/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 x y z)
(RULES
mem(x,nil) -> false
mem(x,set(y)) -> =(x,y)
mem(x,union(y,z)) -> or(mem(x,y),mem(x,z))
or(false,false) -> false
or(true,y) -> true
or(x,true) -> true
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 mem(x,nil) -> false
 mem(x,set(y)) -> =(x,y)
 mem(x,union(y,z)) -> or(mem(x,y),mem(x,z))
 or(false,false) -> false
 or(true,y) -> true
 or(x,true) -> true
-> 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,union(y,z)) -> MEM(x,y)
 MEM(x,union(y,z)) -> MEM(x,z)
 MEM(x,union(y,z)) -> OR(mem(x,y),mem(x,z))
-> Rules:
 mem(x,nil) -> false
 mem(x,set(y)) -> =(x,y)
 mem(x,union(y,z)) -> or(mem(x,y),mem(x,z))
 or(false,false) -> false
 or(true,y) -> true
 or(x,true) -> true

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

The problem is finite.