/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 v_NonEmpty:S x:S)
(RULES
f(h(x:S)) -> f(i(x:S))
g(i(x:S)) -> g(h(x:S))
h(a) -> b
i(a) -> b
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(h(x:S)) -> F(i(x:S))
 F(h(x:S)) -> I(x:S)
 G(i(x:S)) -> G(h(x:S))
 G(i(x:S)) -> H(x:S)
-> Rules:
 f(h(x:S)) -> f(i(x:S))
 g(i(x:S)) -> g(h(x:S))
 h(a) -> b
 i(a) -> b

Problem 1: 

SCC Processor:
-> Pairs:
 F(h(x:S)) -> F(i(x:S))
 F(h(x:S)) -> I(x:S)
 G(i(x:S)) -> G(h(x:S))
 G(i(x:S)) -> H(x:S)
-> Rules:
 f(h(x:S)) -> f(i(x:S))
 g(i(x:S)) -> g(h(x:S))
 h(a) -> b
 i(a) -> b
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 G(i(x:S)) -> G(h(x:S))
->->-> Rules:
 f(h(x:S)) -> f(i(x:S))
 g(i(x:S)) -> g(h(x:S))
 h(a) -> b
 i(a) -> b
->->Cycle:
->->-> Pairs:
 F(h(x:S)) -> F(i(x:S))
->->-> Rules:
 f(h(x:S)) -> f(i(x:S))
 g(i(x:S)) -> g(h(x:S))
 h(a) -> b
 i(a) -> b


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Reduction Pair Processor:
-> Pairs:
 G(i(x:S)) -> G(h(x:S))
-> Rules:
 f(h(x:S)) -> f(i(x:S))
 g(i(x:S)) -> g(h(x:S))
 h(a) -> b
 i(a) -> b
-> Usable rules:
 h(a) -> b
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[h](X) = 1
[i](X) = 2.X + 2
[a] = 0
[b] = 1
[G](X) = 2.X

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 f(h(x:S)) -> f(i(x:S))
 g(i(x:S)) -> g(h(x:S))
 h(a) -> b
 i(a) -> b
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Reduction Pair Processor:
-> Pairs:
 F(h(x:S)) -> F(i(x:S))
-> Rules:
 f(h(x:S)) -> f(i(x:S))
 g(i(x:S)) -> g(h(x:S))
 h(a) -> b
 i(a) -> b
-> Usable rules:
 i(a) -> b
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[h](X) = 2.X + 2
[i](X) = 0
[a] = 0
[b] = 0
[F](X) = 2.X

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 f(h(x:S)) -> f(i(x:S))
 g(i(x:S)) -> g(h(x:S))
 h(a) -> b
 i(a) -> b
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.