Termination proof of /tmp/tmp4mAYS8/GCD2.jar

Termination of the given JBC could be proven:

0 JBC

↳1 JBC2FIG (⇒)

↳2 JBCTerminationGraph

↳3 FIGtoITRSProof (⇒)

↳4 IDP

↳5 IDPNonInfProof (⇒)

↳6 IDP

↳7 IDependencyGraphProof (⇔)

↳8 IDP

↳9 UsableRulesProof (⇔)

↳10 IDP

↳11 IDPNonInfProof (⇒)

↳12 AND

    ↳13 IDP

        ↳14 IDependencyGraphProof (⇔)

        ↳15 TRUE

    ↳16 IDP

        ↳17 IDependencyGraphProof (⇔)

        ↳18 TRUE

(0) Obligation:

JBC Problem based on JBC Program:
Manifest-Version: 1.0 Created-By: 1.6.0_16 (Sun Microsystems Inc.) Main-Class: GCD2

public class GCD2 {
  public static int mod(int a, int b) {
    if (a == b) {
      return 0;
    }
    while(a>b) {
      a -= b;
    }
    return a;
  }

  public static int gcd(int a, int b) {
    int tmp;
    while(b != 0 && a >= 0 && b >= 0) {
      tmp = b;
      b = mod(a, b);
      a = tmp;
    }
    return a;
  }

  public static void main(String[] args) {
    Random.args = args;
    int x = Random.random();
    int y = Random.random();
    gcd(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:
GCD2.main([Ljava/lang/String;)V: Graph of 197 nodes with 1 SCC.

(3) FIGtoITRSProof (SOUND transformation)

Transformed FIGraph SCCs to IDPs. Logs:

Log for SCC 0:

Generated 43 rules for P and 8 rules for R.

Combined rules. Obtained 4 rules for P and 1 rules for R.

Filtered ground terms:

1174_0_gcd_EQ(x1, x2, x3, x4) → 1174_0_gcd_EQ(x2, x3, x4)
1265_0_mod_LE(x1, x2, x3, x4, x5) → 1265_0_mod_LE(x2, x3, x4, x5)
1193_0_main_Return(x1) → 1193_0_main_Return

Filtered duplicate args:

1174_0_gcd_EQ(x1, x2, x3) → 1174_0_gcd_EQ(x1, x3)
1265_0_mod_LE(x1, x2, x3, x4) → 1265_0_mod_LE(x3, x4)
1265_1_gcd_InvokeMethod(x1, x2, x3) → 1265_1_gcd_InvokeMethod(x1, x3)

Combined rules. Obtained 4 rules for P and 1 rules for R.

Finished conversion. Obtained 4 rules for P and 1 rules for R. System has predefined symbols.

(4) 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:
1174_1_main_InvokeMethod(1174_0_gcd_EQ(x0, 0)) → 1193_0_main_Return

The integer pair graph contains the following rules and edges:
(0): 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[0], x1[0])) → COND_1174_1_MAIN_INVOKEMETHOD(x1[0] > 0 && x0[0] >= 0 && !(x0[0] = x1[0]), 1174_0_gcd_EQ(x0[0], x1[0]))
(1): COND_1174_1_MAIN_INVOKEMETHOD(TRUE, 1174_0_gcd_EQ(x0[1], x1[1])) → 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))
(2): 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2])) → COND_1265_2_MAIN_INVOKEMETHOD(x1[2] >= x0[2], 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]))
(3): COND_1265_2_MAIN_INVOKEMETHOD(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[3], x1[3]), x1[3])) → 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))
(4): 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[4], x1[4]), x1[4])) → COND_1265_2_MAIN_INVOKEMETHOD1(x1[4] > 0 && x1[4] < x0[4], 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[4], x1[4]), x1[4]))
(5): COND_1265_2_MAIN_INVOKEMETHOD1(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[5], x1[5]), x1[5])) → 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[5] - x1[5], x1[5]), x1[5]))
(6): 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[6], x0[6])) → COND_1174_1_MAIN_INVOKEMETHOD1(x0[6] > 0, 1174_0_gcd_EQ(x0[6], x0[6]))
(7): COND_1174_1_MAIN_INVOKEMETHOD1(TRUE, 1174_0_gcd_EQ(x0[7], x0[7])) → 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[7], 0))

(0) -> (1), if ((x1[0] > 0 && x0[0] >= 0 && !(x0[0] = x1[0]) →^* TRUE)∧(1174_0_gcd_EQ(x0[0], x1[0]) →^* 1174_0_gcd_EQ(x0[1], x1[1])))

(1) -> (2), if ((1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]) →^* 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2])))

(1) -> (4), if ((1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]) →^* 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[4], x1[4]), x1[4])))

(2) -> (3), if ((x1[2] >= x0[2] →^* TRUE)∧(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]) →^* 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[3], x1[3]), x1[3])))

(3) -> (0), if ((1174_0_gcd_EQ(x1[3], x0[3]) →^* 1174_0_gcd_EQ(x0[0], x1[0])))

(3) -> (6), if ((1174_0_gcd_EQ(x1[3], x0[3]) →^* 1174_0_gcd_EQ(x0[6], x0[6])))

(4) -> (5), if ((x1[4] > 0 && x1[4] < x0[4] →^* TRUE)∧(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[4], x1[4]), x1[4]) →^* 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[5], x1[5]), x1[5])))

(5) -> (2), if ((1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[5] - x1[5], x1[5]), x1[5]) →^* 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2])))

(5) -> (4), if ((1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[5] - x1[5], x1[5]), x1[5]) →^* 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[4], x1[4]), x1[4])))

(6) -> (7), if ((x0[6] > 0 →^* TRUE)∧(1174_0_gcd_EQ(x0[6], x0[6]) →^* 1174_0_gcd_EQ(x0[7], x0[7])))

(7) -> (0), if ((1174_0_gcd_EQ(x0[7], 0) →^* 1174_0_gcd_EQ(x0[0], x1[0])))

(7) -> (6), if ((1174_0_gcd_EQ(x0[7], 0) →^* 1174_0_gcd_EQ(x0[6], x0[6])))

The set Q consists of the following terms:
1174_1_main_InvokeMethod(1174_0_gcd_EQ(x0, 0))

(5) 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 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0, x1)) → COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1, 0), >=(x0, 0)), !(=(x0, x1))), 1174_0_gcd_EQ(x0, x1)) the following chains were created:

We consider the chain 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[0], x1[0])) → COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0])), COND_1174_1_MAIN_INVOKEMETHOD(TRUE, 1174_0_gcd_EQ(x0[1], x1[1])) → 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1])) which results in the following constraint:
(1)    (&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0])))=TRUE∧1174_0_gcd_EQ(x0[0], x1[0])=1174_0_gcd_EQ(x0[1], x1[1]) ⇒ 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[0], x1[0]))≥NonInfC∧1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[0], x1[0]))≥COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0]))∧(U^Increasing(COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0]))), ≥))

We simplified constraint (1) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraints:
(2)    (>(x1[0], 0)=TRUE∧>=(x0[0], 0)=TRUE∧<(x0[0], x1[0])=TRUE ⇒ 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[0], x1[0]))≥NonInfC∧1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[0], x1[0]))≥COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0]))∧(U^Increasing(COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0]))), ≥))

(3)    (>(x1[0], 0)=TRUE∧>=(x0[0], 0)=TRUE∧>(x0[0], x1[0])=TRUE ⇒ 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[0], x1[0]))≥NonInfC∧1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[0], x1[0]))≥COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0]))∧(U^Increasing(COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0]))), ≥))

We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(4)    (x1[0] + [-1] ≥ 0∧x0[0] ≥ 0∧x1[0] + [-1] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0]))), ≥)∧[bni_37 + (-1)Bound*bni_37] + [bni_37]x1[0] + [bni_37]x0[0] ≥ 0∧[(-1)bso_38] ≥ 0)

We simplified constraint (3) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(5)    (x1[0] + [-1] ≥ 0∧x0[0] ≥ 0∧x0[0] + [-1] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0]))), ≥)∧[bni_37 + (-1)Bound*bni_37] + [bni_37]x1[0] + [bni_37]x0[0] ≥ 0∧[(-1)bso_38] ≥ 0)

We simplified constraint (4) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(6)    (x1[0] + [-1] ≥ 0∧x0[0] ≥ 0∧x1[0] + [-1] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0]))), ≥)∧[bni_37 + (-1)Bound*bni_37] + [bni_37]x1[0] + [bni_37]x0[0] ≥ 0∧[(-1)bso_38] ≥ 0)

We simplified constraint (5) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(7)    (x1[0] + [-1] ≥ 0∧x0[0] ≥ 0∧x0[0] + [-1] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0]))), ≥)∧[bni_37 + (-1)Bound*bni_37] + [bni_37]x1[0] + [bni_37]x0[0] ≥ 0∧[(-1)bso_38] ≥ 0)

We simplified constraint (6) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(8)    (x1[0] + [-1] ≥ 0∧x0[0] ≥ 0∧x1[0] + [-1] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0]))), ≥)∧[bni_37 + (-1)Bound*bni_37] + [bni_37]x1[0] + [bni_37]x0[0] ≥ 0∧[(-1)bso_38] ≥ 0)

We simplified constraint (7) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(9)    (x1[0] + [-1] ≥ 0∧x0[0] ≥ 0∧x0[0] + [-1] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0]))), ≥)∧[bni_37 + (-1)Bound*bni_37] + [bni_37]x1[0] + [bni_37]x0[0] ≥ 0∧[(-1)bso_38] ≥ 0)

We simplified constraint (8) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(10)    (x1[0] ≥ 0∧x0[0] ≥ 0∧x1[0] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0]))), ≥)∧[(2)bni_37 + (-1)Bound*bni_37] + [bni_37]x1[0] + [bni_37]x0[0] ≥ 0∧[(-1)bso_38] ≥ 0)

We simplified constraint (9) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(11)    (x1[0] ≥ 0∧x0[0] ≥ 0∧x0[0] + [-2] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0]))), ≥)∧[(2)bni_37 + (-1)Bound*bni_37] + [bni_37]x1[0] + [bni_37]x0[0] ≥ 0∧[(-1)bso_38] ≥ 0)

We simplified constraint (10) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(12)    (x0[0] + x1[0] ≥ 0∧x0[0] ≥ 0∧x1[0] ≥ 0 ⇒ (U^Increasing(COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0]))), ≥)∧[(2)bni_37 + (-1)Bound*bni_37] + [(2)bni_37]x0[0] + [bni_37]x1[0] ≥ 0∧[(-1)bso_38] ≥ 0)

We simplified constraint (11) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(13)    (x1[0] ≥ 0∧[2] + x1[0] + x0[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0]))), ≥)∧[(4)bni_37 + (-1)Bound*bni_37] + [(2)bni_37]x1[0] + [bni_37]x0[0] ≥ 0∧[(-1)bso_38] ≥ 0)

For Pair COND_1174_1_MAIN_INVOKEMETHOD(TRUE, 1174_0_gcd_EQ(x0, x1)) → 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0, x1), x1)) the following chains were created:

We consider the chain 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[0], x1[0])) → COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0])), COND_1174_1_MAIN_INVOKEMETHOD(TRUE, 1174_0_gcd_EQ(x0[1], x1[1])) → 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1])), 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2])) → COND_1265_2_MAIN_INVOKEMETHOD(>=(x1[2], x0[2]), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2])) which results in the following constraint:
(14)    (&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0])))=TRUE∧1174_0_gcd_EQ(x0[0], x1[0])=1174_0_gcd_EQ(x0[1], x1[1])∧1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1])=1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]) ⇒ COND_1174_1_MAIN_INVOKEMETHOD(TRUE, 1174_0_gcd_EQ(x0[1], x1[1]))≥NonInfC∧COND_1174_1_MAIN_INVOKEMETHOD(TRUE, 1174_0_gcd_EQ(x0[1], x1[1]))≥1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))∧(U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))), ≥))

