Termination of the given JBC could be proven:

0 JBC
↳1 JBC2FIG (⇐)
↳2 FIGraph
↳3 FIGtoITRSProof (⇐)
↳4 ITRS
↳5 GroundTermsRemoverProof (⇔)
↳6 ITRS
↳7 ITRStoIDPProof (⇔)
↳8 IDP
↳9 UsableRulesProof (⇔)
↳10 IDP
↳11 IDPNonInfProof (⇐)
↳12 AND
    ↳13 IDP
        ↳14 IDependencyGraphProof (⇔)
        ↳15 IDP
        ↳16 IDPNonInfProof (⇐)
        ↳17 IDP
        ↳18 IDependencyGraphProof (⇔)
        ↳19 TRUE
    ↳20 IDP
        ↳21 IDPNonInfProof (⇐)
        ↳22 IDP
        ↳23 IDependencyGraphProof (⇔)
        ↳24 TRUE

(0) Obligation:

JBC Problem based on JBC Program:
Manifest-Version: 1.0 Created-By: 1.6.0_16 (Sun Microsystems Inc.) Main-Class: DivWithoutMinus 
public class DivWithoutMinus{
  // adaption of the algorithm from [Kolbe 95]
  public static void main(String[] args) {
    Random.args = args;

    int x = Random.random();
    int y = Random.random();
    int z = y;
    int res = 0;

    while (z > 0 && (y == 0 || y > 0 && x > 0))	{

      if (y == 0) {
        res++;
        y = z;
      }
      else {
        x--;
        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 213 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:
Load1200(i175, 0, i237, i227) → Cond_Load1200(i237 > 0 && i227 + 1 > 0, i175, 0, i237, i227)
Cond_Load1200(TRUE, i175, 0, i237, i227) → Load1200(i175, i237, i237, i227 + 1)
Load1200(i268, i255, i237, i227) → Cond_Load12001(i255 > 0 && i268 > 0 && i237 > 0, i268, i255, i237, i227)
Cond_Load12001(TRUE, i268, i255, i237, i227) → Load1200(i268 + -1, i255 + -1, i237, i227)
The set Q consists of the following terms:
Cond_Load1200(TRUE, x0, 0, x1, x2)
Load1200(x0, x1, x2, x3)
Cond_Load12001(TRUE, x0, x1, x2, x3)

(5) GroundTermsRemoverProof (EQUIVALENT transformation)

Some arguments are removed because they always contain the same ground term.
We removed the following ground terms:
  • 0

We removed arguments according to the following replacements:

Cond_Load1200(x1, x2, x3, x4, x5) → Cond_Load1200(x1, x2, x4, x5)

(6) 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:
Load1200(i175, 0, i237, i227) → Cond_Load1200(i237 > 0 && i227 + 1 > 0, i175, i237, i227)
Cond_Load1200(TRUE, i175, i237, i227) → Load1200(i175, i237, i237, i227 + 1)
Load1200(i268, i255, i237, i227) → Cond_Load12001(i255 > 0 && i268 > 0 && i237 > 0, i268, i255, i237, i227)
Cond_Load12001(TRUE, i268, i255, i237, i227) → Load1200(i268 + -1, i255 + -1, i237, i227)
The set Q consists of the following terms:
Cond_Load1200(TRUE, x0, x1, x2)
Load1200(x0, x1, x2, x3)
Cond_Load12001(TRUE, x0, x1, x2, x3)

(7) ITRStoIDPProof (EQUIVALENT transformation)

Added dependency pairs

(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


The ITRS R consists of the following rules:
Load1200(i175, 0, i237, i227) → Cond_Load1200(i237 > 0 && i227 + 1 > 0, i175, i237, i227)
Cond_Load1200(TRUE, i175, i237, i227) → Load1200(i175, i237, i237, i227 + 1)
Load1200(i268, i255, i237, i227) → Cond_Load12001(i255 > 0 && i268 > 0 && i237 > 0, i268, i255, i237, i227)
Cond_Load12001(TRUE, i268, i255, i237, i227) → Load1200(i268 + -1, i255 + -1, i237, i227)

The integer pair graph contains the following rules and edges:
(0): LOAD1200(i175[0], 0, i237[0], i227[0]) → COND_LOAD1200(i237[0] > 0 && i227[0] + 1 > 0, i175[0], i237[0], i227[0])
(1): COND_LOAD1200(TRUE, i175[1], i237[1], i227[1]) → LOAD1200(i175[1], i237[1], i237[1], i227[1] + 1)
(2): LOAD1200(i268[2], i255[2], i237[2], i227[2]) → COND_LOAD12001(i255[2] > 0 && i268[2] > 0 && i237[2] > 0, i268[2], i255[2], i237[2], i227[2])
(3): COND_LOAD12001(TRUE, i268[3], i255[3], i237[3], i227[3]) → LOAD1200(i268[3] + -1, i255[3] + -1, i237[3], i227[3])

(0) -> (1), if ((i237[0] →* i237[1])∧(i175[0] →* i175[1])∧(i237[0] > 0 && i227[0] + 1 > 0 →* TRUE)∧(i227[0] →* i227[1]))


(1) -> (0), if ((i237[1] →* i237[0])∧(i227[1] + 1 →* i227[0])∧(i237[1] →* 0)∧(i175[1] →* i175[0]))


(1) -> (2), if ((i237[1] →* i237[2])∧(i175[1] →* i268[2])∧(i227[1] + 1 →* i227[2])∧(i237[1] →* i255[2]))


(2) -> (3), if ((i255[2] > 0 && i268[2] > 0 && i237[2] > 0 →* TRUE)∧(i255[2] →* i255[3])∧(i227[2] →* i227[3])∧(i237[2] →* i237[3])∧(i268[2] →* i268[3]))


(3) -> (0), if ((i255[3] + -1 →* 0)∧(i237[3] →* i237[0])∧(i227[3] →* i227[0])∧(i268[3] + -1 →* i175[0]))


(3) -> (2), if ((i255[3] + -1 →* i255[2])∧(i237[3] →* i237[2])∧(i268[3] + -1 →* i268[2])∧(i227[3] →* i227[2]))



The set Q consists of the following terms:
Cond_Load1200(TRUE, x0, x1, x2)
Load1200(x0, x1, x2, x3)
Cond_Load12001(TRUE, x0, x1, x2, x3)

(9) 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.

