SRS Standard pair #487091394

details

property	value
status	complete
benchmark	z002.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n146.star.cs.uiowa.edu
space	Zantema_04

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	15.5784 seconds
cpu usage	15.3896
user time	14.4488
system time	0.940761
max virtual memory	760460.0
max residence set size	52988.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

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