/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


YES

Problem 1: 

(VAR v_NonEmpty:S x:S y:S z:S)
(RULES
*(*(x:S,y:S),z:S) -> *(x:S,*(y:S,z:S))
*(+(y:S,z:S),x:S) -> +(*(x:S,y: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))
)

Problem 1: 

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

Problem 1: 

SCC Processor:
-> Pairs:
 *#(*(x:S,y:S),z:S) -> *#(x:S,*(y:S,z:S))
 *#(*(x:S,y:S),z:S) -> *#(y:S,z:S)
 *#(+(y:S,z:S),x:S) -> *#(x:S,y:S)
 *#(+(y:S,z:S),x:S) -> *#(x:S,z:S)
 *#(+(y:S,z:S),x:S) -> +#(*(x:S,y:S),*(x: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,*(y:S,z:S))
 *(+(y:S,z:S),x:S) -> +(*(x:S,y: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))
->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,*(y:S,z:S))
 *(+(y:S,z:S),x:S) -> +(*(x:S,y: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))
->->Cycle:
->->-> Pairs:
 *#(*(x:S,y:S),z:S) -> *#(x:S,*(y:S,z:S))
 *#(*(x:S,y:S),z:S) -> *#(y:S,z:S)
 *#(+(y:S,z:S),x:S) -> *#(x:S,y:S)
 *#(+(y:S,z:S),x:S) -> *#(x: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,*(y:S,z:S))
 *(+(y:S,z:S),x:S) -> +(*(x:S,y: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))


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,*(y:S,z:S))
 *(+(y:S,z:S),x:S) -> +(*(x:S,y: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))
->Projection:
 pi(+#) = 1

Problem 1.1: 

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

The problem is finite.

Problem 1.2: 

Reduction Pair Processor:
-> Pairs:
 *#(*(x:S,y:S),z:S) -> *#(x:S,*(y:S,z:S))
 *#(*(x:S,y:S),z:S) -> *#(y:S,z:S)
 *#(+(y:S,z:S),x:S) -> *#(x:S,y:S)
 *#(+(y:S,z:S),x:S) -> *#(x: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,*(y:S,z:S))
 *(+(y:S,z:S),x:S) -> +(*(x:S,y: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))
-> Usable rules:
 *(*(x:S,y:S),z:S) -> *(x:S,*(y:S,z:S))
 *(+(y:S,z:S),x:S) -> +(*(x:S,y: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))
->Interpretation type:
 Simple mixed
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[*](X1,X2) = 2.X1.X2 + 2.X1 + 2.X2 + 1
[+](X1,X2) = 2.X1 + X2 + 2
[*#](X1,X2) = X1.X2 + X1

Problem 1.2: 

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

Problem 1.2: 

Reduction Pair Processor:
-> Pairs:
 *#(*(x:S,y:S),z:S) -> *#(y:S,z:S)
 *#(+(y:S,z:S),x:S) -> *#(x:S,y:S)
 *#(+(y:S,z:S),x:S) -> *#(x: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,*(y:S,z:S))
 *(+(y:S,z:S),x:S) -> +(*(x:S,y: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))
-> Usable rules:
 Empty
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[*](X1,X2) = 2.X2 + 1
[+](X1,X2) = 2.X1 + 2.X2
[*#](X1,X2) = 2.X1 + 2.X2

Problem 1.2: 

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

Problem 1.2: 

Reduction Pair Processor:
-> Pairs:
 *#(+(y:S,z:S),x:S) -> *#(x:S,y:S)
 *#(+(y:S,z:S),x:S) -> *#(x: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,*(y:S,z:S))
 *(+(y:S,z:S),x:S) -> +(*(x:S,y: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))
-> Usable rules:
 Empty
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[+](X1,X2) = 2.X1 + 2.X2 + 1
[*#](X1,X2) = 2.X1 + 2.X2

Problem 1.2: 

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

Problem 1.2: 

Reduction Pair Processor:
-> Pairs:
 *#(+(y:S,z:S),x:S) -> *#(x: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,*(y:S,z:S))
 *(+(y:S,z:S),x:S) -> +(*(x:S,y: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))
-> Usable rules:
 Empty
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[+](X1,X2) = 2.X1 + 2.X2 + 2
[*#](X1,X2) = 2.X1 + 2.X2

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

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,*(y:S,z:S))
 *(+(y:S,z:S),x:S) -> +(*(x:S,y: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))
->Projection:
 pi(*#) = 2

Problem 1.2: 

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

The problem is finite.