Termination proof of /tmp/tmpBrRUtI/GCD4.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 TRUE

(0) Obligation:

JBC Problem based on JBC Program:
Manifest-Version: 1.0 Created-By: 1.6.0_16 (Sun Microsystems Inc.) Main-Class: GCD4

public class GCD4 {
  public static int mod(int a, int b) {
    while(a>=b && b > 0) {
      a -= b;
    }
    return a;
  }

  public static int gcd(int a, int b) {
    int tmp;
    while(b > 0 && a > 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:
GCD4.main([Ljava/lang/String;)V: Graph of 188 nodes with 1 SCC.

(3) FIGtoITRSProof (SOUND transformation)

Transformed FIGraph SCCs to IDPs. Logs:

Log for SCC 0:

Generated 33 rules for P and 8 rules for R.

Combined rules. Obtained 2 rules for P and 0 rules for R.

Filtered ground terms:

1329_0_mod_LT(x1, x2, x3, x4, x5) → 1329_0_mod_LT(x2, x3, x4, x5)

Filtered duplicate args:

1329_0_mod_LT(x1, x2, x3, x4) → 1329_0_mod_LT(x3, x4)
1329_1_gcd_InvokeMethod(x1, x2, x3) → 1329_1_gcd_InvokeMethod(x1, x3)

Combined rules. Obtained 2 rules for P and 0 rules for R.

Finished conversion. Obtained 2 rules for P and 0 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

R is empty.

The integer pair graph contains the following rules and edges:
(0): 1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[0], x1[0]), x1[0])) → COND_1329_2_MAIN_INVOKEMETHOD(x1[0] > x0[0] && x1[0] > 0 && x0[0] > 0, 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[0], x1[0]), x1[0]))
(1): COND_1329_2_MAIN_INVOKEMETHOD(TRUE, 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[1], x1[1]), x1[1])) → 1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x1[1], x0[1]), x0[1]))
(2): 1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[2], x1[2]), x1[2])) → COND_1329_2_MAIN_INVOKEMETHOD1(x1[2] > 0 && x1[2] <= x0[2], 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[2], x1[2]), x1[2]))
(3): COND_1329_2_MAIN_INVOKEMETHOD1(TRUE, 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[3], x1[3]), x1[3])) → 1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[3] - x1[3], x1[3]), x1[3]))

(0) -> (1), if ((x1[0] > x0[0] && x1[0] > 0 && x0[0] > 0 →^* TRUE)∧(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[0], x1[0]), x1[0]) →^* 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[1], x1[1]), x1[1])))

(1) -> (0), if ((1329_1_gcd_InvokeMethod(1329_0_mod_LT(x1[1], x0[1]), x0[1]) →^* 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[0], x1[0]), x1[0])))

(1) -> (2), if ((1329_1_gcd_InvokeMethod(1329_0_mod_LT(x1[1], x0[1]), x0[1]) →^* 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[2], x1[2]), x1[2])))

(2) -> (3), if ((x1[2] > 0 && x1[2] <= x0[2] →^* TRUE)∧(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[2], x1[2]), x1[2]) →^* 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[3], x1[3]), x1[3])))

(3) -> (0), if ((1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[3] - x1[3], x1[3]), x1[3]) →^* 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[0], x1[0]), x1[0])))

(3) -> (2), if ((1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[3] - x1[3], x1[3]), x1[3]) →^* 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[2], x1[2]), x1[2])))

The set Q is empty.

(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 1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0, x1), x1)) → COND_1329_2_MAIN_INVOKEMETHOD(&&(&&(>(x1, x0), >(x1, 0)), >(x0, 0)), 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0, x1), x1)) the following chains were created:

We consider the chain 1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[0], x1[0]), x1[0])) → COND_1329_2_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], x0[0]), >(x1[0], 0)), >(x0[0], 0)), 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[0], x1[0]), x1[0])), COND_1329_2_MAIN_INVOKEMETHOD(TRUE, 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[1], x1[1]), x1[1])) → 1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x1[1], x0[1]), x0[1])) which results in the following constraint:
(1)    (&&(&&(>(x1[0], x0[0]), >(x1[0], 0)), >(x0[0], 0))=TRUE∧1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[0], x1[0]), x1[0])=1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[1], x1[1]), x1[1]) ⇒ 1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[0], x1[0]), x1[0]))≥NonInfC∧1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[0], x1[0]), x1[0]))≥COND_1329_2_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], x0[0]), >(x1[0], 0)), >(x0[0], 0)), 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[0], x1[0]), x1[0]))∧(U^Increasing(COND_1329_2_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], x0[0]), >(x1[0], 0)), >(x0[0], 0)), 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[0], x1[0]), x1[0]))), ≥))

