/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 h:S t:S x:S)
(RULES
app(app(fmap,app(app(cons,f:S),t_f)),x:S) -> app(app(cons,app(f:S,x:S)),app(app(fmap,t_f),x:S))
app(app(fmap,nil),x:S) -> nil
app(app(map,f:S),app(app(cons,h:S),t:S)) -> app(app(cons,app(f:S,h:S)),app(app(map,f:S),t:S))
app(app(map,f:S),nil) -> nil
app(app(twice,f:S),x:S) -> app(f:S,app(f:S,x:S))
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 app(app(fmap,app(app(cons,f:S),t_f)),x:S) -> app(app(cons,app(f:S,x:S)),app(app(fmap,t_f),x:S))
 app(app(fmap,nil),x:S) -> nil
 app(app(map,f:S),app(app(cons,h:S),t:S)) -> app(app(cons,app(f:S,h:S)),app(app(map,f:S),t:S))
 app(app(map,f:S),nil) -> nil
 app(app(twice,f:S),x:S) -> app(f:S,app(f:S,x: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(fmap,app(app(cons,f:S),t_f)),x:S) -> APP(app(cons,app(f:S,x:S)),app(app(fmap,t_f),x:S))
 APP(app(fmap,app(app(cons,f:S),t_f)),x:S) -> APP(cons,app(f:S,x:S))
 APP(app(fmap,app(app(cons,f:S),t_f)),x:S) -> APP(f:S,x:S)
 APP(app(map,f:S),app(app(cons,h:S),t:S)) -> APP(app(cons,app(f:S,h:S)),app(app(map,f:S),t:S))
 APP(app(map,f:S),app(app(cons,h:S),t:S)) -> APP(app(map,f:S),t:S)
 APP(app(map,f:S),app(app(cons,h:S),t:S)) -> APP(cons,app(f:S,h:S))
 APP(app(map,f:S),app(app(cons,h:S),t:S)) -> APP(f:S,h:S)
 APP(app(twice,f:S),x:S) -> APP(f:S,app(f:S,x:S))
 APP(app(twice,f:S),x:S) -> APP(f:S,x:S)
-> Rules:
 app(app(fmap,app(app(cons,f:S),t_f)),x:S) -> app(app(cons,app(f:S,x:S)),app(app(fmap,t_f),x:S))
 app(app(fmap,nil),x:S) -> nil
 app(app(map,f:S),app(app(cons,h:S),t:S)) -> app(app(cons,app(f:S,h:S)),app(app(map,f:S),t:S))
 app(app(map,f:S),nil) -> nil
 app(app(twice,f:S),x:S) -> app(f:S,app(f:S,x:S))

Problem 1: 

SCC Processor:
-> Pairs:
 APP(app(fmap,app(app(cons,f:S),t_f)),x:S) -> APP(app(cons,app(f:S,x:S)),app(app(fmap,t_f),x:S))
 APP(app(fmap,app(app(cons,f:S),t_f)),x:S) -> APP(cons,app(f:S,x:S))
 APP(app(fmap,app(app(cons,f:S),t_f)),x:S) -> APP(f:S,x:S)
 APP(app(map,f:S),app(app(cons,h:S),t:S)) -> APP(app(cons,app(f:S,h:S)),app(app(map,f:S),t:S))
 APP(app(map,f:S),app(app(cons,h:S),t:S)) -> APP(app(map,f:S),t:S)
 APP(app(map,f:S),app(app(cons,h:S),t:S)) -> APP(cons,app(f:S,h:S))
 APP(app(map,f:S),app(app(cons,h:S),t:S)) -> APP(f:S,h:S)
 APP(app(twice,f:S),x:S) -> APP(f:S,app(f:S,x:S))
 APP(app(twice,f:S),x:S) -> APP(f:S,x:S)
-> Rules:
 app(app(fmap,app(app(cons,f:S),t_f)),x:S) -> app(app(cons,app(f:S,x:S)),app(app(fmap,t_f),x:S))
 app(app(fmap,nil),x:S) -> nil
 app(app(map,f:S),app(app(cons,h:S),t:S)) -> app(app(cons,app(f:S,h:S)),app(app(map,f:S),t:S))
 app(app(map,f:S),nil) -> nil
 app(app(twice,f:S),x:S) -> app(f:S,app(f:S,x:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 APP(app(fmap,app(app(cons,f:S),t_f)),x:S) -> APP(f:S,x:S)
 APP(app(map,f:S),app(app(cons,h:S),t:S)) -> APP(app(map,f:S),t:S)
 APP(app(map,f:S),app(app(cons,h:S),t:S)) -> APP(f:S,h:S)
 APP(app(twice,f:S),x:S) -> APP(f:S,app(f:S,x:S))
 APP(app(twice,f:S),x:S) -> APP(f:S,x:S)
->->-> Rules:
 app(app(fmap,app(app(cons,f:S),t_f)),x:S) -> app(app(cons,app(f:S,x:S)),app(app(fmap,t_f),x:S))
 app(app(fmap,nil),x:S) -> nil
 app(app(map,f:S),app(app(cons,h:S),t:S)) -> app(app(cons,app(f:S,h:S)),app(app(map,f:S),t:S))
 app(app(map,f:S),nil) -> nil
 app(app(twice,f:S),x:S) -> app(f:S,app(f:S,x:S))

