> A(x1:S)
-> Rules:
 a(x1:S) -> b(b(x1:S))
 b(b(b(x1:S))) -> a(x1:S)
->Projection:
 pi(A) = 1
 pi(B) = 1

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