TRS Standard pair #516967809

details

property	value
status	complete
benchmark	log2.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n009.star.cs.uiowa.edu
space	CiME_04

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	3.03097200394 seconds
cpu usage	9.963449594
max memory	4.5617152E8

stage attributes

key	value
output-size	33073
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem:
 0(#()) -> #()
 +(#(),x) -> x
 +(x,#()) -> x
 +(0(x),0(y)) -> 0(+(x,y))
 +(0(x),1(y)) -> 1(+(x,y))
 +(1(x),0(y)) -> 1(+(x,y))
 +(1(x),1(y)) -> 0(+(+(x,y),1(#())))
 +(+(x,y),z) -> +(x,+(y,z))
 -(#(),x) -> #()
 -(x,#()) -> x
 -(0(x),0(y)) -> 0(-(x,y))
 -(0(x),1(y)) -> 1(-(-(x,y),1(#())))
 -(1(x),0(y)) -> 1(-(x,y))
 -(1(x),1(y)) -> 0(-(x,y))
 not(true()) -> false()
 not(false()) -> true()
 if(true(),x,y) -> x
 if(false(),x,y) -> y
 ge(0(x),0(y)) -> ge(x,y)
 ge(0(x),1(y)) -> not(ge(y,x))
 ge(1(x),0(y)) -> ge(x,y)
 ge(1(x),1(y)) -> ge(x,y)
 ge(x,#()) -> true()
 ge(#(),0(x)) -> ge(#(),x)
 ge(#(),1(x)) -> false()
 log(x) -> -(log'(x),1(#()))
 log'(#()) -> #()
 log'(1(x)) -> +(log'(x),1(#()))
 log'(0(x)) -> if(ge(x,1(#())),+(log'(x),1(#())),#())

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [-](x0, x1) = x0 + x1,
   
   [if](x0, x1, x2) = x0 + x1 + x2,
   
   [0](x0) = 2x0,
   
   [1](x0) = 2x0,
   
   [true] = 0,
   
   [log](x0) = 4x0 + 4,
   
   [#] = 0,
   
   [false] = 0,
   
   [log'](x0) = 4x0 + 1,
   
   [ge](x0, x1) = x0 + x1,
   
   [not](x0) = 2x0,
   
   [+](x0, x1) = x0 + x1
  orientation:
   0(#()) = 0 >= 0 = #()
   
   +(#(),x) = x >= x = x
   
   +(x,#()) = x >= x = x
   
   +(0(x),0(y)) = 2x + 2y >= 2x + 2y = 0(+(x,y))
   
   +(0(x),1(y)) = 2x + 2y >= 2x + 2y = 1(+(x,y))
   
   +(1(x),0(y)) = 2x + 2y >= 2x + 2y = 1(+(x,y))
   
   +(1(x),1(y)) = 2x + 2y >= 2x + 2y = 0(+(+(x,y),1(#())))
   
   +(+(x,y),z) = x + y + z >= x + y + z = +(x,+(y,z))
   
   -(#(),x) = x >= 0 = #()
   
   -(x,#()) = x >= x = x
   
   -(0(x),0(y)) = 2x + 2y >= 2x + 2y = 0(-(x,y))
   
   -(0(x),1(y)) = 2x + 2y >= 2x + 2y = 1(-(-(x,y),1(#())))
   
   -(1(x),0(y)) = 2x + 2y >= 2x + 2y = 1(-(x,y))
   
   -(1(x),1(y)) = 2x + 2y >= 2x + 2y = 0(-(x,y))
   
   not(true()) = 0 >= 0 = false()
   
   not(false()) = 0 >= 0 = true()
   
   if(true(),x,y) = x + y >= x = x

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