TRS Standard pair #487068237

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	n175.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	0.648927 seconds
cpu usage	1.35565
user time	1.09968
system time	0.255977
max virtual memory	1764464.0
max residence set size	69580.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem:
 msort(nil()) -> nil()
 msort(.(x,y)) -> .(min(x,y),msort(del(min(x,y),.(x,y))))
 min(x,nil()) -> x
 min(x,.(y,z)) -> if(<=(x,y),min(x,z),min(y,z))
 del(x,nil()) -> nil()
 del(x,.(y,z)) -> if(=(x,y),z,.(y,del(x,z)))

Proof:
 DP Processor:
  DPs:
   msort#(.(x,y)) -> del#(min(x,y),.(x,y))
   msort#(.(x,y)) -> msort#(del(min(x,y),.(x,y)))
   msort#(.(x,y)) -> min#(x,y)
   min#(x,.(y,z)) -> min#(y,z)
   min#(x,.(y,z)) -> min#(x,z)
   del#(x,.(y,z)) -> del#(x,z)
  TRS:
   msort(nil()) -> nil()
   msort(.(x,y)) -> .(min(x,y),msort(del(min(x,y),.(x,y))))
   min(x,nil()) -> x
   min(x,.(y,z)) -> if(<=(x,y),min(x,z),min(y,z))
   del(x,nil()) -> nil()
   del(x,.(y,z)) -> if(=(x,y),z,.(y,del(x,z)))
  TDG Processor:
   DPs:
    msort#(.(x,y)) -> del#(min(x,y),.(x,y))
    msort#(.(x,y)) -> msort#(del(min(x,y),.(x,y)))
    msort#(.(x,y)) -> min#(x,y)
    min#(x,.(y,z)) -> min#(y,z)
    min#(x,.(y,z)) -> min#(x,z)
    del#(x,.(y,z)) -> del#(x,z)
   TRS:
    msort(nil()) -> nil()
    msort(.(x,y)) -> .(min(x,y),msort(del(min(x,y),.(x,y))))
    min(x,nil()) -> x
    min(x,.(y,z)) -> if(<=(x,y),min(x,z),min(y,z))
    del(x,nil()) -> nil()
    del(x,.(y,z)) -> if(=(x,y),z,.(y,del(x,z)))
   graph:
    min#(x,.(y,z)) -> min#(y,z) -> min#(x,.(y,z)) -> min#(x,z)
    min#(x,.(y,z)) -> min#(y,z) -> min#(x,.(y,z)) -> min#(y,z)
    min#(x,.(y,z)) -> min#(x,z) -> min#(x,.(y,z)) -> min#(x,z)
    min#(x,.(y,z)) -> min#(x,z) -> min#(x,.(y,z)) -> min#(y,z)
    del#(x,.(y,z)) -> del#(x,z) -> del#(x,.(y,z)) -> del#(x,z)
    msort#(.(x,y)) -> min#(x,y) -> min#(x,.(y,z)) -> min#(x,z)
    msort#(.(x,y)) -> min#(x,y) ->
    min#(x,.(y,z)) -> min#(y,z)
    msort#(.(x,y)) -> del#(min(x,y),.(x,y)) ->
    del#(x,.(y,z)) -> del#(x,z)
    msort#(.(x,y)) -> msort#(del(min(x,y),.(x,y))) ->
    msort#(.(x,y)) -> min#(x,y)
    msort#(.(x,y)) -> msort#(del(min(x,y),.(x,y))) ->
    msort#(.(x,y)) -> msort#(del(min(x,y),.(x,y)))
    msort#(.(x,y)) -> msort#(del(min(x,y),.(x,y))) -> msort#(.(x,y)) -> del#(min(x,y),.(x,y))
   SCC Processor:
    #sccs: 3
    #rules: 4
    #arcs: 11/36
    DPs:
     msort#(.(x,y)) -> msort#(del(min(x,y),.(x,y)))
    TRS:
     msort(nil()) -> nil()
     msort(.(x,y)) -> .(min(x,y),msort(del(min(x,y),.(x,y))))
     min(x,nil()) -> x
     min(x,.(y,z)) -> if(<=(x,y),min(x,z),min(y,z))
     del(x,nil()) -> nil()
     del(x,.(y,z)) -> if(=(x,y),z,.(y,del(x,z)))
    EDG Processor:
     DPs:
      msort#(.(x,y)) -> msort#(del(min(x,y),.(x,y)))
     TRS:
      msort(nil()) -> nil()
      msort(.(x,y)) -> .(min(x,y),msort(del(min(x,y),.(x,y))))
      min(x,nil()) -> x
      min(x,.(y,z)) -> if(<=(x,y),min(x,z),min(y,z))
      del(x,nil()) -> nil()
      del(x,.(y,z)) -> if(=(x,y),z,.(y,del(x,z)))
     graph:
      
     SCC Processor:
      #sccs: 0
      #rules: 0
      #arcs: 0/1
      
    
    DPs:
     del#(x,.(y,z)) -> del#(x,z)
    TRS:
     msort(nil()) -> nil()
     msort(.(x,y)) -> .(min(x,y),msort(del(min(x,y),.(x,y))))
     min(x,nil()) -> x
     min(x,.(y,z)) -> if(<=(x,y),min(x,z),min(y,z))
     del(x,nil()) -> nil()
     del(x,.(y,z)) -> if(=(x,y),z,.(y,del(x,z)))
    Subterm Criterion Processor:
     simple projection:
      pi(del#) = 1

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