/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 z:S)
(RULES
mem(x:S,nil) -> ffalse
mem(x:S,set(y:S)) -> =(x:S,y:S)
mem(x:S,union(y:S,z:S)) -> or(mem(x:S,y:S),mem(x:S,z:S))
or(ffalse,ffalse) -> ffalse
or(ttrue,y:S) -> ttrue
or(x:S,ttrue) -> ttrue
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 mem(x:S,nil) -> ffalse
 mem(x:S,set(y:S)) -> =(x:S,y:S)
 mem(x:S,union(y:S,z:S)) -> or(mem(x:S,y:S),mem(x:S,z:S))
 or(ffalse,ffalse) -> ffalse
 or(ttrue,y:S) -> ttrue
 or(x:S,ttrue) -> ttrue
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 MEM(x:S,union(y:S,z:S)) -> MEM(x:S,y:S)
 MEM(x:S,union(y:S,z:S)) -> MEM(x:S,z:S)
 MEM(x:S,union(y:S,z:S)) -> OR(mem(x:S,y:S),mem(x:S,z:S))
-> Rules:
 mem(x:S,nil) -> ffalse
 mem(x:S,set(y:S)) -> =(x:S,y:S)
 mem(x:S,union(y:S,z:S)) -> or(mem(x:S,y:S),mem(x:S,z:S))
 or(ffalse,ffalse) -> ffalse
 or(ttrue,y:S) -> ttrue
 or(x:S,ttrue) -> ttrue

Problem 1: 

SCC Processor:
-> Pairs:
 MEM(x:S,union(y:S,z:S)) -> MEM(x:S,y:S)
 MEM(x:S,union(y:S,z:S)) -> MEM(x:S,z:S)
 MEM(x:S,union(y:S,z:S)) -> OR(mem(x:S,y:S),mem(x:S,z:S))
-> Rules:
 mem(x:S,nil) -> ffalse
 mem(x:S,set(y:S)) -> =(x:S,y:S)
 mem(x:S,union(y:S,z:S)) -> or(mem(x:S,y:S),mem(x:S,z:S))
 or(ffalse,ffalse) -> ffalse
 or(ttrue,y:S) -> ttrue
 or(x:S,ttrue) -> ttrue
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 MEM(x:S,union(y:S,z:S)) -> MEM(x:S,y:S)
 MEM(x:S,union(y:S,z:S)) -> MEM(x:S,z:S)
->->-> Rules:
 mem(x:S,nil) -> ffalse
 mem(x:S,set(y:S)) -> =(x:S,y:S)
 mem(x:S,union(y:S,z:S)) -> or(mem(x:S,y:S),mem(x:S,z:S))
 or(ffalse,ffalse) -> ffalse
 or(ttrue,y:S) -> ttrue
 or(x:S,ttrue) -> ttrue

Problem 1: 

Subterm Processor:
-> Pairs:
 MEM(x:S,union(y:S,z:S)) -> MEM(x:S,y:S)
 MEM(x:S,union(y:S,z:S)) -> MEM(x:S,z:S)
-> Rules:
 mem(x:S,nil) -> ffalse
 mem(x:S,set(y:S)) -> =(x:S,y:S)
 mem(x:S,union(y:S,z:S)) -> or(mem(x:S,y:S),mem(x:S,z:S))
 or(ffalse,ffalse) -> ffalse
 or(ttrue,y:S) -> ttrue
 or(x:S,ttrue) -> ttrue
->Projection:
 pi(MEM) = 2

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 mem(x:S,nil) -> ffalse
 mem(x:S,set(y:S)) -> =(x:S,y:S)
 mem(x:S,union(y:S,z:S)) -> or(mem(x:S,y:S),mem(x:S,z:S))
 or(ffalse,ffalse) -> ffalse
 or(ttrue,y:S) -> ttrue
 or(x:S,ttrue) -> ttrue
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.