We simplified constraint (1) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(2)    (>(x0[0], 0)=TRUE∧>(x1[0], x0[0])=TRUE∧>(x1[0], 0)=TRUE ⇒ 1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[0], x1[0]), x1[0]))≥NonInfC∧1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[0], x1[0]), x1[0]))≥COND_1329_2_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], x0[0]), >(x1[0], 0)), >(x0[0], 0)), 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[0], x1[0]), x1[0]))∧(U^Increasing(COND_1329_2_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], x0[0]), >(x1[0], 0)), >(x0[0], 0)), 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[0], x1[0]), x1[0]))), ≥))

We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(3)    (x0[0] + [-1] ≥ 0∧x1[0] + [-1] + [-1]x0[0] ≥ 0∧x1[0] + [-1] ≥ 0 ⇒ (U^Increasing(COND_1329_2_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], x0[0]), >(x1[0], 0)), >(x0[0], 0)), 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[0], x1[0]), x1[0]))), ≥)∧[bni_20 + (-1)Bound*bni_20] + [(2)bni_20]x1[0] + [bni_20]x0[0] ≥ 0∧[(-1)bso_21] ≥ 0)

We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(4)    (x0[0] + [-1] ≥ 0∧x1[0] + [-1] + [-1]x0[0] ≥ 0∧x1[0] + [-1] ≥ 0 ⇒ (U^Increasing(COND_1329_2_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], x0[0]), >(x1[0], 0)), >(x0[0], 0)), 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[0], x1[0]), x1[0]))), ≥)∧[bni_20 + (-1)Bound*bni_20] + [(2)bni_20]x1[0] + [bni_20]x0[0] ≥ 0∧[(-1)bso_21] ≥ 0)

We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(5)    (x0[0] + [-1] ≥ 0∧x1[0] + [-1] + [-1]x0[0] ≥ 0∧x1[0] + [-1] ≥ 0 ⇒ (U^Increasing(COND_1329_2_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], x0[0]), >(x1[0], 0)), >(x0[0], 0)), 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[0], x1[0]), x1[0]))), ≥)∧[bni_20 + (-1)Bound*bni_20] + [(2)bni_20]x1[0] + [bni_20]x0[0] ≥ 0∧[(-1)bso_21] ≥ 0)

We simplified constraint (5) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(6)    (x0[0] ≥ 0∧x1[0] + [-2] + [-1]x0[0] ≥ 0∧x1[0] + [-1] ≥ 0 ⇒ (U^Increasing(COND_1329_2_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], x0[0]), >(x1[0], 0)), >(x0[0], 0)), 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[0], x1[0]), x1[0]))), ≥)∧[(2)bni_20 + (-1)Bound*bni_20] + [(2)bni_20]x1[0] + [bni_20]x0[0] ≥ 0∧[(-1)bso_21] ≥ 0)

We simplified constraint (6) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(7)    (x0[0] ≥ 0∧x1[0] ≥ 0∧[1] + x0[0] + x1[0] ≥ 0 ⇒ (U^Increasing(COND_1329_2_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], x0[0]), >(x1[0], 0)), >(x0[0], 0)), 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[0], x1[0]), x1[0]))), ≥)∧[(6)bni_20 + (-1)Bound*bni_20] + [(3)bni_20]x0[0] + [(2)bni_20]x1[0] ≥ 0∧[(-1)bso_21] ≥ 0)

For Pair COND_1329_2_MAIN_INVOKEMETHOD(TRUE, 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0, x1), x1)) → 1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x1, x0), x0)) the following chains were created:

We consider the chain 1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[0], x1[0]), x1[0])) → COND_1329_2_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], x0[0]), >(x1[0], 0)), >(x0[0], 0)), 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[0], x1[0]), x1[0])), COND_1329_2_MAIN_INVOKEMETHOD(TRUE, 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[1], x1[1]), x1[1])) → 1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x1[1], x0[1]), x0[1])), 1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[0], x1[0]), x1[0])) → COND_1329_2_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], x0[0]), >(x1[0], 0)), >(x0[0], 0)), 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[0], x1[0]), x1[0])) which results in the following constraint:
(8)    (&&(&&(>(x1[0], x0[0]), >(x1[0], 0)), >(x0[0], 0))=TRUE∧1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[0], x1[0]), x1[0])=1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[1], x1[1]), x1[1])∧1329_1_gcd_InvokeMethod(1329_0_mod_LT(x1[1], x0[1]), x0[1])=1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[0]1, x1[0]1), x1[0]1) ⇒ COND_1329_2_MAIN_INVOKEMETHOD(TRUE, 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[1], x1[1]), x1[1]))≥NonInfC∧COND_1329_2_MAIN_INVOKEMETHOD(TRUE, 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[1], x1[1]), x1[1]))≥1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x1[1], x0[1]), x0[1]))∧(U^Increasing(1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x1[1], x0[1]), x0[1]))), ≥))

