Termination of the given JBC could be proven:

0 JBC
↳1 JBC2FIG (⇒)
↳2 JBCTerminationGraph
↳3 FIGtoITRSProof (⇒)
↳4 IDP
↳5 IDPNonInfProof (⇒)
↳6 AND
    ↳7 IDP
        ↳8 IDependencyGraphProof (⇔)
        ↳9 IDP
        ↳10 IDPNonInfProof (⇒)
        ↳11 IDP
        ↳12 IDependencyGraphProof (⇔)
        ↳13 IDP
        ↳14 IDPNonInfProof (⇒)
        ↳15 AND
            ↳16 IDP
                ↳17 IDependencyGraphProof (⇔)
                ↳18 TRUE
            ↳19 IDP
                ↳20 IDependencyGraphProof (⇔)
                ↳21 TRUE
    ↳22 IDP
        ↳23 IDependencyGraphProof (⇔)
        ↳24 IDP
        ↳25 IDPNonInfProof (⇒)
        ↳26 AND
            ↳27 IDP
                ↳28 IDependencyGraphProof (⇔)
                ↳29 TRUE
            ↳30 IDP
                ↳31 IDependencyGraphProof (⇔)
                ↳32 IDP
                ↳33 IDPNonInfProof (⇒)
                ↳34 AND
                    ↳35 IDP
                        ↳36 IDependencyGraphProof (⇔)
                        ↳37 TRUE
                    ↳38 IDP
                        ↳39 IDependencyGraphProof (⇔)
                        ↳40 TRUE

(0) Obligation:

JBC Problem based on JBC Program:
Manifest-Version: 1.0 Created-By: 1.6.0_16 (Sun Microsystems Inc.) Main-Class: BubbleSort 
class BubbleSort {
    public static void main(String[] args) {
	sort(new int[100]);
    }

    public static void sort(int[] x) {
	int n = x.length;
	for (int pass=1; pass < n; pass++)  // count how many times
	    // This next loop becomes shorter and shorter
	    for (int i=0; i < n - pass; i++)
		if (x[i] > x[i+1]) {
		    // exchange elements
		    int temp = x[i]; x[i] = x[i+1];  x[i+1] = temp;
		}
    }
}


(1) JBC2FIG (SOUND transformation)

Constructed FIGraph.

(2) Obligation:

FIGraph based on JBC Program:
BubbleSort.main([Ljava/lang/String;)V: Graph of 170 nodes with 1 SCC.


(3) FIGtoITRSProof (SOUND transformation)

Transformed FIGraph SCCs to IDPs. Logs:

Log for SCC 0:

Generated 58 rules for P and 102 rules for R.


Combined rules. Obtained 5 rules for P and 0 rules for R.


Filtered ground terms:


1729_1_main_InvokeMethod(x1, x2) → 1729_1_main_InvokeMethod(x1)
DATA_100(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43, x44, x45, x46, x47, x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59, x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70, x71, x72, x73, x74, x75, x76, x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87, x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99, x100) → DATA_100
ARRAY(x1, x2) → ARRAY
java.lang.Object(x1) → java.lang.Object
1729_0_sort_GE(x1, x2, x3, x4, x5, x6, x7) → 1729_0_sort_GE(x4, x5, x6, x7)
Cond_1810_1_main_InvokeMethod(x1, x2, x3) → Cond_1810_1_main_InvokeMethod(x1, x2)
1810_0_sort_LE(x1, x2, x3, x4, x5, x6, x7) → 1810_0_sort_LE(x4, x5, x6, x7)
1810_1_main_InvokeMethod(x1, x2) → 1810_1_main_InvokeMethod(x1)
Cond_1809_1_main_InvokeMethod(x1, x2, x3) → Cond_1809_1_main_InvokeMethod(x1, x2)
1809_0_sort_LE(x1, x2, x3, x4, x5, x6, x7) → 1809_0_sort_LE(x4, x5, x6, x7)
1809_1_main_InvokeMethod(x1, x2) → 1809_1_main_InvokeMethod(x1)
Cond_1729_1_main_InvokeMethod2(x1, x2, x3) → Cond_1729_1_main_InvokeMethod2(x1, x2)
Cond_1729_1_main_InvokeMethod1(x1, x2, x3) → Cond_1729_1_main_InvokeMethod1(x1, x2)
Cond_1729_1_main_InvokeMethod(x1, x2, x3) → Cond_1729_1_main_InvokeMethod(x1, x2)

Filtered duplicate args:


1729_0_sort_GE(x1, x2, x3, x4) → 1729_0_sort_GE(x1, x3, x4)

Combined rules. Obtained 5 rules for P and 0 rules for R.


