/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 X1 X2 XS)
(RULES
a__tail(cons(X,XS)) -> mark(XS)
a__tail(X) -> tail(X)
a__zeros -> cons(0,zeros)
a__zeros -> zeros
mark(0) -> 0
mark(cons(X1,X2)) -> cons(mark(X1),X2)
mark(tail(X)) -> a__tail(mark(X))
mark(zeros) -> a__zeros
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 A__TAIL(cons(X,XS)) -> MARK(XS)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(tail(X)) -> A__TAIL(mark(X))
 MARK(tail(X)) -> MARK(X)
 MARK(zeros) -> A__ZEROS
-> Rules:
 a__tail(cons(X,XS)) -> mark(XS)
 a__tail(X) -> tail(X)
 a__zeros -> cons(0,zeros)
 a__zeros -> zeros
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(tail(X)) -> a__tail(mark(X))
 mark(zeros) -> a__zeros

Problem 1: 

SCC Processor:
-> Pairs:
 A__TAIL(cons(X,XS)) -> MARK(XS)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(tail(X)) -> A__TAIL(mark(X))
 MARK(tail(X)) -> MARK(X)
 MARK(zeros) -> A__ZEROS
-> Rules:
 a__tail(cons(X,XS)) -> mark(XS)
 a__tail(X) -> tail(X)
 a__zeros -> cons(0,zeros)
 a__zeros -> zeros
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(tail(X)) -> a__tail(mark(X))
 mark(zeros) -> a__zeros
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A__TAIL(cons(X,XS)) -> MARK(XS)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(tail(X)) -> A__TAIL(mark(X))
 MARK(tail(X)) -> MARK(X)
->->-> Rules:
 a__tail(cons(X,XS)) -> mark(XS)
 a__tail(X) -> tail(X)
 a__zeros -> cons(0,zeros)
 a__zeros -> zeros
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(tail(X)) -> a__tail(mark(X))
 mark(zeros) -> a__zeros

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A__TAIL(cons(X,XS)) -> MARK(XS)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(tail(X)) -> A__TAIL(mark(X))
 MARK(tail(X)) -> MARK(X)
-> Rules:
 a__tail(cons(X,XS)) -> mark(XS)
 a__tail(X) -> tail(X)
 a__zeros -> cons(0,zeros)
 a__zeros -> zeros
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(tail(X)) -> a__tail(mark(X))
 mark(zeros) -> a__zeros
-> Usable rules:
 a__tail(cons(X,XS)) -> mark(XS)
 a__tail(X) -> tail(X)
 a__zeros -> cons(0,zeros)
 a__zeros -> zeros
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(tail(X)) -> a__tail(mark(X))
 mark(zeros) -> a__zeros
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a__tail](X) = 2.X + 2
[a__zeros] = 2
[mark](X) = 2.X + 1
[0] = 0
[cons](X1,X2) = 2.X1 + X2 + 1
[tail](X) = 2.X + 2
[zeros] = 1
[A__TAIL](X) = 2.X + 1
[MARK](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(tail(X)) -> A__TAIL(mark(X))
 MARK(tail(X)) -> MARK(X)
-> Rules:
 a__tail(cons(X,XS)) -> mark(XS)
 a__tail(X) -> tail(X)
 a__zeros -> cons(0,zeros)
 a__zeros -> zeros
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(tail(X)) -> a__tail(mark(X))
 mark(zeros) -> a__zeros
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(tail(X)) -> MARK(X)
->->-> Rules:
 a__tail(cons(X,XS)) -> mark(XS)
 a__tail(X) -> tail(X)
 a__zeros -> cons(0,zeros)
 a__zeros -> zeros
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(tail(X)) -> a__tail(mark(X))
 mark(zeros) -> a__zeros

Problem 1: 

Subterm Processor:
-> Pairs:
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(tail(X)) -> MARK(X)
-> Rules:
 a__tail(cons(X,XS)) -> mark(XS)
 a__tail(X) -> tail(X)
 a__zeros -> cons(0,zeros)
 a__zeros -> zeros
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(tail(X)) -> a__tail(mark(X))
 mark(zeros) -> a__zeros
->Projection:
 pi(MARK) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 a__tail(cons(X,XS)) -> mark(XS)
 a__tail(X) -> tail(X)
 a__zeros -> cons(0,zeros)
 a__zeros -> zeros
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(tail(X)) -> a__tail(mark(X))
 mark(zeros) -> a__zeros
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.