/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 X1 X2 Y Z)
(RULES
a__first(0,X) -> nil
a__first(s(X),cons(Y,Z)) -> cons(mark(Y),first(X,Z))
a__first(X1,X2) -> first(X1,X2)
a__from(X) -> cons(mark(X),from(s(X)))
a__from(X) -> from(X)
mark(0) -> 0
mark(cons(X1,X2)) -> cons(mark(X1),X2)
mark(first(X1,X2)) -> a__first(mark(X1),mark(X2))
mark(from(X)) -> a__from(mark(X))
mark(nil) -> nil
mark(s(X)) -> s(mark(X))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 A__FIRST(s(X),cons(Y,Z)) -> MARK(Y)
 A__FROM(X) -> MARK(X)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(first(X1,X2)) -> A__FIRST(mark(X1),mark(X2))
 MARK(first(X1,X2)) -> MARK(X1)
 MARK(first(X1,X2)) -> MARK(X2)
 MARK(from(X)) -> A__FROM(mark(X))
 MARK(from(X)) -> MARK(X)
 MARK(s(X)) -> MARK(X)
-> Rules:
 a__first(0,X) -> nil
 a__first(s(X),cons(Y,Z)) -> cons(mark(Y),first(X,Z))
 a__first(X1,X2) -> first(X1,X2)
 a__from(X) -> cons(mark(X),from(s(X)))
 a__from(X) -> from(X)
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(first(X1,X2)) -> a__first(mark(X1),mark(X2))
 mark(from(X)) -> a__from(mark(X))
 mark(nil) -> nil
 mark(s(X)) -> s(mark(X))

Problem 1: 

SCC Processor:
-> Pairs:
 A__FIRST(s(X),cons(Y,Z)) -> MARK(Y)
 A__FROM(X) -> MARK(X)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(first(X1,X2)) -> A__FIRST(mark(X1),mark(X2))
 MARK(first(X1,X2)) -> MARK(X1)
 MARK(first(X1,X2)) -> MARK(X2)
 MARK(from(X)) -> A__FROM(mark(X))
 MARK(from(X)) -> MARK(X)
 MARK(s(X)) -> MARK(X)
-> Rules:
 a__first(0,X) -> nil
 a__first(s(X),cons(Y,Z)) -> cons(mark(Y),first(X,Z))
 a__first(X1,X2) -> first(X1,X2)
 a__from(X) -> cons(mark(X),from(s(X)))
 a__from(X) -> from(X)
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(first(X1,X2)) -> a__first(mark(X1),mark(X2))
 mark(from(X)) -> a__from(mark(X))
 mark(nil) -> nil
 mark(s(X)) -> s(mark(X))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A__FIRST(s(X),cons(Y,Z)) -> MARK(Y)
 A__FROM(X) -> MARK(X)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(first(X1,X2)) -> A__FIRST(mark(X1),mark(X2))
 MARK(first(X1,X2)) -> MARK(X1)
 MARK(first(X1,X2)) -> MARK(X2)
 MARK(from(X)) -> A__FROM(mark(X))
 MARK(from(X)) -> MARK(X)
 MARK(s(X)) -> MARK(X)
->->-> Rules:
 a__first(0,X) -> nil
 a__first(s(X),cons(Y,Z)) -> cons(mark(Y),first(X,Z))
 a__first(X1,X2) -> first(X1,X2)
 a__from(X) -> cons(mark(X),from(s(X)))
 a__from(X) -> from(X)
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(first(X1,X2)) -> a__first(mark(X1),mark(X2))
 mark(from(X)) -> a__from(mark(X))
 mark(nil) -> nil
 mark(s(X)) -> s(mark(X))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A__FIRST(s(X),cons(Y,Z)) -> MARK(Y)
 A__FROM(X) -> MARK(X)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(first(X1,X2)) -> A__FIRST(mark(X1),mark(X2))
 MARK(first(X1,X2)) -> MARK(X1)
 MARK(first(X1,X2)) -> MARK(X2)
 MARK(from(X)) -> A__FROM(mark(X))
 MARK(from(X)) -> MARK(X)
