TRS Standard pair #487068759

details

property	value
status	complete
benchmark	jw13.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n183.star.cs.uiowa.edu
space	Zantema_05

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.083084 seconds
cpu usage	0.077888
user time	0.037107
system time	0.040781
max virtual memory	113188.0
max residence set size	5412.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 F(a,f(a,x:S)) -> F(f(a,x:S),f(a,a))
 F(a,f(a,x:S)) -> F(a,f(f(a,x:S),f(a,a)))
-> Rules:
 f(a,f(a,x:S)) -> f(a,f(f(a,x:S),f(a,a)))
-> Usable rules:
 f(a,f(a,x:S)) -> 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] = 2
[F](X1,X2) = 2.X1 + 2.X2

Problem 1: 

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

Problem 1: 

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

Problem 1: 

SCC Processor:
-> Pairs:
 Empty

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