We simplified constraint (14) using rules (I), (II), (III), (IV), (IDP_BOOLEAN) which results in the following new constraints:
(15)    (>(x1[0], 0)=TRUE∧>=(x0[0], 0)=TRUE∧<(x0[0], x1[0])=TRUE ⇒ COND_1174_1_MAIN_INVOKEMETHOD(TRUE, 1174_0_gcd_EQ(x0[0], x1[0]))≥NonInfC∧COND_1174_1_MAIN_INVOKEMETHOD(TRUE, 1174_0_gcd_EQ(x0[0], x1[0]))≥1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[0], x1[0]), x1[0]))∧(U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))), ≥))

(16)    (>(x1[0], 0)=TRUE∧>=(x0[0], 0)=TRUE∧>(x0[0], x1[0])=TRUE ⇒ COND_1174_1_MAIN_INVOKEMETHOD(TRUE, 1174_0_gcd_EQ(x0[0], x1[0]))≥NonInfC∧COND_1174_1_MAIN_INVOKEMETHOD(TRUE, 1174_0_gcd_EQ(x0[0], x1[0]))≥1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[0], x1[0]), x1[0]))∧(U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))), ≥))

We simplified constraint (15) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(17)    (x1[0] + [-1] ≥ 0∧x0[0] ≥ 0∧x1[0] + [-1] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))), ≥)∧[bni_39 + (-1)Bound*bni_39] + [bni_39]x1[0] + [bni_39]x0[0] ≥ 0∧[(-1)bso_40] ≥ 0)

We simplified constraint (16) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(18)    (x1[0] + [-1] ≥ 0∧x0[0] ≥ 0∧x0[0] + [-1] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))), ≥)∧[bni_39 + (-1)Bound*bni_39] + [bni_39]x1[0] + [bni_39]x0[0] ≥ 0∧[(-1)bso_40] ≥ 0)

We simplified constraint (17) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(19)    (x1[0] + [-1] ≥ 0∧x0[0] ≥ 0∧x1[0] + [-1] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))), ≥)∧[bni_39 + (-1)Bound*bni_39] + [bni_39]x1[0] + [bni_39]x0[0] ≥ 0∧[(-1)bso_40] ≥ 0)

We simplified constraint (18) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(20)    (x1[0] + [-1] ≥ 0∧x0[0] ≥ 0∧x0[0] + [-1] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))), ≥)∧[bni_39 + (-1)Bound*bni_39] + [bni_39]x1[0] + [bni_39]x0[0] ≥ 0∧[(-1)bso_40] ≥ 0)

We simplified constraint (19) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(21)    (x1[0] + [-1] ≥ 0∧x0[0] ≥ 0∧x1[0] + [-1] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))), ≥)∧[bni_39 + (-1)Bound*bni_39] + [bni_39]x1[0] + [bni_39]x0[0] ≥ 0∧[(-1)bso_40] ≥ 0)

We simplified constraint (20) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(22)    (x1[0] + [-1] ≥ 0∧x0[0] ≥ 0∧x0[0] + [-1] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))), ≥)∧[bni_39 + (-1)Bound*bni_39] + [bni_39]x1[0] + [bni_39]x0[0] ≥ 0∧[(-1)bso_40] ≥ 0)

We simplified constraint (21) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(23)    (x1[0] ≥ 0∧x0[0] ≥ 0∧x1[0] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))), ≥)∧[(2)bni_39 + (-1)Bound*bni_39] + [bni_39]x1[0] + [bni_39]x0[0] ≥ 0∧[(-1)bso_40] ≥ 0)

We simplified constraint (22) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(24)    (x1[0] ≥ 0∧x0[0] ≥ 0∧x0[0] + [-2] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))), ≥)∧[(2)bni_39 + (-1)Bound*bni_39] + [bni_39]x1[0] + [bni_39]x0[0] ≥ 0∧[(-1)bso_40] ≥ 0)

We simplified constraint (23) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(25)    (x0[0] + x1[0] ≥ 0∧x0[0] ≥ 0∧x1[0] ≥ 0 ⇒ (U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))), ≥)∧[(2)bni_39 + (-1)Bound*bni_39] + [(2)bni_39]x0[0] + [bni_39]x1[0] ≥ 0∧[(-1)bso_40] ≥ 0)

We simplified constraint (24) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(26)    (x1[0] ≥ 0∧[2] + x1[0] + x0[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))), ≥)∧[(4)bni_39 + (-1)Bound*bni_39] + [(2)bni_39]x1[0] + [bni_39]x0[0] ≥ 0∧[(-1)bso_40] ≥ 0)
We consider the chain 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[0], x1[0])) → COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0])), COND_1174_1_MAIN_INVOKEMETHOD(TRUE, 1174_0_gcd_EQ(x0[1], x1[1])) → 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1])), 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[4], x1[4]), x1[4])) → COND_1265_2_MAIN_INVOKEMETHOD1(&&(>(x1[4], 0), <(x1[4], x0[4])), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[4], x1[4]), x1[4])) which results in the following constraint:
(27)    (&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0])))=TRUE∧1174_0_gcd_EQ(x0[0], x1[0])=1174_0_gcd_EQ(x0[1], x1[1])∧1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1])=1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[4], x1[4]), x1[4]) ⇒ COND_1174_1_MAIN_INVOKEMETHOD(TRUE, 1174_0_gcd_EQ(x0[1], x1[1]))≥NonInfC∧COND_1174_1_MAIN_INVOKEMETHOD(TRUE, 1174_0_gcd_EQ(x0[1], x1[1]))≥1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))∧(U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))), ≥))

We simplified constraint (27) using rules (I), (II), (III), (IV), (IDP_BOOLEAN) which results in the following new constraints:
(28)    (>(x1[0], 0)=TRUE∧>=(x0[0], 0)=TRUE∧<(x0[0], x1[0])=TRUE ⇒ COND_1174_1_MAIN_INVOKEMETHOD(TRUE, 1174_0_gcd_EQ(x0[0], x1[0]))≥NonInfC∧COND_1174_1_MAIN_INVOKEMETHOD(TRUE, 1174_0_gcd_EQ(x0[0], x1[0]))≥1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[0], x1[0]), x1[0]))∧(U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))), ≥))

(29)    (>(x1[0], 0)=TRUE∧>=(x0[0], 0)=TRUE∧>(x0[0], x1[0])=TRUE ⇒ COND_1174_1_MAIN_INVOKEMETHOD(TRUE, 1174_0_gcd_EQ(x0[0], x1[0]))≥NonInfC∧COND_1174_1_MAIN_INVOKEMETHOD(TRUE, 1174_0_gcd_EQ(x0[0], x1[0]))≥1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[0], x1[0]), x1[0]))∧(U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))), ≥))

We simplified constraint (28) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(30)    (x1[0] + [-1] ≥ 0∧x0[0] ≥ 0∧x1[0] + [-1] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))), ≥)∧[bni_39 + (-1)Bound*bni_39] + [bni_39]x1[0] + [bni_39]x0[0] ≥ 0∧[(-1)bso_40] ≥ 0)

We simplified constraint (29) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(31)    (x1[0] + [-1] ≥ 0∧x0[0] ≥ 0∧x0[0] + [-1] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))), ≥)∧[bni_39 + (-1)Bound*bni_39] + [bni_39]x1[0] + [bni_39]x0[0] ≥ 0∧[(-1)bso_40] ≥ 0)

We simplified constraint (30) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(32)    (x1[0] + [-1] ≥ 0∧x0[0] ≥ 0∧x1[0] + [-1] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))), ≥)∧[bni_39 + (-1)Bound*bni_39] + [bni_39]x1[0] + [bni_39]x0[0] ≥ 0∧[(-1)bso_40] ≥ 0)

We simplified constraint (31) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(33)    (x1[0] + [-1] ≥ 0∧x0[0] ≥ 0∧x0[0] + [-1] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))), ≥)∧[bni_39 + (-1)Bound*bni_39] + [bni_39]x1[0] + [bni_39]x0[0] ≥ 0∧[(-1)bso_40] ≥ 0)

We simplified constraint (32) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(34)    (x1[0] + [-1] ≥ 0∧x0[0] ≥ 0∧x1[0] + [-1] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))), ≥)∧[bni_39 + (-1)Bound*bni_39] + [bni_39]x1[0] + [bni_39]x0[0] ≥ 0∧[(-1)bso_40] ≥ 0)

We simplified constraint (33) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(35)    (x1[0] + [-1] ≥ 0∧x0[0] ≥ 0∧x0[0] + [-1] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))), ≥)∧[bni_39 + (-1)Bound*bni_39] + [bni_39]x1[0] + [bni_39]x0[0] ≥ 0∧[(-1)bso_40] ≥ 0)

We simplified constraint (34) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(36)    (x1[0] ≥ 0∧x0[0] ≥ 0∧x1[0] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))), ≥)∧[(2)bni_39 + (-1)Bound*bni_39] + [bni_39]x1[0] + [bni_39]x0[0] ≥ 0∧[(-1)bso_40] ≥ 0)

We simplified constraint (35) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(37)    (x1[0] ≥ 0∧x0[0] ≥ 0∧x0[0] + [-2] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))), ≥)∧[(2)bni_39 + (-1)Bound*bni_39] + [bni_39]x1[0] + [bni_39]x0[0] ≥ 0∧[(-1)bso_40] ≥ 0)

We simplified constraint (36) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(38)    (x0[0] + x1[0] ≥ 0∧x0[0] ≥ 0∧x1[0] ≥ 0 ⇒ (U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))), ≥)∧[(2)bni_39 + (-1)Bound*bni_39] + [(2)bni_39]x0[0] + [bni_39]x1[0] ≥ 0∧[(-1)bso_40] ≥ 0)

We simplified constraint (37) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(39)    (x1[0] ≥ 0∧[2] + x1[0] + x0[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))), ≥)∧[(4)bni_39 + (-1)Bound*bni_39] + [(2)bni_39]x1[0] + [bni_39]x0[0] ≥ 0∧[(-1)bso_40] ≥ 0)

For Pair 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0, x1), x1)) → COND_1265_2_MAIN_INVOKEMETHOD(>=(x1, x0), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0, x1), x1)) the following chains were created:

We consider the chain 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2])) → COND_1265_2_MAIN_INVOKEMETHOD(>=(x1[2], x0[2]), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2])), COND_1265_2_MAIN_INVOKEMETHOD(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[3], x1[3]), x1[3])) → 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3])) which results in the following constraint:
(40)    (>=(x1[2], x0[2])=TRUE∧1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2])=1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[3], x1[3]), x1[3]) ⇒ 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]))≥NonInfC∧1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]))≥COND_1265_2_MAIN_INVOKEMETHOD(>=(x1[2], x0[2]), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]))∧(U^Increasing(COND_1265_2_MAIN_INVOKEMETHOD(>=(x1[2], x0[2]), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]))), ≥))

We simplified constraint (40) using rules (I), (II), (IV) which results in the following new constraint:
(41)    (>=(x1[2], x0[2])=TRUE ⇒ 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]))≥NonInfC∧1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]))≥COND_1265_2_MAIN_INVOKEMETHOD(>=(x1[2], x0[2]), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]))∧(U^Increasing(COND_1265_2_MAIN_INVOKEMETHOD(>=(x1[2], x0[2]), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]))), ≥))

We simplified constraint (41) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(42)    (x1[2] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(COND_1265_2_MAIN_INVOKEMETHOD(>=(x1[2], x0[2]), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]))), ≥)∧[bni_41 + (-1)Bound*bni_41] + [bni_41]x1[2] + [bni_41]x0[2] ≥ 0∧[(-1)bso_42] ≥ 0)

We simplified constraint (42) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(43)    (x1[2] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(COND_1265_2_MAIN_INVOKEMETHOD(>=(x1[2], x0[2]), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]))), ≥)∧[bni_41 + (-1)Bound*bni_41] + [bni_41]x1[2] + [bni_41]x0[2] ≥ 0∧[(-1)bso_42] ≥ 0)

We simplified constraint (43) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(44)    (x1[2] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(COND_1265_2_MAIN_INVOKEMETHOD(>=(x1[2], x0[2]), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]))), ≥)∧[bni_41 + (-1)Bound*bni_41] + [bni_41]x1[2] + [bni_41]x0[2] ≥ 0∧[(-1)bso_42] ≥ 0)

