(0) Obligation:

JBC Problem based on JBC Program:
/**
* Example taken from "A Term Rewriting Approach to the Automated Termination
* Analysis of Imperative Programs" (http://www.cs.unm.edu/~spf/papers/2009-02.pdf)
* and converted to Java.
*/

public class PastaB4 {
public static void main(String[] args) {
Random.args = args;
int x = Random.random();
int y = Random.random();

while (x > y) {
int t = x;
x = y;
y = t;
}
}
}


public class Random {
static String[] args;
static int index = 0;

public static int random() {
String string = args[index];
index++;
return string.length();
}
}


(1) JBCToGraph (SOUND transformation)

Constructed TerminationGraph.

(2) Obligation:

Termination Graph based on JBC Program:
PastaB4.main([Ljava/lang/String;)V: Graph of 179 nodes with 1 SCC.


(3) TerminationGraphToSCCProof (SOUND transformation)

Splitted TerminationGraph to 1 SCCs.

(4) Obligation:

SCC of termination graph based on JBC Program.
SCC contains nodes from the following methods: PastaB4.main([Ljava/lang/String;)V
SCC calls the following helper methods:
Performed SCC analyses:
  • Used field analysis yielded the following read fields:
  • Marker field analysis yielded the following relations that could be markers:

(5) SCCToIntTRSProof (SOUND transformation)

Transformed FIGraph SCCs to intTRSs. Log:

Generated rules. Obtained 12 IRules

P rules:
f328_0_main_Load(EOS, i18, i44, i18) → f335_0_main_LE(EOS, i18, i44, i18, i44)
f335_0_main_LE(EOS, i18, i44, i18, i44) → f355_0_main_LE(EOS, i18, i44, i18, i44)
f355_0_main_LE(EOS, i18, i44, i18, i44) → f367_0_main_Load(EOS, i18, i44) | >(i18, i44)
f367_0_main_Load(EOS, i18, i44) → f377_0_main_Store(EOS, i44, i18)
f377_0_main_Store(EOS, i44, i18) → f390_0_main_Load(EOS, i44, i18)
f390_0_main_Load(EOS, i44, i18) → f404_0_main_Store(EOS, i18, i44)
f404_0_main_Store(EOS, i18, i44) → f417_0_main_Load(EOS, i44, i18)
f417_0_main_Load(EOS, i44, i18) → f427_0_main_Store(EOS, i44, i18)
f427_0_main_Store(EOS, i44, i18) → f443_0_main_JMP(EOS, i44, i18)
f443_0_main_JMP(EOS, i44, i18) → f483_0_main_Load(EOS, i44, i18)
f483_0_main_Load(EOS, i44, i18) → f318_0_main_Load(EOS, i44, i18)
f318_0_main_Load(EOS, i18, i44) → f328_0_main_Load(EOS, i18, i44, i18)

Combined rules. Obtained 1 IRules

P rules:
f328_0_main_Load(EOS, x0, x1, x0) → f328_0_main_Load(EOS, x1, x0, x1) | <(x1, x0)

Filtered ground terms:


f328_0_main_Load(x1, x2, x3, x4) → f328_0_main_Load(x2, x3, x4)
Cond_f328_0_main_Load(x1, x2, x3, x4, x5) → Cond_f328_0_main_Load(x1, x3, x4, x5)

Filtered duplicate terms:


f328_0_main_Load(x1, x2, x3) → f328_0_main_Load(x2, x3)
Cond_f328_0_main_Load(x1, x2, x3, x4) → Cond_f328_0_main_Load(x1, x3, x4)

Prepared 1 rules for path length conversion:

P rules:
f328_0_main_Load(x1, x0) → f328_0_main_Load(x0, x1) | <(x1, x0)

Finished conversion. Obtained 1 rules.

P rules:
f328_0_main_Load(x0, x1) → f328_0_main_Load(x1, x0) | >(x1, x0)

(6) Obligation:

Rules:
f328_0_main_Load(x0, x1) → f328_0_main_Load(x1, x0) | >(x1, x0)

(7) TerminationGraphProcessor (EQUIVALENT transformation)

Constructed the termination graph and obtained no non-trivial SCC(s).


(8) YES