/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,+(y:S,z:S))
+(f(x:S),+(f(y:S),z:S)) -> +(f(+(x:S,y:S)),z:S)
+(f(x:S),f(y:S)) -> f(+(x:S,y: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)
 +#(f(x:S),+(f(y:S),z:S)) -> +#(f(+(x:S,y:S)),z:S)
 +#(f(x:S),+(f(y:S),z:S)) -> +#(x:S,y:S)
 +#(f(x:S),f(y:S)) -> +#(x:S,y:S)
-> Rules:
 +(+(x:S,y:S),z:S) -> +(x:S,+(y:S,z:S))
 +(f(x:S),+(f(y:S),z:S)) -> +(f(+(x:S,y:S)),z:S)
 +(f(x:S),f(y:S)) -> f(+(x:S,y: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)
 +#(f(x:S),+(f(y:S),z:S)) -> +#(f(+(x:S,y:S)),z:S)
 +#(f(x:S),+(f(y:S),z:S)) -> +#(x:S,y:S)
 +#(f(x:S),f(y:S)) -> +#(x:S,y:S)
-> Rules:
 +(+(x:S,y:S),z:S) -> +(x:S,+(y:S,z:S))
 +(f(x:S),+(f(y:S),z:S)) -> +(f(+(x:S,y:S)),z:S)
 +(f(x:S),f(y:S)) -> f(+(x:S,y: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)
 +#(f(x:S),+(f(y:S),z:S)) -> +#(f(+(x:S,y:S)),z:S)
 +#(f(x:S),+(f(y:S),z:S)) -> +#(x:S,y:S)
 +#(f(x:S),f(y:S)) -> +#(x:S,y:S)
->->-> Rules:
 +(+(x:S,y:S),z:S) -> +(x:S,+(y:S,z:S))
 +(f(x:S),+(f(y:S),z:S)) -> +(f(+(x:S,y:S)),z:S)
 +(f(x:S),f(y:S)) -> f(+(x:S,y:S))

Problem 1: 

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)
 +#(f(x:S),+(f(y:S),z:S)) -> +#(f(+(x:S,y:S)),z:S)
 +#(f(x:S),+(f(y:S),z:S)) -> +#(x:S,y:S)
 +#(f(x:S),f(y:S)) -> +#(x:S,y:S)
-> Rules:
 +(+(x:S,y:S),z:S) -> +(x:S,+(y:S,z:S))
 +(f(x:S),+(f(y:S),z:S)) -> +(f(+(x:S,y:S)),z:S)
 +(f(x:S),f(y:S)) -> f(+(x:S,y:S))
-> Usable rules:
 +(+(x:S,y:S),z:S) -> +(x:S,+(y:S,z:S))
 +(f(x:S),+(f(y:S),z:S)) -> +(f(+(x:S,y:S)),z:S)
 +(f(x:S),f(y:S)) -> f(+(x:S,y:S))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[+](X1,X2) = X1 + X2 + 2
[f](X) = 2.X + 2
[+#](X1,X2) = X1 + X2

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

The problem is finite.