We simplified constraint (8) using rules (I), (II), (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(9)    (>(x0[0], 0)=TRUE∧>(x1[0], x0[0])=TRUE∧>(x1[0], 0)=TRUE ⇒ COND_1329_2_MAIN_INVOKEMETHOD(TRUE, 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[0], x1[0]), x1[0]))≥NonInfC∧COND_1329_2_MAIN_INVOKEMETHOD(TRUE, 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[0], x1[0]), x1[0]))≥1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x1[0], x0[0]), x0[0]))∧(U^Increasing(1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x1[1], x0[1]), x0[1]))), ≥))

We simplified constraint (9) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(10)    (x0[0] + [-1] ≥ 0∧x1[0] + [-1] + [-1]x0[0] ≥ 0∧x1[0] + [-1] ≥ 0 ⇒ (U^Increasing(1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x1[1], x0[1]), x0[1]))), ≥)∧[bni_22 + (-1)Bound*bni_22] + [(2)bni_22]x1[0] + [bni_22]x0[0] ≥ 0∧[(-1)bso_23] + x1[0] + [-1]x0[0] ≥ 0)

We simplified constraint (10) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(11)    (x0[0] + [-1] ≥ 0∧x1[0] + [-1] + [-1]x0[0] ≥ 0∧x1[0] + [-1] ≥ 0 ⇒ (U^Increasing(1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x1[1], x0[1]), x0[1]))), ≥)∧[bni_22 + (-1)Bound*bni_22] + [(2)bni_22]x1[0] + [bni_22]x0[0] ≥ 0∧[(-1)bso_23] + x1[0] + [-1]x0[0] ≥ 0)

We simplified constraint (11) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(12)    (x0[0] + [-1] ≥ 0∧x1[0] + [-1] + [-1]x0[0] ≥ 0∧x1[0] + [-1] ≥ 0 ⇒ (U^Increasing(1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x1[1], x0[1]), x0[1]))), ≥)∧[bni_22 + (-1)Bound*bni_22] + [(2)bni_22]x1[0] + [bni_22]x0[0] ≥ 0∧[(-1)bso_23] + x1[0] + [-1]x0[0] ≥ 0)

We simplified constraint (12) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(13)    (x0[0] ≥ 0∧x1[0] + [-2] + [-1]x0[0] ≥ 0∧x1[0] + [-1] ≥ 0 ⇒ (U^Increasing(1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x1[1], x0[1]), x0[1]))), ≥)∧[(2)bni_22 + (-1)Bound*bni_22] + [(2)bni_22]x1[0] + [bni_22]x0[0] ≥ 0∧[-1 + (-1)bso_23] + x1[0] + [-1]x0[0] ≥ 0)

We simplified constraint (13) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(14)    (x0[0] ≥ 0∧x1[0] ≥ 0∧[1] + x0[0] + x1[0] ≥ 0 ⇒ (U^Increasing(1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x1[1], x0[1]), x0[1]))), ≥)∧[(6)bni_22 + (-1)Bound*bni_22] + [(3)bni_22]x0[0] + [(2)bni_22]x1[0] ≥ 0∧[1 + (-1)bso_23] + x1[0] ≥ 0)
We consider the chain 1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[0], x1[0]), x1[0])) → COND_1329_2_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], x0[0]), >(x1[0], 0)), >(x0[0], 0)), 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[0], x1[0]), x1[0])), COND_1329_2_MAIN_INVOKEMETHOD(TRUE, 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[1], x1[1]), x1[1])) → 1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x1[1], x0[1]), x0[1])), 1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[2], x1[2]), x1[2])) → COND_1329_2_MAIN_INVOKEMETHOD1(&&(>(x1[2], 0), <=(x1[2], x0[2])), 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[2], x1[2]), x1[2])) which results in the following constraint:
(15)    (&&(&&(>(x1[0], x0[0]), >(x1[0], 0)), >(x0[0], 0))=TRUE∧1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[0], x1[0]), x1[0])=1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[1], x1[1]), x1[1])∧1329_1_gcd_InvokeMethod(1329_0_mod_LT(x1[1], x0[1]), x0[1])=1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[2], x1[2]), x1[2]) ⇒ COND_1329_2_MAIN_INVOKEMETHOD(TRUE, 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[1], x1[1]), x1[1]))≥NonInfC∧COND_1329_2_MAIN_INVOKEMETHOD(TRUE, 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[1], x1[1]), x1[1]))≥1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x1[1], x0[1]), x0[1]))∧(U^Increasing(1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x1[1], x0[1]), x0[1]))), ≥))

