/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 xs:S y:S ys:S)
(RULES
isnoc(cons(x:S,ys:S)) -> tp2(cons(x:S,xs:S),y:S) | isnoc(ys:S) ->* tp2(xs:S,y:S)
isnoc(cons(y:S,nil)) -> tp2(nil,y:S)
)

Problem 1: 
Valid CTRS Processor:
-> Rules:
 isnoc(cons(x:S,ys:S)) -> tp2(cons(x:S,xs:S),y:S) | isnoc(ys:S) ->* tp2(xs:S,y:S)
 isnoc(cons(y:S,nil)) -> tp2(nil,y:S)
-> The system is a deterministic 3-CTRS.

Problem 1: 

Dependency Pairs Processor:

Conditional Termination Problem 1:
-> Pairs:
 Empty
-> QPairs:
 Empty
-> Rules:
 isnoc(cons(x:S,ys:S)) -> tp2(cons(x:S,xs:S),y:S) | isnoc(ys:S) ->* tp2(xs:S,y:S)
 isnoc(cons(y:S,nil)) -> tp2(nil,y:S)

Conditional Termination Problem 2:
-> Pairs:
 ISNOC(cons(x:S,ys:S)) -> ISNOC(ys:S)
-> QPairs:
 Empty
-> Rules:
 isnoc(cons(x:S,ys:S)) -> tp2(cons(x:S,xs:S),y:S) | isnoc(ys:S) ->* tp2(xs:S,y:S)
 isnoc(cons(y:S,nil)) -> tp2(nil,y:S)


The problem is decomposed in 2 subproblems.

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> QPairs:
 Empty
-> Rules:
 isnoc(cons(x:S,ys:S)) -> tp2(cons(x:S,xs:S),y:S) | isnoc(ys:S) ->* tp2(xs:S,y:S)
 isnoc(cons(y:S,nil)) -> tp2(nil,y:S)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

SCC Processor:
-> Pairs:
 ISNOC(cons(x:S,ys:S)) -> ISNOC(ys:S)
-> QPairs:
 Empty
-> Rules:
 isnoc(cons(x:S,ys:S)) -> tp2(cons(x:S,xs:S),y:S) | isnoc(ys:S) ->* tp2(xs:S,y:S)
 isnoc(cons(y:S,nil)) -> tp2(nil,y:S)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ISNOC(cons(x:S,ys:S)) -> ISNOC(ys:S)
-> QPairs:
 Empty
->->-> Rules:
 isnoc(cons(x:S,ys:S)) -> tp2(cons(x:S,xs:S),y:S) | isnoc(ys:S) ->* tp2(xs:S,y:S)
 isnoc(cons(y:S,nil)) -> tp2(nil,y:S)

Problem 1.2: 

Conditional Subterm Processor:
-> Pairs:
 ISNOC(cons(x:S,ys:S)) -> ISNOC(ys:S)
-> QPairs:
 Empty
-> Rules:
 isnoc(cons(x:S,ys:S)) -> tp2(cons(x:S,xs:S),y:S) | isnoc(ys:S) ->* tp2(xs:S,y:S)
 isnoc(cons(y:S,nil)) -> tp2(nil,y:S)
->Projection:
 pi(ISNOC) = 1

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> QPairs:
 Empty
-> Rules:
 isnoc(cons(x:S,ys:S)) -> tp2(cons(x:S,xs:S),y:S) | isnoc(ys:S) ->* tp2(xs:S,y:S)
 isnoc(cons(y:S,nil)) -> tp2(nil,y:S)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.