We simplified constraint (44) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(45)    (x1[2] ≥ 0 ⇒ (U^Increasing(COND_1265_2_MAIN_INVOKEMETHOD(>=(x1[2], x0[2]), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]))), ≥)∧[bni_41 + (-1)Bound*bni_41] + [(2)bni_41]x0[2] + [bni_41]x1[2] ≥ 0∧[(-1)bso_42] ≥ 0)

We simplified constraint (45) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(46)    (x1[2] ≥ 0∧x0[2] ≥ 0 ⇒ (U^Increasing(COND_1265_2_MAIN_INVOKEMETHOD(>=(x1[2], x0[2]), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]))), ≥)∧[bni_41 + (-1)Bound*bni_41] + [(-2)bni_41]x0[2] + [bni_41]x1[2] ≥ 0∧[(-1)bso_42] ≥ 0)

(47)    (x1[2] ≥ 0∧x0[2] ≥ 0 ⇒ (U^Increasing(COND_1265_2_MAIN_INVOKEMETHOD(>=(x1[2], x0[2]), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]))), ≥)∧[bni_41 + (-1)Bound*bni_41] + [(2)bni_41]x0[2] + [bni_41]x1[2] ≥ 0∧[(-1)bso_42] ≥ 0)

For Pair COND_1265_2_MAIN_INVOKEMETHOD(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0, x1), x1)) → 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1, x0)) the following chains were created:

We consider the chain 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2])) → COND_1265_2_MAIN_INVOKEMETHOD(>=(x1[2], x0[2]), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2])), COND_1265_2_MAIN_INVOKEMETHOD(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[3], x1[3]), x1[3])) → 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3])), 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[0], x1[0])) → COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0])) which results in the following constraint:
(48)    (>=(x1[2], x0[2])=TRUE∧1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2])=1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[3], x1[3]), x1[3])∧1174_0_gcd_EQ(x1[3], x0[3])=1174_0_gcd_EQ(x0[0], x1[0]) ⇒ COND_1265_2_MAIN_INVOKEMETHOD(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[3], x1[3]), x1[3]))≥NonInfC∧COND_1265_2_MAIN_INVOKEMETHOD(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[3], x1[3]), x1[3]))≥1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))∧(U^Increasing(1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))), ≥))

We simplified constraint (48) using rules (I), (II), (III), (IV) which results in the following new constraint:
(49)    (>=(x1[2], x0[2])=TRUE ⇒ COND_1265_2_MAIN_INVOKEMETHOD(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]))≥NonInfC∧COND_1265_2_MAIN_INVOKEMETHOD(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]))≥1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[2], x0[2]))∧(U^Increasing(1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))), ≥))

We simplified constraint (49) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(50)    (x1[2] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))), ≥)∧[bni_43 + (-1)Bound*bni_43] + [bni_43]x1[2] + [bni_43]x0[2] ≥ 0∧[(-1)bso_44] ≥ 0)

We simplified constraint (50) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(51)    (x1[2] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))), ≥)∧[bni_43 + (-1)Bound*bni_43] + [bni_43]x1[2] + [bni_43]x0[2] ≥ 0∧[(-1)bso_44] ≥ 0)

We simplified constraint (51) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(52)    (x1[2] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))), ≥)∧[bni_43 + (-1)Bound*bni_43] + [bni_43]x1[2] + [bni_43]x0[2] ≥ 0∧[(-1)bso_44] ≥ 0)

We simplified constraint (52) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(53)    (x1[2] ≥ 0 ⇒ (U^Increasing(1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))), ≥)∧[bni_43 + (-1)Bound*bni_43] + [(2)bni_43]x0[2] + [bni_43]x1[2] ≥ 0∧[(-1)bso_44] ≥ 0)

We simplified constraint (53) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(54)    (x1[2] ≥ 0∧x0[2] ≥ 0 ⇒ (U^Increasing(1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))), ≥)∧[bni_43 + (-1)Bound*bni_43] + [(2)bni_43]x0[2] + [bni_43]x1[2] ≥ 0∧[(-1)bso_44] ≥ 0)

(55)    (x1[2] ≥ 0∧x0[2] ≥ 0 ⇒ (U^Increasing(1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))), ≥)∧[bni_43 + (-1)Bound*bni_43] + [(-2)bni_43]x0[2] + [bni_43]x1[2] ≥ 0∧[(-1)bso_44] ≥ 0)
We consider the chain 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2])) → COND_1265_2_MAIN_INVOKEMETHOD(>=(x1[2], x0[2]), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2])), COND_1265_2_MAIN_INVOKEMETHOD(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[3], x1[3]), x1[3])) → 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3])), 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[6], x0[6])) → COND_1174_1_MAIN_INVOKEMETHOD1(>(x0[6], 0), 1174_0_gcd_EQ(x0[6], x0[6])) which results in the following constraint:
(56)    (>=(x1[2], x0[2])=TRUE∧1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2])=1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[3], x1[3]), x1[3])∧1174_0_gcd_EQ(x1[3], x0[3])=1174_0_gcd_EQ(x0[6], x0[6]) ⇒ COND_1265_2_MAIN_INVOKEMETHOD(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[3], x1[3]), x1[3]))≥NonInfC∧COND_1265_2_MAIN_INVOKEMETHOD(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[3], x1[3]), x1[3]))≥1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))∧(U^Increasing(1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))), ≥))

We simplified constraint (56) using rules (I), (II), (III) which results in the following new constraint:
(57)    (>=(x0[2], x0[2])=TRUE ⇒ COND_1265_2_MAIN_INVOKEMETHOD(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x0[2]), x0[2]))≥NonInfC∧COND_1265_2_MAIN_INVOKEMETHOD(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x0[2]), x0[2]))≥1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[2], x0[2]))∧(U^Increasing(1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))), ≥))

We simplified constraint (57) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(58)    (0 ≥ 0 ⇒ (U^Increasing(1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))), ≥)∧[bni_43 + (-1)Bound*bni_43] + [(2)bni_43]x0[2] ≥ 0∧[(-1)bso_44] ≥ 0)

We simplified constraint (58) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(59)    (0 ≥ 0 ⇒ (U^Increasing(1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))), ≥)∧[bni_43 + (-1)Bound*bni_43] + [(2)bni_43]x0[2] ≥ 0∧[(-1)bso_44] ≥ 0)

We simplified constraint (59) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(60)    (0 ≥ 0 ⇒ (U^Increasing(1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))), ≥)∧[bni_43 + (-1)Bound*bni_43] + [(2)bni_43]x0[2] ≥ 0∧[(-1)bso_44] ≥ 0)

We simplified constraint (60) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(61)    (0 ≥ 0 ⇒ (U^Increasing(1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))), ≥)∧[(2)bni_43] = 0∧[bni_43 + (-1)Bound*bni_43] ≥ 0∧0 = 0∧[(-1)bso_44] ≥ 0)

For Pair 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0, x1), x1)) → COND_1265_2_MAIN_INVOKEMETHOD1(&&(>(x1, 0), <(x1, x0)), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0, x1), x1)) the following chains were created:

We consider the chain 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[4], x1[4]), x1[4])) → COND_1265_2_MAIN_INVOKEMETHOD1(&&(>(x1[4], 0), <(x1[4], x0[4])), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[4], x1[4]), x1[4])), COND_1265_2_MAIN_INVOKEMETHOD1(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[5], x1[5]), x1[5])) → 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(-(x0[5], x1[5]), x1[5]), x1[5])) which results in the following constraint:
(62)    (&&(>(x1[4], 0), <(x1[4], x0[4]))=TRUE∧1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[4], x1[4]), x1[4])=1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[5], x1[5]), x1[5]) ⇒ 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[4], x1[4]), x1[4]))≥NonInfC∧1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[4], x1[4]), x1[4]))≥COND_1265_2_MAIN_INVOKEMETHOD1(&&(>(x1[4], 0), <(x1[4], x0[4])), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[4], x1[4]), x1[4]))∧(U^Increasing(COND_1265_2_MAIN_INVOKEMETHOD1(&&(>(x1[4], 0), <(x1[4], x0[4])), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[4], x1[4]), x1[4]))), ≥))

We simplified constraint (62) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(63)    (>(x1[4], 0)=TRUE∧<(x1[4], x0[4])=TRUE ⇒ 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[4], x1[4]), x1[4]))≥NonInfC∧1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[4], x1[4]), x1[4]))≥COND_1265_2_MAIN_INVOKEMETHOD1(&&(>(x1[4], 0), <(x1[4], x0[4])), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[4], x1[4]), x1[4]))∧(U^Increasing(COND_1265_2_MAIN_INVOKEMETHOD1(&&(>(x1[4], 0), <(x1[4], x0[4])), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[4], x1[4]), x1[4]))), ≥))

We simplified constraint (63) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(64)    (x1[4] + [-1] ≥ 0∧x0[4] + [-1] + [-1]x1[4] ≥ 0 ⇒ (U^Increasing(COND_1265_2_MAIN_INVOKEMETHOD1(&&(>(x1[4], 0), <(x1[4], x0[4])), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[4], x1[4]), x1[4]))), ≥)∧[bni_45 + (-1)Bound*bni_45] + [bni_45]x1[4] + [bni_45]x0[4] ≥ 0∧[1 + (-1)bso_46] ≥ 0)

We simplified constraint (64) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(65)    (x1[4] + [-1] ≥ 0∧x0[4] + [-1] + [-1]x1[4] ≥ 0 ⇒ (U^Increasing(COND_1265_2_MAIN_INVOKEMETHOD1(&&(>(x1[4], 0), <(x1[4], x0[4])), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[4], x1[4]), x1[4]))), ≥)∧[bni_45 + (-1)Bound*bni_45] + [bni_45]x1[4] + [bni_45]x0[4] ≥ 0∧[1 + (-1)bso_46] ≥ 0)

We simplified constraint (65) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(66)    (x1[4] + [-1] ≥ 0∧x0[4] + [-1] + [-1]x1[4] ≥ 0 ⇒ (U^Increasing(COND_1265_2_MAIN_INVOKEMETHOD1(&&(>(x1[4], 0), <(x1[4], x0[4])), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[4], x1[4]), x1[4]))), ≥)∧[bni_45 + (-1)Bound*bni_45] + [bni_45]x1[4] + [bni_45]x0[4] ≥ 0∧[1 + (-1)bso_46] ≥ 0)

We simplified constraint (66) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(67)    (x1[4] ≥ 0∧x0[4] + [-2] + [-1]x1[4] ≥ 0 ⇒ (U^Increasing(COND_1265_2_MAIN_INVOKEMETHOD1(&&(>(x1[4], 0), <(x1[4], x0[4])), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[4], x1[4]), x1[4]))), ≥)∧[(2)bni_45 + (-1)Bound*bni_45] + [bni_45]x1[4] + [bni_45]x0[4] ≥ 0∧[1 + (-1)bso_46] ≥ 0)

We simplified constraint (67) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(68)    (x1[4] ≥ 0∧x0[4] ≥ 0 ⇒ (U^Increasing(COND_1265_2_MAIN_INVOKEMETHOD1(&&(>(x1[4], 0), <(x1[4], x0[4])), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[4], x1[4]), x1[4]))), ≥)∧[(4)bni_45 + (-1)Bound*bni_45] + [(2)bni_45]x1[4] + [bni_45]x0[4] ≥ 0∧[1 + (-1)bso_46] ≥ 0)

For Pair COND_1265_2_MAIN_INVOKEMETHOD1(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0, x1), x1)) → 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(-(x0, x1), x1), x1)) the following chains were created:

We consider the chain 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[4], x1[4]), x1[4])) → COND_1265_2_MAIN_INVOKEMETHOD1(&&(>(x1[4], 0), <(x1[4], x0[4])), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[4], x1[4]), x1[4])), COND_1265_2_MAIN_INVOKEMETHOD1(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[5], x1[5]), x1[5])) → 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(-(x0[5], x1[5]), x1[5]), x1[5])), 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2])) → COND_1265_2_MAIN_INVOKEMETHOD(>=(x1[2], x0[2]), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2])) which results in the following constraint:
(69)    (&&(>(x1[4], 0), <(x1[4], x0[4]))=TRUE∧1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[4], x1[4]), x1[4])=1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[5], x1[5]), x1[5])∧1265_1_gcd_InvokeMethod(1265_0_mod_LE(-(x0[5], x1[5]), x1[5]), x1[5])=1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]) ⇒ COND_1265_2_MAIN_INVOKEMETHOD1(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[5], x1[5]), x1[5]))≥NonInfC∧COND_1265_2_MAIN_INVOKEMETHOD1(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[5], x1[5]), x1[5]))≥1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(-(x0[5], x1[5]), x1[5]), x1[5]))∧(U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(-(x0[5], x1[5]), x1[5]), x1[5]))), ≥))

We simplified constraint (69) using rules (I), (II), (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(70)    (>(x1[4], 0)=TRUE∧<(x1[4], x0[4])=TRUE ⇒ COND_1265_2_MAIN_INVOKEMETHOD1(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[4], x1[4]), x1[4]))≥NonInfC∧COND_1265_2_MAIN_INVOKEMETHOD1(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[4], x1[4]), x1[4]))≥1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(-(x0[4], x1[4]), x1[4]), x1[4]))∧(U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(-(x0[5], x1[5]), x1[5]), x1[5]))), ≥))

We simplified constraint (70) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(71)    (x1[4] + [-1] ≥ 0∧x0[4] + [-1] + [-1]x1[4] ≥ 0 ⇒ (U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(-(x0[5], x1[5]), x1[5]), x1[5]))), ≥)∧[(-1)Bound*bni_47] + [bni_47]x1[4] + [bni_47]x0[4] ≥ 0∧[-1 + (-1)bso_48] + x1[4] ≥ 0)

We simplified constraint (71) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(72)    (x1[4] + [-1] ≥ 0∧x0[4] + [-1] + [-1]x1[4] ≥ 0 ⇒ (U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(-(x0[5], x1[5]), x1[5]), x1[5]))), ≥)∧[(-1)Bound*bni_47] + [bni_47]x1[4] + [bni_47]x0[4] ≥ 0∧[-1 + (-1)bso_48] + x1[4] ≥ 0)

We simplified constraint (72) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(73)    (x1[4] + [-1] ≥ 0∧x0[4] + [-1] + [-1]x1[4] ≥ 0 ⇒ (U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(-(x0[5], x1[5]), x1[5]), x1[5]))), ≥)∧[(-1)Bound*bni_47] + [bni_47]x1[4] + [bni_47]x0[4] ≥ 0∧[-1 + (-1)bso_48] + x1[4] ≥ 0)

We simplified constraint (73) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(74)    (x1[4] ≥ 0∧x0[4] + [-2] + [-1]x1[4] ≥ 0 ⇒ (U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(-(x0[5], x1[5]), x1[5]), x1[5]))), ≥)∧[(-1)Bound*bni_47 + bni_47] + [bni_47]x1[4] + [bni_47]x0[4] ≥ 0∧[(-1)bso_48] + x1[4] ≥ 0)

We simplified constraint (74) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(75)    (x1[4] ≥ 0∧x0[4] ≥ 0 ⇒ (U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(-(x0[5], x1[5]), x1[5]), x1[5]))), ≥)∧[(-1)Bound*bni_47 + (3)bni_47] + [(2)bni_47]x1[4] + [bni_47]x0[4] ≥ 0∧[(-1)bso_48] + x1[4] ≥ 0)
We consider the chain 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[4], x1[4]), x1[4])) → COND_1265_2_MAIN_INVOKEMETHOD1(&&(>(x1[4], 0), <(x1[4], x0[4])), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[4], x1[4]), x1[4])), COND_1265_2_MAIN_INVOKEMETHOD1(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[5], x1[5]), x1[5])) → 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(-(x0[5], x1[5]), x1[5]), x1[5])), 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[4], x1[4]), x1[4])) → COND_1265_2_MAIN_INVOKEMETHOD1(&&(>(x1[4], 0), <(x1[4], x0[4])), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[4], x1[4]), x1[4])) which results in the following constraint:
(76)    (&&(>(x1[4], 0), <(x1[4], x0[4]))=TRUE∧1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[4], x1[4]), x1[4])=1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[5], x1[5]), x1[5])∧1265_1_gcd_InvokeMethod(1265_0_mod_LE(-(x0[5], x1[5]), x1[5]), x1[5])=1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[4]1, x1[4]1), x1[4]1) ⇒ COND_1265_2_MAIN_INVOKEMETHOD1(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[5], x1[5]), x1[5]))≥NonInfC∧COND_1265_2_MAIN_INVOKEMETHOD1(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[5], x1[5]), x1[5]))≥1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(-(x0[5], x1[5]), x1[5]), x1[5]))∧(U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(-(x0[5], x1[5]), x1[5]), x1[5]))), ≥))

We simplified constraint (76) using rules (I), (II), (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(77)    (>(x1[4], 0)=TRUE∧<(x1[4], x0[4])=TRUE ⇒ COND_1265_2_MAIN_INVOKEMETHOD1(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[4], x1[4]), x1[4]))≥NonInfC∧COND_1265_2_MAIN_INVOKEMETHOD1(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[4], x1[4]), x1[4]))≥1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(-(x0[4], x1[4]), x1[4]), x1[4]))∧(U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(-(x0[5], x1[5]), x1[5]), x1[5]))), ≥))

We simplified constraint (77) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(78)    (x1[4] + [-1] ≥ 0∧x0[4] + [-1] + [-1]x1[4] ≥ 0 ⇒ (U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(-(x0[5], x1[5]), x1[5]), x1[5]))), ≥)∧[(-1)Bound*bni_47] + [bni_47]x1[4] + [bni_47]x0[4] ≥ 0∧[-1 + (-1)bso_48] + x1[4] ≥ 0)

We simplified constraint (78) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(79)    (x1[4] + [-1] ≥ 0∧x0[4] + [-1] + [-1]x1[4] ≥ 0 ⇒ (U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(-(x0[5], x1[5]), x1[5]), x1[5]))), ≥)∧[(-1)Bound*bni_47] + [bni_47]x1[4] + [bni_47]x0[4] ≥ 0∧[-1 + (-1)bso_48] + x1[4] ≥ 0)

We simplified constraint (79) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(80)    (x1[4] + [-1] ≥ 0∧x0[4] + [-1] + [-1]x1[4] ≥ 0 ⇒ (U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(-(x0[5], x1[5]), x1[5]), x1[5]))), ≥)∧[(-1)Bound*bni_47] + [bni_47]x1[4] + [bni_47]x0[4] ≥ 0∧[-1 + (-1)bso_48] + x1[4] ≥ 0)

We simplified constraint (80) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(81)    (x1[4] ≥ 0∧x0[4] + [-2] + [-1]x1[4] ≥ 0 ⇒ (U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(-(x0[5], x1[5]), x1[5]), x1[5]))), ≥)∧[(-1)Bound*bni_47 + bni_47] + [bni_47]x1[4] + [bni_47]x0[4] ≥ 0∧[(-1)bso_48] + x1[4] ≥ 0)

We simplified constraint (81) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(82)    (x1[4] ≥ 0∧x0[4] ≥ 0 ⇒ (U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(-(x0[5], x1[5]), x1[5]), x1[5]))), ≥)∧[(-1)Bound*bni_47 + (3)bni_47] + [(2)bni_47]x1[4] + [bni_47]x0[4] ≥ 0∧[(-1)bso_48] + x1[4] ≥ 0)

For Pair 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0, x0)) → COND_1174_1_MAIN_INVOKEMETHOD1(>(x0, 0), 1174_0_gcd_EQ(x0, x0)) the following chains were created:

We consider the chain 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[6], x0[6])) → COND_1174_1_MAIN_INVOKEMETHOD1(>(x0[6], 0), 1174_0_gcd_EQ(x0[6], x0[6])), COND_1174_1_MAIN_INVOKEMETHOD1(TRUE, 1174_0_gcd_EQ(x0[7], x0[7])) → 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[7], 0)) which results in the following constraint:
(83)    (>(x0[6], 0)=TRUE∧1174_0_gcd_EQ(x0[6], x0[6])=1174_0_gcd_EQ(x0[7], x0[7]) ⇒ 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[6], x0[6]))≥NonInfC∧1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[6], x0[6]))≥COND_1174_1_MAIN_INVOKEMETHOD1(>(x0[6], 0), 1174_0_gcd_EQ(x0[6], x0[6]))∧(U^Increasing(COND_1174_1_MAIN_INVOKEMETHOD1(>(x0[6], 0), 1174_0_gcd_EQ(x0[6], x0[6]))), ≥))

We simplified constraint (83) using rules (I), (II), (IV) which results in the following new constraint:
(84)    (>(x0[6], 0)=TRUE ⇒ 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[6], x0[6]))≥NonInfC∧1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[6], x0[6]))≥COND_1174_1_MAIN_INVOKEMETHOD1(>(x0[6], 0), 1174_0_gcd_EQ(x0[6], x0[6]))∧(U^Increasing(COND_1174_1_MAIN_INVOKEMETHOD1(>(x0[6], 0), 1174_0_gcd_EQ(x0[6], x0[6]))), ≥))

We simplified constraint (84) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(85)    (x0[6] + [-1] ≥ 0 ⇒ (U^Increasing(COND_1174_1_MAIN_INVOKEMETHOD1(>(x0[6], 0), 1174_0_gcd_EQ(x0[6], x0[6]))), ≥)∧[bni_49 + (-1)Bound*bni_49] + [(2)bni_49]x0[6] ≥ 0∧[(-1)bso_50] ≥ 0)

We simplified constraint (85) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(86)    (x0[6] + [-1] ≥ 0 ⇒ (U^Increasing(COND_1174_1_MAIN_INVOKEMETHOD1(>(x0[6], 0), 1174_0_gcd_EQ(x0[6], x0[6]))), ≥)∧[bni_49 + (-1)Bound*bni_49] + [(2)bni_49]x0[6] ≥ 0∧[(-1)bso_50] ≥ 0)

We simplified constraint (86) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(87)    (x0[6] + [-1] ≥ 0 ⇒ (U^Increasing(COND_1174_1_MAIN_INVOKEMETHOD1(>(x0[6], 0), 1174_0_gcd_EQ(x0[6], x0[6]))), ≥)∧[bni_49 + (-1)Bound*bni_49] + [(2)bni_49]x0[6] ≥ 0∧[(-1)bso_50] ≥ 0)

We simplified constraint (87) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(88)    (x0[6] ≥ 0 ⇒ (U^Increasing(COND_1174_1_MAIN_INVOKEMETHOD1(>(x0[6], 0), 1174_0_gcd_EQ(x0[6], x0[6]))), ≥)∧[(3)bni_49 + (-1)Bound*bni_49] + [(2)bni_49]x0[6] ≥ 0∧[(-1)bso_50] ≥ 0)

For Pair COND_1174_1_MAIN_INVOKEMETHOD1(TRUE, 1174_0_gcd_EQ(x0, x0)) → 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0, 0)) the following chains were created:

We consider the chain 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[6], x0[6])) → COND_1174_1_MAIN_INVOKEMETHOD1(>(x0[6], 0), 1174_0_gcd_EQ(x0[6], x0[6])), COND_1174_1_MAIN_INVOKEMETHOD1(TRUE, 1174_0_gcd_EQ(x0[7], x0[7])) → 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[7], 0)), 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[0], x1[0])) → COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0])) which results in the following constraint:
(89)    (>(x0[6], 0)=TRUE∧1174_0_gcd_EQ(x0[6], x0[6])=1174_0_gcd_EQ(x0[7], x0[7])∧1174_0_gcd_EQ(x0[7], 0)=1174_0_gcd_EQ(x0[0], x1[0]) ⇒ COND_1174_1_MAIN_INVOKEMETHOD1(TRUE, 1174_0_gcd_EQ(x0[7], x0[7]))≥NonInfC∧COND_1174_1_MAIN_INVOKEMETHOD1(TRUE, 1174_0_gcd_EQ(x0[7], x0[7]))≥1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[7], 0))∧(U^Increasing(1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[7], 0))), ≥))