We simplified constraint (15) using rules (I), (II), (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(16)    (>(x0[0], 0)=TRUE∧>(x1[0], x0[0])=TRUE∧>(x1[0], 0)=TRUE ⇒ COND_1329_2_MAIN_INVOKEMETHOD(TRUE, 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[0], x1[0]), x1[0]))≥NonInfC∧COND_1329_2_MAIN_INVOKEMETHOD(TRUE, 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[0], x1[0]), x1[0]))≥1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x1[0], x0[0]), x0[0]))∧(U^Increasing(1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x1[1], x0[1]), x0[1]))), ≥))

We simplified constraint (16) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(17)    (x0[0] + [-1] ≥ 0∧x1[0] + [-1] + [-1]x0[0] ≥ 0∧x1[0] + [-1] ≥ 0 ⇒ (U^Increasing(1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x1[1], x0[1]), x0[1]))), ≥)∧[bni_22 + (-1)Bound*bni_22] + [(2)bni_22]x1[0] + [bni_22]x0[0] ≥ 0∧[(-1)bso_23] + x1[0] + [-1]x0[0] ≥ 0)

We simplified constraint (17) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(18)    (x0[0] + [-1] ≥ 0∧x1[0] + [-1] + [-1]x0[0] ≥ 0∧x1[0] + [-1] ≥ 0 ⇒ (U^Increasing(1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x1[1], x0[1]), x0[1]))), ≥)∧[bni_22 + (-1)Bound*bni_22] + [(2)bni_22]x1[0] + [bni_22]x0[0] ≥ 0∧[(-1)bso_23] + x1[0] + [-1]x0[0] ≥ 0)

We simplified constraint (18) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(19)    (x0[0] + [-1] ≥ 0∧x1[0] + [-1] + [-1]x0[0] ≥ 0∧x1[0] + [-1] ≥ 0 ⇒ (U^Increasing(1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x1[1], x0[1]), x0[1]))), ≥)∧[bni_22 + (-1)Bound*bni_22] + [(2)bni_22]x1[0] + [bni_22]x0[0] ≥ 0∧[(-1)bso_23] + x1[0] + [-1]x0[0] ≥ 0)

We simplified constraint (19) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(20)    (x0[0] ≥ 0∧x1[0] + [-2] + [-1]x0[0] ≥ 0∧x1[0] + [-1] ≥ 0 ⇒ (U^Increasing(1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x1[1], x0[1]), x0[1]))), ≥)∧[(2)bni_22 + (-1)Bound*bni_22] + [(2)bni_22]x1[0] + [bni_22]x0[0] ≥ 0∧[-1 + (-1)bso_23] + x1[0] + [-1]x0[0] ≥ 0)

We simplified constraint (20) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(21)    (x0[0] ≥ 0∧x1[0] ≥ 0∧[1] + x0[0] + x1[0] ≥ 0 ⇒ (U^Increasing(1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x1[1], x0[1]), x0[1]))), ≥)∧[(6)bni_22 + (-1)Bound*bni_22] + [(3)bni_22]x0[0] + [(2)bni_22]x1[0] ≥ 0∧[1 + (-1)bso_23] + x1[0] ≥ 0)

For Pair 1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0, x1), x1)) → COND_1329_2_MAIN_INVOKEMETHOD1(&&(>(x1, 0), <=(x1, x0)), 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0, x1), x1)) the following chains were created:

We consider the chain 1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[2], x1[2]), x1[2])) → COND_1329_2_MAIN_INVOKEMETHOD1(&&(>(x1[2], 0), <=(x1[2], x0[2])), 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[2], x1[2]), x1[2])), COND_1329_2_MAIN_INVOKEMETHOD1(TRUE, 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[3], x1[3]), x1[3])) → 1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(-(x0[3], x1[3]), x1[3]), x1[3])) which results in the following constraint:
(22)    (&&(>(x1[2], 0), <=(x1[2], x0[2]))=TRUE∧1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[2], x1[2]), x1[2])=1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[3], x1[3]), x1[3]) ⇒ 1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[2], x1[2]), x1[2]))≥NonInfC∧1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[2], x1[2]), x1[2]))≥COND_1329_2_MAIN_INVOKEMETHOD1(&&(>(x1[2], 0), <=(x1[2], x0[2])), 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[2], x1[2]), x1[2]))∧(U^Increasing(COND_1329_2_MAIN_INVOKEMETHOD1(&&(>(x1[2], 0), <=(x1[2], x0[2])), 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[2], x1[2]), x1[2]))), ≥))

