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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 F(f(a,x),y) -> F(x,f(a,f(h(a),a)))
 F(f(a,x),y) -> F(y,f(x,f(a,f(h(a),a))))
-> Rules:
 f(f(a,x),y) -> f(y,f(x,f(a,f(h(a),a))))
-> Usable rules:
 f(f(a,x),y) -> f(y,f(x,f(a,f(h(a),a))))
->Interpretation type:
 Simple mixed
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[f](X1,X2) = X1.X2 + 1/2.X1
[a] = 2
[h](X) = 0
[F](X1,X2) = X1.X2 + X1

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

The problem is finite.