/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
dfib(s(s(x)),y) -> dfib(s(x),dfib(x,y))
)

Problem 1: 

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

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 DFIB(s(s(x)),y) -> DFIB(s(x),dfib(x,y))
 DFIB(s(s(x)),y) -> DFIB(x,y)
-> Rules:
 dfib(s(s(x)),y) -> dfib(s(x),dfib(x,y))

Problem 1: 

SCC Processor:
-> Pairs:
 DFIB(s(s(x)),y) -> DFIB(s(x),dfib(x,y))
 DFIB(s(s(x)),y) -> DFIB(x,y)
-> Rules:
 dfib(s(s(x)),y) -> dfib(s(x),dfib(x,y))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 DFIB(s(s(x)),y) -> DFIB(s(x),dfib(x,y))
 DFIB(s(s(x)),y) -> DFIB(x,y)
->->-> Rules:
 dfib(s(s(x)),y) -> dfib(s(x),dfib(x,y))

Problem 1: 

Subterm Processor:
-> Pairs:
 DFIB(s(s(x)),y) -> DFIB(s(x),dfib(x,y))
 DFIB(s(s(x)),y) -> DFIB(x,y)
-> Rules:
 dfib(s(s(x)),y) -> dfib(s(x),dfib(x,y))
->Projection:
 pi(DFIB) = 1

Problem 1: 

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

The problem is finite.