/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 v_NonEmpty:S x:S y:S z:S)
(RULES
and(or(y:S,z:S),x:S) -> or(and(x:S,y:S),and(x:S,z:S))
and(x:S,or(y:S,z:S)) -> or(and(x:S,y:S),and(x:S,z:S))
not(and(x:S,y:S)) -> or(not(x:S),not(y:S))
not(not(x:S)) -> x:S
not(or(x:S,y:S)) -> and(not(x:S),not(y:S))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 AND(or(y:S,z:S),x:S) -> AND(x:S,y:S)
 AND(or(y:S,z:S),x:S) -> AND(x:S,z:S)
 AND(x:S,or(y:S,z:S)) -> AND(x:S,y:S)
 AND(x:S,or(y:S,z:S)) -> AND(x:S,z:S)
 NOT(and(x:S,y:S)) -> NOT(x:S)
 NOT(and(x:S,y:S)) -> NOT(y:S)
 NOT(or(x:S,y:S)) -> AND(not(x:S),not(y:S))
 NOT(or(x:S,y:S)) -> NOT(x:S)
 NOT(or(x:S,y:S)) -> NOT(y:S)
-> Rules:
 and(or(y:S,z:S),x:S) -> or(and(x:S,y:S),and(x:S,z:S))
 and(x:S,or(y:S,z:S)) -> or(and(x:S,y:S),and(x:S,z:S))
 not(and(x:S,y:S)) -> or(not(x:S),not(y:S))
 not(not(x:S)) -> x:S
 not(or(x:S,y:S)) -> and(not(x:S),not(y:S))

Problem 1: 

SCC Processor:
-> Pairs:
 AND(or(y:S,z:S),x:S) -> AND(x:S,y:S)
 AND(or(y:S,z:S),x:S) -> AND(x:S,z:S)
 AND(x:S,or(y:S,z:S)) -> AND(x:S,y:S)
 AND(x:S,or(y:S,z:S)) -> AND(x:S,z:S)
 NOT(and(x:S,y:S)) -> NOT(x:S)
 NOT(and(x:S,y:S)) -> NOT(y:S)
 NOT(or(x:S,y:S)) -> AND(not(x:S),not(y:S))
 NOT(or(x:S,y:S)) -> NOT(x:S)
 NOT(or(x:S,y:S)) -> NOT(y:S)
-> Rules:
 and(or(y:S,z:S),x:S) -> or(and(x:S,y:S),and(x:S,z:S))
 and(x:S,or(y:S,z:S)) -> or(and(x:S,y:S),and(x:S,z:S))
 not(and(x:S,y:S)) -> or(not(x:S),not(y:S))
 not(not(x:S)) -> x:S
 not(or(x:S,y:S)) -> and(not(x:S),not(y:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 AND(or(y:S,z:S),x:S) -> AND(x:S,y:S)
 AND(or(y:S,z:S),x:S) -> AND(x:S,z:S)
 AND(x:S,or(y:S,z:S)) -> AND(x:S,y:S)
 AND(x:S,or(y:S,z:S)) -> AND(x:S,z:S)
->->-> Rules:
 and(or(y:S,z:S),x:S) -> or(and(x:S,y:S),and(x:S,z:S))
 and(x:S,or(y:S,z:S)) -> or(and(x:S,y:S),and(x:S,z:S))
 not(and(x:S,y:S)) -> or(not(x:S),not(y:S))
 not(not(x:S)) -> x:S
 not(or(x:S,y:S)) -> and(not(x:S),not(y:S))
->->Cycle:
->->-> Pairs:
 NOT(and(x:S,y:S)) -> NOT(x:S)
 NOT(and(x:S,y:S)) -> NOT(y:S)
 NOT(or(x:S,y:S)) -> NOT(x:S)
 NOT(or(x:S,y:S)) -> NOT(y:S)
->->-> Rules:
 and(or(y:S,z:S),x:S) -> or(and(x:S,y:S),and(x:S,z:S))
 and(x:S,or(y:S,z:S)) -> or(and(x:S,y:S),and(x:S,z:S))
 not(and(x:S,y:S)) -> or(not(x:S),not(y:S))
 not(not(x:S)) -> x:S
 not(or(x:S,y:S)) -> and(not(x:S),not(y:S))


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Reduction Pair Processor:
-> Pairs:
 AND(or(y:S,z:S),x:S) -> AND(x:S,y:S)
 AND(or(y:S,z:S),x:S) -> AND(x:S,z:S)
 AND(x:S,or(y:S,z:S)) -> AND(x:S,y:S)
 AND(x:S,or(y:S,z:S)) -> AND(x:S,z:S)
-> Rules:
 and(or(y:S,z:S),x:S) -> or(and(x:S,y:S),and(x:S,z:S))
 and(x:S,or(y:S,z:S)) -> or(and(x:S,y:S),and(x:S,z:S))
 not(and(x:S,y:S)) -> or(not(x:S),not(y:S))
 not(not(x:S)) -> x:S
 not(or(x:S,y:S)) -> and(not(x:S),not(y:S))
-> Usable rules:
 Empty
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[or](X1,X2) = 2.X1 + 2.X2 + 1
[AND](X1,X2) = 2.X1 + 2.X2

Problem 1.1: 

