/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 x y z)
(RULES
+(x,+(y,z)) -> +(+(x,y),z)
f(+(x,0)) -> f(x)
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 +#(x,+(y,z)) -> +#(+(x,y),z)
 +#(x,+(y,z)) -> +#(x,y)
 F(+(x,0)) -> F(x)
-> Rules:
 +(x,+(y,z)) -> +(+(x,y),z)
 f(+(x,0)) -> f(x)

Problem 1: 

SCC Processor:
-> Pairs:
 +#(x,+(y,z)) -> +#(+(x,y),z)
 +#(x,+(y,z)) -> +#(x,y)
 F(+(x,0)) -> F(x)
-> Rules:
 +(x,+(y,z)) -> +(+(x,y),z)
 f(+(x,0)) -> f(x)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(+(x,0)) -> F(x)
->->-> Rules:
 +(x,+(y,z)) -> +(+(x,y),z)
 f(+(x,0)) -> f(x)
->->Cycle:
->->-> Pairs:
 +#(x,+(y,z)) -> +#(+(x,y),z)
 +#(x,+(y,z)) -> +#(x,y)
->->-> Rules:
 +(x,+(y,z)) -> +(+(x,y),z)
 f(+(x,0)) -> f(x)


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 F(+(x,0)) -> F(x)
-> Rules:
 +(x,+(y,z)) -> +(+(x,y),z)
 f(+(x,0)) -> f(x)
->Projection:
 pi(F) = 1

Problem 1.1: 

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

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 +#(x,+(y,z)) -> +#(+(x,y),z)
 +#(x,+(y,z)) -> +#(x,y)
-> Rules:
 +(x,+(y,z)) -> +(+(x,y),z)
 f(+(x,0)) -> f(x)
->Projection:
 pi(+#) = 2

Problem 1.2: 

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

The problem is finite.