/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 p x xs)
(RULES
app(app(and,false),false) -> false
app(app(and,false),true) -> false
app(app(and,true),false) -> false
app(app(and,true),true) -> true
app(app(forall,p),app(app(cons,x),xs)) -> app(app(and,app(p,x)),app(app(forall,p),xs))
app(app(forall,p),nil) -> true
app(app(forsome,p),app(app(cons,x),xs)) -> app(app(or,app(p,x)),app(app(forsome,p),xs))
app(app(forsome,p),nil) -> false
app(app(or,false),false) -> false
app(app(or,false),true) -> true
app(app(or,true),false) -> true
app(app(or,true),true) -> true
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 app(app(and,false),false) -> false
 app(app(and,false),true) -> false
 app(app(and,true),false) -> false
 app(app(and,true),true) -> true
 app(app(forall,p),app(app(cons,x),xs)) -> app(app(and,app(p,x)),app(app(forall,p),xs))
 app(app(forall,p),nil) -> true
 app(app(forsome,p),app(app(cons,x),xs)) -> app(app(or,app(p,x)),app(app(forsome,p),xs))
 app(app(forsome,p),nil) -> false
 app(app(or,false),false) -> false
 app(app(or,false),true) -> true
 app(app(or,true),false) -> true
 app(app(or,true),true) -> true
-> 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(forall,p),app(app(cons,x),xs)) -> APP(app(and,app(p,x)),app(app(forall,p),xs))
 APP(app(forall,p),app(app(cons,x),xs)) -> APP(app(forall,p),xs)
 APP(app(forall,p),app(app(cons,x),xs)) -> APP(and,app(p,x))
 APP(app(forall,p),app(app(cons,x),xs)) -> APP(p,x)
 APP(app(forsome,p),app(app(cons,x),xs)) -> APP(app(forsome,p),xs)
 APP(app(forsome,p),app(app(cons,x),xs)) -> APP(app(or,app(p,x)),app(app(forsome,p),xs))
 APP(app(forsome,p),app(app(cons,x),xs)) -> APP(or,app(p,x))
 APP(app(forsome,p),app(app(cons,x),xs)) -> APP(p,x)
-> Rules:
 app(app(and,false),false) -> false
 app(app(and,false),true) -> false
 app(app(and,true),false) -> false
 app(app(and,true),true) -> true
 app(app(forall,p),app(app(cons,x),xs)) -> app(app(and,app(p,x)),app(app(forall,p),xs))
 app(app(forall,p),nil) -> true
 app(app(forsome,p),app(app(cons,x),xs)) -> app(app(or,app(p,x)),app(app(forsome,p),xs))
 app(app(forsome,p),nil) -> false
 app(app(or,false),false) -> false
 app(app(or,false),true) -> true
 app(app(or,true),false) -> true
 app(app(or,true),true) -> true

Problem 1: 

