TRS Standard pair #487069034

details

property	value
status	complete
benchmark	2.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n070.star.cs.uiowa.edu
space	Mixed_TRS

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.562321 seconds
cpu usage	0.541431
user time	0.418638
system time	0.122793
max virtual memory	113188.0
max residence set size	5640.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

Subterm Processor:
-> Pairs:
 F(a,f(f(a,a),x:S)) -> F(a,x:S)
-> Rules:
 f(a,f(f(a,a),x:S)) -> f(f(a,a),f(a,f(a,x:S)))
->Projection:
 pi(F) = 2

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 f(a,f(f(a,a),x:S)) -> f(f(a,a),f(a,f(a,x:S)))

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