We simplified constraint (22) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(23)    (>(x1[2], 0)=TRUE∧<=(x1[2], x0[2])=TRUE ⇒ 1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[2], x1[2]), x1[2]))≥NonInfC∧1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[2], x1[2]), x1[2]))≥COND_1329_2_MAIN_INVOKEMETHOD1(&&(>(x1[2], 0), <=(x1[2], x0[2])), 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[2], x1[2]), x1[2]))∧(U^Increasing(COND_1329_2_MAIN_INVOKEMETHOD1(&&(>(x1[2], 0), <=(x1[2], x0[2])), 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[2], x1[2]), x1[2]))), ≥))

We simplified constraint (23) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(24)    (x1[2] + [-1] ≥ 0∧x0[2] + [-1]x1[2] ≥ 0 ⇒ (U^Increasing(COND_1329_2_MAIN_INVOKEMETHOD1(&&(>(x1[2], 0), <=(x1[2], x0[2])), 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[2], x1[2]), x1[2]))), ≥)∧[bni_24 + (-1)Bound*bni_24] + [(2)bni_24]x1[2] + [bni_24]x0[2] ≥ 0∧[(-1)bso_25] ≥ 0)

We simplified constraint (24) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(25)    (x1[2] + [-1] ≥ 0∧x0[2] + [-1]x1[2] ≥ 0 ⇒ (U^Increasing(COND_1329_2_MAIN_INVOKEMETHOD1(&&(>(x1[2], 0), <=(x1[2], x0[2])), 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[2], x1[2]), x1[2]))), ≥)∧[bni_24 + (-1)Bound*bni_24] + [(2)bni_24]x1[2] + [bni_24]x0[2] ≥ 0∧[(-1)bso_25] ≥ 0)

We simplified constraint (25) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(26)    (x1[2] + [-1] ≥ 0∧x0[2] + [-1]x1[2] ≥ 0 ⇒ (U^Increasing(COND_1329_2_MAIN_INVOKEMETHOD1(&&(>(x1[2], 0), <=(x1[2], x0[2])), 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[2], x1[2]), x1[2]))), ≥)∧[bni_24 + (-1)Bound*bni_24] + [(2)bni_24]x1[2] + [bni_24]x0[2] ≥ 0∧[(-1)bso_25] ≥ 0)

We simplified constraint (26) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(27)    (x1[2] ≥ 0∧x0[2] + [-1] + [-1]x1[2] ≥ 0 ⇒ (U^Increasing(COND_1329_2_MAIN_INVOKEMETHOD1(&&(>(x1[2], 0), <=(x1[2], x0[2])), 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[2], x1[2]), x1[2]))), ≥)∧[(3)bni_24 + (-1)Bound*bni_24] + [(2)bni_24]x1[2] + [bni_24]x0[2] ≥ 0∧[(-1)bso_25] ≥ 0)

We simplified constraint (27) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(28)    (x1[2] ≥ 0∧x0[2] ≥ 0 ⇒ (U^Increasing(COND_1329_2_MAIN_INVOKEMETHOD1(&&(>(x1[2], 0), <=(x1[2], x0[2])), 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[2], x1[2]), x1[2]))), ≥)∧[(4)bni_24 + (-1)Bound*bni_24] + [(3)bni_24]x1[2] + [bni_24]x0[2] ≥ 0∧[(-1)bso_25] ≥ 0)

For Pair COND_1329_2_MAIN_INVOKEMETHOD1(TRUE, 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0, x1), x1)) → 1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(-(x0, x1), x1), x1)) the following chains were created:

We consider the chain 1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[2], x1[2]), x1[2])) → COND_1329_2_MAIN_INVOKEMETHOD1(&&(>(x1[2], 0), <=(x1[2], x0[2])), 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[2], x1[2]), x1[2])), COND_1329_2_MAIN_INVOKEMETHOD1(TRUE, 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[3], x1[3]), x1[3])) → 1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(-(x0[3], x1[3]), x1[3]), x1[3])), 1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[0], x1[0]), x1[0])) → COND_1329_2_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], x0[0]), >(x1[0], 0)), >(x0[0], 0)), 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[0], x1[0]), x1[0])) which results in the following constraint:
(29)    (&&(>(x1[2], 0), <=(x1[2], x0[2]))=TRUE∧1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[2], x1[2]), x1[2])=1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[3], x1[3]), x1[3])∧1329_1_gcd_InvokeMethod(1329_0_mod_LT(-(x0[3], x1[3]), x1[3]), x1[3])=1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[0], x1[0]), x1[0]) ⇒ COND_1329_2_MAIN_INVOKEMETHOD1(TRUE, 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[3], x1[3]), x1[3]))≥NonInfC∧COND_1329_2_MAIN_INVOKEMETHOD1(TRUE, 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[3], x1[3]), x1[3]))≥1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(-(x0[3], x1[3]), x1[3]), x1[3]))∧(U^Increasing(1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(-(x0[3], x1[3]), x1[3]), x1[3]))), ≥))

