SRS Standard pair #516969077

details

property	value
status	complete
benchmark	uni-5.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n056.star.cs.uiowa.edu
space	Waldmann_06_SRS

run statistics

property	value
solver	MnM 3.18b
configuration	default
runtime (wallclock)	4.67938995361 seconds
cpu usage	16.024193616
max memory	2.918621184E9

stage attributes

key	value
output-size	87249
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 ⟶ 2 2 2 2 ,
  2 2 ⟶ 0 2 1 }

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

After renaming modulo the bijection { (1,↑) ↦ 0, (1,↓) ↦ 1, (2,↑) ↦ 2, (2,↓) ↦ 3, (0,↑) ↦ 4, (0,↓) ↦ 5 },
it remains to prove termination of the 10-rule system
{ 0 1 ⟶ 2 3 3 3 ,
  0 1 ⟶ 2 3 3 ,
  0 1 ⟶ 2 3 ,
  0 1 ⟶ 2 ,
  2 3 ⟶ 4 3 1 ,
  2 3 ⟶ 2 1 ,
  2 3 ⟶ 0 ,
  5 5 →= ,
  1 1 →= 3 3 3 3 ,
  3 3 →= 5 3 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 1 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

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

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

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

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 5 ↦ 4 },
it remains to prove termination of the 9-rule system
{ 0 1 ⟶ 2 3 3 3 ,
  0 1 ⟶ 2 3 3 ,
  0 1 ⟶ 2 3 ,
  0 1 ⟶ 2 ,
  2 3 ⟶ 2 1 ,
  2 3 ⟶ 0 ,
  4 4 →= ,
  1 1 →= 3 3 3 3 ,
  3 3 →= 4 3 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, (5,2) ↦ 3, (2,3) ↦ 4, (3,3) ↦ 5, (3,1) ↦ 6, (1,3) ↦ 7, (1,4) ↦ 8, (3,4) ↦ 9, (1,6) ↦ 10, (3,6) ↦ 11, (2,1) ↦ 12, (2,4) ↦ 13, (2,6) ↦ 14, (0,3) ↦ 15, (0,4) ↦ 16, (0,6) ↦ 17, (4,4) ↦ 18, (4,3) ↦ 19, (5,4) ↦ 20, (5,3) ↦ 21 },
it remains to prove termination of the 76-rule system
{ 0 1 2 ⟶ 3 4 5 5 6 ,
  0 1 7 ⟶ 3 4 5 5 5 ,
  0 1 8 ⟶ 3 4 5 5 9 ,
  0 1 10 ⟶ 3 4 5 5 11 ,
  0 1 2 ⟶ 3 4 5 6 ,
  0 1 7 ⟶ 3 4 5 5 ,
  0 1 8 ⟶ 3 4 5 9 ,
  0 1 10 ⟶ 3 4 5 11 ,
  0 1 2 ⟶ 3 4 6 ,
  0 1 7 ⟶ 3 4 5 ,
  0 1 8 ⟶ 3 4 9 ,
  0 1 10 ⟶ 3 4 11 ,
  0 1 2 ⟶ 3 12 ,
  0 1 7 ⟶ 3 4 ,
  0 1 8 ⟶ 3 13 ,
  0 1 10 ⟶ 3 14 ,
  3 4 6 ⟶ 3 12 2 ,
  3 4 5 ⟶ 3 12 7 ,
  3 4 9 ⟶ 3 12 8 ,
  3 4 11 ⟶ 3 12 10 ,
  3 4 6 ⟶ 0 1 ,
  3 4 5 ⟶ 0 15 ,

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