/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)
(RULES
sqr(x:S) -> *(x:S,x:S)
sum(0) -> 0
sum(s(x:S)) -> +(sqr(s(x:S)),sum(x:S))
sum(s(x:S)) -> +(*(s(x:S),s(x:S)),sum(x:S))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 SUM(s(x:S)) -> SQR(s(x:S))
 SUM(s(x:S)) -> SUM(x:S)
-> Rules:
 sqr(x:S) -> *(x:S,x:S)
 sum(0) -> 0
 sum(s(x:S)) -> +(sqr(s(x:S)),sum(x:S))
 sum(s(x:S)) -> +(*(s(x:S),s(x:S)),sum(x:S))

Problem 1: 

SCC Processor:
-> Pairs:
 SUM(s(x:S)) -> SQR(s(x:S))
 SUM(s(x:S)) -> SUM(x:S)
-> Rules:
 sqr(x:S) -> *(x:S,x:S)
 sum(0) -> 0
 sum(s(x:S)) -> +(sqr(s(x:S)),sum(x:S))
 sum(s(x:S)) -> +(*(s(x:S),s(x:S)),sum(x:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 SUM(s(x:S)) -> SUM(x:S)
->->-> Rules:
 sqr(x:S) -> *(x:S,x:S)
 sum(0) -> 0
 sum(s(x:S)) -> +(sqr(s(x:S)),sum(x:S))
 sum(s(x:S)) -> +(*(s(x:S),s(x:S)),sum(x:S))

Problem 1: 

Subterm Processor:
-> Pairs:
 SUM(s(x:S)) -> SUM(x:S)
-> Rules:
 sqr(x:S) -> *(x:S,x:S)
 sum(0) -> 0
 sum(s(x:S)) -> +(sqr(s(x:S)),sum(x:S))
 sum(s(x:S)) -> +(*(s(x:S),s(x:S)),sum(x:S))
->Projection:
 pi(SUM) = 1

Problem 1: 

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

The problem is finite.