/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 x1)
(RULES
0(0(0(0(x1)))) -> 0(1(1(1(x1))))
1(0(0(1(x1)))) -> 0(0(0(0(x1))))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 0#(0(0(0(x1)))) -> 0#(1(1(1(x1))))
 0#(0(0(0(x1)))) -> 1#(1(1(x1)))
 0#(0(0(0(x1)))) -> 1#(1(x1))
 0#(0(0(0(x1)))) -> 1#(x1)
 1#(0(0(1(x1)))) -> 0#(0(0(0(x1))))
 1#(0(0(1(x1)))) -> 0#(0(0(x1)))
 1#(0(0(1(x1)))) -> 0#(0(x1))
 1#(0(0(1(x1)))) -> 0#(x1)
-> Rules:
 0(0(0(0(x1)))) -> 0(1(1(1(x1))))
 1(0(0(1(x1)))) -> 0(0(0(0(x1))))

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(0(x1)))) -> 0#(1(1(1(x1))))
 0#(0(0(0(x1)))) -> 1#(1(1(x1)))
 0#(0(0(0(x1)))) -> 1#(1(x1))
 0#(0(0(0(x1)))) -> 1#(x1)
 1#(0(0(1(x1)))) -> 0#(0(0(0(x1))))
 1#(0(0(1(x1)))) -> 0#(0(0(x1)))
 1#(0(0(1(x1)))) -> 0#(0(x1))
 1#(0(0(1(x1)))) -> 0#(x1)
-> Rules:
 0(0(0(0(x1)))) -> 0(1(1(1(x1))))
 1(0(0(1(x1)))) -> 0(0(0(0(x1))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(0(x1)))) -> 0#(1(1(1(x1))))
 0#(0(0(0(x1)))) -> 1#(1(1(x1)))
 0#(0(0(0(x1)))) -> 1#(1(x1))
 0#(0(0(0(x1)))) -> 1#(x1)
 1#(0(0(1(x1)))) -> 0#(0(0(0(x1))))
 1#(0(0(1(x1)))) -> 0#(0(0(x1)))
 1#(0(0(1(x1)))) -> 0#(0(x1))
 1#(0(0(1(x1)))) -> 0#(x1)
->->-> Rules:
 0(0(0(0(x1)))) -> 0(1(1(1(x1))))
 1(0(0(1(x1)))) -> 0(0(0(0(x1))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(0(x1)))) -> 0#(1(1(1(x1))))
 0#(0(0(0(x1)))) -> 1#(1(1(x1)))
 0#(0(0(0(x1)))) -> 1#(1(x1))
 0#(0(0(0(x1)))) -> 1#(x1)
 1#(0(0(1(x1)))) -> 0#(0(0(0(x1))))
 1#(0(0(1(x1)))) -> 0#(0(0(x1)))
 1#(0(0(1(x1)))) -> 0#(0(x1))
 1#(0(0(1(x1)))) -> 0#(x1)
-> Rules:
 0(0(0(0(x1)))) -> 0(1(1(1(x1))))
 1(0(0(1(x1)))) -> 0(0(0(0(x1))))
-> Usable rules:
 0(0(0(0(x1)))) -> 0(1(1(1(x1))))
 1(0(0(1(x1)))) -> 0(0(0(0(x1))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[1](X) = 2.X + 2
[0#](X) = X + 1
[1#](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(0(x1)))) -> 0#(1(1(1(x1))))
 0#(0(0(0(x1)))) -> 1#(1(x1))
 0#(0(0(0(x1)))) -> 1#(x1)
 1#(0(0(1(x1)))) -> 0#(0(0(0(x1))))
 1#(0(0(1(x1)))) -> 0#(0(0(x1)))
 1#(0(0(1(x1)))) -> 0#(0(x1))
 1#(0(0(1(x1)))) -> 0#(x1)
-> Rules:
 0(0(0(0(x1)))) -> 0(1(1(1(x1))))
 1(0(0(1(x1)))) -> 0(0(0(0(x1))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(0(x1)))) -> 0#(1(1(1(x1))))
 0#(0(0(0(x1)))) -> 1#(1(x1))
 0#(0(0(0(x1)))) -> 1#(x1)
 1#(0(0(1(x1)))) -> 0#(0(0(0(x1))))
 1#(0(0(1(x1)))) -> 0#(0(0(x1)))
 1#(0(0(1(x1)))) -> 0#(0(x1))
 1#(0(0(1(x1)))) -> 0#(x1)
->->-> Rules:
 0(0(0(0(x1)))) -> 0(1(1(1(x1))))
 1(0(0(1(x1)))) -> 0(0(0(0(x1))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(0(x1)))) -> 0#(1(1(1(x1))))
 0#(0(0(0(x1)))) -> 1#(1(x1))
 0#(0(0(0(x1)))) -> 1#(x1)
 1#(0(0(1(x1)))) -> 0#(0(0(0(x1))))
 1#(0(0(1(x1)))) -> 0#(0(0(x1)))
 1#(0(0(1(x1)))) -> 0#(0(x1))
 1#(0(0(1(x1)))) -> 0#(x1)
-> Rules:
 0(0(0(0(x1)))) -> 0(1(1(1(x1))))
 1(0(0(1(x1)))) -> 0(0(0(0(x1))))
-> Usable rules:
 0(0(0(0(x1)))) -> 0(1(1(1(x1))))
 1(0(0(1(x1)))) -> 0(0(0(0(x1))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[1](X) = 2.X + 2
[0#](X) = X + 2
[1#](X) = X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(0(x1)))) -> 0#(1(1(1(x1))))
 0#(0(0(0(x1)))) -> 1#(x1)
 1#(0(0(1(x1)))) -> 0#(0(0(0(x1))))
 1#(0(0(1(x1)))) -> 0#(0(0(x1)))
 1#(0(0(1(x1)))) -> 0#(0(x1))
