TRS Relative pair #487081835

details

property	value
status	complete
benchmark	relsubst.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n137.star.cs.uiowa.edu
space	Mixed_relative_TRS

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	9.52536 seconds
cpu usage	36.3973
user time	33.7675
system time	2.62981
max virtual memory	5537396.0
max residence set size	136956.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem:
 strict:
  o(lambda(x),y) -> lambda(o(x,d(1(),o(y,p()))))
  o(d(x,y),z) -> d(o(x,z),o(y,z))
  o(o(x,y),z) -> o(x,o(y,z))
  lambda(x) -> x
  o(x,y) -> x
  o(x,y) -> y
  d(x,y) -> x
  d(x,y) -> y
 weak:
  o(x,y) -> d(x,y)
  o(x,y) -> d(y,x)

Proof:
 RT Transformation Processor:
  o(lambda(x),y) -> lambda(o(x,d(1(),o(y,p()))))
  o(d(x,y),z) -> d(o(x,z),o(y,z))
  o(o(x,y),z) -> o(x,o(y,z))
  lambda(x) -> x
  o(x,y) -> x
  o(x,y) -> y
  d(x,y) -> x
  d(x,y) -> y
  o(x,y) -> d(x,y)
  o(x,y) -> d(y,x)
  DP Processor:
   DPs:
    o#(lambda(x),y) -> o#(y,p())
    o#(lambda(x),y) -> d#(1(),o(y,p()))
    o#(lambda(x),y) -> o#(x,d(1(),o(y,p())))
    o#(lambda(x),y) -> lambda#(o(x,d(1(),o(y,p()))))
    o#(d(x,y),z) -> o#(y,z)
    o#(d(x,y),z) -> o#(x,z)
    o#(d(x,y),z) -> d#(o(x,z),o(y,z))
    o#(o(x,y),z) -> o#(y,z)
    o#(o(x,y),z) -> o#(x,o(y,z))
    o#(x,y) -> d#(x,y)
    o#(x,y) -> d#(y,x)
   TRS:
    o(lambda(x),y) -> lambda(o(x,d(1(),o(y,p()))))
    o(d(x,y),z) -> d(o(x,z),o(y,z))
    o(o(x,y),z) -> o(x,o(y,z))
    lambda(x) -> x
    o(x,y) -> x
    o(x,y) -> y
    d(x,y) -> x
    d(x,y) -> y
    o(x,y) -> d(x,y)
    o(x,y) -> d(y,x)
   TDG Processor:
    DPs:
     o#(lambda(x),y) -> o#(y,p())
     o#(lambda(x),y) -> d#(1(),o(y,p()))
     o#(lambda(x),y) -> o#(x,d(1(),o(y,p())))
     o#(lambda(x),y) -> lambda#(o(x,d(1(),o(y,p()))))
     o#(d(x,y),z) -> o#(y,z)
     o#(d(x,y),z) -> o#(x,z)
     o#(d(x,y),z) -> d#(o(x,z),o(y,z))
     o#(o(x,y),z) -> o#(y,z)
     o#(o(x,y),z) -> o#(x,o(y,z))
     o#(x,y) -> d#(x,y)
     o#(x,y) -> d#(y,x)
    TRS:
     o(lambda(x),y) -> lambda(o(x,d(1(),o(y,p()))))
     o(d(x,y),z) -> d(o(x,z),o(y,z))
     o(o(x,y),z) -> o(x,o(y,z))
     lambda(x) -> x
     o(x,y) -> x
     o(x,y) -> y
     d(x,y) -> x
     d(x,y) -> y
     o(x,y) -> d(x,y)
     o(x,y) -> d(y,x)
    graph:
     o#(d(x,y),z) -> o#(y,z) -> o#(x,y) -> d#(y,x)
     o#(d(x,y),z) -> o#(y,z) -> o#(x,y) -> d#(x,y)
     o#(d(x,y),z) -> o#(y,z) -> o#(o(x,y),z) -> o#(x,o(y,z))
     o#(d(x,y),z) -> o#(y,z) -> o#(o(x,y),z) -> o#(y,z)
     o#(d(x,y),z) -> o#(y,z) -> o#(d(x,y),z) -> d#(o(x,z),o(y,z))
     o#(d(x,y),z) -> o#(y,z) -> o#(d(x,y),z) -> o#(x,z)
     o#(d(x,y),z) -> o#(y,z) -> o#(d(x,y),z) -> o#(y,z)
     o#(d(x,y),z) -> o#(y,z) ->
     o#(lambda(x),y) -> lambda#(o(x,d(1(),o(y,p()))))
     o#(d(x,y),z) -> o#(y,z) -> o#(lambda(x),y) -> o#(x,d(1(),o(y,p())))
     o#(d(x,y),z) -> o#(y,z) -> o#(lambda(x),y) -> d#(1(),o(y,p()))
     o#(d(x,y),z) -> o#(y,z) -> o#(lambda(x),y) -> o#(y,p())
     o#(d(x,y),z) -> o#(x,z) -> o#(x,y) -> d#(y,x)
     o#(d(x,y),z) -> o#(x,z) -> o#(x,y) -> d#(x,y)
     o#(d(x,y),z) -> o#(x,z) -> o#(o(x,y),z) -> o#(x,o(y,z))
     o#(d(x,y),z) -> o#(x,z) -> o#(o(x,y),z) -> o#(y,z)
     o#(d(x,y),z) -> o#(x,z) -> o#(d(x,y),z) -> d#(o(x,z),o(y,z))
     o#(d(x,y),z) -> o#(x,z) -> o#(d(x,y),z) -> o#(x,z)
     o#(d(x,y),z) -> o#(x,z) -> o#(d(x,y),z) -> o#(y,z)
     o#(d(x,y),z) -> o#(x,z) ->
     o#(lambda(x),y) -> lambda#(o(x,d(1(),o(y,p()))))
     o#(d(x,y),z) -> o#(x,z) -> o#(lambda(x),y) -> o#(x,d(1(),o(y,p())))
     o#(d(x,y),z) -> o#(x,z) -> o#(lambda(x),y) -> d#(1(),o(y,p()))

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job log

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