We simplified constraint (89) using rules (I), (II), (III), (IV) which results in the following new constraint:
(90)    (>(x0[6], 0)=TRUE ⇒ COND_1174_1_MAIN_INVOKEMETHOD1(TRUE, 1174_0_gcd_EQ(x0[6], x0[6]))≥NonInfC∧COND_1174_1_MAIN_INVOKEMETHOD1(TRUE, 1174_0_gcd_EQ(x0[6], x0[6]))≥1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[6], 0))∧(U^Increasing(1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[7], 0))), ≥))

We simplified constraint (90) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(91)    (x0[6] + [-1] ≥ 0 ⇒ (U^Increasing(1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[7], 0))), ≥)∧[bni_51 + (-1)Bound*bni_51] + [(2)bni_51]x0[6] ≥ 0∧[(-1)bso_52] + x0[6] ≥ 0)

We simplified constraint (91) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(92)    (x0[6] + [-1] ≥ 0 ⇒ (U^Increasing(1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[7], 0))), ≥)∧[bni_51 + (-1)Bound*bni_51] + [(2)bni_51]x0[6] ≥ 0∧[(-1)bso_52] + x0[6] ≥ 0)

We simplified constraint (92) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(93)    (x0[6] + [-1] ≥ 0 ⇒ (U^Increasing(1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[7], 0))), ≥)∧[bni_51 + (-1)Bound*bni_51] + [(2)bni_51]x0[6] ≥ 0∧[(-1)bso_52] + x0[6] ≥ 0)

We simplified constraint (93) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(94)    (x0[6] ≥ 0 ⇒ (U^Increasing(1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[7], 0))), ≥)∧[(3)bni_51 + (-1)Bound*bni_51] + [(2)bni_51]x0[6] ≥ 0∧[1 + (-1)bso_52] + x0[6] ≥ 0)
We consider the chain 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[6], x0[6])) → COND_1174_1_MAIN_INVOKEMETHOD1(>(x0[6], 0), 1174_0_gcd_EQ(x0[6], x0[6])), COND_1174_1_MAIN_INVOKEMETHOD1(TRUE, 1174_0_gcd_EQ(x0[7], x0[7])) → 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[7], 0)), 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[6], x0[6])) → COND_1174_1_MAIN_INVOKEMETHOD1(>(x0[6], 0), 1174_0_gcd_EQ(x0[6], x0[6])) which results in the following constraint:
(95) (>(x0[6], 0)=TRUE∧1174_0_gcd_EQ(x0[6], x0[6])=1174_0_gcd_EQ(x0[7], x0[7])∧1174_0_gcd_EQ(x0[7], 0)=1174_0_gcd_EQ(x0[6]1, x0[6]1) ⇒ COND_1174_1_MAIN_INVOKEMETHOD1(TRUE, 1174_0_gcd_EQ(x0[7], x0[7]))≥NonInfC∧COND_1174_1_MAIN_INVOKEMETHOD1(TRUE, 1174_0_gcd_EQ(x0[7], x0[7]))≥1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[7], 0))∧(U^Increasing(1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[7], 0))), ≥))

We solved constraint (95) using rules (I), (II), (III), (IDP_CONSTANT_FOLD).

To summarize, we get the following constraints P_≥ for the following pairs.

1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0, x1)) → COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1, 0), >=(x0, 0)), !(=(x0, x1))), 1174_0_gcd_EQ(x0, x1))
- (x0[0] + x1[0] ≥ 0∧x0[0] ≥ 0∧x1[0] ≥ 0 ⇒ (U^Increasing(COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0]))), ≥)∧[(2)bni_37 + (-1)Bound*bni_37] + [(2)bni_37]x0[0] + [bni_37]x1[0] ≥ 0∧[(-1)bso_38] ≥ 0)
- (x1[0] ≥ 0∧[2] + x1[0] + x0[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0]))), ≥)∧[(4)bni_37 + (-1)Bound*bni_37] + [(2)bni_37]x1[0] + [bni_37]x0[0] ≥ 0∧[(-1)bso_38] ≥ 0)
COND_1174_1_MAIN_INVOKEMETHOD(TRUE, 1174_0_gcd_EQ(x0, x1)) → 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0, x1), x1))
- (x0[0] + x1[0] ≥ 0∧x0[0] ≥ 0∧x1[0] ≥ 0 ⇒ (U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))), ≥)∧[(2)bni_39 + (-1)Bound*bni_39] + [(2)bni_39]x0[0] + [bni_39]x1[0] ≥ 0∧[(-1)bso_40] ≥ 0)
- (x1[0] ≥ 0∧[2] + x1[0] + x0[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))), ≥)∧[(4)bni_39 + (-1)Bound*bni_39] + [(2)bni_39]x1[0] + [bni_39]x0[0] ≥ 0∧[(-1)bso_40] ≥ 0)
- (x0[0] + x1[0] ≥ 0∧x0[0] ≥ 0∧x1[0] ≥ 0 ⇒ (U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))), ≥)∧[(2)bni_39 + (-1)Bound*bni_39] + [(2)bni_39]x0[0] + [bni_39]x1[0] ≥ 0∧[(-1)bso_40] ≥ 0)
- (x1[0] ≥ 0∧[2] + x1[0] + x0[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))), ≥)∧[(4)bni_39 + (-1)Bound*bni_39] + [(2)bni_39]x1[0] + [bni_39]x0[0] ≥ 0∧[(-1)bso_40] ≥ 0)
1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0, x1), x1)) → COND_1265_2_MAIN_INVOKEMETHOD(>=(x1, x0), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0, x1), x1))
- (x1[2] ≥ 0∧x0[2] ≥ 0 ⇒ (U^Increasing(COND_1265_2_MAIN_INVOKEMETHOD(>=(x1[2], x0[2]), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]))), ≥)∧[bni_41 + (-1)Bound*bni_41] + [(-2)bni_41]x0[2] + [bni_41]x1[2] ≥ 0∧[(-1)bso_42] ≥ 0)
- (x1[2] ≥ 0∧x0[2] ≥ 0 ⇒ (U^Increasing(COND_1265_2_MAIN_INVOKEMETHOD(>=(x1[2], x0[2]), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]))), ≥)∧[bni_41 + (-1)Bound*bni_41] + [(2)bni_41]x0[2] + [bni_41]x1[2] ≥ 0∧[(-1)bso_42] ≥ 0)
COND_1265_2_MAIN_INVOKEMETHOD(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0, x1), x1)) → 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1, x0))
- (x1[2] ≥ 0∧x0[2] ≥ 0 ⇒ (U^Increasing(1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))), ≥)∧[bni_43 + (-1)Bound*bni_43] + [(2)bni_43]x0[2] + [bni_43]x1[2] ≥ 0∧[(-1)bso_44] ≥ 0)
- (x1[2] ≥ 0∧x0[2] ≥ 0 ⇒ (U^Increasing(1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))), ≥)∧[bni_43 + (-1)Bound*bni_43] + [(-2)bni_43]x0[2] + [bni_43]x1[2] ≥ 0∧[(-1)bso_44] ≥ 0)
- (0 ≥ 0 ⇒ (U^Increasing(1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))), ≥)∧[(2)bni_43] = 0∧[bni_43 + (-1)Bound*bni_43] ≥ 0∧0 = 0∧[(-1)bso_44] ≥ 0)
1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0, x1), x1)) → COND_1265_2_MAIN_INVOKEMETHOD1(&&(>(x1, 0), <(x1, x0)), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0, x1), x1))
- (x1[4] ≥ 0∧x0[4] ≥ 0 ⇒ (U^Increasing(COND_1265_2_MAIN_INVOKEMETHOD1(&&(>(x1[4], 0), <(x1[4], x0[4])), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[4], x1[4]), x1[4]))), ≥)∧[(4)bni_45 + (-1)Bound*bni_45] + [(2)bni_45]x1[4] + [bni_45]x0[4] ≥ 0∧[1 + (-1)bso_46] ≥ 0)
COND_1265_2_MAIN_INVOKEMETHOD1(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0, x1), x1)) → 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(-(x0, x1), x1), x1))
- (x1[4] ≥ 0∧x0[4] ≥ 0 ⇒ (U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(-(x0[5], x1[5]), x1[5]), x1[5]))), ≥)∧[(-1)Bound*bni_47 + (3)bni_47] + [(2)bni_47]x1[4] + [bni_47]x0[4] ≥ 0∧[(-1)bso_48] + x1[4] ≥ 0)
- (x1[4] ≥ 0∧x0[4] ≥ 0 ⇒ (U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(-(x0[5], x1[5]), x1[5]), x1[5]))), ≥)∧[(-1)Bound*bni_47 + (3)bni_47] + [(2)bni_47]x1[4] + [bni_47]x0[4] ≥ 0∧[(-1)bso_48] + x1[4] ≥ 0)
1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0, x0)) → COND_1174_1_MAIN_INVOKEMETHOD1(>(x0, 0), 1174_0_gcd_EQ(x0, x0))
- (x0[6] ≥ 0 ⇒ (U^Increasing(COND_1174_1_MAIN_INVOKEMETHOD1(>(x0[6], 0), 1174_0_gcd_EQ(x0[6], x0[6]))), ≥)∧[(3)bni_49 + (-1)Bound*bni_49] + [(2)bni_49]x0[6] ≥ 0∧[(-1)bso_50] ≥ 0)
COND_1174_1_MAIN_INVOKEMETHOD1(TRUE, 1174_0_gcd_EQ(x0, x0)) → 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0, 0))
- (x0[6] ≥ 0 ⇒ (U^Increasing(1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[7], 0))), ≥)∧[(3)bni_51 + (-1)Bound*bni_51] + [(2)bni_51]x0[6] ≥ 0∧[1 + (-1)bso_52] + x0[6] ≥ 0)

The constraints for P_> respective P_bound 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 P_bound.
Using the following integer polynomial ordering the resulting constraints can be solved
Polynomial interpretation over integers[POLO]:

POL(TRUE) = [1]
POL(FALSE) = 0
POL(1174_1_main_InvokeMethod(x₁)) = [-1] + [-1]x₁
POL(1174_0_gcd_EQ(x₁, x₂)) = [1] + [-1]x₂ + [-1]x₁
POL(0) = 0
POL(1193_0_main_Return) = [-1]
POL(1174_1_MAIN_INVOKEMETHOD(x₁)) = [2] + [-1]x₁
POL(COND_1174_1_MAIN_INVOKEMETHOD(x₁, x₂)) = [2] + [-1]x₂
POL(&&(x₁, x₂)) = [-1]
POL(>(x₁, x₂)) = [-1]
POL(>=(x₁, x₂)) = [-1]
POL(!(x₁)) = [-1]
POL(=(x₁, x₂)) = [-1]
POL(1265_2_MAIN_INVOKEMETHOD(x₁)) = [-1]x₁
POL(1265_1_gcd_InvokeMethod(x₁, x₂)) = [-1]x₂ + x₁
POL(1265_0_mod_LE(x₁, x₂)) = [-1] + [-1]x₁
POL(COND_1265_2_MAIN_INVOKEMETHOD(x₁, x₂)) = [-1]x₂
POL(COND_1265_2_MAIN_INVOKEMETHOD1(x₁, x₂)) = [-1] + [-1]x₂
POL(<(x₁, x₂)) = [-1]
POL(-(x₁, x₂)) = x₁ + [-1]x₂
POL(COND_1174_1_MAIN_INVOKEMETHOD1(x₁, x₂)) = [2] + [-1]x₂

The following pairs are in P_>:

1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[4], x1[4]), x1[4])) → COND_1265_2_MAIN_INVOKEMETHOD1(&&(>(x1[4], 0), <(x1[4], x0[4])), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[4], x1[4]), x1[4]))
COND_1174_1_MAIN_INVOKEMETHOD1(TRUE, 1174_0_gcd_EQ(x0[7], x0[7])) → 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[7], 0))

The following pairs are in P_bound:

