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

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 +(0,y) -> y
 +(s(x),0) -> s(x)
 +(s(x),s(y)) -> s(+(s(x),+(y,0)))
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

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

Problem 1: 

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

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 +#(s(x),s(y)) -> +#(s(x),+(y,0))
-> Rules:
 +(0,y) -> y
 +(s(x),0) -> s(x)
 +(s(x),s(y)) -> s(+(s(x),+(y,0)))
-> Usable rules:
 +(0,y) -> y
 +(s(x),0) -> s(x)
 +(s(x),s(y)) -> s(+(s(x),+(y,0)))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[+](X1,X2) = X1 + 2.X2 + 1
[0] = 0
[s](X) = X + 2
[+#](X1,X2) = X2

Problem 1: 

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

The problem is finite.