/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 x y)
(RULES
f(f(x,a),y) -> f(y,f(x,y))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(f(x,a),y) -> F(x,y)
 F(f(x,a),y) -> F(y,f(x,y))
-> Rules:
 f(f(x,a),y) -> f(y,f(x,y))

Problem 1: 

SCC Processor:
-> Pairs:
 F(f(x,a),y) -> F(x,y)
 F(f(x,a),y) -> F(y,f(x,y))
-> Rules:
 f(f(x,a),y) -> f(y,f(x,y))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(f(x,a),y) -> F(x,y)
 F(f(x,a),y) -> F(y,f(x,y))
->->-> Rules:
 f(f(x,a),y) -> f(y,f(x,y))

Problem 1: 

Forward Instantiation Processor:
-> Pairs:
 F(f(x,a),y) -> F(x,y)
 F(f(x,a),y) -> F(y,f(x,y))
-> Rules:
 f(f(x,a),y) -> f(y,f(x,y))
->Instantiated Pairs:
->->Original Pair:
 F(f(x,a),y) -> F(x,y)
->-> Instantiated pairs:
 F(f(f(x2,a),a),y) -> F(f(x2,a),y)
 F(f(f(x4,a),a),y) -> F(f(x4,a),y)
->->Original Pair:
 F(f(x,a),y) -> F(y,f(x,y))
->-> Instantiated pairs:
 F(f(x,a),f(x2,a)) -> F(f(x2,a),f(x,f(x2,a)))
 F(f(x,a),f(x4,a)) -> F(f(x4,a),f(x,f(x4,a)))

Problem 1: 

SCC Processor:
-> Pairs:
 F(f(f(x2,a),a),y) -> F(f(x2,a),y)
 F(f(f(x4,a),a),y) -> F(f(x4,a),y)
 F(f(x,a),f(x2,a)) -> F(f(x2,a),f(x,f(x2,a)))
 F(f(x,a),f(x4,a)) -> F(f(x4,a),f(x,f(x4,a)))
-> Rules:
 f(f(x,a),y) -> f(y,f(x,y))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(f(f(x2,a),a),y) -> F(f(x2,a),y)
 F(f(f(x4,a),a),y) -> F(f(x4,a),y)
 F(f(x,a),f(x2,a)) -> F(f(x2,a),f(x,f(x2,a)))
 F(f(x,a),f(x4,a)) -> F(f(x4,a),f(x,f(x4,a)))
->->-> Rules:
 f(f(x,a),y) -> f(y,f(x,y))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 F(f(f(x2,a),a),y) -> F(f(x2,a),y)
 F(f(f(x4,a),a),y) -> F(f(x4,a),y)
 F(f(x,a),f(x2,a)) -> F(f(x2,a),f(x,f(x2,a)))
 F(f(x,a),f(x4,a)) -> F(f(x4,a),f(x,f(x4,a)))
-> Rules:
 f(f(x,a),y) -> f(y,f(x,y))
-> Usable rules:
 f(f(x,a),y) -> f(y,f(x,y))
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[f](X1,X2) = 1/2.X2
[a] = 2
[F](X1,X2) = X2

Problem 1: 

SCC Processor:
-> Pairs:
 F(f(f(x2,a),a),y) -> F(f(x2,a),y)
 F(f(f(x4,a),a),y) -> F(f(x4,a),y)
 F(f(x,a),f(x4,a)) -> F(f(x4,a),f(x,f(x4,a)))
-> Rules:
 f(f(x,a),y) -> f(y,f(x,y))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(f(f(x2,a),a),y) -> F(f(x2,a),y)
 F(f(f(x4,a),a),y) -> F(f(x4,a),y)
 F(f(x,a),f(x4,a)) -> F(f(x4,a),f(x,f(x4,a)))
->->-> Rules:
 f(f(x,a),y) -> f(y,f(x,y))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 F(f(f(x2,a),a),y) -> F(f(x2,a),y)
 F(f(f(x4,a),a),y) -> F(f(x4,a),y)
 F(f(x,a),f(x4,a)) -> F(f(x4,a),f(x,f(x4,a)))
-> Rules:
 f(f(x,a),y) -> f(y,f(x,y))
-> Usable rules:
 f(f(x,a),y) -> f(y,f(x,y))
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[f](X1,X2) = 1/2.X2
[a] = 2
[F](X1,X2) = X2

Problem 1: 

SCC Processor:
-> Pairs:
 F(f(f(x2,a),a),y) -> F(f(x2,a),y)
 F(f(f(x4,a),a),y) -> F(f(x4,a),y)
-> Rules:
 f(f(x,a),y) -> f(y,f(x,y))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(f(f(x2,a),a),y) -> F(f(x2,a),y)
 F(f(f(x4,a),a),y) -> F(f(x4,a),y)
->->-> Rules:
 f(f(x,a),y) -> f(y,f(x,y))

Problem 1: 

Subterm Processor:
-> Pairs:
 F(f(f(x2,a),a),y) -> F(f(x2,a),y)
 F(f(f(x4,a),a),y) -> F(f(x4,a),y)
-> Rules:
 f(f(x,a),y) -> f(y,f(x,y))
->Projection:
 pi(F) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 f(f(x,a),y) -> f(y,f(x,y))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.