/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 x y z)
(RULES
and(false,y) -> false
and(x,and(y,y)) -> and(x,y)
and(x,or(y,z)) -> or(and(x,y),and(x,z))
and(x,true) -> x
and(x,x) -> x
or(or(x,y),and(y,z)) -> or(x,y)
or(true,y) -> true
or(x,and(x,y)) -> x
or(x,or(y,y)) -> or(x,y)
or(x,false) -> x
or(x,x) -> x
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 AND(x,and(y,y)) -> AND(x,y)
 AND(x,or(y,z)) -> AND(x,y)
 AND(x,or(y,z)) -> AND(x,z)
 AND(x,or(y,z)) -> OR(and(x,y),and(x,z))
 OR(x,or(y,y)) -> OR(x,y)
-> Rules:
 and(false,y) -> false
 and(x,and(y,y)) -> and(x,y)
 and(x,or(y,z)) -> or(and(x,y),and(x,z))
 and(x,true) -> x
 and(x,x) -> x
 or(or(x,y),and(y,z)) -> or(x,y)
 or(true,y) -> true
 or(x,and(x,y)) -> x
 or(x,or(y,y)) -> or(x,y)
 or(x,false) -> x
 or(x,x) -> x

Problem 1: 

SCC Processor:
-> Pairs:
 AND(x,and(y,y)) -> AND(x,y)
 AND(x,or(y,z)) -> AND(x,y)
 AND(x,or(y,z)) -> AND(x,z)
 AND(x,or(y,z)) -> OR(and(x,y),and(x,z))
 OR(x,or(y,y)) -> OR(x,y)
-> Rules:
 and(false,y) -> false
 and(x,and(y,y)) -> and(x,y)
 and(x,or(y,z)) -> or(and(x,y),and(x,z))
 and(x,true) -> x
 and(x,x) -> x
 or(or(x,y),and(y,z)) -> or(x,y)
 or(true,y) -> true
 or(x,and(x,y)) -> x
 or(x,or(y,y)) -> or(x,y)
 or(x,false) -> x
 or(x,x) -> x
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 OR(x,or(y,y)) -> OR(x,y)
->->-> Rules:
 and(false,y) -> false
 and(x,and(y,y)) -> and(x,y)
 and(x,or(y,z)) -> or(and(x,y),and(x,z))
 and(x,true) -> x
 and(x,x) -> x
 or(or(x,y),and(y,z)) -> or(x,y)
 or(true,y) -> true
 or(x,and(x,y)) -> x
 or(x,or(y,y)) -> or(x,y)
 or(x,false) -> x
 or(x,x) -> x
->->Cycle:
->->-> Pairs:
 AND(x,and(y,y)) -> AND(x,y)
 AND(x,or(y,z)) -> AND(x,y)
 AND(x,or(y,z)) -> AND(x,z)
->->-> Rules:
 and(false,y) -> false
 and(x,and(y,y)) -> and(x,y)
 and(x,or(y,z)) -> or(and(x,y),and(x,z))
 and(x,true) -> x
 and(x,x) -> x
 or(or(x,y),and(y,z)) -> or(x,y)
 or(true,y) -> true
 or(x,and(x,y)) -> x
 or(x,or(y,y)) -> or(x,y)
 or(x,false) -> x
 or(x,x) -> x


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 OR(x,or(y,y)) -> OR(x,y)
-> Rules:
 and(false,y) -> false
 and(x,and(y,y)) -> and(x,y)
 and(x,or(y,z)) -> or(and(x,y),and(x,z))
 and(x,true) -> x
 and(x,x) -> x
 or(or(x,y),and(y,z)) -> or(x,y)
 or(true,y) -> true
 or(x,and(x,y)) -> x
 or(x,or(y,y)) -> or(x,y)
 or(x,false) -> x
 or(x,x) -> x
->Projection:
 pi(OR) = 2

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 and(false,y) -> false
 and(x,and(y,y)) -> and(x,y)
 and(x,or(y,z)) -> or(and(x,y),and(x,z))
 and(x,true) -> x
 and(x,x) -> x
 or(or(x,y),and(y,z)) -> or(x,y)
 or(true,y) -> true
 or(x,and(x,y)) -> x
 or(x,or(y,y)) -> or(x,y)
 or(x,false) -> x
 or(x,x) -> x
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 AND(x,and(y,y)) -> AND(x,y)
 AND(x,or(y,z)) -> AND(x,y)
 AND(x,or(y,z)) -> AND(x,z)
-> Rules:
 and(false,y) -> false
 and(x,and(y,y)) -> and(x,y)
 and(x,or(y,z)) -> or(and(x,y),and(x,z))
 and(x,true) -> x
 and(x,x) -> x
 or(or(x,y),and(y,z)) -> or(x,y)
 or(true,y) -> true
 or(x,and(x,y)) -> x
 or(x,or(y,y)) -> or(x,y)
 or(x,false) -> x
 or(x,x) -> x
->Projection:
 pi(AND) = 2

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 and(false,y) -> false
 and(x,and(y,y)) -> and(x,y)
 and(x,or(y,z)) -> or(and(x,y),and(x,z))
 and(x,true) -> x
 and(x,x) -> x
 or(or(x,y),and(y,z)) -> or(x,y)
 or(true,y) -> true
 or(x,and(x,y)) -> x
 or(x,or(y,y)) -> or(x,y)
 or(x,false) -> x
 or(x,x) -> x
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.