TRS Standard pair #487072397

details

property	value
status	complete
benchmark	#3.16.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n192.star.cs.uiowa.edu
space	Applicative_first_order_05

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	0.850131 seconds
cpu usage	1.80367
user time	1.54088
system time	0.262788
max virtual memory	1857416.0
max residence set size	72152.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem:
 app(app(times(),x),0()) -> 0()
 app(app(times(),x),app(s(),y)) -> app(app(plus(),app(app(times(),x),y)),x)
 app(app(plus(),x),0()) -> x
 app(app(plus(),0()),x) -> x
 app(app(plus(),x),app(s(),y)) -> app(s(),app(app(plus(),x),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))
 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
   plus ==> plus0/0 plus1/1 plus2/2
   s ==> s0/0 s1/1
   0 ==> 00/0
   times ==> times0/0 times1/1 times2/2
   
  uncurry-rules:
   app(times1(x4),x5) -> times2(x4,x5)
   app(times0(),x4) -> times1(x4)
   app(s0(),x8) -> s1(x8)
   app(plus1(x10),x11) -> plus2(x10,x11)
   app(plus0(),x10) -> plus1(x10)
   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:
   times2(x,00()) -> 00()
   times2(x,s1(y)) -> plus2(times2(x,y),x)
   plus2(x,00()) -> x
   plus2(00(),x) -> x
   plus2(x,s1(y)) -> s1(plus2(x,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))
   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(times1(x4),x5) -> times2(x4,x5)
   app(times0(),x4) -> times1(x4)
   app(s0(),x8) -> s1(x8)
   app(plus1(x10),x11) -> plus2(x10,x11)
   app(plus0(),x10) -> plus1(x10)
   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:
    times{2,#}(x,s1(y)) -> times{2,#}(x,y)
    times{2,#}(x,s1(y)) -> plus{2,#}(times2(x,y),x)
    plus{2,#}(x,s1(y)) -> plus{2,#}(x,y)
    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)
    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#(times1(x4),x5) -> times{2,#}(x4,x5)
    app#(plus1(x10),x11) -> plus{2,#}(x10,x11)
    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:
    times2(x,00()) -> 00()
    times2(x,s1(y)) -> plus2(times2(x,y),x)
    plus2(x,00()) -> x
    plus2(00(),x) -> x

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