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

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 +(0,y) -> y
 +(s(x),y) -> s(+(x,y))
 -(0,y) -> 0
 -(s(x),s(y)) -> -(x,y)
 -(x,0) -> x
-> 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),y) -> +#(x,y)
 -#(s(x),s(y)) -> -#(x,y)
-> Rules:
 +(0,y) -> y
 +(s(x),y) -> s(+(x,y))
 -(0,y) -> 0
 -(s(x),s(y)) -> -(x,y)
 -(x,0) -> x

Problem 1: 

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


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 -#(s(x),s(y)) -> -#(x,y)
-> Rules:
 +(0,y) -> y
 +(s(x),y) -> s(+(x,y))
 -(0,y) -> 0
 -(s(x),s(y)) -> -(x,y)
 -(x,0) -> x
->Projection:
 pi(-#) = 1

Problem 1.1: 

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

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 +#(s(x),y) -> +#(x,y)
-> Rules:
 +(0,y) -> y
 +(s(x),y) -> s(+(x,y))
 -(0,y) -> 0
 -(s(x),s(y)) -> -(x,y)
 -(x,0) -> x
->Projection:
 pi(+#) = 1

Problem 1.2: 

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

The problem is finite.