SRS Standard pair #487091778

details

property	value
status	complete
benchmark	z018.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n141.star.cs.uiowa.edu
space	Zantema_04

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.753186 seconds
cpu usage	0.709413
user time	0.535192
system time	0.174221
max virtual memory	710456.0
max residence set size	6824.0

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)))
b(a(x1:S)) -> a(c(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)))
 B(a(x1:S)) -> A(c(b(x1:S)))
 B(a(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)))
 b(a(x1:S)) -> a(c(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)))
 B(a(x1:S)) -> A(c(b(x1:S)))
 B(a(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)))
 b(a(x1:S)) -> a(c(b(x1:S)))
 b(c(x1:S)) -> c(b(b(x1:S)))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 B(a(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)))
 b(a(x1:S)) -> a(c(b(x1:S)))
 b(c(x1:S)) -> c(b(b(x1:S)))
->->Cycle:
->->-> Pairs:
 A(b(x1:S)) -> A(x1:S)
->->-> Rules:
 a(b(x1:S)) -> b(c(a(x1:S)))
 b(a(x1:S)) -> a(c(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(a(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)))
 b(a(x1:S)) -> a(c(b(x1:S)))
 b(c(x1:S)) -> c(b(b(x1:S)))
-> Usable rules:
 a(b(x1:S)) -> b(c(a(x1:S)))
 b(a(x1:S)) -> a(c(b(x1:S)))
 b(c(x1:S)) -> c(b(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
[B](X) = 2.X

Problem 1.1: 

SCC 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)))
 b(a(x1:S)) -> a(c(b(x1:S)))

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