TRS Stand 20472 pair #381711029

details

property	value
status	complete
benchmark	#3.52.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n093.star.cs.uiowa.edu
space	Applicative_first_order_05

run statistics

property	value
solver	ttt2-1.17+nonreach
configuration	ttt2-1.17+nonreach
runtime (wallclock)	1.00833821297 seconds
cpu usage	2.610593005
max memory	2.53927424E8

stage attributes

key	value
output-size	20944
starexec-result	YES

output

/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES

Problem:
 app(app(app(f(),0()),1()),x) -> app(app(app(f(),app(s(),x)),x),x)
 app(app(app(f(),x),y),app(s(),z)) -> app(s(),app(app(app(f(),0()),1()),z))
 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
   s ==> s0/0 s1/1
   1 ==> 10/0
   0 ==> 00/0
   f ==> f0/0 f1/1 f2/2 f3/3
   
  uncurry-rules:
   app(f2(x5,x6),x7) -> f3(x5,x6,x7)
   app(f1(x5),x6) -> f2(x5,x6)
   app(f0(),x5) -> f1(x5)
   app(s0(),x11) -> s1(x11)
   app(map1(x13),x14) -> map2(x13,x14)
   app(map0(),x13) -> map1(x13)
   app(cons1(x17),x18) -> cons2(x17,x18)
   app(cons0(),x17) -> cons1(x17)
   app(filter1(x20),x21) -> filter2(x20,x21)
   app(filter0(),x20) -> filter1(x20)
   app(filter23(x23,x24,x25),x26) -> filter24(x23,x24,x25,x26)
   app(filter22(x23,x24),x25) -> filter23(x23,x24,x25)
   app(filter21(x23),x24) -> filter22(x23,x24)
   app(filter20(),x23) -> filter21(x23)
  eta-rules:
   
  problem:
   f3(00(),10(),x) -> f3(s1(x),x,x)
   f3(x,y,s1(z)) -> s1(f3(00(),10(),z))
   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(f2(x5,x6),x7) -> f3(x5,x6,x7)
   app(f1(x5),x6) -> f2(x5,x6)
   app(f0(),x5) -> f1(x5)
   app(s0(),x11) -> s1(x11)
   app(map1(x13),x14) -> map2(x13,x14)
   app(map0(),x13) -> map1(x13)
   app(cons1(x17),x18) -> cons2(x17,x18)
   app(cons0(),x17) -> cons1(x17)
   app(filter1(x20),x21) -> filter2(x20,x21)
   app(filter0(),x20) -> filter1(x20)
   app(filter23(x23,x24,x25),x26) -> filter24(x23,x24,x25,x26)
   app(filter22(x23,x24),x25) -> filter23(x23,x24,x25)
   app(filter21(x23),x24) -> filter22(x23,x24)
   app(filter20(),x23) -> filter21(x23)
  DP Processor:
   DPs:
    f{3,#}(00(),10(),x) -> f{3,#}(s1(x),x,x)
    f{3,#}(x,y,s1(z)) -> f{3,#}(00(),10(),z)
    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#(f2(x5,x6),x7) -> f{3,#}(x5,x6,x7)
    app#(map1(x13),x14) -> map{2,#}(x13,x14)
    app#(filter1(x20),x21) -> filter{2,#}(x20,x21)
    app#(filter23(x23,x24,x25),x26) -> filter2{4,#}(x23,x24,x25,x26)
   TRS:
    f3(00(),10(),x) -> f3(s1(x),x,x)
    f3(x,y,s1(z)) -> s1(f3(00(),10(),z))
    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(f2(x5,x6),x7) -> f3(x5,x6,x7)
    app(f1(x5),x6) -> f2(x5,x6)
    app(f0(),x5) -> f1(x5)

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