/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)
(RULES
f(a,a) -> f(a,b)
f(a,b) -> f(s(a),c)
f(c,c) -> f(a,a)
f(s(X),c) -> f(X,c)
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 f(a,a) -> f(a,b)
 f(a,b) -> f(s(a),c)
 f(c,c) -> f(a,a)
 f(s(X),c) -> f(X,c)
-> 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,a) -> F(a,b)
 F(a,b) -> F(s(a),c)
 F(c,c) -> F(a,a)
 F(s(X),c) -> F(X,c)
-> Rules:
 f(a,a) -> f(a,b)
 f(a,b) -> f(s(a),c)
 f(c,c) -> f(a,a)
 f(s(X),c) -> f(X,c)

Problem 1: 

SCC Processor:
-> Pairs:
 F(a,a) -> F(a,b)
 F(a,b) -> F(s(a),c)
 F(c,c) -> F(a,a)
 F(s(X),c) -> F(X,c)
-> Rules:
 f(a,a) -> f(a,b)
 f(a,b) -> f(s(a),c)
 f(c,c) -> f(a,a)
 f(s(X),c) -> f(X,c)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(a,a) -> F(a,b)
 F(a,b) -> F(s(a),c)
 F(c,c) -> F(a,a)
 F(s(X),c) -> F(X,c)
->->-> Rules:
 f(a,a) -> f(a,b)
 f(a,b) -> f(s(a),c)
 f(c,c) -> f(a,a)
 f(s(X),c) -> f(X,c)

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 F(a,a) -> F(a,b)
 F(a,b) -> F(s(a),c)
 F(c,c) -> F(a,a)
 F(s(X),c) -> F(X,c)
-> Rules:
 f(a,a) -> f(a,b)
 f(a,b) -> f(s(a),c)
 f(c,c) -> f(a,a)
 f(s(X),c) -> f(X,c)
-> Usable rules:
 Empty
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a] = 1
[b] = 2
[c] = 2
[s](X) = X
[F](X1,X2) = X1

Problem 1: 

SCC Processor:
-> Pairs:
 F(a,a) -> F(a,b)
 F(a,b) -> F(s(a),c)
 F(s(X),c) -> F(X,c)
-> Rules:
 f(a,a) -> f(a,b)
 f(a,b) -> f(s(a),c)
 f(c,c) -> f(a,a)
 f(s(X),c) -> f(X,c)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(s(X),c) -> F(X,c)
->->-> Rules:
 f(a,a) -> f(a,b)
 f(a,b) -> f(s(a),c)
 f(c,c) -> f(a,a)
 f(s(X),c) -> f(X,c)

Problem 1: 

Subterm Processor:
-> Pairs:
 F(s(X),c) -> F(X,c)
-> Rules:
 f(a,a) -> f(a,b)
 f(a,b) -> f(s(a),c)
 f(c,c) -> f(a,a)
 f(s(X),c) -> f(X,c)
->Projection:
 pi(F) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 f(a,a) -> f(a,b)
 f(a,b) -> f(s(a),c)
 f(c,c) -> f(a,a)
 f(s(X),c) -> f(X,c)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.