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<b>let </b><font color="Maroon" title="c1">i1</font>, <font color="Maroon" title="c2">i2</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>;<br/><b>let </b><font color="Maroon" title="c3">s</font> be    <a href="scm_1.html#M1" title="SCM_1:mode.1">State-consisting</a> of 0,0,0,<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K8" title="AMI_3:func.8">goto</a> <span class="p3">(<span class="default"><a href="ami_3.html#K16" title="AMI_3:func.16">il.</a> 1</span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>,<span class="p1"><a href="scm_1.html#K1" title="SCM_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c1">i1</font></span><a href="scm_1.html#K1" title="SCM_1:func.1">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="scm_1.html#K1" title="SCM_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c2">i2</font></span><a href="scm_1.html#K1" title="SCM_1:func.1">*&gt;</a></span>;<br/>



<a NAME="E1:35"/><i><font color="Green" title="E26">A1</font></i>: 
(  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K16" title="AMI_3:func.16">il.</a> 0 &amp; <font color="Maroon" title="c3">s</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16" title="AMI_3:func.16">il.</a> 0</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K8" title="AMI_3:func.8">goto</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16" title="AMI_3:func.16">il.</a> 1</span>)</span> &amp; <font color="Maroon" title="c3">s</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16" title="AMI_3:func.16">il.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  &amp; <font color="Maroon" title="c3">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15" title="AMI_3:func.15">dl.</a> 0</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i1</font> &amp; <font color="Maroon" title="c3">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15" title="AMI_3:func.15">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">i2</font> )
 
<b>by </b><i><a class="ref" href="scm_1.html#T15" target="_self" title="SCM_1:th.15">Th15</a></i>;<br/>
<b>set </b><font color="Maroon" title="c4">s1</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>;<br/>
<a NAME="E2:35"/><i><font color="Green" title="E27">A2</font></i>: 
<font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 0
 
<b>by </b><i><a class="ref" href="ami_1.html#D19" title="AMI_1:def.19">AMI_1:def 19</a></i>;<br/>
<a NAME="E3:35"/><b>then </b><i><font color="Green" title="E28">A3</font></i>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default">0 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K16" title="AMI_3:func.16">il.</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="scm_1.html#E1:35"><i><font color="Green" title="E26">A1</font></i></a>, <a class="ref" href="scm_1.html#T23" target="_self" title="SCM_1:th.23">Th23</a></i>;<br/>
<b>hence </b><a NAME="E4:35"/>
<font color="Maroon" title="c3">s</font> is <a href="ami_1.html#V9" title="AMI_1:attr.9">halting</a>
 <b>by </b><i><a class="txt" href="scm_1.html#E1:35"><i><font color="Green" title="E26">A1</font></i></a>, <a class="ref" href="scm_1.html#T3" target="_self" title="SCM_1:th.3">Th3</a></i>;<br/>

<a NAME="E5:35"/>
 <a href="ami_3.html#K16" title="AMI_3:func.16">il.</a> 0 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_3.html#K16" title="AMI_3:func.16">il.</a> 1
 
<b>by </b><i><a class="ref" href="ami_3.html#T53" title="AMI_3:th.53">AMI_3:53</a></i>;<br/>
<b>hence </b><a NAME="E6:35"/>
 <a href="scm_1.html#K2" title="SCM_1:func.2">Complexity</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <b>by </b><i><a class="txt" href="scm_1.html#E1:35"><i><font color="Green" title="E26">A1</font></i></a>, <a class="txt" href="scm_1.html#E2:35"><i><font color="Green" title="E27">A2</font></i></a>, <a class="txt" href="scm_1.html#E3:35"><i><font color="Green" title="E28">A3</font></i></a>, <a class="ref" href="scm_1.html#T17" target="_self" title="SCM_1:th.17">Th17</a></i>;<br/>

<b>let </b><font color="Maroon" title="c5">d</font> be    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> ;<br/>

<b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K12" title="AMI_1:func.12">Result</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">d</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default">0 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">d</font>
<b>by </b><i><a class="txt" href="scm_1.html#E1:35"><i><font color="Green" title="E26">A1</font></i></a>, <a class="txt" href="scm_1.html#E3:35"><i><font color="Green" title="E28">A3</font></i></a>, <a class="ref" href="scm_1.html#T4" target="_self" title="SCM_1:th.4">Th4</a></i>
<br/>.= 
<font color="Maroon" title="c3">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">d</font>
<b>by </b><i><a class="txt" href="scm_1.html#E1:35"><i><font color="Green" title="E26">A1</font></i></a>, <a class="txt" href="scm_1.html#E2:35"><i><font color="Green" title="E27">A2</font></i></a>, <a class="ref" href="scm_1.html#T23" target="_self" title="SCM_1:th.23">Th23</a></i>
;<br/>


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