/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 v_NonEmpty:S x:S y:S)
(RULES
+(0,s(y:S)) -> s(y:S)
+(x:S,s(y:S)) -> s(+(x:S,y:S))
+(x:S,0) -> x:S
s(+(0,y:S)) -> s(y:S)
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 +#(x:S,s(y:S)) -> +#(x:S,y:S)
 +#(x:S,s(y:S)) -> S(+(x:S,y:S))
 S(+(0,y:S)) -> S(y:S)
-> Rules:
 +(0,s(y:S)) -> s(y:S)
 +(x:S,s(y:S)) -> s(+(x:S,y:S))
 +(x:S,0) -> x:S
 s(+(0,y:S)) -> s(y:S)

Problem 1: 

SCC Processor:
-> Pairs:
 +#(x:S,s(y:S)) -> +#(x:S,y:S)
 +#(x:S,s(y:S)) -> S(+(x:S,y:S))
 S(+(0,y:S)) -> S(y:S)
-> Rules:
 +(0,s(y:S)) -> s(y:S)
 +(x:S,s(y:S)) -> s(+(x:S,y:S))
 +(x:S,0) -> x:S
 s(+(0,y:S)) -> s(y:S)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 S(+(0,y:S)) -> S(y:S)
->->-> Rules:
 +(0,s(y:S)) -> s(y:S)
 +(x:S,s(y:S)) -> s(+(x:S,y:S))
 +(x:S,0) -> x:S
 s(+(0,y:S)) -> s(y:S)
->->Cycle:
->->-> Pairs:
 +#(x:S,s(y:S)) -> +#(x:S,y:S)
->->-> Rules:
 +(0,s(y:S)) -> s(y:S)
 +(x:S,s(y:S)) -> s(+(x:S,y:S))
 +(x:S,0) -> x:S
 s(+(0,y:S)) -> s(y:S)


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 S(+(0,y:S)) -> S(y:S)
-> Rules:
 +(0,s(y:S)) -> s(y:S)
 +(x:S,s(y:S)) -> s(+(x:S,y:S))
 +(x:S,0) -> x:S
 s(+(0,y:S)) -> s(y:S)
->Projection:
 pi(S) = 1

Problem 1.1: 

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

The problem is finite.

Problem 1.2: 

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

Problem 1.2: 

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

The problem is finite.