Problem 1: 

Subterm Processor:
-> Pairs:
 APP(app(fmap,app(app(cons,f:S),t_f)),x:S) -> APP(f:S,x:S)
 APP(app(map,f:S),app(app(cons,h:S),t:S)) -> APP(app(map,f:S),t:S)
 APP(app(map,f:S),app(app(cons,h:S),t:S)) -> APP(f:S,h:S)
 APP(app(twice,f:S),x:S) -> APP(f:S,app(f:S,x:S))
 APP(app(twice,f:S),x:S) -> APP(f:S,x:S)
-> Rules:
 app(app(fmap,app(app(cons,f:S),t_f)),x:S) -> app(app(cons,app(f:S,x:S)),app(app(fmap,t_f),x:S))
 app(app(fmap,nil),x:S) -> nil
 app(app(map,f:S),app(app(cons,h:S),t:S)) -> app(app(cons,app(f:S,h:S)),app(app(map,f:S),t:S))
 app(app(map,f:S),nil) -> nil
 app(app(twice,f:S),x:S) -> app(f:S,app(f:S,x:S))
->Projection:
 pi(APP) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 APP(app(map,f:S),app(app(cons,h:S),t:S)) -> APP(app(map,f:S),t:S)
-> Rules:
 app(app(fmap,app(app(cons,f:S),t_f)),x:S) -> app(app(cons,app(f:S,x:S)),app(app(fmap,t_f),x:S))
 app(app(fmap,nil),x:S) -> nil
 app(app(map,f:S),app(app(cons,h:S),t:S)) -> app(app(cons,app(f:S,h:S)),app(app(map,f:S),t:S))
 app(app(map,f:S),nil) -> nil
 app(app(twice,f:S),x:S) -> app(f:S,app(f:S,x:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 APP(app(map,f:S),app(app(cons,h:S),t:S)) -> APP(app(map,f:S),t:S)
->->-> Rules:
 app(app(fmap,app(app(cons,f:S),t_f)),x:S) -> app(app(cons,app(f:S,x:S)),app(app(fmap,t_f),x:S))
 app(app(fmap,nil),x:S) -> nil
 app(app(map,f:S),app(app(cons,h:S),t:S)) -> app(app(cons,app(f:S,h:S)),app(app(map,f:S),t:S))
 app(app(map,f:S),nil) -> nil
 app(app(twice,f:S),x:S) -> app(f:S,app(f:S,x:S))

Problem 1: 

Subterm Processor:
-> Pairs:
 APP(app(map,f:S),app(app(cons,h:S),t:S)) -> APP(app(map,f:S),t:S)
-> Rules:
 app(app(fmap,app(app(cons,f:S),t_f)),x:S) -> app(app(cons,app(f:S,x:S)),app(app(fmap,t_f),x:S))
 app(app(fmap,nil),x:S) -> nil
 app(app(map,f:S),app(app(cons,h:S),t:S)) -> app(app(cons,app(f:S,h:S)),app(app(map,f:S),t:S))
 app(app(map,f:S),nil) -> nil
 app(app(twice,f:S),x:S) -> app(f:S,app(f:S,x:S))
->Projection:
 pi(APP) = 2

Problem 1: 

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

The problem is finite.