SCC Processor:
-> Pairs:
 APP(app(forall,p),app(app(cons,x),xs)) -> APP(app(and,app(p,x)),app(app(forall,p),xs))
 APP(app(forall,p),app(app(cons,x),xs)) -> APP(app(forall,p),xs)
 APP(app(forall,p),app(app(cons,x),xs)) -> APP(and,app(p,x))
 APP(app(forall,p),app(app(cons,x),xs)) -> APP(p,x)
 APP(app(forsome,p),app(app(cons,x),xs)) -> APP(app(forsome,p),xs)
 APP(app(forsome,p),app(app(cons,x),xs)) -> APP(app(or,app(p,x)),app(app(forsome,p),xs))
 APP(app(forsome,p),app(app(cons,x),xs)) -> APP(or,app(p,x))
 APP(app(forsome,p),app(app(cons,x),xs)) -> APP(p,x)
-> Rules:
 app(app(and,false),false) -> false
 app(app(and,false),true) -> false
 app(app(and,true),false) -> false
 app(app(and,true),true) -> true
 app(app(forall,p),app(app(cons,x),xs)) -> app(app(and,app(p,x)),app(app(forall,p),xs))
 app(app(forall,p),nil) -> true
 app(app(forsome,p),app(app(cons,x),xs)) -> app(app(or,app(p,x)),app(app(forsome,p),xs))
 app(app(forsome,p),nil) -> false
 app(app(or,false),false) -> false
 app(app(or,false),true) -> true
 app(app(or,true),false) -> true
 app(app(or,true),true) -> true
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 APP(app(forall,p),app(app(cons,x),xs)) -> APP(app(forall,p),xs)
 APP(app(forall,p),app(app(cons,x),xs)) -> APP(p,x)
 APP(app(forsome,p),app(app(cons,x),xs)) -> APP(app(forsome,p),xs)
 APP(app(forsome,p),app(app(cons,x),xs)) -> APP(p,x)
->->-> Rules:
 app(app(and,false),false) -> false
 app(app(and,false),true) -> false
 app(app(and,true),false) -> false
 app(app(and,true),true) -> true
 app(app(forall,p),app(app(cons,x),xs)) -> app(app(and,app(p,x)),app(app(forall,p),xs))
 app(app(forall,p),nil) -> true
 app(app(forsome,p),app(app(cons,x),xs)) -> app(app(or,app(p,x)),app(app(forsome,p),xs))
 app(app(forsome,p),nil) -> false
 app(app(or,false),false) -> false
 app(app(or,false),true) -> true
 app(app(or,true),false) -> true
 app(app(or,true),true) -> true

Problem 1: 

Subterm Processor:
-> Pairs:
 APP(app(forall,p),app(app(cons,x),xs)) -> APP(app(forall,p),xs)
 APP(app(forall,p),app(app(cons,x),xs)) -> APP(p,x)
 APP(app(forsome,p),app(app(cons,x),xs)) -> APP(app(forsome,p),xs)
 APP(app(forsome,p),app(app(cons,x),xs)) -> APP(p,x)
-> Rules:
 app(app(and,false),false) -> false
 app(app(and,false),true) -> false
 app(app(and,true),false) -> false
 app(app(and,true),true) -> true
 app(app(forall,p),app(app(cons,x),xs)) -> app(app(and,app(p,x)),app(app(forall,p),xs))
 app(app(forall,p),nil) -> true
 app(app(forsome,p),app(app(cons,x),xs)) -> app(app(or,app(p,x)),app(app(forsome,p),xs))
 app(app(forsome,p),nil) -> false
 app(app(or,false),false) -> false
 app(app(or,false),true) -> true
 app(app(or,true),false) -> true
 app(app(or,true),true) -> true
->Projection:
 pi(APP) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 APP(app(forall,p),app(app(cons,x),xs)) -> APP(app(forall,p),xs)
 APP(app(forsome,p),app(app(cons,x),xs)) -> APP(app(forsome,p),xs)
-> Rules:
 app(app(and,false),false) -> false
 app(app(and,false),true) -> false
 app(app(and,true),false) -> false
 app(app(and,true),true) -> true
 app(app(forall,p),app(app(cons,x),xs)) -> app(app(and,app(p,x)),app(app(forall,p),xs))
 app(app(forall,p),nil) -> true
 app(app(forsome,p),app(app(cons,x),xs)) -> app(app(or,app(p,x)),app(app(forsome,p),xs))
 app(app(forsome,p),nil) -> false
 app(app(or,false),false) -> false
 app(app(or,false),true) -> true
 app(app(or,true),false) -> true
 app(app(or,true),true) -> true
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 APP(app(forsome,p),app(app(cons,x),xs)) -> APP(app(forsome,p),xs)
->->-> Rules:
 app(app(and,false),false) -> false
 app(app(and,false),true) -> false
 app(app(and,true),false) -> false
 app(app(and,true),true) -> true
 app(app(forall,p),app(app(cons,x),xs)) -> app(app(and,app(p,x)),app(app(forall,p),xs))
 app(app(forall,p),nil) -> true
 app(app(forsome,p),app(app(cons,x),xs)) -> app(app(or,app(p,x)),app(app(forsome,p),xs))
 app(app(forsome,p),nil) -> false
 app(app(or,false),false) -> false
 app(app(or,false),true) -> true
 app(app(or,true),false) -> true
 app(app(or,true),true) -> true
->->Cycle:
->->-> Pairs:
 APP(app(forall,p),app(app(cons,x),xs)) -> APP(app(forall,p),xs)
->->-> Rules:
 app(app(and,false),false) -> false
 app(app(and,false),true) -> false
 app(app(and,true),false) -> false
 app(app(and,true),true) -> true
 app(app(forall,p),app(app(cons,x),xs)) -> app(app(and,app(p,x)),app(app(forall,p),xs))
 app(app(forall,p),nil) -> true
 app(app(forsome,p),app(app(cons,x),xs)) -> app(app(or,app(p,x)),app(app(forsome,p),xs))
 app(app(forsome,p),nil) -> false
 app(app(or,false),false) -> false
 app(app(or,false),true) -> true
 app(app(or,true),false) -> true
 app(app(or,true),true) -> true


