TRS Standard pair #487072482

details

property	value
status	complete
benchmark	06.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n183.star.cs.uiowa.edu
space	Applicative_first_order_05

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	0.643275 seconds
cpu usage	1.42109
user time	1.15953
system time	0.261557
max virtual memory	1871276.0
max residence set size	71524.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem:
 app(f(),app(g(),x)) -> app(g(),app(g(),app(f(),x)))
 app(f(),app(g(),x)) -> app(g(),app(g(),app(g(),x)))
 app(app(map(),fun),nil()) -> nil()
 app(app(map(),fun),app(app(cons(),x),xs)) -> app(app(cons(),app(fun,x)),app(app(map(),fun),xs))
 app(app(filter(),fun),nil()) -> nil()
 app(app(filter(),fun),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(fun,x)),fun),x),xs)
 app(app(app(app(filter2(),true()),fun),x),xs) -> app(app(cons(),x),app(app(filter(),fun),xs))
 app(app(app(app(filter2(),false()),fun),x),xs) -> app(app(filter(),fun),xs)

Proof:
 Extended Uncurrying Processor:
  application symbol: app
  symbol table:
   false ==> false0/0
   true ==> true0/0
   filter2 ==> filter20/0 filter21/1 filter22/2 filter23/3 filter24/4
   filter ==> filter0/0 filter1/1 filter2/2
   cons ==> cons0/0 cons1/1 cons2/2
   nil ==> nil0/0
   map ==> map0/0 map1/1 map2/2
   g ==> g0/0 g1/1
   f ==> f0/0 f1/1
   
  uncurry-rules:
   app(f0(),x3) -> f1(x3)
   app(g0(),x5) -> g1(x5)
   app(map1(x7),x8) -> map2(x7,x8)
   app(map0(),x7) -> map1(x7)
   app(cons1(x11),x12) -> cons2(x11,x12)
   app(cons0(),x11) -> cons1(x11)
   app(filter1(x14),x15) -> filter2(x14,x15)
   app(filter0(),x14) -> filter1(x14)
   app(filter23(x17,x18,x19),x20) -> filter24(x17,x18,x19,x20)
   app(filter22(x17,x18),x19) -> filter23(x17,x18,x19)
   app(filter21(x17),x18) -> filter22(x17,x18)
   app(filter20(),x17) -> filter21(x17)
  eta-rules:
   
  problem:
   f1(g1(x)) -> g1(g1(f1(x)))
   f1(g1(x)) -> g1(g1(g1(x)))
   map2(fun,nil0()) -> nil0()
   map2(fun,cons2(x,xs)) -> cons2(app(fun,x),map2(fun,xs))
   filter2(fun,nil0()) -> nil0()
   filter2(fun,cons2(x,xs)) -> filter24(app(fun,x),fun,x,xs)
   filter24(true0(),fun,x,xs) -> cons2(x,filter2(fun,xs))
   filter24(false0(),fun,x,xs) -> filter2(fun,xs)
   app(f0(),x3) -> f1(x3)
   app(g0(),x5) -> g1(x5)
   app(map1(x7),x8) -> map2(x7,x8)
   app(map0(),x7) -> map1(x7)
   app(cons1(x11),x12) -> cons2(x11,x12)
   app(cons0(),x11) -> cons1(x11)
   app(filter1(x14),x15) -> filter2(x14,x15)
   app(filter0(),x14) -> filter1(x14)
   app(filter23(x17,x18,x19),x20) -> filter24(x17,x18,x19,x20)
   app(filter22(x17,x18),x19) -> filter23(x17,x18,x19)
   app(filter21(x17),x18) -> filter22(x17,x18)
   app(filter20(),x17) -> filter21(x17)
  DP Processor:
   DPs:
    f{1,#}(g1(x)) -> f{1,#}(x)
    map{2,#}(fun,cons2(x,xs)) -> map{2,#}(fun,xs)
    map{2,#}(fun,cons2(x,xs)) -> app#(fun,x)
    filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x)
    filter{2,#}(fun,cons2(x,xs)) -> filter2{4,#}(app(fun,x),fun,x,xs)
    filter2{4,#}(true0(),fun,x,xs) -> filter{2,#}(fun,xs)
    filter2{4,#}(false0(),fun,x,xs) -> filter{2,#}(fun,xs)
    app#(f0(),x3) -> f{1,#}(x3)
    app#(map1(x7),x8) -> map{2,#}(x7,x8)
    app#(filter1(x14),x15) -> filter{2,#}(x14,x15)
    app#(filter23(x17,x18,x19),x20) -> filter2{4,#}(x17,x18,x19,x20)
   TRS:
    f1(g1(x)) -> g1(g1(f1(x)))
    f1(g1(x)) -> g1(g1(g1(x)))
    map2(fun,nil0()) -> nil0()
    map2(fun,cons2(x,xs)) -> cons2(app(fun,x),map2(fun,xs))
    filter2(fun,nil0()) -> nil0()
    filter2(fun,cons2(x,xs)) -> filter24(app(fun,x),fun,x,xs)
    filter24(true0(),fun,x,xs) -> cons2(x,filter2(fun,xs))
    filter24(false0(),fun,x,xs) -> filter2(fun,xs)
    app(f0(),x3) -> f1(x3)
    app(g0(),x5) -> g1(x5)
    app(map1(x7),x8) -> map2(x7,x8)
    app(map0(),x7) -> map1(x7)
    app(cons1(x11),x12) -> cons2(x11,x12)
    app(cons0(),x11) -> cons1(x11)
    app(filter1(x14),x15) -> filter2(x14,x15)
    app(filter0(),x14) -> filter1(x14)
    app(filter23(x17,x18,x19),x20) -> filter24(x17,x18,x19,x20)
    app(filter22(x17,x18),x19) -> filter23(x17,x18,x19)
    app(filter21(x17),x18) -> filter22(x17,x18)
    app(filter20(),x17) -> filter21(x17)
   TDG Processor:
    DPs:
     f{1,#}(g1(x)) -> f{1,#}(x)
     map{2,#}(fun,cons2(x,xs)) -> map{2,#}(fun,xs)

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