Finished conversion. Obtained 5 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): 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[0], x103[0], x104[0])) → COND_1729_1_MAIN_INVOKEMETHOD(x104[0] <= x103[0] && x102[0] > 0 && 100 > x102[0] + 1 && 0 < x102[0] + 1, 1729_0_sort_GE(x102[0], x103[0], x104[0]))
(1): COND_1729_1_MAIN_INVOKEMETHOD(TRUE, 1729_0_sort_GE(x102[1], x103[1], x104[1])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[1] + 1, 0, 100 - x102[1] + 1))
(2): 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2])) → COND_1729_1_MAIN_INVOKEMETHOD1(x104[2] > x103[2] && x103[2] >= 0 && x103[2] <= 99 && 99 >= x103[2] + 1 && 1 <= x103[2] + 1, 1729_0_sort_GE(x102[2], x103[2], x104[2]))
(3): COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3])) → 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))
(4): 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[4], x103[4], x104[4])) → COND_1729_1_MAIN_INVOKEMETHOD2(x104[4] > x103[4] && x103[4] >= 0 && x103[4] <= 99 && 99 >= x103[4] + 1 && 1 <= x103[4] + 1, 1729_0_sort_GE(x102[4], x103[4], x104[4]))
(5): COND_1729_1_MAIN_INVOKEMETHOD2(TRUE, 1729_0_sort_GE(x102[5], x103[5], x104[5])) → 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5]))
(6): 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])) → COND_1809_1_MAIN_INVOKEMETHOD(x105[6] >= x104[6] && x103[6] >= 0 && x102[6] > 0, 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))
(7): COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], x103[7] + 1, 100 - x102[7]))
(8): 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8])) → COND_1810_1_MAIN_INVOKEMETHOD(x3[8] < x2[8] && x1[8] >= 0 && x1[8] <= 99 && x0[8] > 0 && 99 >= x1[8] + 1 && 1 <= x1[8] + 1, 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))
(9): COND_1810_1_MAIN_INVOKEMETHOD(TRUE, 1810_0_sort_LE(x0[9], x1[9], x2[9], x3[9])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0[9], x1[9] + 1, 100 - x0[9]))

(0) -> (1), if ((x104[0] <= x103[0] && x102[0] > 0 && 100 > x102[0] + 1 && 0 < x102[0] + 1 →* TRUE)∧(1729_0_sort_GE(x102[0], x103[0], x104[0]) →* 1729_0_sort_GE(x102[1], x103[1], x104[1])))


(1) -> (0), if ((1729_0_sort_GE(x102[1] + 1, 0, 100 - x102[1] + 1) →* 1729_0_sort_GE(x102[0], x103[0], x104[0])))


(1) -> (2), if ((1729_0_sort_GE(x102[1] + 1, 0, 100 - x102[1] + 1) →* 1729_0_sort_GE(x102[2], x103[2], x104[2])))


(1) -> (4), if ((1729_0_sort_GE(x102[1] + 1, 0, 100 - x102[1] + 1) →* 1729_0_sort_GE(x102[4], x103[4], x104[4])))


(2) -> (3), if ((x104[2] > x103[2] && x103[2] >= 0 && x103[2] <= 99 && 99 >= x103[2] + 1 && 1 <= x103[2] + 1 →* TRUE)∧(1729_0_sort_GE(x102[2], x103[2], x104[2]) →* 1729_0_sort_GE(x102[3], x103[3], x104[3])))


(3) -> (6), if ((1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]) →* 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])))


(4) -> (5), if ((x104[4] > x103[4] && x103[4] >= 0 && x103[4] <= 99 && 99 >= x103[4] + 1 && 1 <= x103[4] + 1 →* TRUE)∧(1729_0_sort_GE(x102[4], x103[4], x104[4]) →* 1729_0_sort_GE(x102[5], x103[5], x104[5])))


(5) -> (8), if ((1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5]) →* 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8])))


(6) -> (7), if ((x105[6] >= x104[6] && x103[6] >= 0 && x102[6] > 0 →* TRUE)∧(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]) →* 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])))


(7) -> (0), if ((1729_0_sort_GE(x102[7], x103[7] + 1, 100 - x102[7]) →* 1729_0_sort_GE(x102[0], x103[0], x104[0])))


(7) -> (2), if ((1729_0_sort_GE(x102[7], x103[7] + 1, 100 - x102[7]) →* 1729_0_sort_GE(x102[2], x103[2], x104[2])))


