/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 f l r x)
(RULES
app(app(mapbt,f),app(app(app(branch,x),l),r)) -> app(app(app(branch,app(f,x)),app(app(mapbt,f),l)),app(app(mapbt,f),r))
app(app(mapbt,f),app(leaf,x)) -> app(leaf,app(f,x))
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 app(app(mapbt,f),app(app(app(branch,x),l),r)) -> app(app(app(branch,app(f,x)),app(app(mapbt,f),l)),app(app(mapbt,f),r))
 app(app(mapbt,f),app(leaf,x)) -> app(leaf,app(f,x))
-> 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(mapbt,f),app(app(app(branch,x),l),r)) -> APP(app(app(branch,app(f,x)),app(app(mapbt,f),l)),app(app(mapbt,f),r))
 APP(app(mapbt,f),app(app(app(branch,x),l),r)) -> APP(app(branch,app(f,x)),app(app(mapbt,f),l))
 APP(app(mapbt,f),app(app(app(branch,x),l),r)) -> APP(app(mapbt,f),l)
 APP(app(mapbt,f),app(app(app(branch,x),l),r)) -> APP(app(mapbt,f),r)
 APP(app(mapbt,f),app(app(app(branch,x),l),r)) -> APP(branch,app(f,x))
 APP(app(mapbt,f),app(app(app(branch,x),l),r)) -> APP(f,x)
 APP(app(mapbt,f),app(leaf,x)) -> APP(leaf,app(f,x))
 APP(app(mapbt,f),app(leaf,x)) -> APP(f,x)
-> Rules:
 app(app(mapbt,f),app(app(app(branch,x),l),r)) -> app(app(app(branch,app(f,x)),app(app(mapbt,f),l)),app(app(mapbt,f),r))
 app(app(mapbt,f),app(leaf,x)) -> app(leaf,app(f,x))

Problem 1: 

SCC Processor:
-> Pairs:
 APP(app(mapbt,f),app(app(app(branch,x),l),r)) -> APP(app(app(branch,app(f,x)),app(app(mapbt,f),l)),app(app(mapbt,f),r))
 APP(app(mapbt,f),app(app(app(branch,x),l),r)) -> APP(app(branch,app(f,x)),app(app(mapbt,f),l))
 APP(app(mapbt,f),app(app(app(branch,x),l),r)) -> APP(app(mapbt,f),l)
 APP(app(mapbt,f),app(app(app(branch,x),l),r)) -> APP(app(mapbt,f),r)
 APP(app(mapbt,f),app(app(app(branch,x),l),r)) -> APP(branch,app(f,x))
 APP(app(mapbt,f),app(app(app(branch,x),l),r)) -> APP(f,x)
 APP(app(mapbt,f),app(leaf,x)) -> APP(leaf,app(f,x))
 APP(app(mapbt,f),app(leaf,x)) -> APP(f,x)
-> Rules:
 app(app(mapbt,f),app(app(app(branch,x),l),r)) -> app(app(app(branch,app(f,x)),app(app(mapbt,f),l)),app(app(mapbt,f),r))
 app(app(mapbt,f),app(leaf,x)) -> app(leaf,app(f,x))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 APP(app(mapbt,f),app(app(app(branch,x),l),r)) -> APP(app(mapbt,f),l)
 APP(app(mapbt,f),app(app(app(branch,x),l),r)) -> APP(app(mapbt,f),r)
 APP(app(mapbt,f),app(app(app(branch,x),l),r)) -> APP(f,x)
 APP(app(mapbt,f),app(leaf,x)) -> APP(f,x)
->->-> Rules:
 app(app(mapbt,f),app(app(app(branch,x),l),r)) -> app(app(app(branch,app(f,x)),app(app(mapbt,f),l)),app(app(mapbt,f),r))
 app(app(mapbt,f),app(leaf,x)) -> app(leaf,app(f,x))

Problem 1: 

Subterm Processor:
-> Pairs:
 APP(app(mapbt,f),app(app(app(branch,x),l),r)) -> APP(app(mapbt,f),l)
 APP(app(mapbt,f),app(app(app(branch,x),l),r)) -> APP(app(mapbt,f),r)
 APP(app(mapbt,f),app(app(app(branch,x),l),r)) -> APP(f,x)
 APP(app(mapbt,f),app(leaf,x)) -> APP(f,x)
-> Rules:
 app(app(mapbt,f),app(app(app(branch,x),l),r)) -> app(app(app(branch,app(f,x)),app(app(mapbt,f),l)),app(app(mapbt,f),r))
 app(app(mapbt,f),app(leaf,x)) -> app(leaf,app(f,x))
->Projection:
 pi(APP) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 APP(app(mapbt,f),app(app(app(branch,x),l),r)) -> APP(app(mapbt,f),l)
 APP(app(mapbt,f),app(app(app(branch,x),l),r)) -> APP(app(mapbt,f),r)
-> Rules:
 app(app(mapbt,f),app(app(app(branch,x),l),r)) -> app(app(app(branch,app(f,x)),app(app(mapbt,f),l)),app(app(mapbt,f),r))
 app(app(mapbt,f),app(leaf,x)) -> app(leaf,app(f,x))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 APP(app(mapbt,f),app(app(app(branch,x),l),r)) -> APP(app(mapbt,f),l)
 APP(app(mapbt,f),app(app(app(branch,x),l),r)) -> APP(app(mapbt,f),r)
->->-> Rules:
 app(app(mapbt,f),app(app(app(branch,x),l),r)) -> app(app(app(branch,app(f,x)),app(app(mapbt,f),l)),app(app(mapbt,f),r))
 app(app(mapbt,f),app(leaf,x)) -> app(leaf,app(f,x))

Problem 1: 

Subterm Processor:
-> Pairs:
 APP(app(mapbt,f),app(app(app(branch,x),l),r)) -> APP(app(mapbt,f),l)
 APP(app(mapbt,f),app(app(app(branch,x),l),r)) -> APP(app(mapbt,f),r)
-> Rules:
 app(app(mapbt,f),app(app(app(branch,x),l),r)) -> app(app(app(branch,app(f,x)),app(app(mapbt,f),l)),app(app(mapbt,f),r))
 app(app(mapbt,f),app(leaf,x)) -> app(leaf,app(f,x))
->Projection:
 pi(APP) = 2

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 app(app(mapbt,f),app(app(app(branch,x),l),r)) -> app(app(app(branch,app(f,x)),app(app(mapbt,f),l)),app(app(mapbt,f),r))
 app(app(mapbt,f),app(leaf,x)) -> app(leaf,app(f,x))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.