Termination proof of /tmp/tmpSV2cuz/PastaB11.jar

Termination of the given JBC could be proven:

0 JBC

↳1 JBC2FIG (⇐)

↳2 FIGraph

↳3 FIGtoITRSProof (⇐)

↳4 ITRS

↳5 ITRStoIDPProof (⇔)

↳6 IDP

↳7 UsableRulesProof (⇔)

↳8 IDP

↳9 IDPNonInfProof (⇐)

↳10 AND

    ↳11 IDP

        ↳12 IDependencyGraphProof (⇔)

        ↳13 TRUE

    ↳14 IDP

        ↳15 IDependencyGraphProof (⇔)

        ↳16 TRUE

(0) Obligation:

JBC Problem based on JBC Program:
Manifest-Version: 1.0 Created-By: 1.6.0_16 (Sun Microsystems Inc.) Main-Class: PastaB11

/**
 * 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 PastaB11 {
    public static void main(String[] args) {
        Random.args = args;
        int x = Random.random();
        int y = Random.random();

        while (x + y > 0) {
            if (x > y) {
                x--;
            } else if (x == y) {
                x--;
            } else {
                y--;
            }     
        }
    }
}


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

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

(1) JBC2FIG (SOUND transformation)

Constructed FIGraph.

(2) Obligation:

FIGraph based on JBC Program:
Graph of 201 nodes with 1 SCC.

(3) FIGtoITRSProof (SOUND transformation)

Transformed FIGraph to ITRS rules

(4) Obligation:

ITRS problem:

The following function symbols are pre-defined:

!=	~	Neq: (Integer, Integer) -> Boolean
*	~	Mul: (Integer, Integer) -> Integer
>=	~	Ge: (Integer, Integer) -> Boolean
-1	~	UnaryMinus: (Integer) -> Integer
\|	~	Bwor: (Integer, Integer) -> Integer
/	~	Div: (Integer, Integer) -> Integer
=	~	Eq: (Integer, Integer) -> Boolean
	~	Bwxor: (Integer, Integer) -> Integer
\|\|	~	Lor: (Boolean, Boolean) -> Boolean
!	~	Lnot: (Boolean) -> Boolean
<	~	Lt: (Integer, Integer) -> Boolean
-	~	Sub: (Integer, Integer) -> Integer
<=	~	Le: (Integer, Integer) -> Boolean
>	~	Gt: (Integer, Integer) -> Boolean
~	~	Bwnot: (Integer) -> Integer
%	~	Mod: (Integer, Integer) -> Integer
&	~	Bwand: (Integer, Integer) -> Integer
+	~	Add: (Integer, Integer) -> Integer
&&	~	Land: (Boolean, Boolean) -> Boolean

The TRS R consists of the following rules:
Load576(i14, i23) → Cond_Load576(i14 < i23 && i14 + i23 > 0, i14, i23)
Cond_Load576(TRUE, i14, i23) → Load576(i14, i23 + -1)
Load576(i23, i23) → Cond_Load5761(i23 + i23 > 0, i23, i23)
Cond_Load5761(TRUE, i23, i23) → Load576(i23 + -1, i23)
Load576(i14, i23) → Cond_Load5762(i14 > i23 && i14 + i23 > 0, i14, i23)
Cond_Load5762(TRUE, i14, i23) → Load576(i14 + -1, i23)
The set Q consists of the following terms:
Load576(x0, x1)
Cond_Load576(TRUE, x0, x1)
Cond_Load5761(TRUE, x0, x0)
Cond_Load5762(TRUE, x0, x1)

(5) ITRStoIDPProof (EQUIVALENT transformation)

Added dependency pairs

(6) Obligation:

IDP problem:
The following function symbols are pre-defined:

!=	~	Neq: (Integer, Integer) -> Boolean
*	~	Mul: (Integer, Integer) -> Integer
>=	~	Ge: (Integer, Integer) -> Boolean
-1	~	UnaryMinus: (Integer) -> Integer
\|	~	Bwor: (Integer, Integer) -> Integer
/	~	Div: (Integer, Integer) -> Integer
=	~	Eq: (Integer, Integer) -> Boolean
	~	Bwxor: (Integer, Integer) -> Integer
\|\|	~	Lor: (Boolean, Boolean) -> Boolean
!	~	Lnot: (Boolean) -> Boolean
<	~	Lt: (Integer, Integer) -> Boolean
-	~	Sub: (Integer, Integer) -> Integer
<=	~	Le: (Integer, Integer) -> Boolean
>	~	Gt: (Integer, Integer) -> Boolean
~	~	Bwnot: (Integer) -> Integer
%	~	Mod: (Integer, Integer) -> Integer
&	~	Bwand: (Integer, Integer) -> Integer
+	~	Add: (Integer, Integer) -> Integer
&&	~	Land: (Boolean, Boolean) -> Boolean

The following domains are used:

Boolean, Integer

The ITRS R consists of the following rules:
Load576(i14, i23) → Cond_Load576(i14 < i23 && i14 + i23 > 0, i14, i23)
Cond_Load576(TRUE, i14, i23) → Load576(i14, i23 + -1)
Load576(i23, i23) → Cond_Load5761(i23 + i23 > 0, i23, i23)
Cond_Load5761(TRUE, i23, i23) → Load576(i23 + -1, i23)
Load576(i14, i23) → Cond_Load5762(i14 > i23 && i14 + i23 > 0, i14, i23)
Cond_Load5762(TRUE, i14, i23) → Load576(i14 + -1, i23)