(10) 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): LOAD1200(i175[0], 0, i237[0], i227[0]) → COND_LOAD1200(i237[0] > 0 && i227[0] + 1 > 0, i175[0], i237[0], i227[0])
(1): COND_LOAD1200(TRUE, i175[1], i237[1], i227[1]) → LOAD1200(i175[1], i237[1], i237[1], i227[1] + 1)
(2): LOAD1200(i268[2], i255[2], i237[2], i227[2]) → COND_LOAD12001(i255[2] > 0 && i268[2] > 0 && i237[2] > 0, i268[2], i255[2], i237[2], i227[2])
(3): COND_LOAD12001(TRUE, i268[3], i255[3], i237[3], i227[3]) → LOAD1200(i268[3] + -1, i255[3] + -1, i237[3], i227[3])

(0) -> (1), if ((i237[0] →* i237[1])∧(i175[0] →* i175[1])∧(i237[0] > 0 && i227[0] + 1 > 0 →* TRUE)∧(i227[0] →* i227[1]))


(1) -> (0), if ((i237[1] →* i237[0])∧(i227[1] + 1 →* i227[0])∧(i237[1] →* 0)∧(i175[1] →* i175[0]))


(1) -> (2), if ((i237[1] →* i237[2])∧(i175[1] →* i268[2])∧(i227[1] + 1 →* i227[2])∧(i237[1] →* i255[2]))


(2) -> (3), if ((i255[2] > 0 && i268[2] > 0 && i237[2] > 0 →* TRUE)∧(i255[2] →* i255[3])∧(i227[2] →* i227[3])∧(i237[2] →* i237[3])∧(i268[2] →* i268[3]))


(3) -> (0), if ((i255[3] + -1 →* 0)∧(i237[3] →* i237[0])∧(i227[3] →* i227[0])∧(i268[3] + -1 →* i175[0]))


(3) -> (2), if ((i255[3] + -1 →* i255[2])∧(i237[3] →* i237[2])∧(i268[3] + -1 →* i268[2])∧(i227[3] →* i227[2]))



The set Q consists of the following terms:
Cond_Load1200(TRUE, x0, x1, x2)
Load1200(x0, x1, x2, x3)
Cond_Load12001(TRUE, x0, x1, x2, x3)

(11) IDPNonInfProof (SOUND transformation)

The constraints were generated the following way:
The DP Problem is simplified using the Induction Calculus [NONINF] with the following steps:
Note that final constraints are written in bold face.


For Pair LOAD1200(i175, 0, i237, i227) → COND_LOAD1200(&&(>(i237, 0), >(+(i227, 1), 0)), i175, i237, i227) the following chains were created:
  • We consider the chain LOAD1200(i175[0], 0, i237[0], i227[0]) → COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0]), COND_LOAD1200(TRUE, i175[1], i237[1], i227[1]) → LOAD1200(i175[1], i237[1], i237[1], +(i227[1], 1)) which results in the following constraint:

    (1)    (i237[0]=i237[1]∧i175[0]=i175[1]∧&&(>(i237[0], 0), >(+(i227[0], 1), 0))=TRUE∧i227[0]=i227[1] ⇒ LOAD1200(i175[0], 0, i237[0], i227[0])≥NonInfC∧LOAD1200(i175[0], 0, i237[0], i227[0])≥COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0])∧(UIncreasing(COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0])), ≥))



    We simplified constraint (1) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (2)    (>(i237[0], 0)=TRUE∧>(+(i227[0], 1), 0)=TRUE ⇒ LOAD1200(i175[0], 0, i237[0], i227[0])≥NonInfC∧LOAD1200(i175[0], 0, i237[0], i227[0])≥COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0])∧(UIncreasing(COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0])), ≥))



    We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (3)    (i237[0] + [-1] ≥ 0∧i227[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0])), ≥)∧[(-1)bni_21 + (-1)Bound*bni_21] + [bni_21]i175[0] ≥ 0∧[(-1)bso_22] ≥ 0)



    We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (4)    (i237[0] + [-1] ≥ 0∧i227[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0])), ≥)∧[(-1)bni_21 + (-1)Bound*bni_21] + [bni_21]i175[0] ≥ 0∧[(-1)bso_22] ≥ 0)



    We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (5)    (i237[0] + [-1] ≥ 0∧i227[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0])), ≥)∧[(-1)bni_21 + (-1)Bound*bni_21] + [bni_21]i175[0] ≥ 0∧[(-1)bso_22] ≥ 0)



    We simplified constraint (5) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (6)    (i237[0] + [-1] ≥ 0∧i227[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0])), ≥)∧[bni_21] = 0∧[(-1)bni_21 + (-1)Bound*bni_21] ≥ 0∧0 = 0∧[(-1)bso_22] ≥ 0)



    We simplified constraint (6) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (7)    (i237[0] ≥ 0∧i227[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0])), ≥)∧[bni_21] = 0∧[(-1)bni_21 + (-1)Bound*bni_21] ≥ 0∧0 = 0∧[(-1)bso_22] ≥ 0)







For Pair COND_LOAD1200(TRUE, i175, i237, i227) → LOAD1200(i175, i237, i237, +(i227, 1)) the following chains were created:
  • We consider the chain LOAD1200(i175[0], 0, i237[0], i227[0]) → COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0]), COND_LOAD1200(TRUE, i175[1], i237[1], i227[1]) → LOAD1200(i175[1], i237[1], i237[1], +(i227[1], 1)), LOAD1200(i175[0], 0, i237[0], i227[0]) → COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0]) which results in the following constraint:

    (8)    (i237[0]=i237[1]∧i175[0]=i175[1]∧&&(>(i237[0], 0), >(+(i227[0], 1), 0))=TRUE∧i227[0]=i227[1]∧i237[1]=i237[0]1∧+(i227[1], 1)=i227[0]1∧i237[1]=0∧i175[1]=i175[0]1 ⇒ COND_LOAD1200(TRUE, i175[1], i237[1], i227[1])≥NonInfC∧COND_LOAD1200(TRUE, i175[1], i237[1], i227[1])≥LOAD1200(i175[1], i237[1], i237[1], +(i227[1], 1))∧(UIncreasing(LOAD1200(i175[1], i237[1], i237[1], +(i227[1], 1))), ≥))



    We solved constraint (8) using rules (I), (II), (III), (IV), (IDP_CONSTANT_FOLD).
  • We consider the chain LOAD1200(i175[0], 0, i237[0], i227[0]) → COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0]), COND_LOAD1200(TRUE, i175[1], i237[1], i227[1]) → LOAD1200(i175[1], i237[1], i237[1], +(i227[1], 1)), LOAD1200(i268[2], i255[2], i237[2], i227[2]) → COND_LOAD12001(&&(&&(>(i255[2], 0), >(i268[2], 0)), >(i237[2], 0)), i268[2], i255[2], i237[2], i227[2]) which results in the following constraint:

