TRS Standard pair #487073657

details

property	value
status	complete
benchmark	mapDivMinus.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n073.star.cs.uiowa.edu
space	Applicative_05

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	0.846337 seconds
cpu usage	2.22172
user time	1.66518
system time	0.556541
max virtual memory	1647448.0
max residence set size	69244.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem:
 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(minus(),x),0()) -> x
 app(app(minus(),app(s(),x)),app(s(),y)) -> app(app(minus(),x),y)
 app(app(div(),0()),app(s(),y)) -> 0()
 app(app(div(),app(s(),x)),app(s(),y)) -> app(s(),app(app(div(),app(app(minus(),x),y)),app(s(),y)))

Proof:
 Extended Uncurrying Processor:
  application symbol: app
  symbol table:
   div ==> div0/0 div1/1 div2/2
   s ==> s0/0 s1/1
   0 ==> 00/0
   minus ==> minus0/0 minus1/1 minus2/2
   cons ==> cons0/0 cons1/1 cons2/2
   nil ==> nil0/0
   map ==> map0/0 map1/1 map2/2
   
  uncurry-rules:
   app(map1(x4),x5) -> map2(x4,x5)
   app(map0(),x4) -> map1(x4)
   app(cons1(x8),x9) -> cons2(x8,x9)
   app(cons0(),x8) -> cons1(x8)
   app(minus1(x11),x12) -> minus2(x11,x12)
   app(minus0(),x11) -> minus1(x11)
   app(s0(),x15) -> s1(x15)
   app(div1(x17),x18) -> div2(x17,x18)
   app(div0(),x17) -> div1(x17)
  eta-rules:
   
  problem:
   map2(f,nil0()) -> nil0()
   map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
   minus2(x,00()) -> x
   minus2(s1(x),s1(y)) -> minus2(x,y)
   div2(00(),s1(y)) -> 00()
   div2(s1(x),s1(y)) -> s1(div2(minus2(x,y),s1(y)))
   app(map1(x4),x5) -> map2(x4,x5)
   app(map0(),x4) -> map1(x4)
   app(cons1(x8),x9) -> cons2(x8,x9)
   app(cons0(),x8) -> cons1(x8)
   app(minus1(x11),x12) -> minus2(x11,x12)
   app(minus0(),x11) -> minus1(x11)
   app(s0(),x15) -> s1(x15)
   app(div1(x17),x18) -> div2(x17,x18)
   app(div0(),x17) -> div1(x17)
  DP Processor:
   DPs:
    map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
    map{2,#}(f,cons2(x,xs)) -> app#(f,x)
    minus{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y)
    div{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y)
    div{2,#}(s1(x),s1(y)) -> div{2,#}(minus2(x,y),s1(y))
    app#(map1(x4),x5) -> map{2,#}(x4,x5)
    app#(minus1(x11),x12) -> minus{2,#}(x11,x12)
    app#(div1(x17),x18) -> div{2,#}(x17,x18)
   TRS:
    map2(f,nil0()) -> nil0()
    map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
    minus2(x,00()) -> x
    minus2(s1(x),s1(y)) -> minus2(x,y)
    div2(00(),s1(y)) -> 00()
    div2(s1(x),s1(y)) -> s1(div2(minus2(x,y),s1(y)))
    app(map1(x4),x5) -> map2(x4,x5)
    app(map0(),x4) -> map1(x4)
    app(cons1(x8),x9) -> cons2(x8,x9)
    app(cons0(),x8) -> cons1(x8)
    app(minus1(x11),x12) -> minus2(x11,x12)
    app(minus0(),x11) -> minus1(x11)
    app(s0(),x15) -> s1(x15)
    app(div1(x17),x18) -> div2(x17,x18)
    app(div0(),x17) -> div1(x17)
   TDG Processor:
    DPs:
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     minus{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y)
     div{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y)
     div{2,#}(s1(x),s1(y)) -> div{2,#}(minus2(x,y),s1(y))
     app#(map1(x4),x5) -> map{2,#}(x4,x5)
     app#(minus1(x11),x12) -> minus{2,#}(x11,x12)
     app#(div1(x17),x18) -> div{2,#}(x17,x18)
    TRS:
     map2(f,nil0()) -> nil0()
     map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
     minus2(x,00()) -> x
     minus2(s1(x),s1(y)) -> minus2(x,y)
     div2(00(),s1(y)) -> 00()
     div2(s1(x),s1(y)) -> s1(div2(minus2(x,y),s1(y)))
     app(map1(x4),x5) -> map2(x4,x5)
     app(map0(),x4) -> map1(x4)
     app(cons1(x8),x9) -> cons2(x8,x9)
     app(cons0(),x8) -> cons1(x8)
     app(minus1(x11),x12) -> minus2(x11,x12)
     app(minus0(),x11) -> minus1(x11)
     app(s0(),x15) -> s1(x15)

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