/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)
(RULES
a__f(f(a)) -> c(f(g(f(a))))
a__f(X) -> f(X)
mark(a) -> a
mark(c(X)) -> c(X)
mark(f(X)) -> a__f(mark(X))
mark(g(X)) -> g(mark(X))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 MARK(f(X)) -> A__F(mark(X))
 MARK(f(X)) -> MARK(X)
 MARK(g(X)) -> MARK(X)
-> Rules:
 a__f(f(a)) -> c(f(g(f(a))))
 a__f(X) -> f(X)
 mark(a) -> a
 mark(c(X)) -> c(X)
 mark(f(X)) -> a__f(mark(X))
 mark(g(X)) -> g(mark(X))

Problem 1: 

SCC Processor:
-> Pairs:
 MARK(f(X)) -> A__F(mark(X))
 MARK(f(X)) -> MARK(X)
 MARK(g(X)) -> MARK(X)
-> Rules:
 a__f(f(a)) -> c(f(g(f(a))))
 a__f(X) -> f(X)
 mark(a) -> a
 mark(c(X)) -> c(X)
 mark(f(X)) -> a__f(mark(X))
 mark(g(X)) -> g(mark(X))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 MARK(f(X)) -> MARK(X)
 MARK(g(X)) -> MARK(X)
->->-> Rules:
 a__f(f(a)) -> c(f(g(f(a))))
 a__f(X) -> f(X)
 mark(a) -> a
 mark(c(X)) -> c(X)
 mark(f(X)) -> a__f(mark(X))
 mark(g(X)) -> g(mark(X))

Problem 1: 

Subterm Processor:
-> Pairs:
 MARK(f(X)) -> MARK(X)
 MARK(g(X)) -> MARK(X)
-> Rules:
 a__f(f(a)) -> c(f(g(f(a))))
 a__f(X) -> f(X)
 mark(a) -> a
 mark(c(X)) -> c(X)
 mark(f(X)) -> a__f(mark(X))
 mark(g(X)) -> g(mark(X))
->Projection:
 pi(MARK) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 a__f(f(a)) -> c(f(g(f(a))))
 a__f(X) -> f(X)
 mark(a) -> a
 mark(c(X)) -> c(X)
 mark(f(X)) -> a__f(mark(X))
 mark(g(X)) -> g(mark(X))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.