/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES

Problem 1: 

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

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 app(app(app(uncurry,f),x),y) -> app(app(f,x),y)
-> 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),x),y) -> APP(app(f,x),y)
 APP(app(app(uncurry,f),x),y) -> APP(f,x)
-> Rules:
 app(app(app(uncurry,f),x),y) -> app(app(f,x),y)

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

The problem is finite.