 1#(0(0(1(x1)))) -> 0#(x1)
-> Rules:
 0(0(0(0(x1)))) -> 0(1(1(1(x1))))
 1(0(0(1(x1)))) -> 0(0(0(0(x1))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(0(x1)))) -> 0#(1(1(1(x1))))
 0#(0(0(0(x1)))) -> 1#(x1)
 1#(0(0(1(x1)))) -> 0#(0(0(0(x1))))
 1#(0(0(1(x1)))) -> 0#(0(0(x1)))
 1#(0(0(1(x1)))) -> 0#(0(x1))
 1#(0(0(1(x1)))) -> 0#(x1)
->->-> Rules:
 0(0(0(0(x1)))) -> 0(1(1(1(x1))))
 1(0(0(1(x1)))) -> 0(0(0(0(x1))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(0(x1)))) -> 0#(1(1(1(x1))))
 0#(0(0(0(x1)))) -> 1#(x1)
 1#(0(0(1(x1)))) -> 0#(0(0(0(x1))))
 1#(0(0(1(x1)))) -> 0#(0(0(x1)))
 1#(0(0(1(x1)))) -> 0#(0(x1))
 1#(0(0(1(x1)))) -> 0#(x1)
-> Rules:
 0(0(0(0(x1)))) -> 0(1(1(1(x1))))
 1(0(0(1(x1)))) -> 0(0(0(0(x1))))
-> Usable rules:
 0(0(0(0(x1)))) -> 0(1(1(1(x1))))
 1(0(0(1(x1)))) -> 0(0(0(0(x1))))
->Interpretation type:
 Simple mixed
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 1
[1](X) = 2.X + 1
[0#](X) = 1/2.X + 1/2
[1#](X) = 1/2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(0(x1)))) -> 0#(1(1(1(x1))))
 0#(0(0(0(x1)))) -> 1#(x1)
 1#(0(0(1(x1)))) -> 0#(0(0(0(x1))))
 1#(0(0(1(x1)))) -> 0#(0(x1))
 1#(0(0(1(x1)))) -> 0#(x1)
-> Rules:
 0(0(0(0(x1)))) -> 0(1(1(1(x1))))
 1(0(0(1(x1)))) -> 0(0(0(0(x1))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(0(x1)))) -> 0#(1(1(1(x1))))
 0#(0(0(0(x1)))) -> 1#(x1)
 1#(0(0(1(x1)))) -> 0#(0(0(0(x1))))
 1#(0(0(1(x1)))) -> 0#(0(x1))
 1#(0(0(1(x1)))) -> 0#(x1)
->->-> Rules:
 0(0(0(0(x1)))) -> 0(1(1(1(x1))))
 1(0(0(1(x1)))) -> 0(0(0(0(x1))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(0(x1)))) -> 0#(1(1(1(x1))))
 0#(0(0(0(x1)))) -> 1#(x1)
 1#(0(0(1(x1)))) -> 0#(0(0(0(x1))))
 1#(0(0(1(x1)))) -> 0#(0(x1))
 1#(0(0(1(x1)))) -> 0#(x1)
-> Rules:
 0(0(0(0(x1)))) -> 0(1(1(1(x1))))
 1(0(0(1(x1)))) -> 0(0(0(0(x1))))
-> Usable rules:
 0(0(0(0(x1)))) -> 0(1(1(1(x1))))
 1(0(0(1(x1)))) -> 0(0(0(0(x1))))
->Interpretation type:
 Simple mixed
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 1/2.X.X + 1/2.X + 2
[1](X) = 1/2.X.X + 1/2.X + 2
[0#](X) = 1/2.X.X + 1/2
[1#](X) = X.X

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(0(x1)))) -> 1#(x1)
 1#(0(0(1(x1)))) -> 0#(0(0(0(x1))))
 1#(0(0(1(x1)))) -> 0#(0(x1))
 1#(0(0(1(x1)))) -> 0#(x1)
-> Rules:
 0(0(0(0(x1)))) -> 0(1(1(1(x1))))
 1(0(0(1(x1)))) -> 0(0(0(0(x1))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(0(x1)))) -> 1#(x1)
 1#(0(0(1(x1)))) -> 0#(0(0(0(x1))))
 1#(0(0(1(x1)))) -> 0#(0(x1))
 1#(0(0(1(x1)))) -> 0#(x1)
->->-> Rules:
 0(0(0(0(x1)))) -> 0(1(1(1(x1))))
 1(0(0(1(x1)))) -> 0(0(0(0(x1))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(0(x1)))) -> 1#(x1)
 1#(0(0(1(x1)))) -> 0#(0(0(0(x1))))
 1#(0(0(1(x1)))) -> 0#(0(x1))
 1#(0(0(1(x1)))) -> 0#(x1)
-> Rules:
 0(0(0(0(x1)))) -> 0(1(1(1(x1))))
 1(0(0(1(x1)))) -> 0(0(0(0(x1))))
-> Usable rules:
 0(0(0(0(x1)))) -> 0(1(1(1(x1))))
 1(0(0(1(x1)))) -> 0(0(0(0(x1))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[1](X) = 2.X + 2
[0#](X) = X
[1#](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 1#(0(0(1(x1)))) -> 0#(0(0(0(x1))))
 1#(0(0(1(x1)))) -> 0#(0(x1))
 1#(0(0(1(x1)))) -> 0#(x1)
-> Rules:
 0(0(0(0(x1)))) -> 0(1(1(1(x1))))
 1(0(0(1(x1)))) -> 0(0(0(0(x1))))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.