/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
active(f(g(X))) -> mark(g(X))
active(c) -> mark(f(g(c)))
f(active(X)) -> f(X)
f(mark(X)) -> f(X)
g(active(X)) -> g(X)
g(mark(X)) -> g(X)
mark(f(X)) -> active(f(X))
mark(g(X)) -> active(g(X))
mark(c) -> active(c)
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 ACTIVE(f(g(X))) -> MARK(g(X))
 ACTIVE(c) -> MARK(f(g(c)))
 F(active(X)) -> F(X)
 F(mark(X)) -> F(X)
 G(active(X)) -> G(X)
 G(mark(X)) -> G(X)
 MARK(f(X)) -> ACTIVE(f(X))
 MARK(g(X)) -> ACTIVE(g(X))
 MARK(c) -> ACTIVE(c)
-> Rules:
 active(f(g(X))) -> mark(g(X))
 active(c) -> mark(f(g(c)))
 f(active(X)) -> f(X)
 f(mark(X)) -> f(X)
 g(active(X)) -> g(X)
 g(mark(X)) -> g(X)
 mark(f(X)) -> active(f(X))
 mark(g(X)) -> active(g(X))
 mark(c) -> active(c)

Problem 1: 

SCC Processor:
-> Pairs:
 ACTIVE(f(g(X))) -> MARK(g(X))
 ACTIVE(c) -> MARK(f(g(c)))
 F(active(X)) -> F(X)
 F(mark(X)) -> F(X)
 G(active(X)) -> G(X)
 G(mark(X)) -> G(X)
 MARK(f(X)) -> ACTIVE(f(X))
 MARK(g(X)) -> ACTIVE(g(X))
 MARK(c) -> ACTIVE(c)
-> Rules:
 active(f(g(X))) -> mark(g(X))
 active(c) -> mark(f(g(c)))
 f(active(X)) -> f(X)
 f(mark(X)) -> f(X)
 g(active(X)) -> g(X)
 g(mark(X)) -> g(X)
 mark(f(X)) -> active(f(X))
 mark(g(X)) -> active(g(X))
 mark(c) -> active(c)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 G(active(X)) -> G(X)
 G(mark(X)) -> G(X)
->->-> Rules:
 active(f(g(X))) -> mark(g(X))
 active(c) -> mark(f(g(c)))
 f(active(X)) -> f(X)
 f(mark(X)) -> f(X)
 g(active(X)) -> g(X)
 g(mark(X)) -> g(X)
 mark(f(X)) -> active(f(X))
 mark(g(X)) -> active(g(X))
 mark(c) -> active(c)
->->Cycle:
->->-> Pairs:
 F(active(X)) -> F(X)
 F(mark(X)) -> F(X)
->->-> Rules:
 active(f(g(X))) -> mark(g(X))
 active(c) -> mark(f(g(c)))
 f(active(X)) -> f(X)
 f(mark(X)) -> f(X)
 g(active(X)) -> g(X)
 g(mark(X)) -> g(X)
 mark(f(X)) -> active(f(X))
 mark(g(X)) -> active(g(X))
 mark(c) -> active(c)
->->Cycle:
->->-> Pairs:
 ACTIVE(f(g(X))) -> MARK(g(X))
 ACTIVE(c) -> MARK(f(g(c)))
 MARK(f(X)) -> ACTIVE(f(X))
 MARK(g(X)) -> ACTIVE(g(X))
 MARK(c) -> ACTIVE(c)
->->-> Rules:
 active(f(g(X))) -> mark(g(X))
 active(c) -> mark(f(g(c)))
 f(active(X)) -> f(X)
 f(mark(X)) -> f(X)
 g(active(X)) -> g(X)
 g(mark(X)) -> g(X)
 mark(f(X)) -> active(f(X))
 mark(g(X)) -> active(g(X))
 mark(c) -> active(c)


The problem is decomposed in 3 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 G(active(X)) -> G(X)
 G(mark(X)) -> G(X)
-> Rules:
 active(f(g(X))) -> mark(g(X))
 active(c) -> mark(f(g(c)))
 f(active(X)) -> f(X)
 f(mark(X)) -> f(X)
 g(active(X)) -> g(X)
 g(mark(X)) -> g(X)
 mark(f(X)) -> active(f(X))
 mark(g(X)) -> active(g(X))
 mark(c) -> active(c)
->Projection:
 pi(G) = 1

Problem 1.1: 

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

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 F(active(X)) -> F(X)
 F(mark(X)) -> F(X)
-> Rules:
 active(f(g(X))) -> mark(g(X))
 active(c) -> mark(f(g(c)))
 f(active(X)) -> f(X)
 f(mark(X)) -> f(X)
 g(active(X)) -> g(X)
 g(mark(X)) -> g(X)
 mark(f(X)) -> active(f(X))
 mark(g(X)) -> active(g(X))
 mark(c) -> active(c)
->Projection:
 pi(F) = 1

Problem 1.2: 

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

The problem is finite.