    (9)    (i237[0]=i237[1]∧i175[0]=i175[1]∧&&(>(i237[0], 0), >(+(i227[0], 1), 0))=TRUE∧i227[0]=i227[1]∧i237[1]=i237[2]∧i175[1]=i268[2]∧+(i227[1], 1)=i227[2]∧i237[1]=i255[2] ⇒ COND_LOAD1200(TRUE, i175[1], i237[1], i227[1])≥NonInfC∧COND_LOAD1200(TRUE, i175[1], i237[1], i227[1])≥LOAD1200(i175[1], i237[1], i237[1], +(i227[1], 1))∧(UIncreasing(LOAD1200(i175[1], i237[1], i237[1], +(i227[1], 1))), ≥))



    We simplified constraint (9) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (10)    (>(i237[0], 0)=TRUE∧>(+(i227[0], 1), 0)=TRUE ⇒ COND_LOAD1200(TRUE, i175[0], i237[0], i227[0])≥NonInfC∧COND_LOAD1200(TRUE, i175[0], i237[0], i227[0])≥LOAD1200(i175[0], i237[0], i237[0], +(i227[0], 1))∧(UIncreasing(LOAD1200(i175[1], i237[1], i237[1], +(i227[1], 1))), ≥))



    We simplified constraint (10) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (11)    (i237[0] + [-1] ≥ 0∧i227[0] ≥ 0 ⇒ (UIncreasing(LOAD1200(i175[1], i237[1], i237[1], +(i227[1], 1))), ≥)∧[(-1)bni_23 + (-1)Bound*bni_23] + [bni_23]i175[0] ≥ 0∧[(-1)bso_24] ≥ 0)



    We simplified constraint (11) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (12)    (i237[0] + [-1] ≥ 0∧i227[0] ≥ 0 ⇒ (UIncreasing(LOAD1200(i175[1], i237[1], i237[1], +(i227[1], 1))), ≥)∧[(-1)bni_23 + (-1)Bound*bni_23] + [bni_23]i175[0] ≥ 0∧[(-1)bso_24] ≥ 0)



    We simplified constraint (12) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (13)    (i237[0] + [-1] ≥ 0∧i227[0] ≥ 0 ⇒ (UIncreasing(LOAD1200(i175[1], i237[1], i237[1], +(i227[1], 1))), ≥)∧[(-1)bni_23 + (-1)Bound*bni_23] + [bni_23]i175[0] ≥ 0∧[(-1)bso_24] ≥ 0)



    We simplified constraint (13) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (14)    (i237[0] + [-1] ≥ 0∧i227[0] ≥ 0 ⇒ (UIncreasing(LOAD1200(i175[1], i237[1], i237[1], +(i227[1], 1))), ≥)∧[bni_23] = 0∧[(-1)bni_23 + (-1)Bound*bni_23] ≥ 0∧0 = 0∧[(-1)bso_24] ≥ 0)



    We simplified constraint (14) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (15)    (i237[0] ≥ 0∧i227[0] ≥ 0 ⇒ (UIncreasing(LOAD1200(i175[1], i237[1], i237[1], +(i227[1], 1))), ≥)∧[bni_23] = 0∧[(-1)bni_23 + (-1)Bound*bni_23] ≥ 0∧0 = 0∧[(-1)bso_24] ≥ 0)







For Pair LOAD1200(i268, i255, i237, i227) → COND_LOAD12001(&&(&&(>(i255, 0), >(i268, 0)), >(i237, 0)), i268, i255, i237, i227) the following chains were created:
  • We consider the chain LOAD1200(i268[2], i255[2], i237[2], i227[2]) → COND_LOAD12001(&&(&&(>(i255[2], 0), >(i268[2], 0)), >(i237[2], 0)), i268[2], i255[2], i237[2], i227[2]), COND_LOAD12001(TRUE, i268[3], i255[3], i237[3], i227[3]) → LOAD1200(+(i268[3], -1), +(i255[3], -1), i237[3], i227[3]) which results in the following constraint:

    (16)    (&&(&&(>(i255[2], 0), >(i268[2], 0)), >(i237[2], 0))=TRUE∧i255[2]=i255[3]∧i227[2]=i227[3]∧i237[2]=i237[3]∧i268[2]=i268[3] ⇒ LOAD1200(i268[2], i255[2], i237[2], i227[2])≥NonInfC∧LOAD1200(i268[2], i255[2], i237[2], i227[2])≥COND_LOAD12001(&&(&&(>(i255[2], 0), >(i268[2], 0)), >(i237[2], 0)), i268[2], i255[2], i237[2], i227[2])∧(UIncreasing(COND_LOAD12001(&&(&&(>(i255[2], 0), >(i268[2], 0)), >(i237[2], 0)), i268[2], i255[2], i237[2], i227[2])), ≥))



    We simplified constraint (16) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (17)    (>(i237[2], 0)=TRUE∧>(i255[2], 0)=TRUE∧>(i268[2], 0)=TRUE ⇒ LOAD1200(i268[2], i255[2], i237[2], i227[2])≥NonInfC∧LOAD1200(i268[2], i255[2], i237[2], i227[2])≥COND_LOAD12001(&&(&&(>(i255[2], 0), >(i268[2], 0)), >(i237[2], 0)), i268[2], i255[2], i237[2], i227[2])∧(UIncreasing(COND_LOAD12001(&&(&&(>(i255[2], 0), >(i268[2], 0)), >(i237[2], 0)), i268[2], i255[2], i237[2], i227[2])), ≥))



    We simplified constraint (17) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (18)    (i237[2] + [-1] ≥ 0∧i255[2] + [-1] ≥ 0∧i268[2] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD12001(&&(&&(>(i255[2], 0), >(i268[2], 0)), >(i237[2], 0)), i268[2], i255[2], i237[2], i227[2])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i268[2] ≥ 0∧[(-1)bso_26] ≥ 0)



    We simplified constraint (18) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (19)    (i237[2] + [-1] ≥ 0∧i255[2] + [-1] ≥ 0∧i268[2] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD12001(&&(&&(>(i255[2], 0), >(i268[2], 0)), >(i237[2], 0)), i268[2], i255[2], i237[2], i227[2])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i268[2] ≥ 0∧[(-1)bso_26] ≥ 0)



    We simplified constraint (19) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (20)    (i237[2] + [-1] ≥ 0∧i255[2] + [-1] ≥ 0∧i268[2] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD12001(&&(&&(>(i255[2], 0), >(i268[2], 0)), >(i237[2], 0)), i268[2], i255[2], i237[2], i227[2])), ≥)∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i268[2] ≥ 0∧[(-1)bso_26] ≥ 0)



