/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(s(x),s(y)) -> f(x,s(c(s(y))))
f(x,c(y)) -> f(x,s(f(y,y)))
)

Problem 1: 

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

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(s(x),s(y)) -> F(x,s(c(s(y))))
 F(x,c(y)) -> F(x,s(f(y,y)))
 F(x,c(y)) -> F(y,y)
-> Rules:
 f(s(x),s(y)) -> f(x,s(c(s(y))))
 f(x,c(y)) -> f(x,s(f(y,y)))

Problem 1: 

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


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 F(s(x),s(y)) -> F(x,s(c(s(y))))
-> Rules:
 f(s(x),s(y)) -> f(x,s(c(s(y))))
 f(x,c(y)) -> f(x,s(f(y,y)))
->Projection:
 pi(F) = 1

Problem 1.1: 

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

The problem is finite.

Problem 1.2: 

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

Problem 1.2: 

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

The problem is finite.