YES

Problem 1: 

(VAR v_NonEmpty:S x:S y:S z:S)
(RULES
+(minus(+(x:S,1)),1) -> minus(x:S)
+(minus(1),1) -> 0
+(0,y:S) -> y:S
+(x:S,+(y:S,z:S)) -> +(+(x:S,y:S),z:S)
+(x:S,minus(y:S)) -> minus(+(minus(x:S),y:S))
+(x:S,0) -> x:S
minus(minus(x:S)) -> x:S
minus(0) -> 0
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 +#(minus(+(x:S,1)),1) -> MINUS(x:S)
 +#(x:S,+(y:S,z:S)) -> +#(+(x:S,y:S),z:S)
 +#(x:S,+(y:S,z:S)) -> +#(x:S,y:S)
 +#(x:S,minus(y:S)) -> +#(minus(x:S),y:S)
 +#(x:S,minus(y:S)) -> MINUS(+(minus(x:S),y:S))
 +#(x:S,minus(y:S)) -> MINUS(x:S)
-> Rules:
 +(minus(+(x:S,1)),1) -> minus(x:S)
 +(minus(1),1) -> 0
 +(0,y:S) -> y:S
 +(x:S,+(y:S,z:S)) -> +(+(x:S,y:S),z:S)
 +(x:S,minus(y:S)) -> minus(+(minus(x:S),y:S))
 +(x:S,0) -> x:S
 minus(minus(x:S)) -> x:S
 minus(0) -> 0

Problem 1: 

SCC Processor:
-> Pairs:
 +#(minus(+(x:S,1)),1) -> MINUS(x:S)
 +#(x:S,+(y:S,z:S)) -> +#(+(x:S,y:S),z:S)
 +#(x:S,+(y:S,z:S)) -> +#(x:S,y:S)
 +#(x:S,minus(y:S)) -> +#(minus(x:S),y:S)
 +#(x:S,minus(y:S)) -> MINUS(+(minus(x:S),y:S))
 +#(x:S,minus(y:S)) -> MINUS(x:S)
-> Rules:
 +(minus(+(x:S,1)),1) -> minus(x:S)
 +(minus(1),1) -> 0
 +(0,y:S) -> y:S
 +(x:S,+(y:S,z:S)) -> +(+(x:S,y:S),z:S)
 +(x:S,minus(y:S)) -> minus(+(minus(x:S),y:S))
 +(x:S,0) -> x:S
 minus(minus(x:S)) -> x:S
 minus(0) -> 0
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 +#(x:S,+(y:S,z:S)) -> +#(+(x:S,y:S),z:S)
 +#(x:S,+(y:S,z:S)) -> +#(x:S,y:S)
 +#(x:S,minus(y:S)) -> +#(minus(x:S),y:S)
->->-> Rules:
 +(minus(+(x:S,1)),1) -> minus(x:S)
 +(minus(1),1) -> 0
 +(0,y:S) -> y:S
 +(x:S,+(y:S,z:S)) -> +(+(x:S,y:S),z:S)
 +(x:S,minus(y:S)) -> minus(+(minus(x:S),y:S))
 +(x:S,0) -> x:S
 minus(minus(x:S)) -> x:S
 minus(0) -> 0

Problem 1: 

Subterm Processor:
-> Pairs:
 +#(x:S,+(y:S,z:S)) -> +#(+(x:S,y:S),z:S)
 +#(x:S,+(y:S,z:S)) -> +#(x:S,y:S)
 +#(x:S,minus(y:S)) -> +#(minus(x:S),y:S)
-> Rules:
 +(minus(+(x:S,1)),1) -> minus(x:S)
 +(minus(1),1) -> 0
 +(0,y:S) -> y:S
 +(x:S,+(y:S,z:S)) -> +(+(x:S,y:S),z:S)
 +(x:S,minus(y:S)) -> minus(+(minus(x:S),y:S))
 +(x:S,0) -> x:S
 minus(minus(x:S)) -> x:S
 minus(0) -> 0
->Projection:
 pi(+#) = 2

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 +(minus(+(x:S,1)),1) -> minus(x:S)
 +(minus(1),1) -> 0
 +(0,y:S) -> y:S
 +(x:S,+(y:S,z:S)) -> +(+(x:S,y:S),z:S)
 +(x:S,minus(y:S)) -> minus(+(minus(x:S),y:S))
 +(x:S,0) -> x:S
 minus(minus(x:S)) -> x:S
 minus(0) -> 0
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.