SRS Standard pair #487519909

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	n057.star.cs.uiowa.edu
space	Zantema_04

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.088222026825 seconds
cpu usage	0.040272146
max memory	3133440.0

stage attributes

key	value
output-size	2958
starexec-result	YES

output

/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


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))

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