SRS Standard pair #487091604

details

property	value
status	complete
benchmark	z022.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)	1.20275 seconds
cpu usage	1.1874
user time	0.688656
system time	0.498741
max virtual memory	570304.0
max residence set size	6388.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

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