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TRS Standard pair #516966461
details
property
value
status
complete
benchmark
4.60.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n136.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.124435901642 seconds
cpu usage
0.04862688
max memory
4124672.0
stage attributes
key
value
output-size
6285
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR v_NonEmpty:S x:S y:S z:S) (RULES del(x:S,.(y:S,z:S)) -> if(=(x:S,y:S),z:S,.(y:S,del(x:S,z:S))) del(x:S,nil) -> nil min(x:S,.(y:S,z:S)) -> if(<=(x:S,y:S),min(x:S,z:S),min(y:S,z:S)) min(x:S,nil) -> x:S msort(.(x:S,y:S)) -> .(min(x:S,y:S),msort(del(min(x:S,y:S),.(x:S,y:S)))) msort(nil) -> nil ) Problem 1: Innermost Equivalent Processor: -> Rules: del(x:S,.(y:S,z:S)) -> if(=(x:S,y:S),z:S,.(y:S,del(x:S,z:S))) del(x:S,nil) -> nil min(x:S,.(y:S,z:S)) -> if(<=(x:S,y:S),min(x:S,z:S),min(y:S,z:S)) min(x:S,nil) -> x:S msort(.(x:S,y:S)) -> .(min(x:S,y:S),msort(del(min(x:S,y:S),.(x:S,y:S)))) msort(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: DEL(x:S,.(y:S,z:S)) -> DEL(x:S,z:S) MIN(x:S,.(y:S,z:S)) -> MIN(x:S,z:S) MIN(x:S,.(y:S,z:S)) -> MIN(y:S,z:S) MSORT(.(x:S,y:S)) -> DEL(min(x:S,y:S),.(x:S,y:S)) MSORT(.(x:S,y:S)) -> MIN(x:S,y:S) MSORT(.(x:S,y:S)) -> MSORT(del(min(x:S,y:S),.(x:S,y:S))) -> Rules: del(x:S,.(y:S,z:S)) -> if(=(x:S,y:S),z:S,.(y:S,del(x:S,z:S))) del(x:S,nil) -> nil min(x:S,.(y:S,z:S)) -> if(<=(x:S,y:S),min(x:S,z:S),min(y:S,z:S)) min(x:S,nil) -> x:S msort(.(x:S,y:S)) -> .(min(x:S,y:S),msort(del(min(x:S,y:S),.(x:S,y:S)))) msort(nil) -> nil Problem 1: SCC Processor: -> Pairs: DEL(x:S,.(y:S,z:S)) -> DEL(x:S,z:S) MIN(x:S,.(y:S,z:S)) -> MIN(x:S,z:S) MIN(x:S,.(y:S,z:S)) -> MIN(y:S,z:S) MSORT(.(x:S,y:S)) -> DEL(min(x:S,y:S),.(x:S,y:S)) MSORT(.(x:S,y:S)) -> MIN(x:S,y:S) MSORT(.(x:S,y:S)) -> MSORT(del(min(x:S,y:S),.(x:S,y:S))) -> Rules: del(x:S,.(y:S,z:S)) -> if(=(x:S,y:S),z:S,.(y:S,del(x:S,z:S))) del(x:S,nil) -> nil min(x:S,.(y:S,z:S)) -> if(<=(x:S,y:S),min(x:S,z:S),min(y:S,z:S)) min(x:S,nil) -> x:S msort(.(x:S,y:S)) -> .(min(x:S,y:S),msort(del(min(x:S,y:S),.(x:S,y:S)))) msort(nil) -> nil ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: MIN(x:S,.(y:S,z:S)) -> MIN(x:S,z:S) MIN(x:S,.(y:S,z:S)) -> MIN(y:S,z:S) ->->-> Rules: del(x:S,.(y:S,z:S)) -> if(=(x:S,y:S),z:S,.(y:S,del(x:S,z:S))) del(x:S,nil) -> nil min(x:S,.(y:S,z:S)) -> if(<=(x:S,y:S),min(x:S,z:S),min(y:S,z:S)) min(x:S,nil) -> x:S msort(.(x:S,y:S)) -> .(min(x:S,y:S),msort(del(min(x:S,y:S),.(x:S,y:S)))) msort(nil) -> nil ->->Cycle: ->->-> Pairs: DEL(x:S,.(y:S,z:S)) -> DEL(x:S,z:S) ->->-> Rules: del(x:S,.(y:S,z:S)) -> if(=(x:S,y:S),z:S,.(y:S,del(x:S,z:S))) del(x:S,nil) -> nil min(x:S,.(y:S,z:S)) -> if(<=(x:S,y:S),min(x:S,z:S),min(y:S,z:S)) min(x:S,nil) -> x:S msort(.(x:S,y:S)) -> .(min(x:S,y:S),msort(del(min(x:S,y:S),.(x:S,y:S)))) msort(nil) -> nil ->->Cycle: ->->-> Pairs: MSORT(.(x:S,y:S)) -> MSORT(del(min(x:S,y:S),.(x:S,y:S))) ->->-> Rules: del(x:S,.(y:S,z:S)) -> if(=(x:S,y:S),z:S,.(y:S,del(x:S,z:S))) del(x:S,nil) -> nil min(x:S,.(y:S,z:S)) -> if(<=(x:S,y:S),min(x:S,z:S),min(y:S,z:S)) min(x:S,nil) -> x:S msort(.(x:S,y:S)) -> .(min(x:S,y:S),msort(del(min(x:S,y:S),.(x:S,y:S)))) msort(nil) -> nil
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