/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem 1: 

(VAR X)
(RULES
a__c(X) -> c(X)
a__c(X) -> d(X)
a__f(f(X)) -> a__c(f(g(f(X))))
a__f(X) -> f(X)
a__h(X) -> a__c(d(X))
a__h(X) -> h(X)
mark(c(X)) -> a__c(X)
mark(d(X)) -> d(X)
mark(f(X)) -> a__f(mark(X))
mark(g(X)) -> g(X)
mark(h(X)) -> a__h(mark(X))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 A__F(f(X)) -> A__C(f(g(f(X))))
 A__H(X) -> A__C(d(X))
 MARK(c(X)) -> A__C(X)
 MARK(f(X)) -> A__F(mark(X))
 MARK(f(X)) -> MARK(X)
 MARK(h(X)) -> A__H(mark(X))
 MARK(h(X)) -> MARK(X)
-> Rules:
 a__c(X) -> c(X)
 a__c(X) -> d(X)
 a__f(f(X)) -> a__c(f(g(f(X))))
 a__f(X) -> f(X)
 a__h(X) -> a__c(d(X))
 a__h(X) -> h(X)
 mark(c(X)) -> a__c(X)
 mark(d(X)) -> d(X)
 mark(f(X)) -> a__f(mark(X))
 mark(g(X)) -> g(X)
 mark(h(X)) -> a__h(mark(X))

Problem 1: 

SCC Processor:
-> Pairs:
 A__F(f(X)) -> A__C(f(g(f(X))))
 A__H(X) -> A__C(d(X))
 MARK(c(X)) -> A__C(X)
 MARK(f(X)) -> A__F(mark(X))
 MARK(f(X)) -> MARK(X)
 MARK(h(X)) -> A__H(mark(X))
 MARK(h(X)) -> MARK(X)
-> Rules:
 a__c(X) -> c(X)
 a__c(X) -> d(X)
 a__f(f(X)) -> a__c(f(g(f(X))))
 a__f(X) -> f(X)
 a__h(X) -> a__c(d(X))
 a__h(X) -> h(X)
 mark(c(X)) -> a__c(X)
 mark(d(X)) -> d(X)
 mark(f(X)) -> a__f(mark(X))
 mark(g(X)) -> g(X)
 mark(h(X)) -> a__h(mark(X))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 MARK(f(X)) -> MARK(X)
 MARK(h(X)) -> MARK(X)
->->-> Rules:
 a__c(X) -> c(X)
 a__c(X) -> d(X)
 a__f(f(X)) -> a__c(f(g(f(X))))
 a__f(X) -> f(X)
 a__h(X) -> a__c(d(X))
 a__h(X) -> h(X)
 mark(c(X)) -> a__c(X)
 mark(d(X)) -> d(X)
 mark(f(X)) -> a__f(mark(X))
 mark(g(X)) -> g(X)
 mark(h(X)) -> a__h(mark(X))

Problem 1: 

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

Problem 1: 

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

The problem is finite.