Termination proof of /tmp/tmpEsPt2B/MinusMin.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 IDPNonInfProof (⇐)

        ↳16 AND

            ↳17 IDP

                ↳18 IDependencyGraphProof (⇔)

                ↳19 TRUE

            ↳20 IDP

                ↳21 IDependencyGraphProof (⇔)

                ↳22 TRUE

(0) Obligation:

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

public class MinusMin{

  public static int min (int x, int y) {

    if (x < y) return x;
    else return y;
  }


  public static void main(String[] args) {
    Random.args = args;
    int x = Random.random();
    int y = Random.random();
    int res = 0;



    while (min(x-1,y) == y) {

      y++;
      res++;

    }


  }

}


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 202 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:
Load1487(i14, i214, i215) → Cond_Load1487(i14 - 1 >= i214, i14, i214, i215)
Cond_Load1487(TRUE, i14, i214, i215) → Load1538(i14, i215, i214)
Load1538(i14, i215, i214) → Load1487(i14, i214 + 1, i215 + 1)
Load1487(i14, i14 - 1, i215) → Cond_Load14871(i14 - 1 < i14 - 1 && i215 + 1 > 0, i14, i14 - 1, i215)
Cond_Load14871(TRUE, i14, i14 - 1, i215) → Load1487(i14, i14 - 1 + 1, i215 + 1)
The set Q consists of the following terms:
Load1487(x0, x1, x2)
Cond_Load1487(TRUE, x0, x1, x2)
Load1538(x0, x1, x2)
Cond_Load14871(TRUE, x0, x0 - 1, 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:

Integer, Boolean

The ITRS R consists of the following rules:
Load1487(i14, i214, i215) → Cond_Load1487(i14 - 1 >= i214, i14, i214, i215)
Cond_Load1487(TRUE, i14, i214, i215) → Load1538(i14, i215, i214)
Load1538(i14, i215, i214) → Load1487(i14, i214 + 1, i215 + 1)
Load1487(i14, i14 - 1, i215) → Cond_Load14871(i14 - 1 < i14 - 1 && i215 + 1 > 0, i14, i14 - 1, i215)
Cond_Load14871(TRUE, i14, i14 - 1, i215) → Load1487(i14, i14 - 1 + 1, i215 + 1)

The integer pair graph contains the following rules and edges:
(0): LOAD1487(i14[0], i214[0], i215[0]) → COND_LOAD1487(i14[0] - 1 >= i214[0], i14[0], i214[0], i215[0])
(1): COND_LOAD1487(TRUE, i14[1], i214[1], i215[1]) → LOAD1538(i14[1], i215[1], i214[1])
(2): LOAD1538(i14[2], i215[2], i214[2]) → LOAD1487(i14[2], i214[2] + 1, i215[2] + 1)
(3): LOAD1487(i14[3], i14[3] - 1, i215[3]) → COND_LOAD14871(i14[3] - 1 < i14[3] - 1 && i215[3] + 1 > 0, i14[3], i14[3] - 1, i215[3])
(4): COND_LOAD14871(TRUE, i14[4], i14[4] - 1, i215[4]) → LOAD1487(i14[4], i14[4] - 1 + 1, i215[4] + 1)

(0) -> (1), if ((i215[0] →^* i215[1])∧(i214[0] →^* i214[1])∧(i14[0] →^* i14[1])∧(i14[0] - 1 >= i214[0] →^* TRUE))

(1) -> (2), if ((i14[1] →^* i14[2])∧(i214[1] →^* i214[2])∧(i215[1] →^* i215[2]))

(2) -> (0), if ((i215[2] + 1 →^* i215[0])∧(i214[2] + 1 →^* i214[0])∧(i14[2] →^* i14[0]))

(2) -> (3), if ((i14[2] →^* i14[3])∧(i214[2] + 1 →^* i14[3] - 1)∧(i215[2] + 1 →^* i215[3]))

(3) -> (4), if ((i14[3] →^* i14[4])∧(i14[3] - 1 < i14[3] - 1 && i215[3] + 1 > 0 →^* TRUE)∧(i215[3] →^* i215[4])∧(i14[3] - 1 →^* i14[4] - 1))

(4) -> (0), if ((i14[4] - 1 + 1 →^* i214[0])∧(i14[4] →^* i14[0])∧(i215[4] + 1 →^* i215[0]))

(4) -> (3), if ((i215[4] + 1 →^* i215[3])∧(i14[4] - 1 + 1 →^* i14[3] - 1)∧(i14[4] →^* i14[3]))

The set Q consists of the following terms:
Load1487(x0, x1, x2)
Cond_Load1487(TRUE, x0, x1, x2)
Load1538(x0, x1, x2)
Cond_Load14871(TRUE, x0, x0 - 1, 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:

Integer, Boolean

R is empty.

The integer pair graph contains the following rules and edges:
(0): LOAD1487(i14[0], i214[0], i215[0]) → COND_LOAD1487(i14[0] - 1 >= i214[0], i14[0], i214[0], i215[0])
(1): COND_LOAD1487(TRUE, i14[1], i214[1], i215[1]) → LOAD1538(i14[1], i215[1], i214[1])
(2): LOAD1538(i14[2], i215[2], i214[2]) → LOAD1487(i14[2], i214[2] + 1, i215[2] + 1)
(3): LOAD1487(i14[3], i14[3] - 1, i215[3]) → COND_LOAD14871(i14[3] - 1 < i14[3] - 1 && i215[3] + 1 > 0, i14[3], i14[3] - 1, i215[3])
(4): COND_LOAD14871(TRUE, i14[4], i14[4] - 1, i215[4]) → LOAD1487(i14[4], i14[4] - 1 + 1, i215[4] + 1)