/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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


YES

Problem 1: 

(VAR a k x y)
(RULES
f(cons(a,k),y) -> f(y,k)
f(empty,cons(a,k)) -> f(cons(a,k),k)
f(x,empty) -> x
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(cons(a,k),y) -> F(y,k)
 F(empty,cons(a,k)) -> F(cons(a,k),k)
-> Rules:
 f(cons(a,k),y) -> f(y,k)
 f(empty,cons(a,k)) -> f(cons(a,k),k)
 f(x,empty) -> x

Problem 1: 

SCC Processor:
-> Pairs:
 F(cons(a,k),y) -> F(y,k)
 F(empty,cons(a,k)) -> F(cons(a,k),k)
-> Rules:
 f(cons(a,k),y) -> f(y,k)
 f(empty,cons(a,k)) -> f(cons(a,k),k)
 f(x,empty) -> x
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(cons(a,k),y) -> F(y,k)
 F(empty,cons(a,k)) -> F(cons(a,k),k)
->->-> Rules:
 f(cons(a,k),y) -> f(y,k)
 f(empty,cons(a,k)) -> f(cons(a,k),k)
 f(x,empty) -> x

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 F(cons(a,k),y) -> F(y,k)
 F(empty,cons(a,k)) -> F(cons(a,k),k)
-> Rules:
 f(cons(a,k),y) -> f(y,k)
 f(empty,cons(a,k)) -> f(cons(a,k),k)
 f(x,empty) -> x
-> Usable rules:
 Empty
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[cons](X1,X2) = 2.X1 + 2.X2 + 2
[empty] = 0
[F](X1,X2) = X1 + 2.X2

Problem 1: 

SCC Processor:
-> Pairs:
 F(empty,cons(a,k)) -> F(cons(a,k),k)
-> Rules:
 f(cons(a,k),y) -> f(y,k)
 f(empty,cons(a,k)) -> f(cons(a,k),k)
 f(x,empty) -> x
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.