/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 v_NonEmpty:S x:S)
(RULES
f(a,f(f(a,a),x:S)) -> f(f(a,a),f(a,f(a,x:S)))
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 f(a,f(f(a,a),x:S)) -> f(f(a,a),f(a,f(a,x:S)))
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

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

Problem 1: 

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

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 F(a,f(f(a,a),x:S)) -> F(a,f(a,x:S))
 F(a,f(f(a,a),x:S)) -> F(a,x:S)
-> Rules:
 f(a,f(f(a,a),x:S)) -> f(f(a,a),f(a,f(a,x:S)))
-> Usable rules:
 f(a,f(f(a,a),x:S)) -> f(f(a,a),f(a,f(a,x:S)))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 2
->Bound:
 1
->Interpretation:
 
[f](X1,X2) = [0 0;1 0].X1 + [0 0;0 1].X2 + [1;0]
[a] = 0
[fSNonEmpty] = 0
[F](X1,X2) = [0 1;0 1].X2

Problem 1: 

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

Problem 1: 

Subterm Processor:
-> Pairs:
 F(a,f(f(a,a),x:S)) -> F(a,x:S)
-> Rules:
 f(a,f(f(a,a),x:S)) -> f(f(a,a),f(a,f(a,x:S)))
->Projection:
 pi(F) = 2

Problem 1: 

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

The problem is finite.