/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 a d k x)
(RULES
f(a,cons(x,k)) -> f(cons(x,a),k)
f(a,empty) -> g(a,empty)
g(cons(x,k),d) -> g(k,cons(x,d))
g(empty,d) -> d
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 f(a,cons(x,k)) -> f(cons(x,a),k)
 f(a,empty) -> g(a,empty)
 g(cons(x,k),d) -> g(k,cons(x,d))
 g(empty,d) -> d
-> 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,cons(x,k)) -> F(cons(x,a),k)
 F(a,empty) -> G(a,empty)
 G(cons(x,k),d) -> G(k,cons(x,d))
-> Rules:
 f(a,cons(x,k)) -> f(cons(x,a),k)
 f(a,empty) -> g(a,empty)
 g(cons(x,k),d) -> g(k,cons(x,d))
 g(empty,d) -> d

Problem 1: 

SCC Processor:
-> Pairs:
 F(a,cons(x,k)) -> F(cons(x,a),k)
 F(a,empty) -> G(a,empty)
 G(cons(x,k),d) -> G(k,cons(x,d))
-> Rules:
 f(a,cons(x,k)) -> f(cons(x,a),k)
 f(a,empty) -> g(a,empty)
 g(cons(x,k),d) -> g(k,cons(x,d))
 g(empty,d) -> d
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 G(cons(x,k),d) -> G(k,cons(x,d))
->->-> Rules:
 f(a,cons(x,k)) -> f(cons(x,a),k)
 f(a,empty) -> g(a,empty)
 g(cons(x,k),d) -> g(k,cons(x,d))
 g(empty,d) -> d
->->Cycle:
->->-> Pairs:
 F(a,cons(x,k)) -> F(cons(x,a),k)
->->-> Rules:
 f(a,cons(x,k)) -> f(cons(x,a),k)
 f(a,empty) -> g(a,empty)
 g(cons(x,k),d) -> g(k,cons(x,d))
 g(empty,d) -> d


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 G(cons(x,k),d) -> G(k,cons(x,d))
-> Rules:
 f(a,cons(x,k)) -> f(cons(x,a),k)
 f(a,empty) -> g(a,empty)
 g(cons(x,k),d) -> g(k,cons(x,d))
 g(empty,d) -> d
->Projection:
 pi(G) = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 f(a,cons(x,k)) -> f(cons(x,a),k)
 f(a,empty) -> g(a,empty)
 g(cons(x,k),d) -> g(k,cons(x,d))
 g(empty,d) -> d
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 F(a,cons(x,k)) -> F(cons(x,a),k)
-> Rules:
 f(a,cons(x,k)) -> f(cons(x,a),k)
 f(a,empty) -> g(a,empty)
 g(cons(x,k),d) -> g(k,cons(x,d))
 g(empty,d) -> d
->Projection:
 pi(F) = 2

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 f(a,cons(x,k)) -> f(cons(x,a),k)
 f(a,empty) -> g(a,empty)
 g(cons(x,k),d) -> g(k,cons(x,d))
 g(empty,d) -> d
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.