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


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YES

Problem 1: 

(VAR f x xs y)
(RULES
app(app(app(if,false),x),y) -> y
app(app(app(if,true),x),y) -> x
app(app(filter,f),app(app(cons,x),xs)) -> app(app(app(if,app(f,x)),app(app(cons,x),app(app(filter,f),xs))),app(app(filter,f),xs))
app(app(filter,f),nil) -> nil
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 app(app(app(if,false),x),y) -> y
 app(app(app(if,true),x),y) -> x
 app(app(filter,f),app(app(cons,x),xs)) -> app(app(app(if,app(f,x)),app(app(cons,x),app(app(filter,f),xs))),app(app(filter,f),xs))
 app(app(filter,f),nil) -> 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(filter,f),app(app(cons,x),xs)) -> APP(app(app(if,app(f,x)),app(app(cons,x),app(app(filter,f),xs))),app(app(filter,f),xs))
 APP(app(filter,f),app(app(cons,x),xs)) -> APP(app(cons,x),app(app(filter,f),xs))
 APP(app(filter,f),app(app(cons,x),xs)) -> APP(app(filter,f),xs)
 APP(app(filter,f),app(app(cons,x),xs)) -> APP(app(if,app(f,x)),app(app(cons,x),app(app(filter,f),xs)))
 APP(app(filter,f),app(app(cons,x),xs)) -> APP(if,app(f,x))
 APP(app(filter,f),app(app(cons,x),xs)) -> APP(f,x)
-> Rules:
 app(app(app(if,false),x),y) -> y
 app(app(app(if,true),x),y) -> x
 app(app(filter,f),app(app(cons,x),xs)) -> app(app(app(if,app(f,x)),app(app(cons,x),app(app(filter,f),xs))),app(app(filter,f),xs))
 app(app(filter,f),nil) -> nil

Problem 1: 

SCC Processor:
-> Pairs:
 APP(app(filter,f),app(app(cons,x),xs)) -> APP(app(app(if,app(f,x)),app(app(cons,x),app(app(filter,f),xs))),app(app(filter,f),xs))
 APP(app(filter,f),app(app(cons,x),xs)) -> APP(app(cons,x),app(app(filter,f),xs))
 APP(app(filter,f),app(app(cons,x),xs)) -> APP(app(filter,f),xs)
 APP(app(filter,f),app(app(cons,x),xs)) -> APP(app(if,app(f,x)),app(app(cons,x),app(app(filter,f),xs)))
 APP(app(filter,f),app(app(cons,x),xs)) -> APP(if,app(f,x))
 APP(app(filter,f),app(app(cons,x),xs)) -> APP(f,x)
-> Rules:
 app(app(app(if,false),x),y) -> y
 app(app(app(if,true),x),y) -> x
 app(app(filter,f),app(app(cons,x),xs)) -> app(app(app(if,app(f,x)),app(app(cons,x),app(app(filter,f),xs))),app(app(filter,f),xs))
 app(app(filter,f),nil) -> nil
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 APP(app(filter,f),app(app(cons,x),xs)) -> APP(app(filter,f),xs)
 APP(app(filter,f),app(app(cons,x),xs)) -> APP(f,x)
->->-> Rules:
 app(app(app(if,false),x),y) -> y
 app(app(app(if,true),x),y) -> x
 app(app(filter,f),app(app(cons,x),xs)) -> app(app(app(if,app(f,x)),app(app(cons,x),app(app(filter,f),xs))),app(app(filter,f),xs))
 app(app(filter,f),nil) -> nil

Problem 1: 

Subterm Processor:
-> Pairs:
 APP(app(filter,f),app(app(cons,x),xs)) -> APP(app(filter,f),xs)
 APP(app(filter,f),app(app(cons,x),xs)) -> APP(f,x)
-> Rules:
 app(app(app(if,false),x),y) -> y
 app(app(app(if,true),x),y) -> x
 app(app(filter,f),app(app(cons,x),xs)) -> app(app(app(if,app(f,x)),app(app(cons,x),app(app(filter,f),xs))),app(app(filter,f),xs))
 app(app(filter,f),nil) -> nil
->Projection:
 pi(APP) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 APP(app(filter,f),app(app(cons,x),xs)) -> APP(app(filter,f),xs)
-> Rules:
 app(app(app(if,false),x),y) -> y
 app(app(app(if,true),x),y) -> x
 app(app(filter,f),app(app(cons,x),xs)) -> app(app(app(if,app(f,x)),app(app(cons,x),app(app(filter,f),xs))),app(app(filter,f),xs))
 app(app(filter,f),nil) -> nil
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 APP(app(filter,f),app(app(cons,x),xs)) -> APP(app(filter,f),xs)
->->-> Rules:
 app(app(app(if,false),x),y) -> y
 app(app(app(if,true),x),y) -> x
 app(app(filter,f),app(app(cons,x),xs)) -> app(app(app(if,app(f,x)),app(app(cons,x),app(app(filter,f),xs))),app(app(filter,f),xs))
 app(app(filter,f),nil) -> nil

Problem 1: 

Subterm Processor:
-> Pairs:
 APP(app(filter,f),app(app(cons,x),xs)) -> APP(app(filter,f),xs)
-> Rules:
 app(app(app(if,false),x),y) -> y
 app(app(app(if,true),x),y) -> x
 app(app(filter,f),app(app(cons,x),xs)) -> app(app(app(if,app(f,x)),app(app(cons,x),app(app(filter,f),xs))),app(app(filter,f),xs))
 app(app(filter,f),nil) -> nil
->Projection:
 pi(APP) = 2

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 app(app(app(if,false),x),y) -> y
 app(app(app(if,true),x),y) -> x
 app(app(filter,f),app(app(cons,x),xs)) -> app(app(app(if,app(f,x)),app(app(cons,x),app(app(filter,f),xs))),app(app(filter,f),xs))
 app(app(filter,f),nil) -> nil
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.