/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 v_NonEmpty:S u:S v:S x:S y:S z:S)
(RULES
++(.(x:S,y:S),z:S) -> .(x:S,++(y:S,z:S))
++(nil,y:S) -> y:S
if(ffalse,x:S,y:S) -> x:S
if(ttrue,x:S,y:S) -> x:S
merge(.(x:S,y:S),.(u:S,v:S)) -> if(<(x:S,u:S),.(x:S,merge(y:S,.(u:S,v:S))),.(u:S,merge(.(x:S,y:S),v:S)))
merge(nil,y:S) -> y:S
merge(x:S,nil) -> x:S
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 ++(.(x:S,y:S),z:S) -> .(x:S,++(y:S,z:S))
 ++(nil,y:S) -> y:S
 if(ffalse,x:S,y:S) -> x:S
 if(ttrue,x:S,y:S) -> x:S
 merge(.(x:S,y:S),.(u:S,v:S)) -> if(<(x:S,u:S),.(x:S,merge(y:S,.(u:S,v:S))),.(u:S,merge(.(x:S,y:S),v:S)))
 merge(nil,y:S) -> y:S
 merge(x:S,nil) -> 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:
 ++#(.(x:S,y:S),z:S) -> ++#(y:S,z:S)
 MERGE(.(x:S,y:S),.(u:S,v:S)) -> IF(<(x:S,u:S),.(x:S,merge(y:S,.(u:S,v:S))),.(u:S,merge(.(x:S,y:S),v:S)))
 MERGE(.(x:S,y:S),.(u:S,v:S)) -> MERGE(.(x:S,y:S),v:S)
 MERGE(.(x:S,y:S),.(u:S,v:S)) -> MERGE(y:S,.(u:S,v:S))
-> Rules:
 ++(.(x:S,y:S),z:S) -> .(x:S,++(y:S,z:S))
 ++(nil,y:S) -> y:S
 if(ffalse,x:S,y:S) -> x:S
 if(ttrue,x:S,y:S) -> x:S
 merge(.(x:S,y:S),.(u:S,v:S)) -> if(<(x:S,u:S),.(x:S,merge(y:S,.(u:S,v:S))),.(u:S,merge(.(x:S,y:S),v:S)))
 merge(nil,y:S) -> y:S
 merge(x:S,nil) -> x:S

Problem 1: 

SCC Processor:
-> Pairs:
 ++#(.(x:S,y:S),z:S) -> ++#(y:S,z:S)
 MERGE(.(x:S,y:S),.(u:S,v:S)) -> IF(<(x:S,u:S),.(x:S,merge(y:S,.(u:S,v:S))),.(u:S,merge(.(x:S,y:S),v:S)))
 MERGE(.(x:S,y:S),.(u:S,v:S)) -> MERGE(.(x:S,y:S),v:S)
 MERGE(.(x:S,y:S),.(u:S,v:S)) -> MERGE(y:S,.(u:S,v:S))
-> Rules:
 ++(.(x:S,y:S),z:S) -> .(x:S,++(y:S,z:S))
 ++(nil,y:S) -> y:S
 if(ffalse,x:S,y:S) -> x:S
 if(ttrue,x:S,y:S) -> x:S
 merge(.(x:S,y:S),.(u:S,v:S)) -> if(<(x:S,u:S),.(x:S,merge(y:S,.(u:S,v:S))),.(u:S,merge(.(x:S,y:S),v:S)))
 merge(nil,y:S) -> y:S
 merge(x:S,nil) -> x:S
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 MERGE(.(x:S,y:S),.(u:S,v:S)) -> MERGE(.(x:S,y:S),v:S)
 MERGE(.(x:S,y:S),.(u:S,v:S)) -> MERGE(y:S,.(u:S,v:S))
->->-> Rules:
 ++(.(x:S,y:S),z:S) -> .(x:S,++(y:S,z:S))
 ++(nil,y:S) -> y:S
 if(ffalse,x:S,y:S) -> x:S
 if(ttrue,x:S,y:S) -> x:S
 merge(.(x:S,y:S),.(u:S,v:S)) -> if(<(x:S,u:S),.(x:S,merge(y:S,.(u:S,v:S))),.(u:S,merge(.(x:S,y:S),v:S)))
 merge(nil,y:S) -> y:S
 merge(x:S,nil) -> x:S
->->Cycle:
->->-> Pairs:
 ++#(.(x:S,y:S),z:S) -> ++#(y:S,z:S)
->->-> Rules:
 ++(.(x:S,y:S),z:S) -> .(x:S,++(y:S,z:S))
 ++(nil,y:S) -> y:S
 if(ffalse,x:S,y:S) -> x:S
 if(ttrue,x:S,y:S) -> x:S
 merge(.(x:S,y:S),.(u:S,v:S)) -> if(<(x:S,u:S),.(x:S,merge(y:S,.(u:S,v:S))),.(u:S,merge(.(x:S,y:S),v:S)))
 merge(nil,y:S) -> y:S
 merge(x:S,nil) -> x:S