    We simplified constraint (20) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (21)    (i237[2] + [-1] ≥ 0∧i255[2] + [-1] ≥ 0∧i268[2] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD12001(&&(&&(>(i255[2], 0), >(i268[2], 0)), >(i237[2], 0)), i268[2], i255[2], i237[2], i227[2])), ≥)∧0 = 0∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i268[2] ≥ 0∧0 = 0∧[(-1)bso_26] ≥ 0)



    We simplified constraint (21) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (22)    (i237[2] ≥ 0∧i255[2] + [-1] ≥ 0∧i268[2] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD12001(&&(&&(>(i255[2], 0), >(i268[2], 0)), >(i237[2], 0)), i268[2], i255[2], i237[2], i227[2])), ≥)∧0 = 0∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i268[2] ≥ 0∧0 = 0∧[(-1)bso_26] ≥ 0)



    We simplified constraint (22) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (23)    (i237[2] ≥ 0∧i255[2] ≥ 0∧i268[2] + [-1] ≥ 0 ⇒ (UIncreasing(COND_LOAD12001(&&(&&(>(i255[2], 0), >(i268[2], 0)), >(i237[2], 0)), i268[2], i255[2], i237[2], i227[2])), ≥)∧0 = 0∧[(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]i268[2] ≥ 0∧0 = 0∧[(-1)bso_26] ≥ 0)



    We simplified constraint (23) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (24)    (i237[2] ≥ 0∧i255[2] ≥ 0∧i268[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD12001(&&(&&(>(i255[2], 0), >(i268[2], 0)), >(i237[2], 0)), i268[2], i255[2], i237[2], i227[2])), ≥)∧0 = 0∧[(-1)Bound*bni_25] + [bni_25]i268[2] ≥ 0∧0 = 0∧[(-1)bso_26] ≥ 0)







For Pair COND_LOAD12001(TRUE, i268, i255, i237, i227) → LOAD1200(+(i268, -1), +(i255, -1), i237, i227) the following chains were created:
  • We consider the chain LOAD1200(i268[2], i255[2], i237[2], i227[2]) → COND_LOAD12001(&&(&&(>(i255[2], 0), >(i268[2], 0)), >(i237[2], 0)), i268[2], i255[2], i237[2], i227[2]), COND_LOAD12001(TRUE, i268[3], i255[3], i237[3], i227[3]) → LOAD1200(+(i268[3], -1), +(i255[3], -1), i237[3], i227[3]), LOAD1200(i175[0], 0, i237[0], i227[0]) → COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0]) which results in the following constraint:

    (25)    (&&(&&(>(i255[2], 0), >(i268[2], 0)), >(i237[2], 0))=TRUE∧i255[2]=i255[3]∧i227[2]=i227[3]∧i237[2]=i237[3]∧i268[2]=i268[3]∧+(i255[3], -1)=0∧i237[3]=i237[0]∧i227[3]=i227[0]∧+(i268[3], -1)=i175[0] ⇒ COND_LOAD12001(TRUE, i268[3], i255[3], i237[3], i227[3])≥NonInfC∧COND_LOAD12001(TRUE, i268[3], i255[3], i237[3], i227[3])≥LOAD1200(+(i268[3], -1), +(i255[3], -1), i237[3], i227[3])∧(UIncreasing(LOAD1200(+(i268[3], -1), +(i255[3], -1), i237[3], i227[3])), ≥))



    We simplified constraint (25) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (26)    (+(i255[2], -1)=0∧>(i237[2], 0)=TRUE∧>(i255[2], 0)=TRUE∧>(i268[2], 0)=TRUE ⇒ COND_LOAD12001(TRUE, i268[2], i255[2], i237[2], i227[2])≥NonInfC∧COND_LOAD12001(TRUE, i268[2], i255[2], i237[2], i227[2])≥LOAD1200(+(i268[2], -1), +(i255[2], -1), i237[2], i227[2])∧(UIncreasing(LOAD1200(+(i268[3], -1), +(i255[3], -1), i237[3], i227[3])), ≥))



    We simplified constraint (26) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (27)    (i255[2] + [-1] ≥ 0∧i237[2] + [-1] ≥ 0∧i255[2] + [-1] ≥ 0∧i268[2] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD1200(+(i268[3], -1), +(i255[3], -1), i237[3], i227[3])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i268[2] ≥ 0∧[1 + (-1)bso_28] ≥ 0)



    We simplified constraint (27) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (28)    (i255[2] + [-1] ≥ 0∧i237[2] + [-1] ≥ 0∧i255[2] + [-1] ≥ 0∧i268[2] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD1200(+(i268[3], -1), +(i255[3], -1), i237[3], i227[3])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i268[2] ≥ 0∧[1 + (-1)bso_28] ≥ 0)



    We simplified constraint (28) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (29)    (i255[2] + [-1] ≥ 0∧i237[2] + [-1] ≥ 0∧i255[2] + [-1] ≥ 0∧i268[2] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD1200(+(i268[3], -1), +(i255[3], -1), i237[3], i227[3])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i268[2] ≥ 0∧[1 + (-1)bso_28] ≥ 0)



    We simplified constraint (29) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (30)    (i255[2] + [-1] ≥ 0∧i237[2] + [-1] ≥ 0∧i255[2] + [-1] ≥ 0∧i268[2] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD1200(+(i268[3], -1), +(i255[3], -1), i237[3], i227[3])), ≥)∧0 = 0∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i268[2] ≥ 0∧0 = 0∧[1 + (-1)bso_28] ≥ 0)



    We simplified constraint (30) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (31)    (i255[2] ≥ 0∧i237[2] + [-1] ≥ 0∧i255[2] ≥ 0∧i268[2] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD1200(+(i268[3], -1), +(i255[3], -1), i237[3], i227[3])), ≥)∧0 = 0∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i268[2] ≥ 0∧0 = 0∧[1 + (-1)bso_28] ≥ 0)



    We simplified constraint (31) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (32)    (i255[2] ≥ 0∧i237[2] ≥ 0∧i255[2] ≥ 0∧i268[2] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD1200(+(i268[3], -1), +(i255[3], -1), i237[3], i227[3])), ≥)∧0 = 0∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i268[2] ≥ 0∧0 = 0∧[1 + (-1)bso_28] ≥ 0)



