SRS Standard pair #487091640

details

property	value
status	complete
benchmark	z010.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)	0.0490009 seconds
cpu usage	0.034701
user time	0.012325
system time	0.022376
max virtual memory	113188.0
max residence set size	4900.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem 1: 

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

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 a(b(x1:S)) -> b(b(a(x1:S)))
 c(b(x1:S)) -> b(c(c(x1:S)))
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

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

Problem 1: 

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


The problem is decomposed in 2 subproblems.

Problem 1.1: 

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

Problem 1.1: 

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

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