YES

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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


The problem is decomposed in 2 subproblems.

Problem 1.1: 

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

Problem 1.1: 

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

The problem is finite.

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

Problem 1.2: 

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

The problem is finite.