 MARK(s(X)) -> MARK(X)
-> Rules:
 a__first(0,X) -> nil
 a__first(s(X),cons(Y,Z)) -> cons(mark(Y),first(X,Z))
 a__first(X1,X2) -> first(X1,X2)
 a__from(X) -> cons(mark(X),from(s(X)))
 a__from(X) -> from(X)
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(first(X1,X2)) -> a__first(mark(X1),mark(X2))
 mark(from(X)) -> a__from(mark(X))
 mark(nil) -> nil
 mark(s(X)) -> s(mark(X))
-> Usable rules:
 a__first(0,X) -> nil
 a__first(s(X),cons(Y,Z)) -> cons(mark(Y),first(X,Z))
 a__first(X1,X2) -> first(X1,X2)
 a__from(X) -> cons(mark(X),from(s(X)))
 a__from(X) -> from(X)
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(first(X1,X2)) -> a__first(mark(X1),mark(X2))
 mark(from(X)) -> a__from(mark(X))
 mark(nil) -> nil
 mark(s(X)) -> s(mark(X))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a__first](X1,X2) = X1 + 2.X2 + 2
[a__from](X) = 2.X + 2
[mark](X) = 2.X + 1
[0] = 2
[cons](X1,X2) = X1 + 1
[first](X1,X2) = X1 + 2.X2 + 2
[from](X) = 2.X + 2
[nil] = 1
[s](X) = X + 2
[A__FIRST](X1,X2) = X1 + 2.X2 + 2
[A__FROM](X) = 2.X + 2
[MARK](X) = 2.X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 A__FROM(X) -> MARK(X)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(first(X1,X2)) -> A__FIRST(mark(X1),mark(X2))
 MARK(first(X1,X2)) -> MARK(X1)
 MARK(first(X1,X2)) -> MARK(X2)
 MARK(from(X)) -> A__FROM(mark(X))
 MARK(from(X)) -> MARK(X)
 MARK(s(X)) -> MARK(X)
-> Rules:
 a__first(0,X) -> nil
 a__first(s(X),cons(Y,Z)) -> cons(mark(Y),first(X,Z))
 a__first(X1,X2) -> first(X1,X2)
 a__from(X) -> cons(mark(X),from(s(X)))
 a__from(X) -> from(X)
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(first(X1,X2)) -> a__first(mark(X1),mark(X2))
 mark(from(X)) -> a__from(mark(X))
 mark(nil) -> nil
 mark(s(X)) -> s(mark(X))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A__FROM(X) -> MARK(X)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(first(X1,X2)) -> MARK(X1)
 MARK(first(X1,X2)) -> MARK(X2)
 MARK(from(X)) -> A__FROM(mark(X))
 MARK(from(X)) -> MARK(X)
 MARK(s(X)) -> MARK(X)
->->-> Rules:
 a__first(0,X) -> nil
 a__first(s(X),cons(Y,Z)) -> cons(mark(Y),first(X,Z))
 a__first(X1,X2) -> first(X1,X2)
 a__from(X) -> cons(mark(X),from(s(X)))
 a__from(X) -> from(X)
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(first(X1,X2)) -> a__first(mark(X1),mark(X2))
 mark(from(X)) -> a__from(mark(X))
 mark(nil) -> nil
 mark(s(X)) -> s(mark(X))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A__FROM(X) -> MARK(X)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(first(X1,X2)) -> MARK(X1)
 MARK(first(X1,X2)) -> MARK(X2)
 MARK(from(X)) -> A__FROM(mark(X))
 MARK(from(X)) -> MARK(X)
 MARK(s(X)) -> MARK(X)
-> Rules:
 a__first(0,X) -> nil
 a__first(s(X),cons(Y,Z)) -> cons(mark(Y),first(X,Z))
 a__first(X1,X2) -> first(X1,X2)
 a__from(X) -> cons(mark(X),from(s(X)))
 a__from(X) -> from(X)
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(first(X1,X2)) -> a__first(mark(X1),mark(X2))
