/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 L X Y)
(STRATEGY CONTEXTSENSITIVE
(eq)
(inf 1)
(length 1)
(take 1 2)
(0)
(cons)
(false)
(nil)
(s)
(true)
)
(RULES
eq(0,0) -> true
eq(s(X),s(Y)) -> eq(X,Y)
eq(X,Y) -> false
inf(X) -> cons(X,inf(s(X)))
length(cons(X,L)) -> s(length(L))
length(nil) -> 0
take(0,X) -> nil
take(s(X),cons(Y,L)) -> cons(Y,take(X,L))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 EQ(s(X),s(Y)) -> EQ(X,Y)
-> Rules:
 eq(0,0) -> true
 eq(s(X),s(Y)) -> eq(X,Y)
 eq(X,Y) -> false
 inf(X) -> cons(X,inf(s(X)))
 length(cons(X,L)) -> s(length(L))
 length(nil) -> 0
 take(0,X) -> nil
 take(s(X),cons(Y,L)) -> cons(Y,take(X,L))
-> Unhiding Rules:
 Empty

Problem 1: 

SCC Processor:
-> Pairs:
 EQ(s(X),s(Y)) -> EQ(X,Y)
-> Rules:
 eq(0,0) -> true
 eq(s(X),s(Y)) -> eq(X,Y)
 eq(X,Y) -> false
 inf(X) -> cons(X,inf(s(X)))
 length(cons(X,L)) -> s(length(L))
 length(nil) -> 0
 take(0,X) -> nil
 take(s(X),cons(Y,L)) -> cons(Y,take(X,L))
-> Unhiding rules:
 Empty
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 EQ(s(X),s(Y)) -> EQ(X,Y)
->->-> Rules:
 eq(0,0) -> true
 eq(s(X),s(Y)) -> eq(X,Y)
 eq(X,Y) -> false
 inf(X) -> cons(X,inf(s(X)))
 length(cons(X,L)) -> s(length(L))
 length(nil) -> 0
 take(0,X) -> nil
 take(s(X),cons(Y,L)) -> cons(Y,take(X,L))
->->-> Unhiding rules:
 Empty

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 EQ(s(X),s(Y)) -> EQ(X,Y)
-> Rules:
 eq(0,0) -> true
 eq(s(X),s(Y)) -> eq(X,Y)
 eq(X,Y) -> false
 inf(X) -> cons(X,inf(s(X)))
 length(cons(X,L)) -> s(length(L))
 length(nil) -> 0
 take(0,X) -> nil
 take(s(X),cons(Y,L)) -> cons(Y,take(X,L))
-> Unhiding rules:
 Empty
-> Usable rules:
 Empty
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[s](X) = 2.X + 2
[EQ](X1,X2) = 2.X1 + 2.X2

Problem 1: 

Basic Processor:
-> Pairs:
 Empty
-> Rules:
 eq(0,0) -> true
 eq(s(X),s(Y)) -> eq(X,Y)
 eq(X,Y) -> false
 inf(X) -> cons(X,inf(s(X)))
 length(cons(X,L)) -> s(length(L))
 length(nil) -> 0
 take(0,X) -> nil
 take(s(X),cons(Y,L)) -> cons(Y,take(X,L))
-> Unhiding rules:
 Empty
-> Result:
 Set P is empty

The problem is finite.