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


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


YES

Problem 1: 

(VAR v_NonEmpty:S)
(RULES
a -> c | b ->* c
b -> c
f(b) -> f(a)
)

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

Problem 1: 

Dependency Pairs Processor:

Conditional Termination Problem 1:
-> Pairs:
 F(b) -> A
 F(b) -> F(a)
-> QPairs:
 Empty
-> Rules:
 a -> c | b ->* c
 b -> c
 f(b) -> f(a)

Conditional Termination Problem 2:
-> Pairs:
 A -> B
-> QPairs:
 Empty
-> Rules:
 a -> c | b ->* c
 b -> c
 f(b) -> f(a)


The problem is decomposed in 2 subproblems.

Problem 1.1: 

SCC Processor:
-> Pairs:
 F(b) -> A
 F(b) -> F(a)
-> QPairs:
 Empty
-> Rules:
 a -> c | b ->* c
 b -> c
 f(b) -> f(a)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(b) -> F(a)
-> QPairs:
 Empty
->->-> Rules:
 a -> c | b ->* c
 b -> c
 f(b) -> f(a)

Problem 1.1: 

Reduction Triple Processor:
-> Pairs:
 F(b) -> F(a)
-> QPairs:
 Empty
-> Rules:
 a -> c | b ->* c
 b -> c
 f(b) -> f(a)
-> Usable rules:
 a -> c | b ->* c
 b -> c
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a] = 1
[b] = 2
[f](X) = 0
[c] = 0
[fSNonEmpty] = 0
[A] = 0
[B] = 0
[F](X) = 2.X

Problem 1.1: 

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

The problem is finite.

Problem 1.2: 

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

The problem is finite.