SRS Standard pair #487091646

details

property	value
status	complete
benchmark	z017.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n142.star.cs.uiowa.edu
space	Zantema_04

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.0457071 seconds
cpu usage	0.036904
user time	0.012528
system time	0.024376
max virtual memory	113188.0
max residence set size	5396.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 B(c(x1:S)) -> B(x1:S)
-> Rules:
 a(a(x1:S)) -> a(c(a(x1:S)))
 a(b(x1:S)) -> b(a(a(x1:S)))
 b(c(x1:S)) -> c(b(x1:S))
->Projection:
 pi(B) = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 a(a(x1:S)) -> a(c(a(x1:S)))
 a(b(x1:S)) -> b(a(a(x1:S)))
 b(c(x1:S)) -> c(b(x1:S))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

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

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