TRS Standard pair #487072422

details

property	value
status	complete
benchmark	hydra.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)	0.950013 seconds
cpu usage	2.5964
user time	2.02172
system time	0.574685
max virtual memory	1875576.0
max residence set size	72588.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem:
 app(f(),app(app(cons(),nil()),y)) -> y
 app(f(),app(app(cons(),app(f(),app(app(cons(),nil()),y))),z)) -> app(app(app(copy(),n()),y),z)
 app(app(app(copy(),0()),y),z) -> app(f(),z)
 app(app(app(copy(),app(s(),x)),y),z) -> app(app(app(copy(),x),y),app(app(cons(),app(f(),y)),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
   map ==> map0/0 map1/1 map2/2
   s ==> s0/0 s1/1
   0 ==> 00/0
   n ==> n0/0
   copy ==> copy0/0 copy1/1 copy2/2 copy3/3
   nil ==> nil0/0
   cons ==> cons0/0 cons1/1 cons2/2
   f ==> f0/0 f1/1
   
  uncurry-rules:
   app(f0(),x5) -> f1(x5)
   app(cons1(x7),x8) -> cons2(x7,x8)
   app(cons0(),x7) -> cons1(x7)
   app(copy2(x11,x12),x13) -> copy3(x11,x12,x13)
   app(copy1(x11),x12) -> copy2(x11,x12)
   app(copy0(),x11) -> copy1(x11)
   app(s0(),x17) -> s1(x17)
   app(map1(x19),x20) -> map2(x19,x20)
   app(map0(),x19) -> map1(x19)
   app(filter1(x22),x23) -> filter2(x22,x23)
   app(filter0(),x22) -> filter1(x22)
   app(filter23(x25,x26,x27),x28) -> filter24(x25,x26,x27,x28)
   app(filter22(x25,x26),x27) -> filter23(x25,x26,x27)
   app(filter21(x25),x26) -> filter22(x25,x26)
   app(filter20(),x25) -> filter21(x25)
  eta-rules:
   
  problem:
   f1(cons2(nil0(),y)) -> y
   f1(cons2(f1(cons2(nil0(),y)),z)) -> copy3(n0(),y,z)
   copy3(00(),y,z) -> f1(z)
   copy3(s1(x),y,z) -> copy3(x,y,cons2(f1(y),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(f0(),x5) -> f1(x5)
   app(cons1(x7),x8) -> cons2(x7,x8)
   app(cons0(),x7) -> cons1(x7)
   app(copy2(x11,x12),x13) -> copy3(x11,x12,x13)
   app(copy1(x11),x12) -> copy2(x11,x12)
   app(copy0(),x11) -> copy1(x11)
   app(s0(),x17) -> s1(x17)
   app(map1(x19),x20) -> map2(x19,x20)
   app(map0(),x19) -> map1(x19)
   app(filter1(x22),x23) -> filter2(x22,x23)
   app(filter0(),x22) -> filter1(x22)
   app(filter23(x25,x26,x27),x28) -> filter24(x25,x26,x27,x28)
   app(filter22(x25,x26),x27) -> filter23(x25,x26,x27)
   app(filter21(x25),x26) -> filter22(x25,x26)
   app(filter20(),x25) -> filter21(x25)
  DP Processor:
   DPs:
    f{1,#}(cons2(f1(cons2(nil0(),y)),z)) -> copy{3,#}(n0(),y,z)
    copy{3,#}(00(),y,z) -> f{1,#}(z)
    copy{3,#}(s1(x),y,z) -> f{1,#}(y)
    copy{3,#}(s1(x),y,z) -> copy{3,#}(x,y,cons2(f1(y),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#(f0(),x5) -> f{1,#}(x5)
    app#(copy2(x11,x12),x13) -> copy{3,#}(x11,x12,x13)
    app#(map1(x19),x20) -> map{2,#}(x19,x20)
    app#(filter1(x22),x23) -> filter{2,#}(x22,x23)
    app#(filter23(x25,x26,x27),x28) -> filter2{4,#}(x25,x26,x27,x28)
   TRS:
    f1(cons2(nil0(),y)) -> y
    f1(cons2(f1(cons2(nil0(),y)),z)) -> copy3(n0(),y,z)
    copy3(00(),y,z) -> f1(z)
    copy3(s1(x),y,z) -> copy3(x,y,cons2(f1(y),z))
    map2(fun,nil0()) -> nil0()
    map2(fun,cons2(x,xs)) -> cons2(app(fun,x),map2(fun,xs))
    filter2(fun,nil0()) -> nil0()

popout

output may be truncated. 'popout' for the full output.

job log

popout

actions all output return to TRS Standard