TRS Standard pair #487068514

details

property	value
status	complete
benchmark	jw08.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n173.star.cs.uiowa.edu
space	Zantema_05

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.951708 seconds
cpu usage	0.769132
user time	0.594015
system time	0.175117
max virtual memory	708240.0
max residence set size	6176.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem 1: 

(VAR v_NonEmpty:S x:S)
(RULES
f(a,f(x:S,a)) -> f(a,f(a,f(f(a,a),x:S)))
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 f(a,f(x:S,a)) -> f(a,f(a,f(f(a,a),x:S)))
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(a,f(x:S,a)) -> F(a,f(f(a,a),x:S))
 F(a,f(x:S,a)) -> F(a,f(a,f(f(a,a),x:S)))
-> Rules:
 f(a,f(x:S,a)) -> f(a,f(a,f(f(a,a),x:S)))

Problem 1: 

SCC Processor:
-> Pairs:
 F(a,f(x:S,a)) -> F(a,f(f(a,a),x:S))
 F(a,f(x:S,a)) -> F(a,f(a,f(f(a,a),x:S)))
-> Rules:
 f(a,f(x:S,a)) -> f(a,f(a,f(f(a,a),x:S)))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(a,f(x:S,a)) -> F(a,f(f(a,a),x:S))
 F(a,f(x:S,a)) -> F(a,f(a,f(f(a,a),x:S)))
->->-> Rules:
 f(a,f(x:S,a)) -> f(a,f(a,f(f(a,a),x:S)))

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 F(a,f(x:S,a)) -> F(a,f(f(a,a),x:S))
 F(a,f(x:S,a)) -> F(a,f(a,f(f(a,a),x:S)))
-> Rules:
 f(a,f(x:S,a)) -> f(a,f(a,f(f(a,a),x:S)))
-> Usable rules:
 f(a,f(x:S,a)) -> f(a,f(a,f(f(a,a),x:S)))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 2
->Bound:
 1
->Interpretation:
 
[f](X1,X2) = [0 1;0 0].X1 + [0 1;0 0].X2
[a] = [0;1]
[fSNonEmpty] = 0
[F](X1,X2) = [1 0;1 0].X2

Problem 1: 

SCC Processor:
-> Pairs:
 F(a,f(x:S,a)) -> F(a,f(a,f(f(a,a),x:S)))
-> Rules:
 f(a,f(x:S,a)) -> f(a,f(a,f(f(a,a),x:S)))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(a,f(x:S,a)) -> F(a,f(a,f(f(a,a),x:S)))
->->-> Rules:
 f(a,f(x:S,a)) -> f(a,f(a,f(f(a,a),x:S)))

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 F(a,f(x:S,a)) -> F(a,f(a,f(f(a,a),x:S)))
-> Rules:
 f(a,f(x:S,a)) -> f(a,f(a,f(f(a,a),x:S)))
-> Usable rules:
 f(a,f(x:S,a)) -> f(a,f(a,f(f(a,a),x:S)))
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 4
->Interpretation:

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