SRS Standard pair #516974873

details

property	value
status	complete
benchmark	size-12-alpha-3-num-470.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n078.star.cs.uiowa.edu
space	Waldmann_07_size12

run statistics

property	value
solver	MnM 3.18b
configuration	default
runtime (wallclock)	4.2814950943 seconds
cpu usage	15.17608927
max memory	2.564612096E9

stage attributes

key	value
output-size	85000
starexec-result	YES

output

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


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YES

After renaming modulo the bijection { a ↦ 0, b ↦ 1, c ↦ 2 },
it remains to prove termination of the 3-rule system
{ 0 0 ⟶ ,
  1 1 ⟶ 0 1 2 ,
  2 2 ⟶ 1 1 1 }

Applying the dependency pairs transformation. Here, ↑ marks so-called defined symbols.

After renaming modulo the bijection { (1,↑) ↦ 0, (1,↓) ↦ 1, (0,↑) ↦ 2, (2,↓) ↦ 3, (2,↑) ↦ 4, (0,↓) ↦ 5 },
it remains to prove termination of the 9-rule system
{ 0 1 ⟶ 2 1 3 ,
  0 1 ⟶ 0 3 ,
  0 1 ⟶ 4 ,
  4 3 ⟶ 0 1 1 ,
  4 3 ⟶ 0 1 ,
  4 3 ⟶ 0 ,
  5 5 →= ,
  1 1 →= 5 1 3 ,
  3 3 →= 1 1 1 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 2:

0 ↦ ⎛     ⎞
    ⎜ 1 1 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

1 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

2 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

3 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

4 ↦ ⎛     ⎞
    ⎜ 1 1 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

5 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 3 ↦ 2, 4 ↦ 3, 5 ↦ 4 },
it remains to prove termination of the 8-rule system
{ 0 1 ⟶ 0 2 ,
  0 1 ⟶ 3 ,
  3 2 ⟶ 0 1 1 ,
  3 2 ⟶ 0 1 ,
  3 2 ⟶ 0 ,
  4 4 →= ,
  1 1 →= 4 1 2 ,
  2 2 →= 1 1 1 }

Applying sparse tiling TROC(2) [Geser/Hofbauer/Waldmann, FSCD 2019].

After renaming modulo the bijection { (5,0) ↦ 0, (0,1) ↦ 1, (1,1) ↦ 2, (0,2) ↦ 3, (2,1) ↦ 4, (1,2) ↦ 5, (2,2) ↦ 6, (1,4) ↦ 7, (2,4) ↦ 8, (1,6) ↦ 9, (2,6) ↦ 10, (5,3) ↦ 11, (3,1) ↦ 12, (3,2) ↦ 13, (3,4) ↦ 14, (3,6) ↦ 15, (0,4) ↦ 16, (0,6) ↦ 17, (4,4) ↦ 18, (4,1) ↦ 19, (5,4) ↦ 20, (5,1) ↦ 21 },
it remains to prove termination of the 72-rule system
{ 0 1 2 ⟶ 0 3 4 ,
  0 1 5 ⟶ 0 3 6 ,
  0 1 7 ⟶ 0 3 8 ,
  0 1 9 ⟶ 0 3 10 ,
  0 1 2 ⟶ 11 12 ,
  0 1 5 ⟶ 11 13 ,
  0 1 7 ⟶ 11 14 ,
  0 1 9 ⟶ 11 15 ,
  11 13 4 ⟶ 0 1 2 2 ,
  11 13 6 ⟶ 0 1 2 5 ,
  11 13 8 ⟶ 0 1 2 7 ,
  11 13 10 ⟶ 0 1 2 9 ,
  11 13 4 ⟶ 0 1 2 ,
  11 13 6 ⟶ 0 1 5 ,
  11 13 8 ⟶ 0 1 7 ,
  11 13 10 ⟶ 0 1 9 ,
  11 13 4 ⟶ 0 1 ,
  11 13 6 ⟶ 0 3 ,
  11 13 8 ⟶ 0 16 ,
  11 13 10 ⟶ 0 17 ,
  16 18 19 →= 1 ,
  16 18 18 →= 16 ,
  7 18 19 →= 2 ,
  7 18 18 →= 7 ,

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