TRS Standard pair #487070982

details

property	value
status	complete
benchmark	ExAppendixB_AEL03_Z.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n174.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	0.781588 seconds
cpu usage	1.75774
user time	1.47737
system time	0.280367
max virtual memory	1755768.0
max residence set size	72620.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem:
 from(X) -> cons(X,n__from(s(X)))
 2ndspos(0(),Z) -> rnil()
 2ndspos(s(N),cons(X,Z)) -> 2ndspos(s(N),cons2(X,activate(Z)))
 2ndspos(s(N),cons2(X,cons(Y,Z))) -> rcons(posrecip(Y),2ndsneg(N,activate(Z)))
 2ndsneg(0(),Z) -> rnil()
 2ndsneg(s(N),cons(X,Z)) -> 2ndsneg(s(N),cons2(X,activate(Z)))
 2ndsneg(s(N),cons2(X,cons(Y,Z))) -> rcons(negrecip(Y),2ndspos(N,activate(Z)))
 pi(X) -> 2ndspos(X,from(0()))
 plus(0(),Y) -> Y
 plus(s(X),Y) -> s(plus(X,Y))
 times(0(),Y) -> 0()
 times(s(X),Y) -> plus(Y,times(X,Y))
 square(X) -> times(X,X)
 from(X) -> n__from(X)
 activate(n__from(X)) -> from(X)
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   2ndspos#(s(N),cons(X,Z)) -> activate#(Z)
   2ndspos#(s(N),cons(X,Z)) -> 2ndspos#(s(N),cons2(X,activate(Z)))
   2ndspos#(s(N),cons2(X,cons(Y,Z))) -> activate#(Z)
   2ndspos#(s(N),cons2(X,cons(Y,Z))) -> 2ndsneg#(N,activate(Z))
   2ndsneg#(s(N),cons(X,Z)) -> activate#(Z)
   2ndsneg#(s(N),cons(X,Z)) -> 2ndsneg#(s(N),cons2(X,activate(Z)))
   2ndsneg#(s(N),cons2(X,cons(Y,Z))) -> activate#(Z)
   2ndsneg#(s(N),cons2(X,cons(Y,Z))) -> 2ndspos#(N,activate(Z))
   pi#(X) -> from#(0())
   pi#(X) -> 2ndspos#(X,from(0()))
   plus#(s(X),Y) -> plus#(X,Y)
   times#(s(X),Y) -> times#(X,Y)
   times#(s(X),Y) -> plus#(Y,times(X,Y))
   square#(X) -> times#(X,X)
   activate#(n__from(X)) -> from#(X)
  TRS:
   from(X) -> cons(X,n__from(s(X)))
   2ndspos(0(),Z) -> rnil()
   2ndspos(s(N),cons(X,Z)) -> 2ndspos(s(N),cons2(X,activate(Z)))
   2ndspos(s(N),cons2(X,cons(Y,Z))) -> rcons(posrecip(Y),2ndsneg(N,activate(Z)))
   2ndsneg(0(),Z) -> rnil()
   2ndsneg(s(N),cons(X,Z)) -> 2ndsneg(s(N),cons2(X,activate(Z)))
   2ndsneg(s(N),cons2(X,cons(Y,Z))) -> rcons(negrecip(Y),2ndspos(N,activate(Z)))
   pi(X) -> 2ndspos(X,from(0()))
   plus(0(),Y) -> Y
   plus(s(X),Y) -> s(plus(X,Y))
   times(0(),Y) -> 0()
   times(s(X),Y) -> plus(Y,times(X,Y))
   square(X) -> times(X,X)
   from(X) -> n__from(X)
   activate(n__from(X)) -> from(X)
   activate(X) -> X
  TDG Processor:
   DPs:
    2ndspos#(s(N),cons(X,Z)) -> activate#(Z)
    2ndspos#(s(N),cons(X,Z)) -> 2ndspos#(s(N),cons2(X,activate(Z)))
    2ndspos#(s(N),cons2(X,cons(Y,Z))) -> activate#(Z)
    2ndspos#(s(N),cons2(X,cons(Y,Z))) -> 2ndsneg#(N,activate(Z))
    2ndsneg#(s(N),cons(X,Z)) -> activate#(Z)
    2ndsneg#(s(N),cons(X,Z)) -> 2ndsneg#(s(N),cons2(X,activate(Z)))
    2ndsneg#(s(N),cons2(X,cons(Y,Z))) -> activate#(Z)
    2ndsneg#(s(N),cons2(X,cons(Y,Z))) -> 2ndspos#(N,activate(Z))
    pi#(X) -> from#(0())
    pi#(X) -> 2ndspos#(X,from(0()))
    plus#(s(X),Y) -> plus#(X,Y)
    times#(s(X),Y) -> times#(X,Y)
    times#(s(X),Y) -> plus#(Y,times(X,Y))
    square#(X) -> times#(X,X)
    activate#(n__from(X)) -> from#(X)
   TRS:
    from(X) -> cons(X,n__from(s(X)))
    2ndspos(0(),Z) -> rnil()
    2ndspos(s(N),cons(X,Z)) -> 2ndspos(s(N),cons2(X,activate(Z)))
    2ndspos(s(N),cons2(X,cons(Y,Z))) -> rcons(posrecip(Y),2ndsneg(N,activate(Z)))
    2ndsneg(0(),Z) -> rnil()
    2ndsneg(s(N),cons(X,Z)) -> 2ndsneg(s(N),cons2(X,activate(Z)))
    2ndsneg(s(N),cons2(X,cons(Y,Z))) -> rcons(negrecip(Y),2ndspos(N,activate(Z)))
    pi(X) -> 2ndspos(X,from(0()))
    plus(0(),Y) -> Y
    plus(s(X),Y) -> s(plus(X,Y))
    times(0(),Y) -> 0()
    times(s(X),Y) -> plus(Y,times(X,Y))
    square(X) -> times(X,X)
    from(X) -> n__from(X)
    activate(n__from(X)) -> from(X)
    activate(X) -> X
   graph:
    square#(X) -> times#(X,X) -> times#(s(X),Y) -> plus#(Y,times(X,Y))
    square#(X) -> times#(X,X) -> times#(s(X),Y) -> times#(X,Y)
    times#(s(X),Y) -> times#(X,Y) ->
    times#(s(X),Y) -> plus#(Y,times(X,Y))
    times#(s(X),Y) -> times#(X,Y) ->
    times#(s(X),Y) -> times#(X,Y)
    times#(s(X),Y) -> plus#(Y,times(X,Y)) -> plus#(s(X),Y) -> plus#(X,Y)
    plus#(s(X),Y) -> plus#(X,Y) -> plus#(s(X),Y) -> plus#(X,Y)
    pi#(X) -> 2ndspos#(X,from(0())) ->
    2ndspos#(s(N),cons2(X,cons(Y,Z))) -> 2ndsneg#(N,activate(Z))

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