    We simplified constraint (32) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (33)    (i255[2] ≥ 0∧i237[2] ≥ 0∧i255[2] ≥ 0∧i268[2] ≥ 0 ⇒ (UIncreasing(LOAD1200(+(i268[3], -1), +(i255[3], -1), i237[3], i227[3])), ≥)∧0 = 0∧[(-1)Bound*bni_27] + [bni_27]i268[2] ≥ 0∧0 = 0∧[1 + (-1)bso_28] ≥ 0)



  • We consider the chain LOAD1200(i268[2], i255[2], i237[2], i227[2]) → COND_LOAD12001(&&(&&(>(i255[2], 0), >(i268[2], 0)), >(i237[2], 0)), i268[2], i255[2], i237[2], i227[2]), COND_LOAD12001(TRUE, i268[3], i255[3], i237[3], i227[3]) → LOAD1200(+(i268[3], -1), +(i255[3], -1), i237[3], i227[3]), LOAD1200(i268[2], i255[2], i237[2], i227[2]) → COND_LOAD12001(&&(&&(>(i255[2], 0), >(i268[2], 0)), >(i237[2], 0)), i268[2], i255[2], i237[2], i227[2]) which results in the following constraint:

    (34)    (&&(&&(>(i255[2], 0), >(i268[2], 0)), >(i237[2], 0))=TRUE∧i255[2]=i255[3]∧i227[2]=i227[3]∧i237[2]=i237[3]∧i268[2]=i268[3]∧+(i255[3], -1)=i255[2]1∧i237[3]=i237[2]1∧+(i268[3], -1)=i268[2]1∧i227[3]=i227[2]1 ⇒ COND_LOAD12001(TRUE, i268[3], i255[3], i237[3], i227[3])≥NonInfC∧COND_LOAD12001(TRUE, i268[3], i255[3], i237[3], i227[3])≥LOAD1200(+(i268[3], -1), +(i255[3], -1), i237[3], i227[3])∧(UIncreasing(LOAD1200(+(i268[3], -1), +(i255[3], -1), i237[3], i227[3])), ≥))



    We simplified constraint (34) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (35)    (>(i237[2], 0)=TRUE∧>(i255[2], 0)=TRUE∧>(i268[2], 0)=TRUE ⇒ COND_LOAD12001(TRUE, i268[2], i255[2], i237[2], i227[2])≥NonInfC∧COND_LOAD12001(TRUE, i268[2], i255[2], i237[2], i227[2])≥LOAD1200(+(i268[2], -1), +(i255[2], -1), i237[2], i227[2])∧(UIncreasing(LOAD1200(+(i268[3], -1), +(i255[3], -1), i237[3], i227[3])), ≥))



    We simplified constraint (35) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (36)    (i237[2] + [-1] ≥ 0∧i255[2] + [-1] ≥ 0∧i268[2] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD1200(+(i268[3], -1), +(i255[3], -1), i237[3], i227[3])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i268[2] ≥ 0∧[1 + (-1)bso_28] ≥ 0)



    We simplified constraint (36) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (37)    (i237[2] + [-1] ≥ 0∧i255[2] + [-1] ≥ 0∧i268[2] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD1200(+(i268[3], -1), +(i255[3], -1), i237[3], i227[3])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i268[2] ≥ 0∧[1 + (-1)bso_28] ≥ 0)



    We simplified constraint (37) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (38)    (i237[2] + [-1] ≥ 0∧i255[2] + [-1] ≥ 0∧i268[2] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD1200(+(i268[3], -1), +(i255[3], -1), i237[3], i227[3])), ≥)∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i268[2] ≥ 0∧[1 + (-1)bso_28] ≥ 0)



    We simplified constraint (38) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (39)    (i237[2] + [-1] ≥ 0∧i255[2] + [-1] ≥ 0∧i268[2] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD1200(+(i268[3], -1), +(i255[3], -1), i237[3], i227[3])), ≥)∧0 = 0∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i268[2] ≥ 0∧0 = 0∧[1 + (-1)bso_28] ≥ 0)



    We simplified constraint (39) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (40)    (i237[2] ≥ 0∧i255[2] + [-1] ≥ 0∧i268[2] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD1200(+(i268[3], -1), +(i255[3], -1), i237[3], i227[3])), ≥)∧0 = 0∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i268[2] ≥ 0∧0 = 0∧[1 + (-1)bso_28] ≥ 0)



    We simplified constraint (40) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (41)    (i237[2] ≥ 0∧i255[2] ≥ 0∧i268[2] + [-1] ≥ 0 ⇒ (UIncreasing(LOAD1200(+(i268[3], -1), +(i255[3], -1), i237[3], i227[3])), ≥)∧0 = 0∧[(-1)bni_27 + (-1)Bound*bni_27] + [bni_27]i268[2] ≥ 0∧0 = 0∧[1 + (-1)bso_28] ≥ 0)



    We simplified constraint (41) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (42)    (i237[2] ≥ 0∧i255[2] ≥ 0∧i268[2] ≥ 0 ⇒ (UIncreasing(LOAD1200(+(i268[3], -1), +(i255[3], -1), i237[3], i227[3])), ≥)∧0 = 0∧[(-1)Bound*bni_27] + [bni_27]i268[2] ≥ 0∧0 = 0∧[1 + (-1)bso_28] ≥ 0)







To summarize, we get the following constraints P≥ for the following pairs.
  • LOAD1200(i175, 0, i237, i227) → COND_LOAD1200(&&(>(i237, 0), >(+(i227, 1), 0)), i175, i237, i227)
    • (i237[0] ≥ 0∧i227[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0])), ≥)∧[bni_21] = 0∧[(-1)bni_21 + (-1)Bound*bni_21] ≥ 0∧0 = 0∧[(-1)bso_22] ≥ 0)

  • COND_LOAD1200(TRUE, i175, i237, i227) → LOAD1200(i175, i237, i237, +(i227, 1))
    • (i237[0] ≥ 0∧i227[0] ≥ 0 ⇒ (UIncreasing(LOAD1200(i175[1], i237[1], i237[1], +(i227[1], 1))), ≥)∧[bni_23] = 0∧[(-1)bni_23 + (-1)Bound*bni_23] ≥ 0∧0 = 0∧[(-1)bso_24] ≥ 0)

  • LOAD1200(i268, i255, i237, i227) → COND_LOAD12001(&&(&&(>(i255, 0), >(i268, 0)), >(i237, 0)), i268, i255, i237, i227)
    • (i237[2] ≥ 0∧i255[2] ≥ 0∧i268[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD12001(&&(&&(>(i255[2], 0), >(i268[2], 0)), >(i237[2], 0)), i268[2], i255[2], i237[2], i227[2])), ≥)∧0 = 0∧[(-1)Bound*bni_25] + [bni_25]i268[2] ≥ 0∧0 = 0∧[(-1)bso_26] ≥ 0)

