SRS Standard pair #487091766

details

property	value
status	complete
benchmark	z072.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n140.star.cs.uiowa.edu
space	Zantema_04

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	1.025 seconds
cpu usage	1.00336
user time	0.915159
system time	0.088204
max virtual memory	582520.0
max residence set size	9380.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem 1: 

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

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 A(l(x1:S)) -> A(x1:S)
 B(l(x1:S)) -> A(r(x1:S))
 B(l(x1:S)) -> B(a(r(x1:S)))
 B(l(x1:S)) -> R(x1:S)
 R(a(a(x1:S))) -> A(a(r(x1:S)))
 R(a(a(x1:S))) -> A(r(x1:S))
 R(a(a(x1:S))) -> R(x1:S)
-> Rules:
 a(l(x1:S)) -> l(a(x1:S))
 b(l(x1:S)) -> b(a(r(x1:S)))
 r(a(a(x1:S))) -> a(a(r(x1:S)))
 r(b(x1:S)) -> l(b(x1:S))

Problem 1: 

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


The problem is decomposed in 3 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 A(l(x1:S)) -> A(x1:S)
-> Rules:
 a(l(x1:S)) -> l(a(x1:S))
 b(l(x1:S)) -> b(a(r(x1:S)))
 r(a(a(x1:S))) -> a(a(r(x1:S)))
 r(b(x1:S)) -> l(b(x1:S))
->Projection:
 pi(A) = 1

Problem 1.1: 

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

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