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TRS Standard pair #487068144
details
property
value
status
complete
benchmark
4.31.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)
0.053957 seconds
cpu usage
0.043353
user time
0.024622
system time
0.018731
max virtual memory
113188.0
max residence set size
5464.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S x:S y:S z:S) (RULES purge(.(x:S,y:S)) -> .(x:S,purge(remove(x:S,y:S))) purge(nil) -> nil remove(x:S,.(y:S,z:S)) -> if(=(x:S,y:S),remove(x:S,z:S),.(y:S,remove(x:S,z:S))) remove(x:S,nil) -> nil ) Problem 1: Innermost Equivalent Processor: -> Rules: purge(.(x:S,y:S)) -> .(x:S,purge(remove(x:S,y:S))) purge(nil) -> nil remove(x:S,.(y:S,z:S)) -> if(=(x:S,y:S),remove(x:S,z:S),.(y:S,remove(x:S,z:S))) remove(x:S,nil) -> nil -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: PURGE(.(x:S,y:S)) -> PURGE(remove(x:S,y:S)) PURGE(.(x:S,y:S)) -> REMOVE(x:S,y:S) REMOVE(x:S,.(y:S,z:S)) -> REMOVE(x:S,z:S) -> Rules: purge(.(x:S,y:S)) -> .(x:S,purge(remove(x:S,y:S))) purge(nil) -> nil remove(x:S,.(y:S,z:S)) -> if(=(x:S,y:S),remove(x:S,z:S),.(y:S,remove(x:S,z:S))) remove(x:S,nil) -> nil Problem 1: SCC Processor: -> Pairs: PURGE(.(x:S,y:S)) -> PURGE(remove(x:S,y:S)) PURGE(.(x:S,y:S)) -> REMOVE(x:S,y:S) REMOVE(x:S,.(y:S,z:S)) -> REMOVE(x:S,z:S) -> Rules: purge(.(x:S,y:S)) -> .(x:S,purge(remove(x:S,y:S))) purge(nil) -> nil remove(x:S,.(y:S,z:S)) -> if(=(x:S,y:S),remove(x:S,z:S),.(y:S,remove(x:S,z:S))) remove(x:S,nil) -> nil ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: REMOVE(x:S,.(y:S,z:S)) -> REMOVE(x:S,z:S) ->->-> Rules: purge(.(x:S,y:S)) -> .(x:S,purge(remove(x:S,y:S))) purge(nil) -> nil remove(x:S,.(y:S,z:S)) -> if(=(x:S,y:S),remove(x:S,z:S),.(y:S,remove(x:S,z:S))) remove(x:S,nil) -> nil ->->Cycle: ->->-> Pairs: PURGE(.(x:S,y:S)) -> PURGE(remove(x:S,y:S)) ->->-> Rules: purge(.(x:S,y:S)) -> .(x:S,purge(remove(x:S,y:S))) purge(nil) -> nil remove(x:S,.(y:S,z:S)) -> if(=(x:S,y:S),remove(x:S,z:S),.(y:S,remove(x:S,z:S))) remove(x:S,nil) -> nil The problem is decomposed in 2 subproblems. Problem 1.1: Subterm Processor: -> Pairs: REMOVE(x:S,.(y:S,z:S)) -> REMOVE(x:S,z:S) -> Rules: purge(.(x:S,y:S)) -> .(x:S,purge(remove(x:S,y:S))) purge(nil) -> nil remove(x:S,.(y:S,z:S)) -> if(=(x:S,y:S),remove(x:S,z:S),.(y:S,remove(x:S,z:S))) remove(x:S,nil) -> nil ->Projection: pi(REMOVE) = 2 Problem 1.1: SCC Processor: -> Pairs: Empty -> Rules: purge(.(x:S,y:S)) -> .(x:S,purge(remove(x:S,y:S))) purge(nil) -> nil remove(x:S,.(y:S,z:S)) -> if(=(x:S,y:S),remove(x:S,z:S),.(y:S,remove(x:S,z:S))) remove(x:S,nil) -> nil ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.2: Reduction Pairs Processor:
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