  • COND_LOAD12001(TRUE, i268, i255, i237, i227) → LOAD1200(+(i268, -1), +(i255, -1), i237, i227)
    • (i255[2] ≥ 0∧i237[2] ≥ 0∧i255[2] ≥ 0∧i268[2] ≥ 0 ⇒ (UIncreasing(LOAD1200(+(i268[3], -1), +(i255[3], -1), i237[3], i227[3])), ≥)∧0 = 0∧[(-1)Bound*bni_27] + [bni_27]i268[2] ≥ 0∧0 = 0∧[1 + (-1)bso_28] ≥ 0)
    • (i237[2] ≥ 0∧i255[2] ≥ 0∧i268[2] ≥ 0 ⇒ (UIncreasing(LOAD1200(+(i268[3], -1), +(i255[3], -1), i237[3], i227[3])), ≥)∧0 = 0∧[(-1)Bound*bni_27] + [bni_27]i268[2] ≥ 0∧0 = 0∧[1 + (-1)bso_28] ≥ 0)




The constraints for P> respective Pbound are constructed from P≥ where we just replace every occurence of "t ≥ s" in P≥ by "t > s" respective "t ≥ c". Here c stands for the fresh constant used for Pbound.
Using the following integer polynomial ordering the resulting constraints can be solved
Polynomial interpretation over integers[POLO]:

POL(TRUE) = 0   
POL(FALSE) = [3]   
POL(LOAD1200(x1, x2, x3, x4)) = [-1] + x1   
POL(0) = 0   
POL(COND_LOAD1200(x1, x2, x3, x4)) = [-1] + x2   
POL(&&(x1, x2)) = [-1]   
POL(>(x1, x2)) = [-1]   
POL(+(x1, x2)) = x1 + x2   
POL(1) = [1]   
POL(COND_LOAD12001(x1, x2, x3, x4, x5)) = [-1] + x2   
POL(-1) = [-1]   

The following pairs are in P>:

COND_LOAD12001(TRUE, i268[3], i255[3], i237[3], i227[3]) → LOAD1200(+(i268[3], -1), +(i255[3], -1), i237[3], i227[3])

The following pairs are in Pbound:

LOAD1200(i268[2], i255[2], i237[2], i227[2]) → COND_LOAD12001(&&(&&(>(i255[2], 0), >(i268[2], 0)), >(i237[2], 0)), i268[2], i255[2], i237[2], i227[2])
COND_LOAD12001(TRUE, i268[3], i255[3], i237[3], i227[3]) → LOAD1200(+(i268[3], -1), +(i255[3], -1), i237[3], i227[3])

The following pairs are in P≥:

LOAD1200(i175[0], 0, i237[0], i227[0]) → COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0])
COND_LOAD1200(TRUE, i175[1], i237[1], i227[1]) → LOAD1200(i175[1], i237[1], i237[1], +(i227[1], 1))
LOAD1200(i268[2], i255[2], i237[2], i227[2]) → COND_LOAD12001(&&(&&(>(i255[2], 0), >(i268[2], 0)), >(i237[2], 0)), i268[2], i255[2], i237[2], i227[2])

At least the following rules have been oriented under context sensitive arithmetic replacement:

TRUE1 → &&(TRUE, TRUE)1
FALSE1 → &&(TRUE, FALSE)1
FALSE1 → &&(FALSE, TRUE)1
FALSE1 → &&(FALSE, FALSE)1

(12) Complex Obligation (AND)

(13) 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): LOAD1200(i175[0], 0, i237[0], i227[0]) → COND_LOAD1200(i237[0] > 0 && i227[0] + 1 > 0, i175[0], i237[0], i227[0])
(1): COND_LOAD1200(TRUE, i175[1], i237[1], i227[1]) → LOAD1200(i175[1], i237[1], i237[1], i227[1] + 1)
(2): LOAD1200(i268[2], i255[2], i237[2], i227[2]) → COND_LOAD12001(i255[2] > 0 && i268[2] > 0 && i237[2] > 0, i268[2], i255[2], i237[2], i227[2])

(1) -> (0), if ((i237[1] →* i237[0])∧(i227[1] + 1 →* i227[0])∧(i237[1] →* 0)∧(i175[1] →* i175[0]))


(0) -> (1), if ((i237[0] →* i237[1])∧(i175[0] →* i175[1])∧(i237[0] > 0 && i227[0] + 1 > 0 →* TRUE)∧(i227[0] →* i227[1]))


(1) -> (2), if ((i237[1] →* i237[2])∧(i175[1] →* i268[2])∧(i227[1] + 1 →* i227[2])∧(i237[1] →* i255[2]))



The set Q consists of the following terms:
Cond_Load1200(TRUE, x0, x1, x2)
Load1200(x0, x1, x2, x3)
Cond_Load12001(TRUE, x0, x1, x2, x3)

(14) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.

(15) 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:
(1): COND_LOAD1200(TRUE, i175[1], i237[1], i227[1]) → LOAD1200(i175[1], i237[1], i237[1], i227[1] + 1)
(0): LOAD1200(i175[0], 0, i237[0], i227[0]) → COND_LOAD1200(i237[0] > 0 && i227[0] + 1 > 0, i175[0], i237[0], i227[0])

(1) -> (0), if ((i237[1] →* i237[0])∧(i227[1] + 1 →* i227[0])∧(i237[1] →* 0)∧(i175[1] →* i175[0]))


(0) -> (1), if ((i237[0] →* i237[1])∧(i175[0] →* i175[1])∧(i237[0] > 0 && i227[0] + 1 > 0 →* TRUE)∧(i227[0] →* i227[1]))



The set Q consists of the following terms:
Cond_Load1200(TRUE, x0, x1, x2)
Load1200(x0, x1, x2, x3)
Cond_Load12001(TRUE, x0, x1, x2, x3)

(16) IDPNonInfProof (SOUND transformation)

The constraints were generated the following way:
The DP Problem is simplified using the Induction Calculus [NONINF] with the following steps:
Note that final constraints are written in bold face.


