/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 v_NonEmpty:S f:S t:S x:S)
(RULES
app(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> app(app(cons,app(f:S,x:S)),app(app(fmap,t:S),x:S))
app(app(fmap,fnil),x:S) -> nil
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 app(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> app(app(cons,app(f:S,x:S)),app(app(fmap,t:S),x:S))
 app(app(fmap,fnil),x:S) -> nil
-> 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(fmap,app(app(fcons,f:S),t:S)),x:S) -> APP(app(cons,app(f:S,x:S)),app(app(fmap,t:S),x:S))
 APP(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> APP(app(fmap,t:S),x:S)
 APP(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> APP(cons,app(f:S,x:S))
 APP(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> APP(f:S,x:S)
-> Rules:
 app(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> app(app(cons,app(f:S,x:S)),app(app(fmap,t:S),x:S))
 app(app(fmap,fnil),x:S) -> nil

Problem 1: 

SCC Processor:
-> Pairs:
 APP(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> APP(app(cons,app(f:S,x:S)),app(app(fmap,t:S),x:S))
 APP(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> APP(app(fmap,t:S),x:S)
 APP(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> APP(cons,app(f:S,x:S))
 APP(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> APP(f:S,x:S)
-> Rules:
 app(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> app(app(cons,app(f:S,x:S)),app(app(fmap,t:S),x:S))
 app(app(fmap,fnil),x:S) -> nil
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 APP(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> APP(app(fmap,t:S),x:S)
 APP(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> APP(f:S,x:S)
->->-> Rules:
 app(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> app(app(cons,app(f:S,x:S)),app(app(fmap,t:S),x:S))
 app(app(fmap,fnil),x:S) -> nil

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 APP(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> APP(app(fmap,t:S),x:S)
 APP(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> APP(f:S,x:S)
-> Rules:
 app(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> app(app(cons,app(f:S,x:S)),app(app(fmap,t:S),x:S))
 app(app(fmap,fnil),x:S) -> nil
-> Usable rules:
 app(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> app(app(cons,app(f:S,x:S)),app(app(fmap,t:S),x:S))
 app(app(fmap,fnil),x:S) -> nil
->Interpretation type:
 Simple mixed
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[app](X1,X2) = 2.X1.X2 + 2.X1
[cons] = 0
[fSNonEmpty] = 0
[fcons] = 2
[fmap] = 2
[fnil] = 1
[nil] = 0
[APP](X1,X2) = 2.X1.X2 + 2.X1

Problem 1: 

SCC Processor:
-> Pairs:
 APP(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> APP(f:S,x:S)
-> Rules:
 app(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> app(app(cons,app(f:S,x:S)),app(app(fmap,t:S),x:S))
 app(app(fmap,fnil),x:S) -> nil
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 APP(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> APP(f:S,x:S)
->->-> Rules:
 app(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> app(app(cons,app(f:S,x:S)),app(app(fmap,t:S),x:S))
 app(app(fmap,fnil),x:S) -> nil

Problem 1: 

Subterm Processor:
-> Pairs:
 APP(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> APP(f:S,x:S)
-> Rules:
 app(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> app(app(cons,app(f:S,x:S)),app(app(fmap,t:S),x:S))
 app(app(fmap,fnil),x:S) -> nil
->Projection:
 pi(APP) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 app(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> app(app(cons,app(f:S,x:S)),app(app(fmap,t:S),x:S))
 app(app(fmap,fnil),x:S) -> nil
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.