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TRS Standard pair #487067834
details
property
value
status
complete
benchmark
2.40.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n179.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0188289 seconds
cpu usage
0.019333
user time
0.005484
system time
0.013849
max virtual memory
113188.0
max residence set size
5284.0
stage attributes
key
value
starexec-result
YES
output
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
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