For Pair COND_LOAD1200(TRUE, i175[1], i237[1], i227[1]) → LOAD1200(i175[1], i237[1], i237[1], +(i227[1], 1)) the following chains were created:
  • We consider the chain LOAD1200(i175[0], 0, i237[0], i227[0]) → COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0]), COND_LOAD1200(TRUE, i175[1], i237[1], i227[1]) → LOAD1200(i175[1], i237[1], i237[1], +(i227[1], 1)), LOAD1200(i175[0], 0, i237[0], i227[0]) → COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0]) which results in the following constraint:

    (1)    (i237[0]=i237[1]∧i175[0]=i175[1]∧&&(>(i237[0], 0), >(+(i227[0], 1), 0))=TRUE∧i227[0]=i227[1]∧i237[1]=i237[0]1∧+(i227[1], 1)=i227[0]1∧i237[1]=0∧i175[1]=i175[0]1 ⇒ COND_LOAD1200(TRUE, i175[1], i237[1], i227[1])≥NonInfC∧COND_LOAD1200(TRUE, i175[1], i237[1], i227[1])≥LOAD1200(i175[1], i237[1], i237[1], +(i227[1], 1))∧(UIncreasing(LOAD1200(i175[1], i237[1], i237[1], +(i227[1], 1))), ≥))



    We solved constraint (1) using rules (I), (II), (III), (IV), (IDP_CONSTANT_FOLD).




For Pair LOAD1200(i175[0], 0, i237[0], i227[0]) → COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0]) the following chains were created:
  • We consider the chain LOAD1200(i175[0], 0, i237[0], i227[0]) → COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0]), COND_LOAD1200(TRUE, i175[1], i237[1], i227[1]) → LOAD1200(i175[1], i237[1], i237[1], +(i227[1], 1)) which results in the following constraint:

    (2)    (i237[0]=i237[1]∧i175[0]=i175[1]∧&&(>(i237[0], 0), >(+(i227[0], 1), 0))=TRUE∧i227[0]=i227[1] ⇒ LOAD1200(i175[0], 0, i237[0], i227[0])≥NonInfC∧LOAD1200(i175[0], 0, i237[0], i227[0])≥COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0])∧(UIncreasing(COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0])), ≥))



    We simplified constraint (2) using rule (IV) which results in the following new constraint:

    (3)    (&&(>(i237[0], 0), >(+(i227[0], 1), 0))=TRUE ⇒ LOAD1200(i175[0], 0, i237[0], i227[0])≥NonInfC∧LOAD1200(i175[0], 0, i237[0], i227[0])≥COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0])∧(UIncreasing(COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0])), ≥))



    We simplified constraint (3) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (4)    (0 ≥ 0 ⇒ (UIncreasing(COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0])), ≥)∧[bni_11 + (-1)Bound*bni_11] + [bni_11]i227[0] + [bni_11]i237[0] + [bni_11]i175[0] ≥ 0∧[2 + (-1)bso_12] + i227[0] + i237[0] + i175[0] ≥ 0)



    We simplified constraint (4) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (5)    (0 ≥ 0 ⇒ (UIncreasing(COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0])), ≥)∧[bni_11 + (-1)Bound*bni_11] + [bni_11]i227[0] + [bni_11]i237[0] + [bni_11]i175[0] ≥ 0∧[2 + (-1)bso_12] + i227[0] + i237[0] + i175[0] ≥ 0)



    We simplified constraint (5) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (6)    (0 ≥ 0 ⇒ (UIncreasing(COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0])), ≥)∧[bni_11 + (-1)Bound*bni_11] + [bni_11]i227[0] + [bni_11]i237[0] + [bni_11]i175[0] ≥ 0∧[2 + (-1)bso_12] + i227[0] + i237[0] + i175[0] ≥ 0)



    We simplified constraint (6) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (7)    (0 ≥ 0 ⇒ (UIncreasing(COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0])), ≥)∧[bni_11] ≥ 0∧[bni_11] ≥ 0∧[bni_11] ≥ 0∧[bni_11 + (-1)Bound*bni_11] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[2 + (-1)bso_12] ≥ 0)







To summarize, we get the following constraints P≥ for the following pairs.
  • COND_LOAD1200(TRUE, i175[1], i237[1], i227[1]) → LOAD1200(i175[1], i237[1], i237[1], +(i227[1], 1))

  • LOAD1200(i175[0], 0, i237[0], i227[0]) → COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0])
    • (0 ≥ 0 ⇒ (UIncreasing(COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0])), ≥)∧[bni_11] ≥ 0∧[bni_11] ≥ 0∧[bni_11] ≥ 0∧[bni_11 + (-1)Bound*bni_11] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[2 + (-1)bso_12] ≥ 0)




The constraints for P> respective Pbound are constructed from P≥ where we just replace every occurence of "t ≥ s" in P≥ by "t > s" respective "t ≥ c". Here c stands for the fresh constant used for Pbound.
Using the following integer polynomial ordering the resulting constraints can be solved
Polynomial interpretation over integers with natural coefficients for non-tuple symbols [NONINF][POLO]:

POL(TRUE) = 0   
POL(FALSE) = 0   
POL(COND_LOAD1200(x1, x2, x3, x4)) = [-1] + [2]x1   
POL(LOAD1200(x1, x2, x3, x4)) = [1] + x4 + x3 + [-1]x2 + x1   
POL(+(x1, x2)) = 0   
POL(1) = 0   
POL(0) = 0   
POL(&&(x1, x2)) = 0   
POL(>(x1, x2)) = 0   

The following pairs are in P>:

COND_LOAD1200(TRUE, i175[1], i237[1], i227[1]) → LOAD1200(i175[1], i237[1], i237[1], +(i227[1], 1))
LOAD1200(i175[0], 0, i237[0], i227[0]) → COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0])

The following pairs are in Pbound:

COND_LOAD1200(TRUE, i175[1], i237[1], i227[1]) → LOAD1200(i175[1], i237[1], i237[1], +(i227[1], 1))
LOAD1200(i175[0], 0, i237[0], i227[0]) → COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0])

The following pairs are in P≥:
none

At least the following rules have been oriented under context sensitive arithmetic replacement:

&&(TRUE, TRUE)1 → TRUE1
&&(TRUE, FALSE)1 → FALSE1
&&(FALSE, TRUE)1 → FALSE1
&&(FALSE, FALSE)1 → FALSE1

(17) 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:
none


R is empty.

The integer pair graph is empty.

The set Q consists of the following terms:
Cond_Load1200(TRUE, x0, x1, x2)
Load1200(x0, x1, x2, x3)
Cond_Load12001(TRUE, x0, x1, x2, x3)

(18) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs.

