TRS Standard pair #487068549

details

property	value
status	complete
benchmark	jw11.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n189.star.cs.uiowa.edu
space	Zantema_05

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.739926 seconds
cpu usage	0.705454
user time	0.522168
system time	0.183286
max virtual memory	452896.0
max residence set size	5936.0

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 F(a,f(x:S,a)) -> F(a,f(f(a,x:S),f(a,a)))
 F(a,f(x:S,a)) -> F(a,x:S)
-> Rules:
 f(a,f(x:S,a)) -> f(a,f(f(a,x:S),f(a,a)))
-> Usable rules:
 f(a,f(x:S,a)) -> f(a,f(f(a,x:S),f(a,a)))
->Interpretation type:
 Linear
->Coefficients:

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