1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[0], x1[0])) → COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0]))
COND_1174_1_MAIN_INVOKEMETHOD(TRUE, 1174_0_gcd_EQ(x0[1], x1[1])) → 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))
1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[4], x1[4]), x1[4])) → COND_1265_2_MAIN_INVOKEMETHOD1(&&(>(x1[4], 0), <(x1[4], x0[4])), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[4], x1[4]), x1[4]))
COND_1265_2_MAIN_INVOKEMETHOD1(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[5], x1[5]), x1[5])) → 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(-(x0[5], x1[5]), x1[5]), x1[5]))
1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[6], x0[6])) → COND_1174_1_MAIN_INVOKEMETHOD1(>(x0[6], 0), 1174_0_gcd_EQ(x0[6], x0[6]))
COND_1174_1_MAIN_INVOKEMETHOD1(TRUE, 1174_0_gcd_EQ(x0[7], x0[7])) → 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[7], 0))

The following pairs are in P_≥:

1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[0], x1[0])) → COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0]))
COND_1174_1_MAIN_INVOKEMETHOD(TRUE, 1174_0_gcd_EQ(x0[1], x1[1])) → 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))
1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2])) → COND_1265_2_MAIN_INVOKEMETHOD(>=(x1[2], x0[2]), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]))
COND_1265_2_MAIN_INVOKEMETHOD(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[3], x1[3]), x1[3])) → 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))
COND_1265_2_MAIN_INVOKEMETHOD1(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[5], x1[5]), x1[5])) → 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(-(x0[5], x1[5]), x1[5]), x1[5]))
1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[6], x0[6])) → COND_1174_1_MAIN_INVOKEMETHOD1(>(x0[6], 0), 1174_0_gcd_EQ(x0[6], x0[6]))

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

(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:
1174_1_main_InvokeMethod(1174_0_gcd_EQ(x0, 0)) → 1193_0_main_Return

The integer pair graph contains the following rules and edges:
(0): 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[0], x1[0])) → COND_1174_1_MAIN_INVOKEMETHOD(x1[0] > 0 && x0[0] >= 0 && !(x0[0] = x1[0]), 1174_0_gcd_EQ(x0[0], x1[0]))
(1): COND_1174_1_MAIN_INVOKEMETHOD(TRUE, 1174_0_gcd_EQ(x0[1], x1[1])) → 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))
(2): 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2])) → COND_1265_2_MAIN_INVOKEMETHOD(x1[2] >= x0[2], 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]))
(3): COND_1265_2_MAIN_INVOKEMETHOD(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[3], x1[3]), x1[3])) → 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))
(5): COND_1265_2_MAIN_INVOKEMETHOD1(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[5], x1[5]), x1[5])) → 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[5] - x1[5], x1[5]), x1[5]))
(6): 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[6], x0[6])) → COND_1174_1_MAIN_INVOKEMETHOD1(x0[6] > 0, 1174_0_gcd_EQ(x0[6], x0[6]))

(3) -> (0), if ((1174_0_gcd_EQ(x1[3], x0[3]) →^* 1174_0_gcd_EQ(x0[0], x1[0])))

(0) -> (1), if ((x1[0] > 0 && x0[0] >= 0 && !(x0[0] = x1[0]) →^* TRUE)∧(1174_0_gcd_EQ(x0[0], x1[0]) →^* 1174_0_gcd_EQ(x0[1], x1[1])))

(1) -> (2), if ((1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]) →^* 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2])))

(5) -> (2), if ((1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[5] - x1[5], x1[5]), x1[5]) →^* 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2])))

(2) -> (3), if ((x1[2] >= x0[2] →^* TRUE)∧(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]) →^* 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[3], x1[3]), x1[3])))

(3) -> (6), if ((1174_0_gcd_EQ(x1[3], x0[3]) →^* 1174_0_gcd_EQ(x0[6], x0[6])))

The set Q consists of the following terms:
1174_1_main_InvokeMethod(1174_0_gcd_EQ(x0, 0))

(7) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.

(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

The ITRS R consists of the following rules:
1174_1_main_InvokeMethod(1174_0_gcd_EQ(x0, 0)) → 1193_0_main_Return

The integer pair graph contains the following rules and edges:
(3): COND_1265_2_MAIN_INVOKEMETHOD(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[3], x1[3]), x1[3])) → 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))
(2): 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2])) → COND_1265_2_MAIN_INVOKEMETHOD(x1[2] >= x0[2], 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]))
(1): COND_1174_1_MAIN_INVOKEMETHOD(TRUE, 1174_0_gcd_EQ(x0[1], x1[1])) → 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))
(0): 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[0], x1[0])) → COND_1174_1_MAIN_INVOKEMETHOD(x1[0] > 0 && x0[0] >= 0 && !(x0[0] = x1[0]), 1174_0_gcd_EQ(x0[0], x1[0]))

(3) -> (0), if ((1174_0_gcd_EQ(x1[3], x0[3]) →^* 1174_0_gcd_EQ(x0[0], x1[0])))

(0) -> (1), if ((x1[0] > 0 && x0[0] >= 0 && !(x0[0] = x1[0]) →^* TRUE)∧(1174_0_gcd_EQ(x0[0], x1[0]) →^* 1174_0_gcd_EQ(x0[1], x1[1])))

(1) -> (2), if ((1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]) →^* 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2])))

(2) -> (3), if ((x1[2] >= x0[2] →^* TRUE)∧(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]) →^* 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[3], x1[3]), x1[3])))

The set Q consists of the following terms:
1174_1_main_InvokeMethod(1174_0_gcd_EQ(x0, 0))

(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:

Integer, Boolean

R is empty.

The integer pair graph contains the following rules and edges:
(3): COND_1265_2_MAIN_INVOKEMETHOD(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[3], x1[3]), x1[3])) → 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))
(2): 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2])) → COND_1265_2_MAIN_INVOKEMETHOD(x1[2] >= x0[2], 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]))
(1): COND_1174_1_MAIN_INVOKEMETHOD(TRUE, 1174_0_gcd_EQ(x0[1], x1[1])) → 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))
(0): 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[0], x1[0])) → COND_1174_1_MAIN_INVOKEMETHOD(x1[0] > 0 && x0[0] >= 0 && !(x0[0] = x1[0]), 1174_0_gcd_EQ(x0[0], x1[0]))

(3) -> (0), if ((1174_0_gcd_EQ(x1[3], x0[3]) →^* 1174_0_gcd_EQ(x0[0], x1[0])))

(0) -> (1), if ((x1[0] > 0 && x0[0] >= 0 && !(x0[0] = x1[0]) →^* TRUE)∧(1174_0_gcd_EQ(x0[0], x1[0]) →^* 1174_0_gcd_EQ(x0[1], x1[1])))

(1) -> (2), if ((1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]) →^* 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2])))

(2) -> (3), if ((x1[2] >= x0[2] →^* TRUE)∧(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]) →^* 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[3], x1[3]), x1[3])))

The set Q consists of the following terms:
1174_1_main_InvokeMethod(1174_0_gcd_EQ(x0, 0))

(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 COND_1265_2_MAIN_INVOKEMETHOD(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[3], x1[3]), x1[3])) → 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3])) the following chains were created:

We consider the chain 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[0], x1[0])) → COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0])), COND_1174_1_MAIN_INVOKEMETHOD(TRUE, 1174_0_gcd_EQ(x0[1], x1[1])) → 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1])), 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2])) → COND_1265_2_MAIN_INVOKEMETHOD(>=(x1[2], x0[2]), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2])), COND_1265_2_MAIN_INVOKEMETHOD(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[3], x1[3]), x1[3])) → 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3])), 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[0], x1[0])) → COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0])), COND_1174_1_MAIN_INVOKEMETHOD(TRUE, 1174_0_gcd_EQ(x0[1], x1[1])) → 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1])) which results in the following constraint:
(1)    (&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0])))=TRUE∧1174_0_gcd_EQ(x0[0], x1[0])=1174_0_gcd_EQ(x0[1], x1[1])∧1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1])=1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2])∧>=(x1[2], x0[2])=TRUE∧1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2])=1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[3], x1[3]), x1[3])∧1174_0_gcd_EQ(x1[3], x0[3])=1174_0_gcd_EQ(x0[0]1, x1[0]1)∧&&(&&(>(x1[0]1, 0), >=(x0[0]1, 0)), !(=(x0[0]1, x1[0]1)))=TRUE∧1174_0_gcd_EQ(x0[0]1, x1[0]1)=1174_0_gcd_EQ(x0[1]1, x1[1]1) ⇒ COND_1265_2_MAIN_INVOKEMETHOD(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[3], x1[3]), x1[3]))≥NonInfC∧COND_1265_2_MAIN_INVOKEMETHOD(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[3], x1[3]), x1[3]))≥1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))∧(U^Increasing(1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))), ≥))

We simplified constraint (1) using rules (I), (II), (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(2)    (>=(x1[0], x0[0])=TRUE∧>(x1[0], 0)=TRUE∧>=(x0[0], 0)=TRUE∧>(x0[0], 0)=TRUE∧>=(x1[0], 0)=TRUE∧<(x0[0], x1[0])=TRUE∧<(x1[0], x0[0])=TRUE ⇒ COND_1265_2_MAIN_INVOKEMETHOD(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[0], x1[0]), x1[0]))≥NonInfC∧COND_1265_2_MAIN_INVOKEMETHOD(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[0], x1[0]), x1[0]))≥1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[0], x0[0]))∧(U^Increasing(1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))), ≥))

We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(3)    (x1[0] + [-1]x0[0] ≥ 0∧x1[0] + [-1] ≥ 0∧x0[0] ≥ 0∧x0[0] + [-1] ≥ 0∧x1[0] ≥ 0∧x1[0] + [-1] + [-1]x0[0] ≥ 0∧x0[0] + [-1] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))), ≥)∧[(-5)bni_27 + (-1)Bound*bni_27] + [(4)bni_27]x1[0] + [(2)bni_27]x0[0] ≥ 0∧[-5 + (-1)bso_28] + [4]x1[0] + x0[0] ≥ 0)

We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(4)    (x1[0] + [-1]x0[0] ≥ 0∧x1[0] + [-1] ≥ 0∧x0[0] ≥ 0∧x0[0] + [-1] ≥ 0∧x1[0] ≥ 0∧x1[0] + [-1] + [-1]x0[0] ≥ 0∧x0[0] + [-1] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))), ≥)∧[(-5)bni_27 + (-1)Bound*bni_27] + [(4)bni_27]x1[0] + [(2)bni_27]x0[0] ≥ 0∧[-5 + (-1)bso_28] + [4]x1[0] + x0[0] ≥ 0)

We simplified constraint (5) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(6)    (x1[0] + [-1]x0[0] ≥ 0∧x1[0] + [-1] ≥ 0∧x0[0] ≥ 0∧x0[0] + [-1] ≥ 0∧x1[0] ≥ 0∧x1[0] + [-1] + [-1]x0[0] ≥ 0∧x1[0] + [-1] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))), ≥)∧[(-5)bni_27 + (-1)Bound*bni_27] + [(4)bni_27]x1[0] + [(2)bni_27]x0[0] ≥ 0∧[-5 + (-1)bso_28] + [4]x1[0] + x0[0] ≥ 0)

We simplified constraint (7) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(8)    (x1[0] + [-1]x0[0] ≥ 0∧x1[0] + [-1] ≥ 0∧x0[0] ≥ 0∧x0[0] + [-1] ≥ 0∧x1[0] ≥ 0∧x0[0] + [-1] + [-1]x1[0] ≥ 0∧x0[0] + [-1] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))), ≥)∧[(-5)bni_27 + (-1)Bound*bni_27] + [(4)bni_27]x1[0] + [(2)bni_27]x0[0] ≥ 0∧[-5 + (-1)bso_28] + [4]x1[0] + x0[0] ≥ 0)

We simplified constraint (9) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(10)    (x1[0] + [-1]x0[0] ≥ 0∧x1[0] + [-1] ≥ 0∧x0[0] ≥ 0∧x0[0] + [-1] ≥ 0∧x1[0] ≥ 0∧x0[0] + [-1] + [-1]x1[0] ≥ 0∧x1[0] + [-1] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))), ≥)∧[(-5)bni_27 + (-1)Bound*bni_27] + [(4)bni_27]x1[0] + [(2)bni_27]x0[0] ≥ 0∧[-5 + (-1)bso_28] + [4]x1[0] + x0[0] ≥ 0)

