/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


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

The problem is finite.