/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES

Problem 1: 

(VAR v_NonEmpty:S x:S y:S)
(RULES
gcd(0,y:S) -> y:S
gcd(s(x:S),s(y:S)) -> if(<(x:S,y:S),gcd(s(x:S),-(y:S,x:S)),gcd(-(x:S,y:S),s(y:S)))
gcd(x:S,0) -> x:S
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 gcd(0,y:S) -> y:S
 gcd(s(x:S),s(y:S)) -> if(<(x:S,y:S),gcd(s(x:S),-(y:S,x:S)),gcd(-(x:S,y:S),s(y:S)))
 gcd(x:S,0) -> x:S
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 Empty
-> Rules:
 gcd(0,y:S) -> y:S
 gcd(s(x:S),s(y:S)) -> if(<(x:S,y:S),gcd(s(x:S),-(y:S,x:S)),gcd(-(x:S,y:S),s(y:S)))
 gcd(x:S,0) -> x:S

Problem 1: 

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

The problem is finite.