TRS Standard pair #516965064

details

property	value
status	complete
benchmark	007.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n003.star.cs.uiowa.edu
space	AotoYamada_05

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	0.587487220764 seconds
cpu usage	0.930479081
max memory	1.81542912E8

stage attributes

key	value
output-size	7386
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


YES

Problem:
 app(app(plus(),0()),y) -> y
 app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
 app(app(map(),f),nil()) -> nil()
 app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
 inc() -> app(map(),app(plus(),app(s(),0())))

Proof:
 Extended Uncurrying Processor:
  application symbol: app
  symbol table:
   inc ==> inc0/0
   cons ==> cons0/0 cons1/1 cons2/2
   nil ==> nil0/0
   map ==> map0/0 map1/1 map2/2
   s ==> s0/0 s1/1
   0 ==> 00/0
   plus ==> plus0/0 plus1/1 plus2/2
   
  uncurry-rules:
   app(plus1(x4),x5) -> plus2(x4,x5)
   app(plus0(),x4) -> plus1(x4)
   app(s0(),x8) -> s1(x8)
   app(map1(x10),x11) -> map2(x10,x11)
   app(map0(),x10) -> map1(x10)
   app(cons1(x14),x15) -> cons2(x14,x15)
   app(cons0(),x14) -> cons1(x14)
  eta-rules:
   
  problem:
   plus2(00(),y) -> y
   plus2(s1(x),y) -> s1(plus2(x,y))
   map2(f,nil0()) -> nil0()
   map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
   inc0() -> map1(plus1(s1(00())))
   app(plus1(x4),x5) -> plus2(x4,x5)
   app(plus0(),x4) -> plus1(x4)
   app(s0(),x8) -> s1(x8)
   app(map1(x10),x11) -> map2(x10,x11)
   app(map0(),x10) -> map1(x10)
   app(cons1(x14),x15) -> cons2(x14,x15)
   app(cons0(),x14) -> cons1(x14)
  DP Processor:
   DPs:
    plus{2,#}(s1(x),y) -> plus{2,#}(x,y)
    map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
    map{2,#}(f,cons2(x,xs)) -> app#(f,x)
    app#(plus1(x4),x5) -> plus{2,#}(x4,x5)
    app#(map1(x10),x11) -> map{2,#}(x10,x11)
   TRS:
    plus2(00(),y) -> y
    plus2(s1(x),y) -> s1(plus2(x,y))
    map2(f,nil0()) -> nil0()
    map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
    inc0() -> map1(plus1(s1(00())))
    app(plus1(x4),x5) -> plus2(x4,x5)
    app(plus0(),x4) -> plus1(x4)
    app(s0(),x8) -> s1(x8)
    app(map1(x10),x11) -> map2(x10,x11)
    app(map0(),x10) -> map1(x10)
    app(cons1(x14),x15) -> cons2(x14,x15)
    app(cons0(),x14) -> cons1(x14)
   TDG Processor:
    DPs:
     plus{2,#}(s1(x),y) -> plus{2,#}(x,y)
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     app#(plus1(x4),x5) -> plus{2,#}(x4,x5)
     app#(map1(x10),x11) -> map{2,#}(x10,x11)
    TRS:
     plus2(00(),y) -> y
     plus2(s1(x),y) -> s1(plus2(x,y))
     map2(f,nil0()) -> nil0()
     map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
     inc0() -> map1(plus1(s1(00())))
     app(plus1(x4),x5) -> plus2(x4,x5)
     app(plus0(),x4) -> plus1(x4)
     app(s0(),x8) -> s1(x8)
     app(map1(x10),x11) -> map2(x10,x11)
     app(map0(),x10) -> map1(x10)
     app(cons1(x14),x15) -> cons2(x14,x15)
     app(cons0(),x14) -> cons1(x14)
    graph:
     app#(map1(x10),x11) -> map{2,#}(x10,x11) ->
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     app#(map1(x10),x11) -> map{2,#}(x10,x11) ->
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     app#(plus1(x4),x5) -> plus{2,#}(x4,x5) ->
     plus{2,#}(s1(x),y) -> plus{2,#}(x,y)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(map1(x10),x11) -> map{2,#}(x10,x11)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->

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