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

Problem 1: 

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

Problem 1: 

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


The problem is decomposed in 2 subproblems.

Problem 1.1: 

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

Problem 1.1: 

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

The problem is finite.

Problem 1.2: 

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

Problem 1.2: 

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

The problem is finite.