TRS Standard pair #516964934

details

property	value
status	complete
benchmark	18.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n167.star.cs.uiowa.edu
space	Applicative_first_order_05

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	0.737905025482 seconds
cpu usage	1.496920916
max memory	2.76496384E8

stage attributes

key	value
output-size	18338
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(*(),x),app(app(+(),y),z)) -> app(app(+(),app(app(*(),x),y)),app(app(*(),x),z))
 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))
 app(app(filter(),f),nil()) -> nil()
 app(app(filter(),f),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(f,x)),f),x),xs)
 app(app(app(app(filter2(),true()),f),x),xs) -> app(app(cons(),x),app(app(filter(),f),xs))
 app(app(app(app(filter2(),false()),f),x),xs) -> app(app(filter(),f),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
   + ==> +0/0 +1/1 +2/2
   * ==> *0/0 *1/1 *2/2
   
  uncurry-rules:
   app(*1(x5),x6) -> *2(x5,x6)
   app(*0(),x5) -> *1(x5)
   app(+1(x8),x9) -> +2(x8,x9)
   app(+0(),x8) -> +1(x8)
   app(map1(x11),x12) -> map2(x11,x12)
   app(map0(),x11) -> map1(x11)
   app(cons1(x15),x16) -> cons2(x15,x16)
   app(cons0(),x15) -> cons1(x15)
   app(filter1(x18),x19) -> filter2(x18,x19)
   app(filter0(),x18) -> filter1(x18)
   app(filter23(x21,x22,x23),x24) -> filter24(x21,x22,x23,x24)
   app(filter22(x21,x22),x23) -> filter23(x21,x22,x23)
   app(filter21(x21),x22) -> filter22(x21,x22)
   app(filter20(),x21) -> filter21(x21)
  eta-rules:
   
  problem:
   *2(x,+2(y,z)) -> +2(*2(x,y),*2(x,z))
   map2(f,nil0()) -> nil0()
   map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
   filter2(f,nil0()) -> nil0()
   filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs)
   filter24(true0(),f,x,xs) -> cons2(x,filter2(f,xs))
   filter24(false0(),f,x,xs) -> filter2(f,xs)
   app(*1(x5),x6) -> *2(x5,x6)
   app(*0(),x5) -> *1(x5)
   app(+1(x8),x9) -> +2(x8,x9)
   app(+0(),x8) -> +1(x8)
   app(map1(x11),x12) -> map2(x11,x12)
   app(map0(),x11) -> map1(x11)
   app(cons1(x15),x16) -> cons2(x15,x16)
   app(cons0(),x15) -> cons1(x15)
   app(filter1(x18),x19) -> filter2(x18,x19)
   app(filter0(),x18) -> filter1(x18)
   app(filter23(x21,x22,x23),x24) -> filter24(x21,x22,x23,x24)
   app(filter22(x21,x22),x23) -> filter23(x21,x22,x23)
   app(filter21(x21),x22) -> filter22(x21,x22)
   app(filter20(),x21) -> filter21(x21)
  DP Processor:
   DPs:
    *{2,#}(x,+2(y,z)) -> *{2,#}(x,z)
    *{2,#}(x,+2(y,z)) -> *{2,#}(x,y)
    map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
    map{2,#}(f,cons2(x,xs)) -> app#(f,x)
    filter{2,#}(f,cons2(x,xs)) -> app#(f,x)
    filter{2,#}(f,cons2(x,xs)) -> filter2{4,#}(app(f,x),f,x,xs)
    filter2{4,#}(true0(),f,x,xs) -> filter{2,#}(f,xs)
    filter2{4,#}(false0(),f,x,xs) -> filter{2,#}(f,xs)
    app#(*1(x5),x6) -> *{2,#}(x5,x6)
    app#(map1(x11),x12) -> map{2,#}(x11,x12)
    app#(filter1(x18),x19) -> filter{2,#}(x18,x19)
    app#(filter23(x21,x22,x23),x24) -> filter2{4,#}(x21,x22,x23,x24)
   TRS:
    *2(x,+2(y,z)) -> +2(*2(x,y),*2(x,z))
    map2(f,nil0()) -> nil0()
    map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
    filter2(f,nil0()) -> nil0()
    filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs)
    filter24(true0(),f,x,xs) -> cons2(x,filter2(f,xs))
    filter24(false0(),f,x,xs) -> filter2(f,xs)
    app(*1(x5),x6) -> *2(x5,x6)
    app(*0(),x5) -> *1(x5)
    app(+1(x8),x9) -> +2(x8,x9)
    app(+0(),x8) -> +1(x8)
    app(map1(x11),x12) -> map2(x11,x12)
    app(map0(),x11) -> map1(x11)
    app(cons1(x15),x16) -> cons2(x15,x16)
    app(cons0(),x15) -> cons1(x15)

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