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


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YES

Problem 1: 

(VAR x y)
(STRATEGY CONTEXTSENSITIVE
(f_1)
(g_1)
(a_0)
(i_0 1)
)
(RULES
f_1(x,i_0(g_1(x))) -> a_0
f_1(x,i_0(x)) -> f_1(x,x)
f_1(x,x) -> f_1(i_0(x),g_1(g_1(x)))
f_1(x,y) -> x
g_1(x) -> i_0(x)
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F_1(x,i_0(x)) -> F_1(x,x)
 F_1(x,x) -> F_1(i_0(x),g_1(g_1(x)))
 F_1(x,y) -> x
 G_1(x) -> x
-> Rules:
 f_1(x,i_0(g_1(x))) -> a_0
 f_1(x,i_0(x)) -> f_1(x,x)
 f_1(x,x) -> f_1(i_0(x),g_1(g_1(x)))
 f_1(x,y) -> x
 g_1(x) -> i_0(x)
-> Unhiding Rules:
 g_1(g_1(x)) -> G_1(g_1(x))
 i_0(x2) -> x2

Problem 1: 

SCC Processor:
-> Pairs:
 F_1(x,i_0(x)) -> F_1(x,x)
 F_1(x,x) -> F_1(i_0(x),g_1(g_1(x)))
 F_1(x,y) -> x
 G_1(x) -> x
-> Rules:
 f_1(x,i_0(g_1(x))) -> a_0
 f_1(x,i_0(x)) -> f_1(x,x)
 f_1(x,x) -> f_1(i_0(x),g_1(g_1(x)))
 f_1(x,y) -> x
 g_1(x) -> i_0(x)
-> Unhiding rules:
 g_1(g_1(x)) -> G_1(g_1(x))
 i_0(x2) -> x2
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 G_1(x) -> x
->->-> Rules:
 f_1(x,i_0(g_1(x))) -> a_0
 f_1(x,i_0(x)) -> f_1(x,x)
 f_1(x,x) -> f_1(i_0(x),g_1(g_1(x)))
 f_1(x,y) -> x
 g_1(x) -> i_0(x)
->->-> Unhiding rules:
 g_1(g_1(x)) -> G_1(g_1(x))
 i_0(x2) -> x2

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 G_1(x) -> x
-> Rules:
 f_1(x,i_0(g_1(x))) -> a_0
 f_1(x,i_0(x)) -> f_1(x,x)
 f_1(x,x) -> f_1(i_0(x),g_1(g_1(x)))
 f_1(x,y) -> x
 g_1(x) -> i_0(x)
-> Unhiding rules:
 g_1(g_1(x)) -> G_1(g_1(x))
 i_0(x2) -> x2
-> Usable rules:
 g_1(x) -> i_0(x)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[g_1](X) = 2.X + 2
[i_0](X) = 2.X
[G_1](X) = 2.X + 2

Problem 1: 

Basic Processor:
-> Pairs:
 Empty
-> Rules:
 f_1(x,i_0(g_1(x))) -> a_0
 f_1(x,i_0(x)) -> f_1(x,x)
 f_1(x,x) -> f_1(i_0(x),g_1(g_1(x)))
 f_1(x,y) -> x
 g_1(x) -> i_0(x)
-> Unhiding rules:
 g_1(g_1(x)) -> G_1(g_1(x))
 i_0(x2) -> x2
-> Result:
 Set P is empty

The problem is finite.