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 MERGE(.(x:S,y:S),.(u:S,v:S)) -> MERGE(.(x:S,y:S),v:S)
 MERGE(.(x:S,y:S),.(u:S,v:S)) -> MERGE(y:S,.(u:S,v:S))
-> Rules:
 ++(.(x:S,y:S),z:S) -> .(x:S,++(y:S,z:S))
 ++(nil,y:S) -> y:S
 if(ffalse,x:S,y:S) -> x:S
 if(ttrue,x:S,y:S) -> x:S
 merge(.(x:S,y:S),.(u:S,v:S)) -> if(<(x:S,u:S),.(x:S,merge(y:S,.(u:S,v:S))),.(u:S,merge(.(x:S,y:S),v:S)))
 merge(nil,y:S) -> y:S
 merge(x:S,nil) -> x:S
->Projection:
 pi(MERGE) = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 MERGE(.(x:S,y:S),.(u:S,v:S)) -> MERGE(.(x:S,y:S),v:S)
-> Rules:
 ++(.(x:S,y:S),z:S) -> .(x:S,++(y:S,z:S))
 ++(nil,y:S) -> y:S
 if(ffalse,x:S,y:S) -> x:S
 if(ttrue,x:S,y:S) -> x:S
 merge(.(x:S,y:S),.(u:S,v:S)) -> if(<(x:S,u:S),.(x:S,merge(y:S,.(u:S,v:S))),.(u:S,merge(.(x:S,y:S),v:S)))
 merge(nil,y:S) -> y:S
 merge(x:S,nil) -> x:S
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 MERGE(.(x:S,y:S),.(u:S,v:S)) -> MERGE(.(x:S,y:S),v:S)
->->-> Rules:
 ++(.(x:S,y:S),z:S) -> .(x:S,++(y:S,z:S))
 ++(nil,y:S) -> y:S
 if(ffalse,x:S,y:S) -> x:S
 if(ttrue,x:S,y:S) -> x:S
 merge(.(x:S,y:S),.(u:S,v:S)) -> if(<(x:S,u:S),.(x:S,merge(y:S,.(u:S,v:S))),.(u:S,merge(.(x:S,y:S),v:S)))
 merge(nil,y:S) -> y:S
 merge(x:S,nil) -> x:S

Problem 1.1: 

Subterm Processor:
-> Pairs:
 MERGE(.(x:S,y:S),.(u:S,v:S)) -> MERGE(.(x:S,y:S),v:S)
-> Rules:
 ++(.(x:S,y:S),z:S) -> .(x:S,++(y:S,z:S))
 ++(nil,y:S) -> y:S
 if(ffalse,x:S,y:S) -> x:S
 if(ttrue,x:S,y:S) -> x:S
 merge(.(x:S,y:S),.(u:S,v:S)) -> if(<(x:S,u:S),.(x:S,merge(y:S,.(u:S,v:S))),.(u:S,merge(.(x:S,y:S),v:S)))
 merge(nil,y:S) -> y:S
 merge(x:S,nil) -> x:S
->Projection:
 pi(MERGE) = 2

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 ++(.(x:S,y:S),z:S) -> .(x:S,++(y:S,z:S))
 ++(nil,y:S) -> y:S
 if(ffalse,x:S,y:S) -> x:S
 if(ttrue,x:S,y:S) -> x:S
 merge(.(x:S,y:S),.(u:S,v:S)) -> if(<(x:S,u:S),.(x:S,merge(y:S,.(u:S,v:S))),.(u:S,merge(.(x:S,y:S),v:S)))
 merge(nil,y:S) -> y:S
 merge(x:S,nil) -> x:S
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 ++#(.(x:S,y:S),z:S) -> ++#(y:S,z:S)
-> Rules:
 ++(.(x:S,y:S),z:S) -> .(x:S,++(y:S,z:S))
 ++(nil,y:S) -> y:S
 if(ffalse,x:S,y:S) -> x:S
 if(ttrue,x:S,y:S) -> x:S
 merge(.(x:S,y:S),.(u:S,v:S)) -> if(<(x:S,u:S),.(x:S,merge(y:S,.(u:S,v:S))),.(u:S,merge(.(x:S,y:S),v:S)))
 merge(nil,y:S) -> y:S
 merge(x:S,nil) -> x:S
->Projection:
 pi(++#) = 1

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 ++(.(x:S,y:S),z:S) -> .(x:S,++(y:S,z:S))
 ++(nil,y:S) -> y:S
 if(ffalse,x:S,y:S) -> x:S
 if(ttrue,x:S,y:S) -> x:S
 merge(.(x:S,y:S),.(u:S,v:S)) -> if(<(x:S,u:S),.(x:S,merge(y:S,.(u:S,v:S))),.(u:S,merge(.(x:S,y:S),v:S)))
 merge(nil,y:S) -> y:S
 merge(x:S,nil) -> x:S
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.