TRS Standard pair #487066662

details

property	value
status	complete
benchmark	13.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n180.star.cs.uiowa.edu
space	Various_04

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	1.87878 seconds
cpu usage	10.9742
user time	8.90264
system time	2.07151
max virtual memory	5939608.0
max residence set size	88140.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem:
 O(0()) -> 0()
 +(0(),x) -> x
 +(x,0()) -> x
 +(O(x),O(y)) -> O(+(x,y))
 +(O(x),I(y)) -> I(+(x,y))
 +(I(x),O(y)) -> I(+(x,y))
 +(I(x),I(y)) -> O(+(+(x,y),I(0())))
 *(0(),x) -> 0()
 *(x,0()) -> 0()
 *(O(x),y) -> O(*(x,y))
 *(I(x),y) -> +(O(*(x,y)),y)
 -(x,0()) -> x
 -(0(),x) -> 0()
 -(O(x),O(y)) -> O(-(x,y))
 -(O(x),I(y)) -> I(-(-(x,y),I(1())))
 -(I(x),O(y)) -> I(-(x,y))
 -(I(x),I(y)) -> O(-(x,y))

Proof:
 DP Processor:
  DPs:
   +#(O(x),O(y)) -> +#(x,y)
   +#(O(x),O(y)) -> O#(+(x,y))
   +#(O(x),I(y)) -> +#(x,y)
   +#(I(x),O(y)) -> +#(x,y)
   +#(I(x),I(y)) -> +#(x,y)
   +#(I(x),I(y)) -> +#(+(x,y),I(0()))
   +#(I(x),I(y)) -> O#(+(+(x,y),I(0())))
   *#(O(x),y) -> *#(x,y)
   *#(O(x),y) -> O#(*(x,y))
   *#(I(x),y) -> *#(x,y)
   *#(I(x),y) -> O#(*(x,y))
   *#(I(x),y) -> +#(O(*(x,y)),y)
   -#(O(x),O(y)) -> -#(x,y)
   -#(O(x),O(y)) -> O#(-(x,y))
   -#(O(x),I(y)) -> -#(x,y)
   -#(O(x),I(y)) -> -#(-(x,y),I(1()))
   -#(I(x),O(y)) -> -#(x,y)
   -#(I(x),I(y)) -> -#(x,y)
   -#(I(x),I(y)) -> O#(-(x,y))
  TRS:
   O(0()) -> 0()
   +(0(),x) -> x
   +(x,0()) -> x
   +(O(x),O(y)) -> O(+(x,y))
   +(O(x),I(y)) -> I(+(x,y))
   +(I(x),O(y)) -> I(+(x,y))
   +(I(x),I(y)) -> O(+(+(x,y),I(0())))
   *(0(),x) -> 0()
   *(x,0()) -> 0()
   *(O(x),y) -> O(*(x,y))
   *(I(x),y) -> +(O(*(x,y)),y)
   -(x,0()) -> x
   -(0(),x) -> 0()
   -(O(x),O(y)) -> O(-(x,y))
   -(O(x),I(y)) -> I(-(-(x,y),I(1())))
   -(I(x),O(y)) -> I(-(x,y))
   -(I(x),I(y)) -> O(-(x,y))
  TDG Processor:
   DPs:
    +#(O(x),O(y)) -> +#(x,y)
    +#(O(x),O(y)) -> O#(+(x,y))
    +#(O(x),I(y)) -> +#(x,y)
    +#(I(x),O(y)) -> +#(x,y)
    +#(I(x),I(y)) -> +#(x,y)
    +#(I(x),I(y)) -> +#(+(x,y),I(0()))
    +#(I(x),I(y)) -> O#(+(+(x,y),I(0())))
    *#(O(x),y) -> *#(x,y)
    *#(O(x),y) -> O#(*(x,y))
    *#(I(x),y) -> *#(x,y)
    *#(I(x),y) -> O#(*(x,y))
    *#(I(x),y) -> +#(O(*(x,y)),y)
    -#(O(x),O(y)) -> -#(x,y)
    -#(O(x),O(y)) -> O#(-(x,y))
    -#(O(x),I(y)) -> -#(x,y)
    -#(O(x),I(y)) -> -#(-(x,y),I(1()))
    -#(I(x),O(y)) -> -#(x,y)
    -#(I(x),I(y)) -> -#(x,y)
    -#(I(x),I(y)) -> O#(-(x,y))
   TRS:
    O(0()) -> 0()
    +(0(),x) -> x
    +(x,0()) -> x
    +(O(x),O(y)) -> O(+(x,y))
    +(O(x),I(y)) -> I(+(x,y))
    +(I(x),O(y)) -> I(+(x,y))
    +(I(x),I(y)) -> O(+(+(x,y),I(0())))
    *(0(),x) -> 0()
    *(x,0()) -> 0()
    *(O(x),y) -> O(*(x,y))
    *(I(x),y) -> +(O(*(x,y)),y)
    -(x,0()) -> x
    -(0(),x) -> 0()
    -(O(x),O(y)) -> O(-(x,y))
    -(O(x),I(y)) -> I(-(-(x,y),I(1())))
    -(I(x),O(y)) -> I(-(x,y))
    -(I(x),I(y)) -> O(-(x,y))

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