SRS Standard pair #487091400

details

property	value
status	complete
benchmark	z005.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n054.star.cs.uiowa.edu
space	Zantema_04

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	59.8322 seconds
cpu usage	59.0606
user time	56.0642
system time	2.99643
max virtual memory	832660.0
max residence set size	73828.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A(a(x1:S)) -> A(b(c(a(x1:S))))
 A(a(x1:S)) -> B(c(a(x1:S)))
 A(c(b(x1:S))) -> A(b(a(x1:S)))
 A(c(b(x1:S))) -> A(x1:S)
 A(c(b(x1:S))) -> B(a(b(a(x1:S))))
 A(c(b(x1:S))) -> B(a(x1:S))
 B(x1:S) -> A(c(x1:S))
-> Rules:
 a(a(x1:S)) -> a(b(c(a(x1:S))))
 a(c(b(x1:S))) -> b(a(b(a(x1:S))))
 b(x1:S) -> c(a(c(x1:S)))
-> Usable rules:
 a(a(x1:S)) -> a(b(c(a(x1:S))))
 a(c(b(x1:S))) -> b(a(b(a(x1:S))))
 b(x1:S) -> c(a(c(x1:S)))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 2
->Bound:
 1
->Interpretation:
 
[a](X) = [1 0;1 0].X
[b](X) = [0 1;1 0].X + [0;1]
[c](X) = [0 1;0 0].X
[A](X) = [1 0;1 0].X + [0;1]
[B](X) = [0 1;0 1].X + [0;1]

Problem 1: 

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

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