TRS Standard pair #487073354

details

property	value
status	complete
benchmark	017.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	AotoYamada_05

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.043858 seconds
cpu usage	0.037078
user time	0.012587
system time	0.024491
max virtual memory	113188.0
max residence set size	5348.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem 1: 

(VAR v_NonEmpty:S f:S x:S y:S)
(RULES
app(app(app(uncurry,f:S),x:S),y:S) -> app(app(f:S,x:S),y:S)
)

Problem 1: 

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

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 APP(app(app(uncurry,f:S),x:S),y:S) -> APP(app(f:S,x:S),y:S)
 APP(app(app(uncurry,f:S),x:S),y:S) -> APP(f:S,x:S)
-> Rules:
 app(app(app(uncurry,f:S),x:S),y:S) -> app(app(f:S,x:S),y:S)

Problem 1: 

SCC Processor:
-> Pairs:
 APP(app(app(uncurry,f:S),x:S),y:S) -> APP(app(f:S,x:S),y:S)
 APP(app(app(uncurry,f:S),x:S),y:S) -> APP(f:S,x:S)
-> Rules:
 app(app(app(uncurry,f:S),x:S),y:S) -> app(app(f:S,x:S),y:S)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 APP(app(app(uncurry,f:S),x:S),y:S) -> APP(app(f:S,x:S),y:S)
 APP(app(app(uncurry,f:S),x:S),y:S) -> APP(f:S,x:S)
->->-> Rules:
 app(app(app(uncurry,f:S),x:S),y:S) -> app(app(f:S,x:S),y:S)

Problem 1: 

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

Problem 1: 

SCC Processor:
-> Pairs:
 APP(app(app(uncurry,f:S),x:S),y:S) -> APP(f:S,x:S)
-> Rules:
 app(app(app(uncurry,f:S),x:S),y:S) -> app(app(f:S,x:S),y:S)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 APP(app(app(uncurry,f:S),x:S),y:S) -> APP(f:S,x:S)
->->-> Rules:
 app(app(app(uncurry,f:S),x:S),y:S) -> app(app(f:S,x:S),y:S)

Problem 1: 

Subterm Processor:
-> Pairs:
 APP(app(app(uncurry,f:S),x:S),y:S) -> APP(f:S,x:S)
-> Rules:
 app(app(app(uncurry,f:S),x:S),y:S) -> app(app(f:S,x:S),y:S)
->Projection:
 pi(APP) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 app(app(app(uncurry,f:S),x:S),y:S) -> app(app(f:S,x:S),y:S)
->Strongly Connected Components:
 There is no strongly connected component

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