SRS Standard pair #487083450

details

property	value
status	complete
benchmark	3.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	Mixed_SRS

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.111441 seconds
cpu usage	0.098231
user time	0.044785
system time	0.053446
max virtual memory	113188.0
max residence set size	5432.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A(a(x1:S)) -> A(b(a(x1:S)))
-> Rules:
 a(a(x1:S)) -> a(b(a(x1:S)))
 b(a(b(x1:S))) -> a(c(a(x1:S)))
-> Usable rules:
 a(a(x1:S)) -> a(b(a(x1:S)))
 b(a(b(x1:S))) -> a(c(a(x1:S)))

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