YES

Problem 1: 

(VAR v_NonEmpty:S x:S y:S)
(RULES
-(-(neg(x:S),neg(x:S)),-(neg(y:S),neg(y:S))) -> -(-(x:S,y:S),-(x:S,y:S))
)

Problem 1: 

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

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 -#(-(neg(x:S),neg(x:S)),-(neg(y:S),neg(y:S))) -> -#(-(x:S,y:S),-(x:S,y:S))
 -#(-(neg(x:S),neg(x:S)),-(neg(y:S),neg(y:S))) -> -#(x:S,y:S)
-> Rules:
 -(-(neg(x:S),neg(x:S)),-(neg(y:S),neg(y:S))) -> -(-(x:S,y:S),-(x:S,y:S))

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

The problem is finite.