Problem 1.3: 

Reduction Pair Processor:
-> Pairs:
 ACTIVE(f(g(X))) -> MARK(g(X))
 ACTIVE(c) -> MARK(f(g(c)))
 MARK(f(X)) -> ACTIVE(f(X))
 MARK(g(X)) -> ACTIVE(g(X))
 MARK(c) -> ACTIVE(c)
-> Rules:
 active(f(g(X))) -> mark(g(X))
 active(c) -> mark(f(g(c)))
 f(active(X)) -> f(X)
 f(mark(X)) -> f(X)
 g(active(X)) -> g(X)
 g(mark(X)) -> g(X)
 mark(f(X)) -> active(f(X))
 mark(g(X)) -> active(g(X))
 mark(c) -> active(c)
-> Usable rules:
 f(active(X)) -> f(X)
 f(mark(X)) -> f(X)
 g(active(X)) -> g(X)
 g(mark(X)) -> g(X)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[active](X) = 0
[f](X) = 2
[g](X) = 0
[mark](X) = 0
[c] = 2
[ACTIVE](X) = 2.X + 2
[MARK](X) = 2.X + 2

Problem 1.3: 

SCC Processor:
-> Pairs:
 ACTIVE(c) -> MARK(f(g(c)))
 MARK(f(X)) -> ACTIVE(f(X))
 MARK(g(X)) -> ACTIVE(g(X))
 MARK(c) -> ACTIVE(c)
-> Rules:
 active(f(g(X))) -> mark(g(X))
 active(c) -> mark(f(g(c)))
 f(active(X)) -> f(X)
 f(mark(X)) -> f(X)
 g(active(X)) -> g(X)
 g(mark(X)) -> g(X)
 mark(f(X)) -> active(f(X))
 mark(g(X)) -> active(g(X))
 mark(c) -> active(c)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVE(c) -> MARK(f(g(c)))
 MARK(f(X)) -> ACTIVE(f(X))
->->-> Rules:
 active(f(g(X))) -> mark(g(X))
 active(c) -> mark(f(g(c)))
 f(active(X)) -> f(X)
 f(mark(X)) -> f(X)
 g(active(X)) -> g(X)
 g(mark(X)) -> g(X)
 mark(f(X)) -> active(f(X))
 mark(g(X)) -> active(g(X))
 mark(c) -> active(c)

Problem 1.3: 

Reduction Pair Processor:
-> Pairs:
 ACTIVE(c) -> MARK(f(g(c)))
 MARK(f(X)) -> ACTIVE(f(X))
-> Rules:
 active(f(g(X))) -> mark(g(X))
 active(c) -> mark(f(g(c)))
 f(active(X)) -> f(X)
 f(mark(X)) -> f(X)
 g(active(X)) -> g(X)
 g(mark(X)) -> g(X)
 mark(f(X)) -> active(f(X))
 mark(g(X)) -> active(g(X))
 mark(c) -> active(c)
-> Usable rules:
 f(active(X)) -> f(X)
 f(mark(X)) -> f(X)
 g(active(X)) -> g(X)
 g(mark(X)) -> g(X)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[active](X) = X
[f](X) = 0
[g](X) = X + 2
[mark](X) = 2.X
[c] = 2
[ACTIVE](X) = 2.X + 1
[MARK](X) = 1

Problem 1.3: 

SCC Processor:
-> Pairs:
 MARK(f(X)) -> ACTIVE(f(X))
-> Rules:
 active(f(g(X))) -> mark(g(X))
 active(c) -> mark(f(g(c)))
 f(active(X)) -> f(X)
 f(mark(X)) -> f(X)
 g(active(X)) -> g(X)
 g(mark(X)) -> g(X)
 mark(f(X)) -> active(f(X))
 mark(g(X)) -> active(g(X))
 mark(c) -> active(c)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.