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 APP(app(forsome,p),app(app(cons,x),xs)) -> APP(app(forsome,p),xs)
-> Rules:
 app(app(and,false),false) -> false
 app(app(and,false),true) -> false
 app(app(and,true),false) -> false
 app(app(and,true),true) -> true
 app(app(forall,p),app(app(cons,x),xs)) -> app(app(and,app(p,x)),app(app(forall,p),xs))
 app(app(forall,p),nil) -> true
 app(app(forsome,p),app(app(cons,x),xs)) -> app(app(or,app(p,x)),app(app(forsome,p),xs))
 app(app(forsome,p),nil) -> false
 app(app(or,false),false) -> false
 app(app(or,false),true) -> true
 app(app(or,true),false) -> true
 app(app(or,true),true) -> true
->Projection:
 pi(APP) = 2

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 app(app(and,false),false) -> false
 app(app(and,false),true) -> false
 app(app(and,true),false) -> false
 app(app(and,true),true) -> true
 app(app(forall,p),app(app(cons,x),xs)) -> app(app(and,app(p,x)),app(app(forall,p),xs))
 app(app(forall,p),nil) -> true
 app(app(forsome,p),app(app(cons,x),xs)) -> app(app(or,app(p,x)),app(app(forsome,p),xs))
 app(app(forsome,p),nil) -> false
 app(app(or,false),false) -> false
 app(app(or,false),true) -> true
 app(app(or,true),false) -> true
 app(app(or,true),true) -> true
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 APP(app(forall,p),app(app(cons,x),xs)) -> APP(app(forall,p),xs)
-> Rules:
 app(app(and,false),false) -> false
 app(app(and,false),true) -> false
 app(app(and,true),false) -> false
 app(app(and,true),true) -> true
 app(app(forall,p),app(app(cons,x),xs)) -> app(app(and,app(p,x)),app(app(forall,p),xs))
 app(app(forall,p),nil) -> true
 app(app(forsome,p),app(app(cons,x),xs)) -> app(app(or,app(p,x)),app(app(forsome,p),xs))
 app(app(forsome,p),nil) -> false
 app(app(or,false),false) -> false
 app(app(or,false),true) -> true
 app(app(or,true),false) -> true
 app(app(or,true),true) -> true
->Projection:
 pi(APP) = 2

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 app(app(and,false),false) -> false
 app(app(and,false),true) -> false
 app(app(and,true),false) -> false
 app(app(and,true),true) -> true
 app(app(forall,p),app(app(cons,x),xs)) -> app(app(and,app(p,x)),app(app(forall,p),xs))
 app(app(forall,p),nil) -> true
 app(app(forsome,p),app(app(cons,x),xs)) -> app(app(or,app(p,x)),app(app(forsome,p),xs))
 app(app(forsome,p),nil) -> false
 app(app(or,false),false) -> false
 app(app(or,false),true) -> true
 app(app(or,true),false) -> true
 app(app(or,true),true) -> true
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.