SRS Standard pair #487091130

details

property	value
status	complete
benchmark	z020.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n184.star.cs.uiowa.edu
space	Zantema_04

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.14477 seconds
cpu usage	0.134047
user time	0.057192
system time	0.076855
max virtual memory	113188.0
max residence set size	5480.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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


The problem is decomposed in 2 subproblems.

Problem 1.1: 

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

Problem 1.1: 

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

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