We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(11)    (x1[0] + [-1]x0[0] ≥ 0∧x1[0] + [-1] ≥ 0∧x0[0] ≥ 0∧x0[0] + [-1] ≥ 0∧x1[0] ≥ 0∧x1[0] + [-1] + [-1]x0[0] ≥ 0∧x0[0] + [-1] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))), ≥)∧[(-5)bni_27 + (-1)Bound*bni_27] + [(4)bni_27]x1[0] + [(2)bni_27]x0[0] ≥ 0∧[-5 + (-1)bso_28] + [4]x1[0] + x0[0] ≥ 0)

We simplified constraint (6) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(12)    (x1[0] + [-1]x0[0] ≥ 0∧x1[0] + [-1] ≥ 0∧x0[0] ≥ 0∧x0[0] + [-1] ≥ 0∧x1[0] ≥ 0∧x1[0] + [-1] + [-1]x0[0] ≥ 0∧x1[0] + [-1] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))), ≥)∧[(-5)bni_27 + (-1)Bound*bni_27] + [(4)bni_27]x1[0] + [(2)bni_27]x0[0] ≥ 0∧[-5 + (-1)bso_28] + [4]x1[0] + x0[0] ≥ 0)

We simplified constraint (8) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(13)    (x1[0] + [-1]x0[0] ≥ 0∧x1[0] + [-1] ≥ 0∧x0[0] ≥ 0∧x0[0] + [-1] ≥ 0∧x1[0] ≥ 0∧x0[0] + [-1] + [-1]x1[0] ≥ 0∧x0[0] + [-1] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))), ≥)∧[(-5)bni_27 + (-1)Bound*bni_27] + [(4)bni_27]x1[0] + [(2)bni_27]x0[0] ≥ 0∧[-5 + (-1)bso_28] + [4]x1[0] + x0[0] ≥ 0)

We simplified constraint (10) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(14)    (x1[0] + [-1]x0[0] ≥ 0∧x1[0] + [-1] ≥ 0∧x0[0] ≥ 0∧x0[0] + [-1] ≥ 0∧x1[0] ≥ 0∧x0[0] + [-1] + [-1]x1[0] ≥ 0∧x1[0] + [-1] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))), ≥)∧[(-5)bni_27 + (-1)Bound*bni_27] + [(4)bni_27]x1[0] + [(2)bni_27]x0[0] ≥ 0∧[-5 + (-1)bso_28] + [4]x1[0] + x0[0] ≥ 0)

We solved constraint (11) using rule (IDP_SMT_SPLIT).We simplified constraint (12) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(15)    (x1[0] ≥ 0∧x0[0] + [-1] + x1[0] ≥ 0∧x0[0] ≥ 0∧x0[0] + [-1] ≥ 0∧x0[0] + x1[0] ≥ 0∧[-1] + x1[0] ≥ 0∧[-1] + x1[0] ≥ 0 ⇒ (U^Increasing(1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))), ≥)∧[(-5)bni_27 + (-1)Bound*bni_27] + [(6)bni_27]x0[0] + [(4)bni_27]x1[0] ≥ 0∧[-5 + (-1)bso_28] + [5]x0[0] + [4]x1[0] ≥ 0)

We solved constraint (13) using rule (IDP_SMT_SPLIT).We solved constraint (14) using rule (IDP_SMT_SPLIT).We simplified constraint (15) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(16)    (x1[0] ≥ 0∧x0[0] + x1[0] ≥ 0∧[1] + x0[0] ≥ 0∧x0[0] ≥ 0∧[1] + x0[0] + x1[0] ≥ 0∧[-1] + x1[0] ≥ 0∧[-1] + x1[0] ≥ 0 ⇒ (U^Increasing(1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))), ≥)∧[bni_27 + (-1)Bound*bni_27] + [(6)bni_27]x0[0] + [(4)bni_27]x1[0] ≥ 0∧[(-1)bso_28] + [5]x0[0] + [4]x1[0] ≥ 0)

We simplified constraint (16) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(17)    ([1] + x1[0] ≥ 0∧[1] + x0[0] + x1[0] ≥ 0∧[1] + x0[0] ≥ 0∧x0[0] ≥ 0∧[2] + x0[0] + x1[0] ≥ 0∧x1[0] ≥ 0∧x1[0] ≥ 0 ⇒ (U^Increasing(1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))), ≥)∧[(5)bni_27 + (-1)Bound*bni_27] + [(6)bni_27]x0[0] + [(4)bni_27]x1[0] ≥ 0∧[4 + (-1)bso_28] + [5]x0[0] + [4]x1[0] ≥ 0)

For Pair 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2])) → COND_1265_2_MAIN_INVOKEMETHOD(>=(x1[2], x0[2]), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2])) the following chains were created:

We consider the chain 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2])) → COND_1265_2_MAIN_INVOKEMETHOD(>=(x1[2], x0[2]), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2])), COND_1265_2_MAIN_INVOKEMETHOD(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[3], x1[3]), x1[3])) → 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3])) which results in the following constraint:
(18)    (>=(x1[2], x0[2])=TRUE∧1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2])=1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[3], x1[3]), x1[3]) ⇒ 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]))≥NonInfC∧1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]))≥COND_1265_2_MAIN_INVOKEMETHOD(>=(x1[2], x0[2]), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]))∧(U^Increasing(COND_1265_2_MAIN_INVOKEMETHOD(>=(x1[2], x0[2]), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]))), ≥))

We simplified constraint (18) using rules (I), (II), (IV) which results in the following new constraint:
(19)    (>=(x1[2], x0[2])=TRUE ⇒ 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]))≥NonInfC∧1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]))≥COND_1265_2_MAIN_INVOKEMETHOD(>=(x1[2], x0[2]), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]))∧(U^Increasing(COND_1265_2_MAIN_INVOKEMETHOD(>=(x1[2], x0[2]), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]))), ≥))

We simplified constraint (19) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(20)    (x1[2] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(COND_1265_2_MAIN_INVOKEMETHOD(>=(x1[2], x0[2]), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]))), ≥)∧[(-3)bni_29 + (-1)Bound*bni_29] + [(4)bni_29]x1[2] + [(2)bni_29]x0[2] ≥ 0∧[2 + (-1)bso_30] ≥ 0)

We simplified constraint (20) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(21)    (x1[2] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(COND_1265_2_MAIN_INVOKEMETHOD(>=(x1[2], x0[2]), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]))), ≥)∧[(-3)bni_29 + (-1)Bound*bni_29] + [(4)bni_29]x1[2] + [(2)bni_29]x0[2] ≥ 0∧[2 + (-1)bso_30] ≥ 0)

We simplified constraint (21) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(22)    (x1[2] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(COND_1265_2_MAIN_INVOKEMETHOD(>=(x1[2], x0[2]), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]))), ≥)∧[(-3)bni_29 + (-1)Bound*bni_29] + [(4)bni_29]x1[2] + [(2)bni_29]x0[2] ≥ 0∧[2 + (-1)bso_30] ≥ 0)

We simplified constraint (22) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(23)    (x1[2] ≥ 0 ⇒ (U^Increasing(COND_1265_2_MAIN_INVOKEMETHOD(>=(x1[2], x0[2]), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]))), ≥)∧[(-3)bni_29 + (-1)Bound*bni_29] + [(6)bni_29]x0[2] + [(4)bni_29]x1[2] ≥ 0∧[2 + (-1)bso_30] ≥ 0)

We simplified constraint (23) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(24)    (x1[2] ≥ 0∧x0[2] ≥ 0 ⇒ (U^Increasing(COND_1265_2_MAIN_INVOKEMETHOD(>=(x1[2], x0[2]), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]))), ≥)∧[(-3)bni_29 + (-1)Bound*bni_29] + [(6)bni_29]x0[2] + [(4)bni_29]x1[2] ≥ 0∧[2 + (-1)bso_30] ≥ 0)

(25)    (x1[2] ≥ 0∧x0[2] ≥ 0 ⇒ (U^Increasing(COND_1265_2_MAIN_INVOKEMETHOD(>=(x1[2], x0[2]), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]))), ≥)∧[(-3)bni_29 + (-1)Bound*bni_29] + [(-6)bni_29]x0[2] + [(4)bni_29]x1[2] ≥ 0∧[2 + (-1)bso_30] ≥ 0)

For Pair COND_1174_1_MAIN_INVOKEMETHOD(TRUE, 1174_0_gcd_EQ(x0[1], x1[1])) → 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1])) the following chains were created:

We consider the chain 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2])) → COND_1265_2_MAIN_INVOKEMETHOD(>=(x1[2], x0[2]), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2])), COND_1265_2_MAIN_INVOKEMETHOD(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[3], x1[3]), x1[3])) → 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3])), 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[0], x1[0])) → COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0])), COND_1174_1_MAIN_INVOKEMETHOD(TRUE, 1174_0_gcd_EQ(x0[1], x1[1])) → 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1])), 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2])) → COND_1265_2_MAIN_INVOKEMETHOD(>=(x1[2], x0[2]), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2])), COND_1265_2_MAIN_INVOKEMETHOD(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[3], x1[3]), x1[3])) → 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3])) which results in the following constraint:
(26)    (>=(x1[2], x0[2])=TRUE∧1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2])=1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[3], x1[3]), x1[3])∧1174_0_gcd_EQ(x1[3], x0[3])=1174_0_gcd_EQ(x0[0], x1[0])∧&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0])))=TRUE∧1174_0_gcd_EQ(x0[0], x1[0])=1174_0_gcd_EQ(x0[1], x1[1])∧1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1])=1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2]1, x1[2]1), x1[2]1)∧>=(x1[2]1, x0[2]1)=TRUE∧1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2]1, x1[2]1), x1[2]1)=1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[3]1, x1[3]1), x1[3]1) ⇒ COND_1174_1_MAIN_INVOKEMETHOD(TRUE, 1174_0_gcd_EQ(x0[1], x1[1]))≥NonInfC∧COND_1174_1_MAIN_INVOKEMETHOD(TRUE, 1174_0_gcd_EQ(x0[1], x1[1]))≥1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))∧(U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))), ≥))

We simplified constraint (26) using rules (I), (II), (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(27)    (>=(x1[2], x0[2])=TRUE∧>=(x0[2], x1[2])=TRUE∧>(x0[2], 0)=TRUE∧>=(x1[2], 0)=TRUE∧<(x1[2], x0[2])=TRUE ⇒ COND_1174_1_MAIN_INVOKEMETHOD(TRUE, 1174_0_gcd_EQ(x1[2], x0[2]))≥NonInfC∧COND_1174_1_MAIN_INVOKEMETHOD(TRUE, 1174_0_gcd_EQ(x1[2], x0[2]))≥1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x1[2], x0[2]), x0[2]))∧(U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))), ≥))

We simplified constraint (27) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(28)    (x1[2] + [-1]x0[2] ≥ 0∧x0[2] + [-1]x1[2] ≥ 0∧x0[2] + [-1] ≥ 0∧x1[2] ≥ 0∧x0[2] + [-1] + [-1]x1[2] ≥ 0 ⇒ (U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [(-2)bni_31]x0[2] ≥ 0∧[2 + (-1)bso_32] + [-6]x0[2] + [-2]x1[2] ≥ 0)

We simplified constraint (28) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(29)    (x1[2] + [-1]x0[2] ≥ 0∧x0[2] + [-1]x1[2] ≥ 0∧x0[2] + [-1] ≥ 0∧x1[2] ≥ 0∧x0[2] + [-1] + [-1]x1[2] ≥ 0 ⇒ (U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [(-2)bni_31]x0[2] ≥ 0∧[2 + (-1)bso_32] + [-6]x0[2] + [-2]x1[2] ≥ 0)

We simplified constraint (30) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(31)    (x1[2] + [-1]x0[2] ≥ 0∧x0[2] + [-1]x1[2] ≥ 0∧x0[2] + [-1] ≥ 0∧x1[2] ≥ 0∧x1[2] + [-1] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [(-2)bni_31]x0[2] ≥ 0∧[2 + (-1)bso_32] + [-6]x0[2] + [-2]x1[2] ≥ 0)

We simplified constraint (29) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(32)    (x1[2] + [-1]x0[2] ≥ 0∧x0[2] + [-1]x1[2] ≥ 0∧x0[2] + [-1] ≥ 0∧x1[2] ≥ 0∧x0[2] + [-1] + [-1]x1[2] ≥ 0 ⇒ (U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [(-2)bni_31]x0[2] ≥ 0∧[2 + (-1)bso_32] + [-6]x0[2] + [-2]x1[2] ≥ 0)

We simplified constraint (31) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(33)    (x1[2] + [-1]x0[2] ≥ 0∧x0[2] + [-1]x1[2] ≥ 0∧x0[2] + [-1] ≥ 0∧x1[2] ≥ 0∧x1[2] + [-1] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [(-2)bni_31]x0[2] ≥ 0∧[2 + (-1)bso_32] + [-6]x0[2] + [-2]x1[2] ≥ 0)

We solved constraint (32) using rule (IDP_SMT_SPLIT).We solved constraint (33) using rule (IDP_SMT_SPLIT).