We simplified constraint (29) using rules (I), (II), (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(30)    (>(x1[2], 0)=TRUE∧<=(x1[2], x0[2])=TRUE ⇒ COND_1329_2_MAIN_INVOKEMETHOD1(TRUE, 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[2], x1[2]), x1[2]))≥NonInfC∧COND_1329_2_MAIN_INVOKEMETHOD1(TRUE, 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[2], x1[2]), x1[2]))≥1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(-(x0[2], x1[2]), x1[2]), x1[2]))∧(U^Increasing(1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(-(x0[3], x1[3]), x1[3]), x1[3]))), ≥))

We simplified constraint (30) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(31)    (x1[2] + [-1] ≥ 0∧x0[2] + [-1]x1[2] ≥ 0 ⇒ (U^Increasing(1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(-(x0[3], x1[3]), x1[3]), x1[3]))), ≥)∧[bni_26 + (-1)Bound*bni_26] + [(2)bni_26]x1[2] + [bni_26]x0[2] ≥ 0∧[(-1)bso_27] + x1[2] ≥ 0)

We simplified constraint (31) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(32)    (x1[2] + [-1] ≥ 0∧x0[2] + [-1]x1[2] ≥ 0 ⇒ (U^Increasing(1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(-(x0[3], x1[3]), x1[3]), x1[3]))), ≥)∧[bni_26 + (-1)Bound*bni_26] + [(2)bni_26]x1[2] + [bni_26]x0[2] ≥ 0∧[(-1)bso_27] + x1[2] ≥ 0)

We simplified constraint (32) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(33)    (x1[2] + [-1] ≥ 0∧x0[2] + [-1]x1[2] ≥ 0 ⇒ (U^Increasing(1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(-(x0[3], x1[3]), x1[3]), x1[3]))), ≥)∧[bni_26 + (-1)Bound*bni_26] + [(2)bni_26]x1[2] + [bni_26]x0[2] ≥ 0∧[(-1)bso_27] + x1[2] ≥ 0)

We simplified constraint (33) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(34)    (x1[2] ≥ 0∧x0[2] + [-1] + [-1]x1[2] ≥ 0 ⇒ (U^Increasing(1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(-(x0[3], x1[3]), x1[3]), x1[3]))), ≥)∧[(3)bni_26 + (-1)Bound*bni_26] + [(2)bni_26]x1[2] + [bni_26]x0[2] ≥ 0∧[1 + (-1)bso_27] + x1[2] ≥ 0)

We simplified constraint (34) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(35)    (x1[2] ≥ 0∧x0[2] ≥ 0 ⇒ (U^Increasing(1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(-(x0[3], x1[3]), x1[3]), x1[3]))), ≥)∧[(4)bni_26 + (-1)Bound*bni_26] + [(3)bni_26]x1[2] + [bni_26]x0[2] ≥ 0∧[1 + (-1)bso_27] + x1[2] ≥ 0)
We consider the chain 1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[2], x1[2]), x1[2])) → COND_1329_2_MAIN_INVOKEMETHOD1(&&(>(x1[2], 0), <=(x1[2], x0[2])), 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[2], x1[2]), x1[2])), COND_1329_2_MAIN_INVOKEMETHOD1(TRUE, 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[3], x1[3]), x1[3])) → 1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(-(x0[3], x1[3]), x1[3]), x1[3])), 1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[2], x1[2]), x1[2])) → COND_1329_2_MAIN_INVOKEMETHOD1(&&(>(x1[2], 0), <=(x1[2], x0[2])), 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[2], x1[2]), x1[2])) which results in the following constraint:
(36)    (&&(>(x1[2], 0), <=(x1[2], x0[2]))=TRUE∧1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[2], x1[2]), x1[2])=1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[3], x1[3]), x1[3])∧1329_1_gcd_InvokeMethod(1329_0_mod_LT(-(x0[3], x1[3]), x1[3]), x1[3])=1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[2]1, x1[2]1), x1[2]1) ⇒ COND_1329_2_MAIN_INVOKEMETHOD1(TRUE, 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[3], x1[3]), x1[3]))≥NonInfC∧COND_1329_2_MAIN_INVOKEMETHOD1(TRUE, 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[3], x1[3]), x1[3]))≥1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(-(x0[3], x1[3]), x1[3]), x1[3]))∧(U^Increasing(1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(-(x0[3], x1[3]), x1[3]), x1[3]))), ≥))

