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


--------------------------------------------------------------------------------


YES

Problem 1: 

(VAR X X1 X2 Y)
(RULES
a__f(g(X),Y) -> a__f(mark(X),f(g(X),Y))
a__f(X1,X2) -> f(X1,X2)
mark(f(X1,X2)) -> a__f(mark(X1),X2)
mark(g(X)) -> g(mark(X))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 A__F(g(X),Y) -> A__F(mark(X),f(g(X),Y))
 A__F(g(X),Y) -> MARK(X)
 MARK(f(X1,X2)) -> A__F(mark(X1),X2)
 MARK(f(X1,X2)) -> MARK(X1)
 MARK(g(X)) -> MARK(X)
-> Rules:
 a__f(g(X),Y) -> a__f(mark(X),f(g(X),Y))
 a__f(X1,X2) -> f(X1,X2)
 mark(f(X1,X2)) -> a__f(mark(X1),X2)
 mark(g(X)) -> g(mark(X))

Problem 1: 

SCC Processor:
-> Pairs:
 A__F(g(X),Y) -> A__F(mark(X),f(g(X),Y))
 A__F(g(X),Y) -> MARK(X)
 MARK(f(X1,X2)) -> A__F(mark(X1),X2)
 MARK(f(X1,X2)) -> MARK(X1)
 MARK(g(X)) -> MARK(X)
-> Rules:
 a__f(g(X),Y) -> a__f(mark(X),f(g(X),Y))
 a__f(X1,X2) -> f(X1,X2)
 mark(f(X1,X2)) -> a__f(mark(X1),X2)
 mark(g(X)) -> g(mark(X))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A__F(g(X),Y) -> A__F(mark(X),f(g(X),Y))
 A__F(g(X),Y) -> MARK(X)
 MARK(f(X1,X2)) -> A__F(mark(X1),X2)
 MARK(f(X1,X2)) -> MARK(X1)
 MARK(g(X)) -> MARK(X)
->->-> Rules:
 a__f(g(X),Y) -> a__f(mark(X),f(g(X),Y))
 a__f(X1,X2) -> f(X1,X2)
 mark(f(X1,X2)) -> a__f(mark(X1),X2)
 mark(g(X)) -> g(mark(X))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A__F(g(X),Y) -> A__F(mark(X),f(g(X),Y))
 A__F(g(X),Y) -> MARK(X)
 MARK(f(X1,X2)) -> A__F(mark(X1),X2)
 MARK(f(X1,X2)) -> MARK(X1)
 MARK(g(X)) -> MARK(X)
-> Rules:
 a__f(g(X),Y) -> a__f(mark(X),f(g(X),Y))
 a__f(X1,X2) -> f(X1,X2)
 mark(f(X1,X2)) -> a__f(mark(X1),X2)
 mark(g(X)) -> g(mark(X))
-> Usable rules:
 a__f(g(X),Y) -> a__f(mark(X),f(g(X),Y))
 a__f(X1,X2) -> f(X1,X2)
 mark(f(X1,X2)) -> a__f(mark(X1),X2)
 mark(g(X)) -> g(mark(X))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a__f](X1,X2) = 2.X1 + 2
[mark](X) = 2.X + 1
[f](X1,X2) = 2.X1 + 2
[g](X) = 2.X + 2
[A__F](X1,X2) = X1
[MARK](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 A__F(g(X),Y) -> MARK(X)
 MARK(f(X1,X2)) -> A__F(mark(X1),X2)
 MARK(f(X1,X2)) -> MARK(X1)
 MARK(g(X)) -> MARK(X)
-> Rules:
 a__f(g(X),Y) -> a__f(mark(X),f(g(X),Y))
 a__f(X1,X2) -> f(X1,X2)
 mark(f(X1,X2)) -> a__f(mark(X1),X2)
 mark(g(X)) -> g(mark(X))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A__F(g(X),Y) -> MARK(X)
 MARK(f(X1,X2)) -> A__F(mark(X1),X2)
 MARK(f(X1,X2)) -> MARK(X1)
 MARK(g(X)) -> MARK(X)
->->-> Rules:
 a__f(g(X),Y) -> a__f(mark(X),f(g(X),Y))
 a__f(X1,X2) -> f(X1,X2)
 mark(f(X1,X2)) -> a__f(mark(X1),X2)
 mark(g(X)) -> g(mark(X))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A__F(g(X),Y) -> MARK(X)
 MARK(f(X1,X2)) -> A__F(mark(X1),X2)
 MARK(f(X1,X2)) -> MARK(X1)
 MARK(g(X)) -> MARK(X)
-> Rules:
 a__f(g(X),Y) -> a__f(mark(X),f(g(X),Y))
 a__f(X1,X2) -> f(X1,X2)
 mark(f(X1,X2)) -> a__f(mark(X1),X2)
 mark(g(X)) -> g(mark(X))
-> Usable rules:
 a__f(g(X),Y) -> a__f(mark(X),f(g(X),Y))
 a__f(X1,X2) -> f(X1,X2)
 mark(f(X1,X2)) -> a__f(mark(X1),X2)
 mark(g(X)) -> g(mark(X))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a__f](X1,X2) = X1 + 2
[mark](X) = 2.X + 2
[f](X1,X2) = X1 + 2
[g](X) = 2.X + 2
[A__F](X1,X2) = X1 + 2
[MARK](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 MARK(f(X1,X2)) -> A__F(mark(X1),X2)
 MARK(f(X1,X2)) -> MARK(X1)
 MARK(g(X)) -> MARK(X)
-> Rules:
 a__f(g(X),Y) -> a__f(mark(X),f(g(X),Y))
 a__f(X1,X2) -> f(X1,X2)
 mark(f(X1,X2)) -> a__f(mark(X1),X2)
 mark(g(X)) -> g(mark(X))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 MARK(f(X1,X2)) -> MARK(X1)
 MARK(g(X)) -> MARK(X)
->->-> Rules:
 a__f(g(X),Y) -> a__f(mark(X),f(g(X),Y))
 a__f(X1,X2) -> f(X1,X2)
 mark(f(X1,X2)) -> a__f(mark(X1),X2)
 mark(g(X)) -> g(mark(X))

Problem 1: 

Subterm Processor:
-> Pairs:
 MARK(f(X1,X2)) -> MARK(X1)
 MARK(g(X)) -> MARK(X)
-> Rules:
 a__f(g(X),Y) -> a__f(mark(X),f(g(X),Y))
 a__f(X1,X2) -> f(X1,X2)
 mark(f(X1,X2)) -> a__f(mark(X1),X2)
 mark(g(X)) -> g(mark(X))
->Projection:
 pi(MARK) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 a__f(g(X),Y) -> a__f(mark(X),f(g(X),Y))
 a__f(X1,X2) -> f(X1,X2)
 mark(f(X1,X2)) -> a__f(mark(X1),X2)
 mark(g(X)) -> g(mark(X))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.