NO

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

Narrowing Processor:
-> Pairs:
 +#(1,x:S) -> +#(+(0,1),x:S)
-> Rules:
 +(0,x:S) -> x:S
 +(1,x:S) -> +(+(0,1),x:S)
->Narrowed Pairs:
->->Original Pair:
 +#(1,x:S) -> +#(+(0,1),x:S)
->-> Narrowed pairs:
 +#(1,x2:S) -> +#(1,x2:S)

Problem 1: 

Infinite Processor:
-> Pairs:
 +#(1,x2:S) -> +#(1,x2:S)
-> Rules:
 +(0,x:S) -> x:S
 +(1,x:S) -> +(+(0,1),x:S)
-> Pairs in cycle:
 +#(1,x2:S) -> +#(1,x2:S)

The problem is infinite.