We simplified constraint (36) using rules (I), (II), (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(37)    (>(x1[2], 0)=TRUE∧<=(x1[2], x0[2])=TRUE ⇒ COND_1329_2_MAIN_INVOKEMETHOD1(TRUE, 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[2], x1[2]), x1[2]))≥NonInfC∧COND_1329_2_MAIN_INVOKEMETHOD1(TRUE, 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[2], x1[2]), x1[2]))≥1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(-(x0[2], x1[2]), x1[2]), x1[2]))∧(U^Increasing(1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(-(x0[3], x1[3]), x1[3]), x1[3]))), ≥))

We simplified constraint (37) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(38)    (x1[2] + [-1] ≥ 0∧x0[2] + [-1]x1[2] ≥ 0 ⇒ (U^Increasing(1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(-(x0[3], x1[3]), x1[3]), x1[3]))), ≥)∧[bni_26 + (-1)Bound*bni_26] + [(2)bni_26]x1[2] + [bni_26]x0[2] ≥ 0∧[(-1)bso_27] + x1[2] ≥ 0)

We simplified constraint (38) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(39)    (x1[2] + [-1] ≥ 0∧x0[2] + [-1]x1[2] ≥ 0 ⇒ (U^Increasing(1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(-(x0[3], x1[3]), x1[3]), x1[3]))), ≥)∧[bni_26 + (-1)Bound*bni_26] + [(2)bni_26]x1[2] + [bni_26]x0[2] ≥ 0∧[(-1)bso_27] + x1[2] ≥ 0)

We simplified constraint (39) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(40)    (x1[2] + [-1] ≥ 0∧x0[2] + [-1]x1[2] ≥ 0 ⇒ (U^Increasing(1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(-(x0[3], x1[3]), x1[3]), x1[3]))), ≥)∧[bni_26 + (-1)Bound*bni_26] + [(2)bni_26]x1[2] + [bni_26]x0[2] ≥ 0∧[(-1)bso_27] + x1[2] ≥ 0)

We simplified constraint (40) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(41)    (x1[2] ≥ 0∧x0[2] + [-1] + [-1]x1[2] ≥ 0 ⇒ (U^Increasing(1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(-(x0[3], x1[3]), x1[3]), x1[3]))), ≥)∧[(3)bni_26 + (-1)Bound*bni_26] + [(2)bni_26]x1[2] + [bni_26]x0[2] ≥ 0∧[1 + (-1)bso_27] + x1[2] ≥ 0)

We simplified constraint (41) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(42)    (x1[2] ≥ 0∧x0[2] ≥ 0 ⇒ (U^Increasing(1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(-(x0[3], x1[3]), x1[3]), x1[3]))), ≥)∧[(4)bni_26 + (-1)Bound*bni_26] + [(3)bni_26]x1[2] + [bni_26]x0[2] ≥ 0∧[1 + (-1)bso_27] + x1[2] ≥ 0)

