/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)
(STRATEGY CONTEXTSENSITIVE
(f_1)
(g_1)
(a_0)
)
(RULES
f_1(x) -> g_1(f_1(x))
g_1(f_1(x)) -> x
g_1(x) -> a_0
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F_1(x) -> G_1(f_1(x))
 G_1(f_1(x)) -> x
-> Rules:
 f_1(x) -> g_1(f_1(x))
 g_1(f_1(x)) -> x
 g_1(x) -> a_0
-> Unhiding Rules:
 f_1(x) -> F_1(x)

Problem 1: 

SCC Processor:
-> Pairs:
 F_1(x) -> G_1(f_1(x))
 G_1(f_1(x)) -> x
-> Rules:
 f_1(x) -> g_1(f_1(x))
 g_1(f_1(x)) -> x
 g_1(x) -> a_0
-> Unhiding rules:
 f_1(x) -> F_1(x)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F_1(x) -> G_1(f_1(x))
 G_1(f_1(x)) -> x
->->-> Rules:
 f_1(x) -> g_1(f_1(x))
 g_1(f_1(x)) -> x
 g_1(x) -> a_0
->->-> Unhiding rules:
 f_1(x) -> F_1(x)

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 F_1(x) -> G_1(f_1(x))
 G_1(f_1(x)) -> x
-> Rules:
 f_1(x) -> g_1(f_1(x))
 g_1(f_1(x)) -> x
 g_1(x) -> a_0
-> Unhiding rules:
 f_1(x) -> F_1(x)
-> Usable rules:
 f_1(x) -> g_1(f_1(x))
 g_1(f_1(x)) -> x
 g_1(x) -> a_0
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[f_1](X) = X + 2
[g_1](X) = X
[a_0] = 0
[F_1](X) = X + 2
[G_1](X) = X

Problem 1: 

SCC Processor:
-> Pairs:
 F_1(x) -> G_1(f_1(x))
-> Rules:
 f_1(x) -> g_1(f_1(x))
 g_1(f_1(x)) -> x
 g_1(x) -> a_0
-> Unhiding rules:
 f_1(x) -> F_1(x)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.