TRS Standard pair #487068699

details

property	value
status	complete
benchmark	jw15.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n181.star.cs.uiowa.edu
space	Zantema_05

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	1.22618 seconds
cpu usage	0.933188
user time	0.766999
system time	0.166189
max virtual memory	707912.0
max residence set size	5656.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 F(x:S,f(a,a)) -> F(f(f(a,a),a),x:S)
 F(x:S,f(a,a)) -> F(a,f(f(f(a,a),a),x:S))
-> Rules:
 f(x:S,f(a,a)) -> f(a,f(f(f(a,a),a),x:S))
-> Usable rules:
 f(x:S,f(a,a)) -> f(a,f(f(f(a,a),a),x:S))
->Interpretation type:
 Simple mixed
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[f](X1,X2) = 1/2.X1.X2
[a] = 1
[fSNonEmpty] = 0
[F](X1,X2) = 2.X1.X2 + 1/2.X2

Problem 1: 

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

Problem 1: 

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

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