SRS Standard pair #487083120

details

property	value
status	complete
benchmark	while2.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n147.star.cs.uiowa.edu
space	Zantema_06

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.221614 seconds
cpu usage	0.20524
user time	0.136778
system time	0.068462
max virtual memory	113188.0
max residence set size	5716.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

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