SCC Processor:
-> Pairs:
 AND(or(y:S,z:S),x:S) -> AND(x:S,z:S)
 AND(x:S,or(y:S,z:S)) -> AND(x:S,y:S)
 AND(x:S,or(y:S,z:S)) -> AND(x:S,z:S)
-> Rules:
 and(or(y:S,z:S),x:S) -> or(and(x:S,y:S),and(x:S,z:S))
 and(x:S,or(y:S,z:S)) -> or(and(x:S,y:S),and(x:S,z:S))
 not(and(x:S,y:S)) -> or(not(x:S),not(y:S))
 not(not(x:S)) -> x:S
 not(or(x:S,y:S)) -> and(not(x:S),not(y:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 AND(or(y:S,z:S),x:S) -> AND(x:S,z:S)
 AND(x:S,or(y:S,z:S)) -> AND(x:S,y:S)
 AND(x:S,or(y:S,z:S)) -> AND(x:S,z:S)
->->-> Rules:
 and(or(y:S,z:S),x:S) -> or(and(x:S,y:S),and(x:S,z:S))
 and(x:S,or(y:S,z:S)) -> or(and(x:S,y:S),and(x:S,z:S))
 not(and(x:S,y:S)) -> or(not(x:S),not(y:S))
 not(not(x:S)) -> x:S
 not(or(x:S,y:S)) -> and(not(x:S),not(y:S))

Problem 1.1: 

Reduction Pair Processor:
-> Pairs:
 AND(or(y:S,z:S),x:S) -> AND(x:S,z:S)
 AND(x:S,or(y:S,z:S)) -> AND(x:S,y:S)
 AND(x:S,or(y:S,z:S)) -> AND(x:S,z:S)
-> Rules:
 and(or(y:S,z:S),x:S) -> or(and(x:S,y:S),and(x:S,z:S))
 and(x:S,or(y:S,z:S)) -> or(and(x:S,y:S),and(x:S,z:S))
 not(and(x:S,y:S)) -> or(not(x:S),not(y:S))
 not(not(x:S)) -> x:S
 not(or(x:S,y:S)) -> and(not(x:S),not(y:S))
-> Usable rules:
 Empty
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[or](X1,X2) = 2.X1 + 2.X2 + 2
[AND](X1,X2) = 2.X1 + 2.X2

Problem 1.1: 

SCC Processor:
-> Pairs:
 AND(x:S,or(y:S,z:S)) -> AND(x:S,y:S)
 AND(x:S,or(y:S,z:S)) -> AND(x:S,z:S)
-> Rules:
 and(or(y:S,z:S),x:S) -> or(and(x:S,y:S),and(x:S,z:S))
 and(x:S,or(y:S,z:S)) -> or(and(x:S,y:S),and(x:S,z:S))
 not(and(x:S,y:S)) -> or(not(x:S),not(y:S))
 not(not(x:S)) -> x:S
 not(or(x:S,y:S)) -> and(not(x:S),not(y:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 AND(x:S,or(y:S,z:S)) -> AND(x:S,y:S)
 AND(x:S,or(y:S,z:S)) -> AND(x:S,z:S)
->->-> Rules:
 and(or(y:S,z:S),x:S) -> or(and(x:S,y:S),and(x:S,z:S))
 and(x:S,or(y:S,z:S)) -> or(and(x:S,y:S),and(x:S,z:S))
 not(and(x:S,y:S)) -> or(not(x:S),not(y:S))
 not(not(x:S)) -> x:S
 not(or(x:S,y:S)) -> and(not(x:S),not(y:S))

Problem 1.1: 

Subterm Processor:
-> Pairs:
 AND(x:S,or(y:S,z:S)) -> AND(x:S,y:S)
 AND(x:S,or(y:S,z:S)) -> AND(x:S,z:S)
-> Rules:
 and(or(y:S,z:S),x:S) -> or(and(x:S,y:S),and(x:S,z:S))
 and(x:S,or(y:S,z:S)) -> or(and(x:S,y:S),and(x:S,z:S))
 not(and(x:S,y:S)) -> or(not(x:S),not(y:S))
 not(not(x:S)) -> x:S
 not(or(x:S,y:S)) -> and(not(x:S),not(y:S))
->Projection:
 pi(AND) = 2

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 and(or(y:S,z:S),x:S) -> or(and(x:S,y:S),and(x:S,z:S))
 and(x:S,or(y:S,z:S)) -> or(and(x:S,y:S),and(x:S,z:S))
 not(and(x:S,y:S)) -> or(not(x:S),not(y:S))
 not(not(x:S)) -> x:S
 not(or(x:S,y:S)) -> and(not(x:S),not(y:S))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 NOT(and(x:S,y:S)) -> NOT(x:S)
 NOT(and(x:S,y:S)) -> NOT(y:S)
 NOT(or(x:S,y:S)) -> NOT(x:S)
 NOT(or(x:S,y:S)) -> NOT(y:S)
-> Rules:
 and(or(y:S,z:S),x:S) -> or(and(x:S,y:S),and(x:S,z:S))
 and(x:S,or(y:S,z:S)) -> or(and(x:S,y:S),and(x:S,z:S))
 not(and(x:S,y:S)) -> or(not(x:S),not(y:S))
 not(not(x:S)) -> x:S
 not(or(x:S,y:S)) -> and(not(x:S),not(y:S))
->Projection:
 pi(NOT) = 1

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 and(or(y:S,z:S),x:S) -> or(and(x:S,y:S),and(x:S,z:S))
 and(x:S,or(y:S,z:S)) -> or(and(x:S,y:S),and(x:S,z:S))
 not(and(x:S,y:S)) -> or(not(x:S),not(y:S))
 not(not(x:S)) -> x:S
 not(or(x:S,y:S)) -> and(not(x:S),not(y:S))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.