 mark(from(X)) -> a__from(mark(X))
 mark(nil) -> nil
 mark(s(X)) -> s(mark(X))
-> Usable rules:
 a__first(0,X) -> nil
 a__first(s(X),cons(Y,Z)) -> cons(mark(Y),first(X,Z))
 a__first(X1,X2) -> first(X1,X2)
 a__from(X) -> cons(mark(X),from(s(X)))
 a__from(X) -> from(X)
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(first(X1,X2)) -> a__first(mark(X1),mark(X2))
 mark(from(X)) -> a__from(mark(X))
 mark(nil) -> nil
 mark(s(X)) -> s(mark(X))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a__first](X1,X2) = X1 + 2.X2 + 2
[a__from](X) = 2.X + 2
[mark](X) = 2.X + 1
[0] = 2
[cons](X1,X2) = X1 + 1
[first](X1,X2) = X1 + 2.X2 + 2
[from](X) = 2.X + 2
[nil] = 2
[s](X) = 2.X + 1
[A__FROM](X) = 2.X + 2
[MARK](X) = 2.X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(first(X1,X2)) -> MARK(X1)
 MARK(first(X1,X2)) -> MARK(X2)
 MARK(from(X)) -> A__FROM(mark(X))
 MARK(from(X)) -> MARK(X)
 MARK(s(X)) -> MARK(X)
-> Rules:
 a__first(0,X) -> nil
 a__first(s(X),cons(Y,Z)) -> cons(mark(Y),first(X,Z))
 a__first(X1,X2) -> first(X1,X2)
 a__from(X) -> cons(mark(X),from(s(X)))
 a__from(X) -> from(X)
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(first(X1,X2)) -> a__first(mark(X1),mark(X2))
 mark(from(X)) -> a__from(mark(X))
 mark(nil) -> nil
 mark(s(X)) -> s(mark(X))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(first(X1,X2)) -> MARK(X1)
 MARK(first(X1,X2)) -> MARK(X2)
 MARK(from(X)) -> MARK(X)
 MARK(s(X)) -> MARK(X)
->->-> Rules:
 a__first(0,X) -> nil
 a__first(s(X),cons(Y,Z)) -> cons(mark(Y),first(X,Z))
 a__first(X1,X2) -> first(X1,X2)
 a__from(X) -> cons(mark(X),from(s(X)))
 a__from(X) -> from(X)
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(first(X1,X2)) -> a__first(mark(X1),mark(X2))
 mark(from(X)) -> a__from(mark(X))
 mark(nil) -> nil
 mark(s(X)) -> s(mark(X))

Problem 1: 

Subterm Processor:
-> Pairs:
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(first(X1,X2)) -> MARK(X1)
 MARK(first(X1,X2)) -> MARK(X2)
 MARK(from(X)) -> MARK(X)
 MARK(s(X)) -> MARK(X)
-> Rules:
 a__first(0,X) -> nil
 a__first(s(X),cons(Y,Z)) -> cons(mark(Y),first(X,Z))
 a__first(X1,X2) -> first(X1,X2)
 a__from(X) -> cons(mark(X),from(s(X)))
 a__from(X) -> from(X)
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(first(X1,X2)) -> a__first(mark(X1),mark(X2))
 mark(from(X)) -> a__from(mark(X))
 mark(nil) -> nil
 mark(s(X)) -> s(mark(X))
->Projection:
 pi(MARK) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 a__first(0,X) -> nil
 a__first(s(X),cons(Y,Z)) -> cons(mark(Y),first(X,Z))
 a__first(X1,X2) -> first(X1,X2)
 a__from(X) -> cons(mark(X),from(s(X)))
 a__from(X) -> from(X)
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(first(X1,X2)) -> a__first(mark(X1),mark(X2))
 mark(from(X)) -> a__from(mark(X))
 mark(nil) -> nil
 mark(s(X)) -> s(mark(X))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.