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


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


YES

Problem 1: 

(VAR x)
(RULES
f(x) -> c | a -> b
g(x,x) -> g(f(a),f(b))
)

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

Problem 1: 

Dependency Pairs Processor:

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

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


The problem is decomposed in 2 subproblems.

Problem 1.1: 

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

Problem 1.1: 

Unsatisfiable Rule Processor:
-> Pairs:
 G(x,x) -> G(f(a),f(b))
-> QPairs:
 Empty
-> Rules:
 f(x) -> c | a -> b
 g(x,x) -> g(f(a),f(b))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[f](X) = 0
[g](X1,X2) = 0
[a] = 0
[b] = 2
[c] = 2
[F](X) = 0
[G](X1,X2) = 0

Problem 1.1: 

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

The problem is finite.

Problem 1.2: 

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

The problem is finite.