/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)
(RULES
a -> b
f(a) -> b
g(x) -> g(a) | f(x) -> x
)

Problem 1: 
Valid CTRS Processor:
-> Rules:
 a -> b
 f(a) -> b
 g(x) -> g(a) | f(x) -> x
-> The system is a deterministic 3-CTRS.

Problem 1: 

Dependency Pairs Processor:

Conditional Termination Problem 1:
-> Pairs:
 G(x) -> A | f(x) -> x
 G(x) -> G(a) | f(x) -> x
-> QPairs:
 Empty
-> Rules:
 a -> b
 f(a) -> b
 g(x) -> g(a) | f(x) -> x

Conditional Termination Problem 2:
-> Pairs:
 G(x) -> F(x)
-> QPairs:
 G(x) -> A | f(x) -> x
 G(x) -> G(a) | f(x) -> x
-> Rules:
 a -> b
 f(a) -> b
 g(x) -> g(a) | f(x) -> x


The problem is decomposed in 2 subproblems.

Problem 1.1: 

SCC Processor:
-> Pairs:
 G(x) -> A | f(x) -> x
 G(x) -> G(a) | f(x) -> x
-> QPairs:
 Empty
-> Rules:
 a -> b
 f(a) -> b
 g(x) -> g(a) | f(x) -> x
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 G(x) -> G(a) | f(x) -> x
->->-> Rules:
 a -> b
 f(a) -> b
 g(x) -> g(a) | f(x) -> x

Problem 1.1: 

Unsatisfiable Rule Processor:
-> Pairs:
 G(x) -> G(a) | f(x) -> x
-> QPairs:
 Empty
-> Rules:
 a -> b
 f(a) -> b
 g(x) -> g(a) | f(x) -> x
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a] = 1
[f](X) = X
[g](X) = 2.X
[b] = 0
[A] = 0
[F](X) = 0
[G](X) = 0

Problem 1.1: 

SCC Processor:
-> Pairs:
 G(x) -> G(a) | f(x) -> x
-> QPairs:
 Empty
-> Rules:
 a -> b
 f(a) -> b
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 G(x) -> G(a) | f(x) -> x
->->-> Rules:
 a -> b
 f(a) -> b

Problem 1.1: 

Unsatisfiable Rule Processor:
-> Pairs:
 G(x) -> G(a) | f(x) -> x
-> QPairs:
 Empty
-> Rules:
 a -> b
 f(a) -> b
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a] = 1
[f](X) = X
[g](X) = 2.X
[b] = 0
[A] = 0
[F](X) = 0
[G](X) = 0

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> QPairs:
 Empty
-> Rules:
 a -> b
 f(a) -> b
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

SCC Processor:
-> Pairs:
 G(x) -> F(x)
-> QPairs:
 G(x) -> A | f(x) -> x
 G(x) -> G(a) | f(x) -> x
-> Rules:
 a -> b
 f(a) -> b
 g(x) -> g(a) | f(x) -> x
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.