TRS Standard pair #487068479

details

property	value
status	complete
benchmark	jw34.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n180.star.cs.uiowa.edu
space	Zantema_05

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	1.15725 seconds
cpu usage	0.987322
user time	0.847385
system time	0.139937
max virtual memory	706716.0
max residence set size	5624.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 F(f(a,a),x:S) -> F(f(x:S,f(a,f(a,a))),a)
 F(f(a,a),x:S) -> F(x:S,f(a,f(a,a)))
-> Rules:
 f(f(a,a),x:S) -> f(f(x:S,f(a,f(a,a))),a)
-> Usable rules:
 f(f(a,a),x:S) -> f(f(x:S,f(a,f(a,a))),a)
->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.X1

Problem 1: 

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

Problem 1: 

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

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