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

Problem 1: 

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

Problem 1: 

SCC Processor:
-> Pairs:
 *#(+(x:S,y:S),z:S) -> *#(x:S,z:S)
 *#(+(x:S,y:S),z:S) -> *#(y:S,z:S)
 *#(+(x:S,y:S),z:S) -> +#(*(x:S,z:S),*(y:S,z:S))
 *#(x:S,+(y:S,z:S)) -> *#(x:S,y:S)
 *#(x:S,+(y:S,z:S)) -> *#(x:S,z:S)
 *#(x:S,+(y:S,z:S)) -> +#(*(x:S,y:S),*(x:S,z:S))
 +#(+(x:S,y:S),z:S) -> +#(x:S,+(y:S,z:S))
 +#(+(x:S,y:S),z:S) -> +#(y:S,z:S)
-> Rules:
 *(+(x:S,y:S),z:S) -> +(*(x:S,z:S),*(y:S,z:S))
 *(x:S,+(y:S,z:S)) -> +(*(x:S,y:S),*(x:S,z:S))
 +(+(x:S,y:S),z:S) -> +(x:S,+(y:S,z:S))
 +(x:S,0) -> x:S
 +(x:S,i(x:S)) -> 0
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 +#(+(x:S,y:S),z:S) -> +#(x:S,+(y:S,z:S))
 +#(+(x:S,y:S),z:S) -> +#(y:S,z:S)
->->-> Rules:
 *(+(x:S,y:S),z:S) -> +(*(x:S,z:S),*(y:S,z:S))
 *(x:S,+(y:S,z:S)) -> +(*(x:S,y:S),*(x:S,z:S))
 +(+(x:S,y:S),z:S) -> +(x:S,+(y:S,z:S))
 +(x:S,0) -> x:S
 +(x:S,i(x:S)) -> 0
->->Cycle:
->->-> Pairs:
 *#(+(x:S,y:S),z:S) -> *#(x:S,z:S)
 *#(+(x:S,y:S),z:S) -> *#(y:S,z:S)
 *#(x:S,+(y:S,z:S)) -> *#(x:S,y:S)
 *#(x:S,+(y:S,z:S)) -> *#(x:S,z:S)
->->-> Rules:
 *(+(x:S,y:S),z:S) -> +(*(x:S,z:S),*(y:S,z:S))
 *(x:S,+(y:S,z:S)) -> +(*(x:S,y:S),*(x:S,z:S))
 +(+(x:S,y:S),z:S) -> +(x:S,+(y:S,z:S))
 +(x:S,0) -> x:S
 +(x:S,i(x:S)) -> 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) -> +#(y:S,z:S)
-> Rules:
 *(+(x:S,y:S),z:S) -> +(*(x:S,z:S),*(y:S,z:S))
 *(x:S,+(y:S,z:S)) -> +(*(x:S,y:S),*(x:S,z:S))
 +(+(x:S,y:S),z:S) -> +(x:S,+(y:S,z:S))
 +(x:S,0) -> x:S
 +(x:S,i(x:S)) -> 0
->Projection:
 pi(+#) = 1

Problem 1.1: 

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

The problem is finite.

Problem 1.2: 

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

Problem 1.2: 

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

Problem 1.2: 

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

Problem 1.2: 

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

The problem is finite.