/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)
(RULES
f(g(a)) -> g(b)
g(a) -> b
h(x) -> h(g(x)) | f(x) -> g(x)
)

Problem 1: 
Valid CTRS Processor:
-> Rules:
 f(g(a)) -> g(b)
 g(a) -> b
 h(x) -> h(g(x)) | f(x) -> g(x)
-> The system is a deterministic 3-CTRS.

Problem 1: 

Dependency Pairs Processor:

Conditional Termination Problem 1:
-> Pairs:
 F(g(a)) -> G(b)
 H(x) -> G(x) | f(x) -> g(x)
 H(x) -> H(g(x)) | f(x) -> g(x)
-> QPairs:
 Empty
-> Rules:
 f(g(a)) -> g(b)
 g(a) -> b
 h(x) -> h(g(x)) | f(x) -> g(x)

Conditional Termination Problem 2:
-> Pairs:
 H(x) -> F(x)
-> QPairs:
 F(g(a)) -> G(b)
 H(x) -> G(x) | f(x) -> g(x)
 H(x) -> H(g(x)) | f(x) -> g(x)
-> Rules:
 f(g(a)) -> g(b)
 g(a) -> b
 h(x) -> h(g(x)) | f(x) -> g(x)


The problem is decomposed in 2 subproblems.

Problem 1.1: 

SCC Processor:
-> Pairs:
 F(g(a)) -> G(b)
 H(x) -> G(x) | f(x) -> g(x)
 H(x) -> H(g(x)) | f(x) -> g(x)
-> QPairs:
 Empty
-> Rules:
 f(g(a)) -> g(b)
 g(a) -> b
 h(x) -> h(g(x)) | f(x) -> g(x)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 H(x) -> H(g(x)) | f(x) -> g(x)
->->-> Rules:
 f(g(a)) -> g(b)
 g(a) -> b
 h(x) -> h(g(x)) | f(x) -> g(x)

Problem 1.1: 

Reduction Triple Processor:
-> Pairs:
 H(x) -> H(g(x)) | f(x) -> g(x)
-> QPairs:
 Empty
-> Rules:
 f(g(a)) -> g(b)
 g(a) -> b
 h(x) -> h(g(x)) | f(x) -> g(x)
-> Usable rules:
 f(g(a)) -> g(b)
 g(a) -> b
->Interpretation type:
 Linear
->Coefficients:
 Integer Numbers
->Dimension:
 1
->Convex Domain:
 D[(x_1)] = ((1 >= 0) /\ (1+x_1 >= 0))
->Interpretation:
 
[delta] = 1
[f](x_1) = x_1
[g](x_1) = 1+x_1
[a] = 0
[b] = 0
[H](x_1) = 0

Problem 1.1: 

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

The problem is finite.

Problem 1.2: 

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

Problem 1.2: 

Reduction Triple Processor:
-> Pairs:
 H(x) -> F(x)
-> QPairs:
 F(g(a)) -> G(b)
 H(x) -> G(x) | f(x) -> g(x)
 H(x) -> H(g(x)) | f(x) -> g(x)
-> Rules:
 f(g(a)) -> g(b)
 g(a) -> b
 h(x) -> h(g(x)) | f(x) -> g(x)
-> Usable rules:
 f(g(a)) -> g(b)
 g(a) -> b
->Interpretation type:
 Linear
->Coefficients:
 Integer Numbers
->Dimension:
 1
->Convex Domain:
 D[(x_1)] = ((1 >= 0) /\ (1+x_1 >= 0))
->Interpretation:
 
[delta] = 1
[f](x_1) = 0
[g](x_1) = 0
[a] = 0
[b] = 0
[F](x_1) = 0
[G](x_1) = -1
[H](x_1) = 0

Problem 1.2: 

SCC Processor:
-> Pairs:
 H(x) -> F(x)
-> QPairs:
 H(x) -> G(x) | f(x) -> g(x)
 H(x) -> H(g(x)) | f(x) -> g(x)
-> Rules:
 f(g(a)) -> g(b)
 g(a) -> b
 h(x) -> h(g(x)) | f(x) -> g(x)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.