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


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YES

Problem 1: 

(VAR X Y)
(RULES
f(0,1,X) -> f(g(X,X),X,X)
g(X,Y) -> X
g(X,Y) -> Y
) 
(STRATEGY INNERMOST)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(0,1,X) -> F(g(X,X),X,X)
 F(0,1,X) -> G(X,X)
-> Rules:
 f(0,1,X) -> f(g(X,X),X,X)
 g(X,Y) -> X
 g(X,Y) -> Y

Problem 1: 

SCC Processor:
-> Pairs:
 F(0,1,X) -> F(g(X,X),X,X)
 F(0,1,X) -> G(X,X)
-> Rules:
 f(0,1,X) -> f(g(X,X),X,X)
 g(X,Y) -> X
 g(X,Y) -> Y
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(0,1,X) -> F(g(X,X),X,X)
->->-> Rules:
 f(0,1,X) -> f(g(X,X),X,X)
 g(X,Y) -> X
 g(X,Y) -> Y

Problem 1: 

Instantiation Processor:
-> Pairs:
 F(0,1,X) -> F(g(X,X),X,X)
-> Rules:
 f(0,1,X) -> f(g(X,X),X,X)
 g(X,Y) -> X
 g(X,Y) -> Y
->Instantiated Pairs:
->->Original Pair:
 F(0,1,X) -> F(g(X,X),X,X)
->-> Instantiated pairs:
 F(0,1,1) -> F(g(1,1),1,1)

Problem 1: 

SCC Processor:
-> Pairs:
 F(0,1,1) -> F(g(1,1),1,1)
-> Rules:
 f(0,1,X) -> f(g(X,X),X,X)
 g(X,Y) -> X
 g(X,Y) -> Y
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(0,1,1) -> F(g(1,1),1,1)
->->-> Rules:
 f(0,1,X) -> f(g(X,X),X,X)
 g(X,Y) -> X
 g(X,Y) -> Y

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 F(0,1,1) -> F(g(1,1),1,1)
-> Rules:
 f(0,1,X) -> f(g(X,X),X,X)
 g(X,Y) -> X
 g(X,Y) -> Y
-> Usable rules:
 g(X,Y) -> X
 g(X,Y) -> Y
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[g](X1,X2) = X1 + 2.X2 + 1
[0] = 2
[1] = 0
[F](X1,X2,X3) = 2.X1

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 f(0,1,X) -> f(g(X,X),X,X)
 g(X,Y) -> X
 g(X,Y) -> Y
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.