If you are happy to insert an extra couple of columns, C & D in the example then you can use the formula listed. Summing the totals is a simple matter of summing Columns C & D.
This does throw up a problem for the last row in the data, you will need to decide how you want to handle this.
Sheet1
<table style="font-family: Arial,Arial; font-size: 10pt; background-color: rgb(255, 255, 255); padding-left: 2pt; padding-right: 2pt;" border="1" cellpadding="0" cellspacing="0"> <colgroup><col style="font-weight: bold; width: 30px;"><col style="width: 64px;"><col style="width: 64px;"><col style="width: 64px;"><col style="width: 64px;"><col style="width: 89px;"><col style="width: 89px;"></colgroup><tbody><tr style="background-color: rgb(202, 202, 202); text-align: center; font-weight: bold; font-size: 8pt;"><td>
</td><td>A</td><td>B</td><td>C</td><td>D</td><td>E</td><td>F</td></tr><tr style="height: 68px;"><td style="font-size: 8pt; background-color: rgb(202, 202, 202); text-align: center;">1</td><td style="background-color: rgb(0, 0, 128); color: rgb(255, 255, 255);">Index</td><td style="background-color: rgb(0, 0, 128); color: rgb(255, 255, 255);">Value</td><td style="background-color: rgb(0, 0, 128); color: rgb(255, 255, 255);">Increment x</td><td style="background-color: rgb(0, 0, 128); color: rgb(255, 255, 255);">Increment y</td><td style="background-color: rgb(0, 0, 128); color: rgb(255, 255, 255);">Higher than x previous cell</td><td style="background-color: rgb(0, 0, 128); color: rgb(255, 255, 255);">Higher than y previous cell</td></tr><tr style="height: 17px;"><td style="font-size: 8pt; background-color: rgb(202, 202, 202); text-align: center;">2</td><td style="text-align: right;">1</td><td style="text-align: right;">-76</td><td style="text-align: right;">1</td><td style="text-align: right;">0</td><td style="text-align: right;">1</td><td style="text-align: right;">0</td></tr><tr style="height: 17px;"><td style="font-size: 8pt; background-color: rgb(202, 202, 202); text-align: center;">3</td><td style="text-align: right;">2</td><td style="text-align: right;">1187</td><td style="text-align: right;">0</td><td style="text-align: right;">1</td><td style="text-align: right;">0</td><td style="text-align: right;">1</td></tr><tr style="height: 17px;"><td style="font-size: 8pt; background-color: rgb(202, 202, 202); text-align: center;">4</td><td style="text-align: right;">3</td><td style="text-align: right;">539</td><td style="text-align: right;">1</td><td style="text-align: right;">0</td><td style="text-align: right;">2</td><td style="text-align: right;">0</td></tr><tr style="height: 17px;"><td style="font-size: 8pt; background-color: rgb(202, 202, 202); text-align: center;">5</td><td style="text-align: right;">4</td><td style="text-align: right;">53520</td><td style="text-align: right;">0</td><td style="text-align: right;">1</td><td style="text-align: right;">0</td><td style="text-align: right;">2</td></tr><tr style="height: 17px;"><td style="font-size: 8pt; background-color: rgb(202, 202, 202); text-align: center;">6</td><td style="text-align: right;">5</td><td style="text-align: right;">35216</td><td style="text-align: right;">1</td><td style="text-align: right;">0</td><td style="text-align: right;">3</td><td style="text-align: right;">0</td></tr></tbody></table>
<table style="border-style: groove; border-color: rgb(0, 255, 0); font-family: Arial; font-size: 10pt; background-color: rgb(255, 252, 249); color: rgb(0, 0, 0);"><tbody><tr><td>Spreadsheet Formulas</td></tr><tr><td><table style="font-family: Arial; font-size: 9pt;" border="1" cellpadding="2" cellspacing="0"><tbody><tr style="background-color: rgb(202, 202, 202); font-size: 10pt;"><td>Cell</td><td>Formula</td></tr><tr><td>C2</td><td>=IF(B2<B3,1,0)<b3,1,0)></b3,1,0)></td></tr><tr><td>D2</td><td>=IF(B2>B3,1,0)</td></tr><tr><td>E2</td><td>=IF(C2=1,1,0)</td></tr><tr><td>F2</td><td>=IF(D2=1,1,0)</td></tr><tr><td>A3</td><td>=+A2+1</td></tr><tr><td>C3</td><td>=IF(B3<b4,1,0)></b4,1,0)></td></tr><tr><td>D3</td><td>=IF(B3>B4,1,0)</td></tr><tr><td>E3</td><td>=IF(C3=0,0,MAX($E$2:E2)+1)</td></tr><tr><td>F3</td><td>=IF(D3=0,0,MAX($F$2:F2)+1)</td></tr><tr><td>A4</td><td>=+A3+1</td></tr><tr><td>C4</td><td>=IF(B4<b5,1,0)></b5,1,0)></td></tr><tr><td>D4</td><td>=IF(B4>B5,1,0)</td></tr><tr><td>E4</td><td>=IF(C4=0,0,MAX($E$2:E3)+1)</td></tr><tr><td>F4</td><td>=IF(D4=0,0,MAX($F$2:F3)+1)</td></tr><tr><td>A5</td><td>=+A4+1</td></tr><tr><td>C5</td><td>=IF(B5<b6,1,0)></b6,1,0)></td></tr><tr><td>D5</td><td>=IF(B5>B6,1,0)</td></tr><tr><td>E5</td><td>=IF(C5=0,0,MAX($E$2:E4)+1)</td></tr><tr><td>F5</td><td>=IF(D5=0,0,MAX($F$2:F4)+1)</td></tr><tr><td>A6</td><td>=+A5+1</td></tr><tr><td>C6</td><td>=IF(B6<b7,1,0)></b7,1,0)></td></tr><tr><td>D6</td><td>=IF(B6>B7,1,0)</td></tr><tr><td>E6</td><td>=IF(C6=0,0,MAX($E$2:E5)+1)</td></tr><tr><td>F6</td><td>=IF(D6=0,0,MAX($F$2:F5)+1)</td></tr></tbody></table></td></tr></tbody></table>