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


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


YES

Problem 1: 

(VAR f g x xs)
(RULES
app(app(app(comp,f),g),x) -> app(f,app(g,x))
app(app(map,f),app(app(cons,x),xs)) -> app(app(cons,app(f,x)),app(app(map,f),xs))
app(app(map,f),nil) -> nil
app(twice,f) -> app(app(comp,f),f)
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 app(app(app(comp,f),g),x) -> app(f,app(g,x))
 app(app(map,f),app(app(cons,x),xs)) -> app(app(cons,app(f,x)),app(app(map,f),xs))
 app(app(map,f),nil) -> nil
 app(twice,f) -> app(app(comp,f),f)
-> 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(comp,f),g),x) -> APP(f,app(g,x))
 APP(app(app(comp,f),g),x) -> APP(g,x)
 APP(app(map,f),app(app(cons,x),xs)) -> APP(app(cons,app(f,x)),app(app(map,f),xs))
 APP(app(map,f),app(app(cons,x),xs)) -> APP(app(map,f),xs)
 APP(app(map,f),app(app(cons,x),xs)) -> APP(cons,app(f,x))
 APP(app(map,f),app(app(cons,x),xs)) -> APP(f,x)
-> Rules:
 app(app(app(comp,f),g),x) -> app(f,app(g,x))
 app(app(map,f),app(app(cons,x),xs)) -> app(app(cons,app(f,x)),app(app(map,f),xs))
 app(app(map,f),nil) -> nil
 app(twice,f) -> app(app(comp,f),f)

Problem 1: 

SCC Processor:
-> Pairs:
 APP(app(app(comp,f),g),x) -> APP(f,app(g,x))
 APP(app(app(comp,f),g),x) -> APP(g,x)
 APP(app(map,f),app(app(cons,x),xs)) -> APP(app(cons,app(f,x)),app(app(map,f),xs))
 APP(app(map,f),app(app(cons,x),xs)) -> APP(app(map,f),xs)
 APP(app(map,f),app(app(cons,x),xs)) -> APP(cons,app(f,x))
 APP(app(map,f),app(app(cons,x),xs)) -> APP(f,x)
-> Rules:
 app(app(app(comp,f),g),x) -> app(f,app(g,x))
 app(app(map,f),app(app(cons,x),xs)) -> app(app(cons,app(f,x)),app(app(map,f),xs))
 app(app(map,f),nil) -> nil
 app(twice,f) -> app(app(comp,f),f)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 APP(app(app(comp,f),g),x) -> APP(f,app(g,x))
 APP(app(app(comp,f),g),x) -> APP(g,x)
 APP(app(map,f),app(app(cons,x),xs)) -> APP(app(map,f),xs)
 APP(app(map,f),app(app(cons,x),xs)) -> APP(f,x)
->->-> Rules:
 app(app(app(comp,f),g),x) -> app(f,app(g,x))
 app(app(map,f),app(app(cons,x),xs)) -> app(app(cons,app(f,x)),app(app(map,f),xs))
 app(app(map,f),nil) -> nil
 app(twice,f) -> app(app(comp,f),f)

Problem 1: 

Subterm Processor:
-> Pairs:
 APP(app(app(comp,f),g),x) -> APP(f,app(g,x))
 APP(app(app(comp,f),g),x) -> APP(g,x)
 APP(app(map,f),app(app(cons,x),xs)) -> APP(app(map,f),xs)
 APP(app(map,f),app(app(cons,x),xs)) -> APP(f,x)
-> Rules:
 app(app(app(comp,f),g),x) -> app(f,app(g,x))
 app(app(map,f),app(app(cons,x),xs)) -> app(app(cons,app(f,x)),app(app(map,f),xs))
 app(app(map,f),nil) -> nil
 app(twice,f) -> app(app(comp,f),f)
->Projection:
 pi(APP) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 APP(app(map,f),app(app(cons,x),xs)) -> APP(app(map,f),xs)
-> Rules:
 app(app(app(comp,f),g),x) -> app(f,app(g,x))
 app(app(map,f),app(app(cons,x),xs)) -> app(app(cons,app(f,x)),app(app(map,f),xs))
 app(app(map,f),nil) -> nil
 app(twice,f) -> app(app(comp,f),f)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 APP(app(map,f),app(app(cons,x),xs)) -> APP(app(map,f),xs)
->->-> Rules:
 app(app(app(comp,f),g),x) -> app(f,app(g,x))
 app(app(map,f),app(app(cons,x),xs)) -> app(app(cons,app(f,x)),app(app(map,f),xs))
 app(app(map,f),nil) -> nil
 app(twice,f) -> app(app(comp,f),f)

Problem 1: 

Subterm Processor:
-> Pairs:
 APP(app(map,f),app(app(cons,x),xs)) -> APP(app(map,f),xs)
-> Rules:
 app(app(app(comp,f),g),x) -> app(f,app(g,x))
 app(app(map,f),app(app(cons,x),xs)) -> app(app(cons,app(f,x)),app(app(map,f),xs))
 app(app(map,f),nil) -> nil
 app(twice,f) -> app(app(comp,f),f)
->Projection:
 pi(APP) = 2

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 app(app(app(comp,f),g),x) -> app(f,app(g,x))
 app(app(map,f),app(app(cons,x),xs)) -> app(app(cons,app(f,x)),app(app(map,f),xs))
 app(app(map,f),nil) -> nil
 app(twice,f) -> app(app(comp,f),f)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.