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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

The problem is finite.