/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 u v x y)
(RULES
f(g(x,y),g(u,v)) -> g(f(x,u),f(y,v))
f(a,y) -> y
f(x,a) -> x
g(a,a) -> a
s(f(x,y)) -> f(s(y),s(x))
s(g(x,y)) -> g(s(x),s(y))
s(s(x)) -> x
s(a) -> a
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(g(x,y),g(u,v)) -> F(x,u)
 F(g(x,y),g(u,v)) -> F(y,v)
 F(g(x,y),g(u,v)) -> G(f(x,u),f(y,v))
 S(f(x,y)) -> F(s(y),s(x))
 S(f(x,y)) -> S(x)
 S(f(x,y)) -> S(y)
 S(g(x,y)) -> G(s(x),s(y))
 S(g(x,y)) -> S(x)
 S(g(x,y)) -> S(y)
-> Rules:
 f(g(x,y),g(u,v)) -> g(f(x,u),f(y,v))
 f(a,y) -> y
 f(x,a) -> x
 g(a,a) -> a
 s(f(x,y)) -> f(s(y),s(x))
 s(g(x,y)) -> g(s(x),s(y))
 s(s(x)) -> x
 s(a) -> a

Problem 1: 

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


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 F(g(x,y),g(u,v)) -> F(x,u)
 F(g(x,y),g(u,v)) -> F(y,v)
-> Rules:
 f(g(x,y),g(u,v)) -> g(f(x,u),f(y,v))
 f(a,y) -> y
 f(x,a) -> x
 g(a,a) -> a
 s(f(x,y)) -> f(s(y),s(x))
 s(g(x,y)) -> g(s(x),s(y))
 s(s(x)) -> x
 s(a) -> a
->Projection:
 pi(F) = 1

Problem 1.1: 

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

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 S(f(x,y)) -> S(x)
 S(f(x,y)) -> S(y)
 S(g(x,y)) -> S(x)
 S(g(x,y)) -> S(y)
-> Rules:
 f(g(x,y),g(u,v)) -> g(f(x,u),f(y,v))
 f(a,y) -> y
 f(x,a) -> x
 g(a,a) -> a
 s(f(x,y)) -> f(s(y),s(x))
 s(g(x,y)) -> g(s(x),s(y))
 s(s(x)) -> x
 s(a) -> a
->Projection:
 pi(S) = 1

Problem 1.2: 

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

The problem is finite.