/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 y)
(RULES
f(g(x),s(0),y) -> f(g(s(0)),y,g(x))
g(0) -> 0
g(s(x)) -> s(g(x))
) 
(STRATEGY INNERMOST)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(g(x),s(0),y) -> F(g(s(0)),y,g(x))
 F(g(x),s(0),y) -> G(s(0))
 G(s(x)) -> G(x)
-> Rules:
 f(g(x),s(0),y) -> f(g(s(0)),y,g(x))
 g(0) -> 0
 g(s(x)) -> s(g(x))

Problem 1: 

SCC Processor:
-> Pairs:
 F(g(x),s(0),y) -> F(g(s(0)),y,g(x))
 F(g(x),s(0),y) -> G(s(0))
 G(s(x)) -> G(x)
-> Rules:
 f(g(x),s(0),y) -> f(g(s(0)),y,g(x))
 g(0) -> 0
 g(s(x)) -> s(g(x))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 G(s(x)) -> G(x)
->->-> Rules:
 f(g(x),s(0),y) -> f(g(s(0)),y,g(x))
 g(0) -> 0
 g(s(x)) -> s(g(x))
->->Cycle:
->->-> Pairs:
 F(g(x),s(0),y) -> F(g(s(0)),y,g(x))
->->-> Rules:
 f(g(x),s(0),y) -> f(g(s(0)),y,g(x))
 g(0) -> 0
 g(s(x)) -> s(g(x))


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 G(s(x)) -> G(x)
-> Rules:
 f(g(x),s(0),y) -> f(g(s(0)),y,g(x))
 g(0) -> 0
 g(s(x)) -> s(g(x))
->Projection:
 pi(G) = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 f(g(x),s(0),y) -> f(g(s(0)),y,g(x))
 g(0) -> 0
 g(s(x)) -> s(g(x))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Instantiation Processor:
-> Pairs:
 F(g(x),s(0),y) -> F(g(s(0)),y,g(x))
-> Rules:
 f(g(x),s(0),y) -> f(g(s(0)),y,g(x))
 g(0) -> 0
 g(s(x)) -> s(g(x))
->Instantiated Pairs:
->->Original Pair:
 F(g(x),s(0),y) -> F(g(s(0)),y,g(x))
->-> Instantiated pairs:
 F(g(x),s(0),g(x3)) -> F(g(s(0)),g(x3),g(x))

Problem 1.2: 

SCC Processor:
-> Pairs:
 F(g(x),s(0),g(x3)) -> F(g(s(0)),g(x3),g(x))
-> Rules:
 f(g(x),s(0),y) -> f(g(s(0)),y,g(x))
 g(0) -> 0
 g(s(x)) -> s(g(x))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.