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

Problem 1: 

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

Problem 1: 

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


The problem is decomposed in 2 subproblems.

Problem 1.1: 

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

Problem 1.1: 

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

The problem is finite.

Problem 1.2: 

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

Problem 1.2: 

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

The problem is finite.