/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(0) -> true
f(1) -> false
f(s(x)) -> f(x)
g(x,c(y)) -> g(x,if(f(x),c(g(s(x),y)),c(y)))
g(x,c(y)) -> c(g(x,y))
if(false,s(x),s(y)) -> s(y)
if(true,s(x),s(y)) -> s(x)
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(s(x)) -> F(x)
 G(x,c(y)) -> F(x)
 G(x,c(y)) -> G(s(x),y)
 G(x,c(y)) -> G(x,if(f(x),c(g(s(x),y)),c(y)))
 G(x,c(y)) -> G(x,y)
 G(x,c(y)) -> IF(f(x),c(g(s(x),y)),c(y))
-> Rules:
 f(0) -> true
 f(1) -> false
 f(s(x)) -> f(x)
 g(x,c(y)) -> g(x,if(f(x),c(g(s(x),y)),c(y)))
 g(x,c(y)) -> c(g(x,y))
 if(false,s(x),s(y)) -> s(y)
 if(true,s(x),s(y)) -> s(x)

Problem 1: 

SCC Processor:
-> Pairs:
 F(s(x)) -> F(x)
 G(x,c(y)) -> F(x)
 G(x,c(y)) -> G(s(x),y)
 G(x,c(y)) -> G(x,if(f(x),c(g(s(x),y)),c(y)))
 G(x,c(y)) -> G(x,y)
 G(x,c(y)) -> IF(f(x),c(g(s(x),y)),c(y))
-> Rules:
 f(0) -> true
 f(1) -> false
 f(s(x)) -> f(x)
 g(x,c(y)) -> g(x,if(f(x),c(g(s(x),y)),c(y)))
 g(x,c(y)) -> c(g(x,y))
 if(false,s(x),s(y)) -> s(y)
 if(true,s(x),s(y)) -> s(x)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(s(x)) -> F(x)
->->-> Rules:
 f(0) -> true
 f(1) -> false
 f(s(x)) -> f(x)
 g(x,c(y)) -> g(x,if(f(x),c(g(s(x),y)),c(y)))
 g(x,c(y)) -> c(g(x,y))
 if(false,s(x),s(y)) -> s(y)
 if(true,s(x),s(y)) -> s(x)
->->Cycle:
->->-> Pairs:
 G(x,c(y)) -> G(s(x),y)
 G(x,c(y)) -> G(x,y)
->->-> Rules:
 f(0) -> true
 f(1) -> false
 f(s(x)) -> f(x)
 g(x,c(y)) -> g(x,if(f(x),c(g(s(x),y)),c(y)))
 g(x,c(y)) -> c(g(x,y))
 if(false,s(x),s(y)) -> s(y)
 if(true,s(x),s(y)) -> s(x)


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 F(s(x)) -> F(x)
-> Rules:
 f(0) -> true
 f(1) -> false
 f(s(x)) -> f(x)
 g(x,c(y)) -> g(x,if(f(x),c(g(s(x),y)),c(y)))
 g(x,c(y)) -> c(g(x,y))
 if(false,s(x),s(y)) -> s(y)
 if(true,s(x),s(y)) -> s(x)
->Projection:
 pi(F) = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 f(0) -> true
 f(1) -> false
 f(s(x)) -> f(x)
 g(x,c(y)) -> g(x,if(f(x),c(g(s(x),y)),c(y)))
 g(x,c(y)) -> c(g(x,y))
 if(false,s(x),s(y)) -> s(y)
 if(true,s(x),s(y)) -> s(x)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 G(x,c(y)) -> G(s(x),y)
 G(x,c(y)) -> G(x,y)
-> Rules:
 f(0) -> true
 f(1) -> false
 f(s(x)) -> f(x)
 g(x,c(y)) -> g(x,if(f(x),c(g(s(x),y)),c(y)))
 g(x,c(y)) -> c(g(x,y))
 if(false,s(x),s(y)) -> s(y)
 if(true,s(x),s(y)) -> s(x)
->Projection:
 pi(G) = 2

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 f(0) -> true
 f(1) -> false
 f(s(x)) -> f(x)
 g(x,c(y)) -> g(x,if(f(x),c(g(s(x),y)),c(y)))
 g(x,c(y)) -> c(g(x,y))
 if(false,s(x),s(y)) -> s(y)
 if(true,s(x),s(y)) -> s(x)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.