For Pair 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[0], x1[0])) → COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0])) the following chains were created:

We consider the chain 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[0], x1[0])) → COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0])), COND_1174_1_MAIN_INVOKEMETHOD(TRUE, 1174_0_gcd_EQ(x0[1], x1[1])) → 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1])) which results in the following constraint:
(34)    (&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0])))=TRUE∧1174_0_gcd_EQ(x0[0], x1[0])=1174_0_gcd_EQ(x0[1], x1[1]) ⇒ 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[0], x1[0]))≥NonInfC∧1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[0], x1[0]))≥COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0]))∧(U^Increasing(COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0]))), ≥))

We simplified constraint (34) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraints:
(35)    (>(x1[0], 0)=TRUE∧>=(x0[0], 0)=TRUE∧<(x0[0], x1[0])=TRUE ⇒ 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[0], x1[0]))≥NonInfC∧1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[0], x1[0]))≥COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0]))∧(U^Increasing(COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0]))), ≥))

(36)    (>(x1[0], 0)=TRUE∧>=(x0[0], 0)=TRUE∧>(x0[0], x1[0])=TRUE ⇒ 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[0], x1[0]))≥NonInfC∧1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[0], x1[0]))≥COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0]))∧(U^Increasing(COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0]))), ≥))

We simplified constraint (35) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(37)    (x1[0] + [-1] ≥ 0∧x0[0] ≥ 0∧x1[0] + [-1] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0]))), ≥)∧[(-1)Bound*bni_33] + [bni_33]x1[0] ≥ 0∧[-3 + (-1)bso_34] + [3]x1[0] ≥ 0)

We simplified constraint (36) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(38)    (x1[0] + [-1] ≥ 0∧x0[0] ≥ 0∧x0[0] + [-1] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0]))), ≥)∧[(-1)Bound*bni_33] + [bni_33]x1[0] ≥ 0∧[-3 + (-1)bso_34] + [3]x1[0] ≥ 0)

We simplified constraint (37) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(39)    (x1[0] + [-1] ≥ 0∧x0[0] ≥ 0∧x1[0] + [-1] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0]))), ≥)∧[(-1)Bound*bni_33] + [bni_33]x1[0] ≥ 0∧[-3 + (-1)bso_34] + [3]x1[0] ≥ 0)

We simplified constraint (38) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(40)    (x1[0] + [-1] ≥ 0∧x0[0] ≥ 0∧x0[0] + [-1] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0]))), ≥)∧[(-1)Bound*bni_33] + [bni_33]x1[0] ≥ 0∧[-3 + (-1)bso_34] + [3]x1[0] ≥ 0)

We simplified constraint (39) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(41)    (x1[0] + [-1] ≥ 0∧x0[0] ≥ 0∧x1[0] + [-1] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0]))), ≥)∧[(-1)Bound*bni_33] + [bni_33]x1[0] ≥ 0∧[-3 + (-1)bso_34] + [3]x1[0] ≥ 0)

We simplified constraint (40) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(42)    (x1[0] + [-1] ≥ 0∧x0[0] ≥ 0∧x0[0] + [-1] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0]))), ≥)∧[(-1)Bound*bni_33] + [bni_33]x1[0] ≥ 0∧[-3 + (-1)bso_34] + [3]x1[0] ≥ 0)

We simplified constraint (41) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(43)    (x1[0] ≥ 0∧x0[0] ≥ 0∧x1[0] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0]))), ≥)∧[(-1)Bound*bni_33 + bni_33] + [bni_33]x1[0] ≥ 0∧[(-1)bso_34] + [3]x1[0] ≥ 0)

We simplified constraint (42) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(44)    (x1[0] ≥ 0∧x0[0] ≥ 0∧x0[0] + [-2] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0]))), ≥)∧[(-1)Bound*bni_33 + bni_33] + [bni_33]x1[0] ≥ 0∧[(-1)bso_34] + [3]x1[0] ≥ 0)

We simplified constraint (43) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(45)    (x0[0] + x1[0] ≥ 0∧x0[0] ≥ 0∧x1[0] ≥ 0 ⇒ (U^Increasing(COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0]))), ≥)∧[(-1)Bound*bni_33 + bni_33] + [bni_33]x0[0] + [bni_33]x1[0] ≥ 0∧[(-1)bso_34] + [3]x0[0] + [3]x1[0] ≥ 0)

We simplified constraint (44) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(46)    (x1[0] ≥ 0∧[2] + x1[0] + x0[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0]))), ≥)∧[(-1)Bound*bni_33 + bni_33] + [bni_33]x1[0] ≥ 0∧[(-1)bso_34] + [3]x1[0] ≥ 0)

To summarize, we get the following constraints P_≥ for the following pairs.

COND_1265_2_MAIN_INVOKEMETHOD(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[3], x1[3]), x1[3])) → 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))
- ([1] + x1[0] ≥ 0∧[1] + x0[0] + x1[0] ≥ 0∧[1] + x0[0] ≥ 0∧x0[0] ≥ 0∧[2] + x0[0] + x1[0] ≥ 0∧x1[0] ≥ 0∧x1[0] ≥ 0 ⇒ (U^Increasing(1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))), ≥)∧[(5)bni_27 + (-1)Bound*bni_27] + [(6)bni_27]x0[0] + [(4)bni_27]x1[0] ≥ 0∧[4 + (-1)bso_28] + [5]x0[0] + [4]x1[0] ≥ 0)
1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2])) → COND_1265_2_MAIN_INVOKEMETHOD(>=(x1[2], x0[2]), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]))
- (x1[2] ≥ 0∧x0[2] ≥ 0 ⇒ (U^Increasing(COND_1265_2_MAIN_INVOKEMETHOD(>=(x1[2], x0[2]), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]))), ≥)∧[(-3)bni_29 + (-1)Bound*bni_29] + [(6)bni_29]x0[2] + [(4)bni_29]x1[2] ≥ 0∧[2 + (-1)bso_30] ≥ 0)
- (x1[2] ≥ 0∧x0[2] ≥ 0 ⇒ (U^Increasing(COND_1265_2_MAIN_INVOKEMETHOD(>=(x1[2], x0[2]), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]))), ≥)∧[(-3)bni_29 + (-1)Bound*bni_29] + [(-6)bni_29]x0[2] + [(4)bni_29]x1[2] ≥ 0∧[2 + (-1)bso_30] ≥ 0)
COND_1174_1_MAIN_INVOKEMETHOD(TRUE, 1174_0_gcd_EQ(x0[1], x1[1])) → 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))
1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[0], x1[0])) → COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0]))
- (x0[0] + x1[0] ≥ 0∧x0[0] ≥ 0∧x1[0] ≥ 0 ⇒ (U^Increasing(COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0]))), ≥)∧[(-1)Bound*bni_33 + bni_33] + [bni_33]x0[0] + [bni_33]x1[0] ≥ 0∧[(-1)bso_34] + [3]x0[0] + [3]x1[0] ≥ 0)
- (x1[0] ≥ 0∧[2] + x1[0] + x0[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0]))), ≥)∧[(-1)Bound*bni_33 + bni_33] + [bni_33]x1[0] ≥ 0∧[(-1)bso_34] + [3]x1[0] ≥ 0)

POL(TRUE) = [3]
POL(FALSE) = 0
POL(COND_1265_2_MAIN_INVOKEMETHOD(x₁, x₂)) = [-1] + [2]x₂
POL(1265_1_gcd_InvokeMethod(x₁, x₂)) = [-1] + [2]x₂ + [-1]x₁
POL(1265_0_mod_LE(x₁, x₂)) = [1] + [-1]x₁
POL(1174_1_MAIN_INVOKEMETHOD(x₁)) = [1] + [-1]x₁
POL(1174_0_gcd_EQ(x₁, x₂)) = [1] + [-1]x₂
POL(1265_2_MAIN_INVOKEMETHOD(x₁)) = [1] + [2]x₁
POL(>=(x₁, x₂)) = [-1]
POL(COND_1174_1_MAIN_INVOKEMETHOD(x₁, x₂)) = [2]x₂ + [-1]x₁
POL(&&(x₁, x₂)) = [-1]
POL(>(x₁, x₂)) = [-1]
POL(0) = 0
POL(!(x₁)) = [-1]
POL(=(x₁, x₂)) = [-1]

The following pairs are in P_>:

COND_1265_2_MAIN_INVOKEMETHOD(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[3], x1[3]), x1[3])) → 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))
1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2])) → COND_1265_2_MAIN_INVOKEMETHOD(>=(x1[2], x0[2]), 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]))
COND_1174_1_MAIN_INVOKEMETHOD(TRUE, 1174_0_gcd_EQ(x0[1], x1[1])) → 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))

The following pairs are in P_bound:

COND_1265_2_MAIN_INVOKEMETHOD(TRUE, 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[3], x1[3]), x1[3])) → 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x1[3], x0[3]))
COND_1174_1_MAIN_INVOKEMETHOD(TRUE, 1174_0_gcd_EQ(x0[1], x1[1])) → 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[1], x1[1]), x1[1]))
1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[0], x1[0])) → COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0]))

The following pairs are in P_≥:

1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[0], x1[0])) → COND_1174_1_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], 0), >=(x0[0], 0)), !(=(x0[0], x1[0]))), 1174_0_gcd_EQ(x0[0], x1[0]))

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): 1174_1_MAIN_INVOKEMETHOD(1174_0_gcd_EQ(x0[0], x1[0])) → COND_1174_1_MAIN_INVOKEMETHOD(x1[0] > 0 && x0[0] >= 0 && !(x0[0] = x1[0]), 1174_0_gcd_EQ(x0[0], x1[0]))

The set Q consists of the following terms:
1174_1_main_InvokeMethod(1174_0_gcd_EQ(x0, 0))

(14) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node.

(15) TRUE

(16) 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

R is empty.

The integer pair graph contains the following rules and edges:
(2): 1265_2_MAIN_INVOKEMETHOD(1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2])) → COND_1265_2_MAIN_INVOKEMETHOD(x1[2] >= x0[2], 1265_1_gcd_InvokeMethod(1265_0_mod_LE(x0[2], x1[2]), x1[2]))

The set Q consists of the following terms:
1174_1_main_InvokeMethod(1174_0_gcd_EQ(x0, 0))

(17) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node.

(0) Obligation:

(1) JBC2FIG (SOUND transformation)

(2) Obligation:

(3) FIGtoITRSProof (SOUND transformation)

(4) Obligation:

(5) IDPNonInfProof (SOUND transformation)

(6) Obligation:

(7) IDependencyGraphProof (EQUIVALENT transformation)

(8) Obligation:

(9) UsableRulesProof (EQUIVALENT transformation)

(10) Obligation:

(11) IDPNonInfProof (SOUND transformation)

(12) Complex Obligation (AND)

(13) Obligation:

(14) IDependencyGraphProof (EQUIVALENT transformation)

(15) TRUE

(16) Obligation:

(17) IDependencyGraphProof (EQUIVALENT transformation)

(18) TRUE