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

1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0, x1), x1)) → COND_1329_2_MAIN_INVOKEMETHOD(&&(&&(>(x1, x0), >(x1, 0)), >(x0, 0)), 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0, x1), x1))
- (x0[0] ≥ 0∧x1[0] ≥ 0∧[1] + x0[0] + x1[0] ≥ 0 ⇒ (U^Increasing(COND_1329_2_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], x0[0]), >(x1[0], 0)), >(x0[0], 0)), 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[0], x1[0]), x1[0]))), ≥)∧[(6)bni_20 + (-1)Bound*bni_20] + [(3)bni_20]x0[0] + [(2)bni_20]x1[0] ≥ 0∧[(-1)bso_21] ≥ 0)
COND_1329_2_MAIN_INVOKEMETHOD(TRUE, 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0, x1), x1)) → 1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x1, x0), x0))
- (x0[0] ≥ 0∧x1[0] ≥ 0∧[1] + x0[0] + x1[0] ≥ 0 ⇒ (U^Increasing(1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x1[1], x0[1]), x0[1]))), ≥)∧[(6)bni_22 + (-1)Bound*bni_22] + [(3)bni_22]x0[0] + [(2)bni_22]x1[0] ≥ 0∧[1 + (-1)bso_23] + x1[0] ≥ 0)
- (x0[0] ≥ 0∧x1[0] ≥ 0∧[1] + x0[0] + x1[0] ≥ 0 ⇒ (U^Increasing(1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x1[1], x0[1]), x0[1]))), ≥)∧[(6)bni_22 + (-1)Bound*bni_22] + [(3)bni_22]x0[0] + [(2)bni_22]x1[0] ≥ 0∧[1 + (-1)bso_23] + x1[0] ≥ 0)
1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0, x1), x1)) → COND_1329_2_MAIN_INVOKEMETHOD1(&&(>(x1, 0), <=(x1, x0)), 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0, x1), x1))
- (x1[2] ≥ 0∧x0[2] ≥ 0 ⇒ (U^Increasing(COND_1329_2_MAIN_INVOKEMETHOD1(&&(>(x1[2], 0), <=(x1[2], x0[2])), 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[2], x1[2]), x1[2]))), ≥)∧[(4)bni_24 + (-1)Bound*bni_24] + [(3)bni_24]x1[2] + [bni_24]x0[2] ≥ 0∧[(-1)bso_25] ≥ 0)
COND_1329_2_MAIN_INVOKEMETHOD1(TRUE, 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0, x1), x1)) → 1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(-(x0, x1), x1), x1))
- (x1[2] ≥ 0∧x0[2] ≥ 0 ⇒ (U^Increasing(1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(-(x0[3], x1[3]), x1[3]), x1[3]))), ≥)∧[(4)bni_26 + (-1)Bound*bni_26] + [(3)bni_26]x1[2] + [bni_26]x0[2] ≥ 0∧[1 + (-1)bso_27] + x1[2] ≥ 0)
- (x1[2] ≥ 0∧x0[2] ≥ 0 ⇒ (U^Increasing(1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(-(x0[3], x1[3]), x1[3]), x1[3]))), ≥)∧[(4)bni_26 + (-1)Bound*bni_26] + [(3)bni_26]x1[2] + [bni_26]x0[2] ≥ 0∧[1 + (-1)bso_27] + x1[2] ≥ 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) = 0
POL(FALSE) = [3]
POL(1329_2_MAIN_INVOKEMETHOD(x₁)) = [-1] + [-1]x₁
POL(1329_1_gcd_InvokeMethod(x₁, x₂)) = [-1] + [-1]x₂ + x₁
POL(1329_0_mod_LT(x₁, x₂)) = [-1] + [-1]x₂ + [-1]x₁
POL(COND_1329_2_MAIN_INVOKEMETHOD(x₁, x₂)) = [-1] + [-1]x₂
POL(&&(x₁, x₂)) = [-1]
POL(>(x₁, x₂)) = [-1]
POL(0) = 0
POL(COND_1329_2_MAIN_INVOKEMETHOD1(x₁, x₂)) = [-1] + [-1]x₂
POL(<=(x₁, x₂)) = [-1]
POL(-(x₁, x₂)) = x₁ + [-1]x₂

The following pairs are in P_>:

COND_1329_2_MAIN_INVOKEMETHOD(TRUE, 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[1], x1[1]), x1[1])) → 1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x1[1], x0[1]), x0[1]))
COND_1329_2_MAIN_INVOKEMETHOD1(TRUE, 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[3], x1[3]), x1[3])) → 1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(-(x0[3], x1[3]), x1[3]), x1[3]))

The following pairs are in P_bound:

1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[0], x1[0]), x1[0])) → COND_1329_2_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], x0[0]), >(x1[0], 0)), >(x0[0], 0)), 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[0], x1[0]), x1[0]))
COND_1329_2_MAIN_INVOKEMETHOD(TRUE, 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[1], x1[1]), x1[1])) → 1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x1[1], x0[1]), x0[1]))
1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[2], x1[2]), x1[2])) → COND_1329_2_MAIN_INVOKEMETHOD1(&&(>(x1[2], 0), <=(x1[2], x0[2])), 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[2], x1[2]), x1[2]))
COND_1329_2_MAIN_INVOKEMETHOD1(TRUE, 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[3], x1[3]), x1[3])) → 1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(-(x0[3], x1[3]), x1[3]), x1[3]))

The following pairs are in P_≥:

1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[0], x1[0]), x1[0])) → COND_1329_2_MAIN_INVOKEMETHOD(&&(&&(>(x1[0], x0[0]), >(x1[0], 0)), >(x0[0], 0)), 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[0], x1[0]), x1[0]))
1329_2_MAIN_INVOKEMETHOD(1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[2], x1[2]), x1[2])) → COND_1329_2_MAIN_INVOKEMETHOD1(&&(>(x1[2], 0), <=(x1[2], x0[2])), 1329_1_gcd_InvokeMethod(1329_0_mod_LT(x0[2], x1[2]), x1[2]))

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

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

(6) Obligation: