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


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


YES

Problem 1: 

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

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 b -> c
 f(x,x) -> f(a,b)
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(x,x) -> B
 F(x,x) -> F(a,b)
-> Rules:
 b -> c
 f(x,x) -> f(a,b)

Problem 1: 

SCC Processor:
-> Pairs:
 F(x,x) -> B
 F(x,x) -> F(a,b)
-> Rules:
 b -> c
 f(x,x) -> f(a,b)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(x,x) -> F(a,b)
->->-> Rules:
 b -> c
 f(x,x) -> f(a,b)

Problem 1: 

Instantiation Processor:
-> Pairs:
 F(x,x) -> F(a,b)
-> Rules:
 b -> c
 f(x,x) -> f(a,b)
->Instantiated Pairs:
->->Original Pair:
 F(x,x) -> F(a,b)
->-> Instantiated pairs:
 F(a,a) -> F(a,b)

Problem 1: 

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

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 F(a,a) -> F(a,b)
-> Rules:
 b -> c
 f(x,x) -> f(a,b)
-> Usable rules:
 b -> c
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[b] = 1
[a] = 2
[c] = 1
[F](X1,X2) = 2.X2

Problem 1: 

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

The problem is finite.