TRS Standard pair #487068684

details

property	value
status	complete
benchmark	jw12.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n191.star.cs.uiowa.edu
space	Zantema_05

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.607431 seconds
cpu usage	0.568758
user time	0.405691
system time	0.163067
max virtual memory	566084.0
max residence set size	5868.0

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(f(a,a),f(a,x:S)))
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 f(a,f(x:S,a)) -> f(a,f(f(a,a),f(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(f(a,a),f(a,x:S))
 F(a,f(x:S,a)) -> F(a,f(f(a,a),f(a,x:S)))
 F(a,f(x:S,a)) -> F(a,x:S)
-> Rules:
 f(a,f(x:S,a)) -> f(a,f(f(a,a),f(a,x:S)))

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

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