TRS Standard pair #487073347

details

property	value
status	complete
benchmark	019.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n177.star.cs.uiowa.edu
space	AotoYamada_05

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	0.638021 seconds
cpu usage	1.39809
user time	0.99433
system time	0.403756
max virtual memory	3493776.0
max residence set size	67980.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem:
 app(app(app(comp(),f),g),x) -> app(f,app(g,x))
 app(twice(),f) -> app(app(comp(),f),f)

Proof:
 Extended Uncurrying Processor:
  application symbol: app
  symbol table:
   twice ==> twice0/0 twice1/1
   comp ==> comp0/0 comp1/1 comp2/2 comp3/3
   
  uncurry-rules:
   app(comp2(x3,x4),x5) -> comp3(x3,x4,x5)
   app(comp1(x3),x4) -> comp2(x3,x4)
   app(comp0(),x3) -> comp1(x3)
   app(twice0(),x7) -> twice1(x7)
  eta-rules:
   
  problem:
   comp3(f,g,x) -> app(f,app(g,x))
   twice1(f) -> comp2(f,f)
   app(comp2(x3,x4),x5) -> comp3(x3,x4,x5)
   app(comp1(x3),x4) -> comp2(x3,x4)
   app(comp0(),x3) -> comp1(x3)
   app(twice0(),x7) -> twice1(x7)
  DP Processor:
   DPs:
    comp{3,#}(f,g,x) -> app#(g,x)
    comp{3,#}(f,g,x) -> app#(f,app(g,x))
    app#(comp2(x3,x4),x5) -> comp{3,#}(x3,x4,x5)
    app#(twice0(),x7) -> twice{1,#}(x7)
   TRS:
    comp3(f,g,x) -> app(f,app(g,x))
    twice1(f) -> comp2(f,f)
    app(comp2(x3,x4),x5) -> comp3(x3,x4,x5)
    app(comp1(x3),x4) -> comp2(x3,x4)
    app(comp0(),x3) -> comp1(x3)
    app(twice0(),x7) -> twice1(x7)
   TDG Processor:
    DPs:
     comp{3,#}(f,g,x) -> app#(g,x)
     comp{3,#}(f,g,x) -> app#(f,app(g,x))
     app#(comp2(x3,x4),x5) -> comp{3,#}(x3,x4,x5)
     app#(twice0(),x7) -> twice{1,#}(x7)
    TRS:
     comp3(f,g,x) -> app(f,app(g,x))
     twice1(f) -> comp2(f,f)
     app(comp2(x3,x4),x5) -> comp3(x3,x4,x5)
     app(comp1(x3),x4) -> comp2(x3,x4)
     app(comp0(),x3) -> comp1(x3)
     app(twice0(),x7) -> twice1(x7)
    graph:
     app#(comp2(x3,x4),x5) -> comp{3,#}(x3,x4,x5) ->
     comp{3,#}(f,g,x) -> app#(f,app(g,x))
     app#(comp2(x3,x4),x5) -> comp{3,#}(x3,x4,x5) ->
     comp{3,#}(f,g,x) -> app#(g,x)
     comp{3,#}(f,g,x) -> app#(g,x) ->
     app#(twice0(),x7) -> twice{1,#}(x7)
     comp{3,#}(f,g,x) -> app#(g,x) ->
     app#(comp2(x3,x4),x5) -> comp{3,#}(x3,x4,x5)
     comp{3,#}(f,g,x) -> app#(f,app(g,x)) ->
     app#(twice0(),x7) -> twice{1,#}(x7)
     comp{3,#}(f,g,x) -> app#(f,app(g,x)) -> app#(comp2(x3,x4),x5) -> comp{3,#}(x3,x4,x5)
    SCC Processor:
     #sccs: 1
     #rules: 3
     #arcs: 6/16
     DPs:
      app#(comp2(x3,x4),x5) -> comp{3,#}(x3,x4,x5)
      comp{3,#}(f,g,x) -> app#(g,x)
      comp{3,#}(f,g,x) -> app#(f,app(g,x))
     TRS:
      comp3(f,g,x) -> app(f,app(g,x))
      twice1(f) -> comp2(f,f)
      app(comp2(x3,x4),x5) -> comp3(x3,x4,x5)
      app(comp1(x3),x4) -> comp2(x3,x4)
      app(comp0(),x3) -> comp1(x3)
      app(twice0(),x7) -> twice1(x7)
     Size-Change Termination Processor:
      DPs:
       
      TRS:
       comp3(f,g,x) -> app(f,app(g,x))
       twice1(f) -> comp2(f,f)
       app(comp2(x3,x4),x5) -> comp3(x3,x4,x5)
       app(comp1(x3),x4) -> comp2(x3,x4)
       app(comp0(),x3) -> comp1(x3)
       app(twice0(),x7) -> twice1(x7)
      The DP: app#(comp2(x3,x4),x5) -> comp{3,#}(x3,x4,x5) has the edges:
        0 >   1
        0 >   0
        1 >=  2
      The DP: comp{3,#}(f,g,x) -> app#(g,x) has the edges:
        1 >=  0
        2 >=  1
      The DP: comp{3,#}(f,g,x) -> app#(f,app(g,x)) has the edges:
        0 >=  0
      Qed

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