(19) TRUE

(20) 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): LOAD1200(i175[0], 0, i237[0], i227[0]) → COND_LOAD1200(i237[0] > 0 && i227[0] + 1 > 0, i175[0], i237[0], i227[0])
(1): COND_LOAD1200(TRUE, i175[1], i237[1], i227[1]) → LOAD1200(i175[1], i237[1], i237[1], i227[1] + 1)

(1) -> (0), if ((i237[1] →* i237[0])∧(i227[1] + 1 →* i227[0])∧(i237[1] →* 0)∧(i175[1] →* i175[0]))


(0) -> (1), if ((i237[0] →* i237[1])∧(i175[0] →* i175[1])∧(i237[0] > 0 && i227[0] + 1 > 0 →* TRUE)∧(i227[0] →* i227[1]))



The set Q consists of the following terms:
Cond_Load1200(TRUE, x0, x1, x2)
Load1200(x0, x1, x2, x3)
Cond_Load12001(TRUE, x0, x1, x2, x3)

(21) IDPNonInfProof (SOUND transformation)

The constraints were generated the following way:
The DP Problem is simplified using the Induction Calculus [NONINF] with the following steps:
Note that final constraints are written in bold face.


For Pair LOAD1200(i175[0], 0, i237[0], i227[0]) → COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0]) the following chains were created:
  • We consider the chain LOAD1200(i175[0], 0, i237[0], i227[0]) → COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0]), COND_LOAD1200(TRUE, i175[1], i237[1], i227[1]) → LOAD1200(i175[1], i237[1], i237[1], +(i227[1], 1)) which results in the following constraint:

    (1)    (i237[0]=i237[1]∧i175[0]=i175[1]∧&&(>(i237[0], 0), >(+(i227[0], 1), 0))=TRUE∧i227[0]=i227[1] ⇒ LOAD1200(i175[0], 0, i237[0], i227[0])≥COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0])∧(UIncreasing(COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0])), ≥))



    We simplified constraint (1) using rule (IV) which results in the following new constraint:

    (2)    (&&(>(i237[0], 0), >(+(i227[0], 1), 0))=TRUE ⇒ LOAD1200(i175[0], 0, i237[0], i227[0])≥COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0])∧(UIncreasing(COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0])), ≥))



    We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (3)    (0 ≥ 0 ⇒ (UIncreasing(COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0])), ≥)∧[2 + (-1)bso_11] + i227[0] + i237[0] + i175[0] ≥ 0)



    We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (4)    (0 ≥ 0 ⇒ (UIncreasing(COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0])), ≥)∧[2 + (-1)bso_11] + i227[0] + i237[0] + i175[0] ≥ 0)



    We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (5)    (0 ≥ 0 ⇒ (UIncreasing(COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0])), ≥)∧[2 + (-1)bso_11] + i227[0] + i237[0] + i175[0] ≥ 0)



    We simplified constraint (5) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (6)    (0 ≥ 0 ⇒ (UIncreasing(COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0])), ≥)∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[2 + (-1)bso_11] ≥ 0)







For Pair COND_LOAD1200(TRUE, i175[1], i237[1], i227[1]) → LOAD1200(i175[1], i237[1], i237[1], +(i227[1], 1)) the following chains were created:
  • We consider the chain LOAD1200(i175[0], 0, i237[0], i227[0]) → COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0]), COND_LOAD1200(TRUE, i175[1], i237[1], i227[1]) → LOAD1200(i175[1], i237[1], i237[1], +(i227[1], 1)), LOAD1200(i175[0], 0, i237[0], i227[0]) → COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0]) which results in the following constraint:

    (7)    (i237[0]=i237[1]∧i175[0]=i175[1]∧&&(>(i237[0], 0), >(+(i227[0], 1), 0))=TRUE∧i227[0]=i227[1]∧i237[1]=i237[0]1∧+(i227[1], 1)=i227[0]1∧i237[1]=0∧i175[1]=i175[0]1 ⇒ COND_LOAD1200(TRUE, i175[1], i237[1], i227[1])≥LOAD1200(i175[1], i237[1], i237[1], +(i227[1], 1))∧(UIncreasing(LOAD1200(i175[1], i237[1], i237[1], +(i227[1], 1))), ≥))



    We solved constraint (7) using rules (I), (II), (III), (IV), (IDP_CONSTANT_FOLD).




To summarize, we get the following constraints P≥ for the following pairs.
  • LOAD1200(i175[0], 0, i237[0], i227[0]) → COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0])
    • (0 ≥ 0 ⇒ (UIncreasing(COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0])), ≥)∧[1] ≥ 0∧[1] ≥ 0∧[1] ≥ 0∧[2 + (-1)bso_11] ≥ 0)

  • COND_LOAD1200(TRUE, i175[1], i237[1], i227[1]) → LOAD1200(i175[1], i237[1], i237[1], +(i227[1], 1))




The constraints for P> respective Pbound are constructed from P≥ where we just replace every occurence of "t ≥ s" in P≥ by "t > s" respective "t ≥ c". Here c stands for the fresh constant used for Pbound.
Using the following integer polynomial ordering the resulting constraints can be solved
Polynomial interpretation over integers with natural coefficients for all symbols [NONINF][POLO]:

POL(TRUE) = 0   
POL(FALSE) = 0   
POL(LOAD1200(x1, x2, x3, x4)) = [2] + [2]x4 + [2]x3 + [2]x1   
POL(0) = 0   
POL(COND_LOAD1200(x1, x2, x3, x4)) = x4 + x3 + x2   
POL(&&(x1, x2)) = 0   
POL(>(x1, x2)) = 0   
POL(+(x1, x2)) = 0   
POL(1) = 0   

The following pairs are in P>:

LOAD1200(i175[0], 0, i237[0], i227[0]) → COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0])
COND_LOAD1200(TRUE, i175[1], i237[1], i227[1]) → LOAD1200(i175[1], i237[1], i237[1], +(i227[1], 1))

The following pairs are in Pbound:

LOAD1200(i175[0], 0, i237[0], i227[0]) → COND_LOAD1200(&&(>(i237[0], 0), >(+(i227[0], 1), 0)), i175[0], i237[0], i227[0])
COND_LOAD1200(TRUE, i175[1], i237[1], i227[1]) → LOAD1200(i175[1], i237[1], i237[1], +(i227[1], 1))

The following pairs are in P≥:
none

At least the following rules have been oriented under context sensitive arithmetic replacement:

&&(TRUE, TRUE)1 → TRUE1
&&(TRUE, FALSE)1 → FALSE1
&&(FALSE, TRUE)1 → FALSE1
&&(FALSE, FALSE)1 → FALSE1

(22) 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:
none


R is empty.

The integer pair graph is empty.

The set Q consists of the following terms:
Cond_Load1200(TRUE, x0, x1, x2)
Load1200(x0, x1, x2, x3)
Cond_Load12001(TRUE, x0, x1, x2, x3)

(23) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs.

(24) TRUE