/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)
(STRATEGY CONTEXTSENSITIVE
(f_1)
(i_1)
(a_0)
(h_0 1)
)
(RULES
f_1(i_1(x)) -> a_0
f_1(h_0(x)) -> f_1(i_1(x))
i_1(x) -> h_0(x)
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F_1(h_0(x)) -> F_1(i_1(x))
 I_1(x) -> x
-> Rules:
 f_1(i_1(x)) -> a_0
 f_1(h_0(x)) -> f_1(i_1(x))
 i_1(x) -> h_0(x)
-> Unhiding Rules:
 i_1(x) -> I_1(x)

Problem 1: 

SCC Processor:
-> Pairs:
 F_1(h_0(x)) -> F_1(i_1(x))
 I_1(x) -> x
-> Rules:
 f_1(i_1(x)) -> a_0
 f_1(h_0(x)) -> f_1(i_1(x))
 i_1(x) -> h_0(x)
-> Unhiding rules:
 i_1(x) -> I_1(x)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 I_1(x) -> x
->->-> Rules:
 f_1(i_1(x)) -> a_0
 f_1(h_0(x)) -> f_1(i_1(x))
 i_1(x) -> h_0(x)
->->-> Unhiding rules:
 i_1(x) -> I_1(x)

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 I_1(x) -> x
-> Rules:
 f_1(i_1(x)) -> a_0
 f_1(h_0(x)) -> f_1(i_1(x))
 i_1(x) -> h_0(x)
-> Unhiding rules:
 i_1(x) -> I_1(x)
-> Usable rules:
 Empty
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[i_1](X) = 2.X + 2
[I_1](X) = 2.X + 2

Problem 1: 

Basic Processor:
-> Pairs:
 Empty
-> Rules:
 f_1(i_1(x)) -> a_0
 f_1(h_0(x)) -> f_1(i_1(x))
 i_1(x) -> h_0(x)
-> Unhiding rules:
 i_1(x) -> I_1(x)
-> Result:
 Set P is empty

The problem is finite.