The integer pair graph contains the following rules and edges:
(0): LOAD576(i14[0], i23[0]) → COND_LOAD576(i14[0] < i23[0] && i14[0] + i23[0] > 0, i14[0], i23[0])
(1): COND_LOAD576(TRUE, i14[1], i23[1]) → LOAD576(i14[1], i23[1] + -1)
(2): LOAD576(i23[2], i23[2]) → COND_LOAD5761(i23[2] + i23[2] > 0, i23[2], i23[2])
(3): COND_LOAD5761(TRUE, i23[3], i23[3]) → LOAD576(i23[3] + -1, i23[3])
(4): LOAD576(i14[4], i23[4]) → COND_LOAD5762(i14[4] > i23[4] && i14[4] + i23[4] > 0, i14[4], i23[4])
(5): COND_LOAD5762(TRUE, i14[5], i23[5]) → LOAD576(i14[5] + -1, i23[5])

(0) -> (1), if ((i14[0] < i23[0] && i14[0] + i23[0] > 0 →^* TRUE)∧(i23[0] →^* i23[1])∧(i14[0] →^* i14[1]))

(1) -> (0), if ((i14[1] →^* i14[0])∧(i23[1] + -1 →^* i23[0]))

(1) -> (2), if ((i14[1] →^* i23[2])∧(i23[1] + -1 →^* i23[2]))

(1) -> (4), if ((i14[1] →^* i14[4])∧(i23[1] + -1 →^* i23[4]))

(2) -> (3), if ((i23[2] →^* i23[3])∧(i23[2] + i23[2] > 0 →^* TRUE))

(3) -> (0), if ((i23[3] + -1 →^* i14[0])∧(i23[3] →^* i23[0]))

(3) -> (2), if ((i23[3] →^* i23[2])∧(i23[3] + -1 →^* i23[2]))

(3) -> (4), if ((i23[3] →^* i23[4])∧(i23[3] + -1 →^* i14[4]))

(4) -> (5), if ((i14[4] > i23[4] && i14[4] + i23[4] > 0 →^* TRUE)∧(i23[4] →^* i23[5])∧(i14[4] →^* i14[5]))

(5) -> (0), if ((i23[5] →^* i23[0])∧(i14[5] + -1 →^* i14[0]))

(5) -> (2), if ((i14[5] + -1 →^* i23[2])∧(i23[5] →^* i23[2]))

(5) -> (4), if ((i23[5] →^* i23[4])∧(i14[5] + -1 →^* i14[4]))

The set Q consists of the following terms:
Load576(x0, x1)
Cond_Load576(TRUE, x0, x1)
Cond_Load5761(TRUE, x0, x0)
Cond_Load5762(TRUE, x0, x1)

(7) UsableRulesProof (EQUIVALENT transformation)

As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R.

(8) Obligation:

IDP problem:
The following function symbols are pre-defined:

!=	~	Neq: (Integer, Integer) -> Boolean
*	~	Mul: (Integer, Integer) -> Integer
>=	~	Ge: (Integer, Integer) -> Boolean
-1	~	UnaryMinus: (Integer) -> Integer
\|	~	Bwor: (Integer, Integer) -> Integer
/	~	Div: (Integer, Integer) -> Integer
=	~	Eq: (Integer, Integer) -> Boolean
	~	Bwxor: (Integer, Integer) -> Integer
\|\|	~	Lor: (Boolean, Boolean) -> Boolean
!	~	Lnot: (Boolean) -> Boolean
<	~	Lt: (Integer, Integer) -> Boolean
-	~	Sub: (Integer, Integer) -> Integer
<=	~	Le: (Integer, Integer) -> Boolean
>	~	Gt: (Integer, Integer) -> Boolean
~	~	Bwnot: (Integer) -> Integer
%	~	Mod: (Integer, Integer) -> Integer
&	~	Bwand: (Integer, Integer) -> Integer
+	~	Add: (Integer, Integer) -> Integer
&&	~	Land: (Boolean, Boolean) -> Boolean

The following domains are used:

Boolean, Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): LOAD576(i14[0], i23[0]) → COND_LOAD576(i14[0] < i23[0] && i14[0] + i23[0] > 0, i14[0], i23[0])
(1): COND_LOAD576(TRUE, i14[1], i23[1]) → LOAD576(i14[1], i23[1] + -1)
(2): LOAD576(i23[2], i23[2]) → COND_LOAD5761(i23[2] + i23[2] > 0, i23[2], i23[2])
(3): COND_LOAD5761(TRUE, i23[3], i23[3]) → LOAD576(i23[3] + -1, i23[3])
(4): LOAD576(i14[4], i23[4]) → COND_LOAD5762(i14[4] > i23[4] && i14[4] + i23[4] > 0, i14[4], i23[4])
(5): COND_LOAD5762(TRUE, i14[5], i23[5]) → LOAD576(i14[5] + -1, i23[5])