(7) -> (4), if ((1729_0_sort_GE(x102[7], x103[7] + 1, 100 - x102[7]) →* 1729_0_sort_GE(x102[4], x103[4], x104[4])))


(8) -> (9), if ((x3[8] < x2[8] && x1[8] >= 0 && x1[8] <= 99 && x0[8] > 0 && 99 >= x1[8] + 1 && 1 <= x1[8] + 1 →* TRUE)∧(1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]) →* 1810_0_sort_LE(x0[9], x1[9], x2[9], x3[9])))


(9) -> (0), if ((1729_0_sort_GE(x0[9], x1[9] + 1, 100 - x0[9]) →* 1729_0_sort_GE(x102[0], x103[0], x104[0])))


(9) -> (2), if ((1729_0_sort_GE(x0[9], x1[9] + 1, 100 - x0[9]) →* 1729_0_sort_GE(x102[2], x103[2], x104[2])))


(9) -> (4), if ((1729_0_sort_GE(x0[9], x1[9] + 1, 100 - x0[9]) →* 1729_0_sort_GE(x102[4], x103[4], x104[4])))



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 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102, x103, x104)) → COND_1729_1_MAIN_INVOKEMETHOD(&&(&&(&&(<=(x104, x103), >(x102, 0)), >(100, +(x102, 1))), <(0, +(x102, 1))), 1729_0_sort_GE(x102, x103, x104)) the following chains were created:
  • We consider the chain 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[0], x103[0], x104[0])) → COND_1729_1_MAIN_INVOKEMETHOD(&&(&&(&&(<=(x104[0], x103[0]), >(x102[0], 0)), >(100, +(x102[0], 1))), <(0, +(x102[0], 1))), 1729_0_sort_GE(x102[0], x103[0], x104[0])), COND_1729_1_MAIN_INVOKEMETHOD(TRUE, 1729_0_sort_GE(x102[1], x103[1], x104[1])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(+(x102[1], 1), 0, -(100, +(x102[1], 1)))) which results in the following constraint:

    (1)    (&&(&&(&&(<=(x104[0], x103[0]), >(x102[0], 0)), >(100, +(x102[0], 1))), <(0, +(x102[0], 1)))=TRUE∧1729_0_sort_GE(x102[0], x103[0], x104[0])=1729_0_sort_GE(x102[1], x103[1], x104[1]) ⇒ 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[0], x103[0], x104[0]))≥NonInfC∧1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[0], x103[0], x104[0]))≥COND_1729_1_MAIN_INVOKEMETHOD(&&(&&(&&(<=(x104[0], x103[0]), >(x102[0], 0)), >(100, +(x102[0], 1))), <(0, +(x102[0], 1))), 1729_0_sort_GE(x102[0], x103[0], x104[0]))∧(UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD(&&(&&(&&(<=(x104[0], x103[0]), >(x102[0], 0)), >(100, +(x102[0], 1))), <(0, +(x102[0], 1))), 1729_0_sort_GE(x102[0], x103[0], x104[0]))), ≥))



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

    (2)    (<(0, +(x102[0], 1))=TRUE∧>(100, +(x102[0], 1))=TRUE∧<=(x104[0], x103[0])=TRUE∧>(x102[0], 0)=TRUE ⇒ 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[0], x103[0], x104[0]))≥NonInfC∧1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[0], x103[0], x104[0]))≥COND_1729_1_MAIN_INVOKEMETHOD(&&(&&(&&(<=(x104[0], x103[0]), >(x102[0], 0)), >(100, +(x102[0], 1))), <(0, +(x102[0], 1))), 1729_0_sort_GE(x102[0], x103[0], x104[0]))∧(UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD(&&(&&(&&(<=(x104[0], x103[0]), >(x102[0], 0)), >(100, +(x102[0], 1))), <(0, +(x102[0], 1))), 1729_0_sort_GE(x102[0], x103[0], x104[0]))), ≥))



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

    (3)    (x102[0] ≥ 0∧[98] + [-1]x102[0] ≥ 0∧x103[0] + [-1]x104[0] ≥ 0∧x102[0] + [-1] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD(&&(&&(&&(<=(x104[0], x103[0]), >(x102[0], 0)), >(100, +(x102[0], 1))), <(0, +(x102[0], 1))), 1729_0_sort_GE(x102[0], x103[0], x104[0]))), ≥)∧[(-1)Bound*bni_38] + [(-1)bni_38]x102[0] ≥ 0∧[(-1)bso_39] ≥ 0)



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

    (4)    (x102[0] ≥ 0∧[98] + [-1]x102[0] ≥ 0∧x103[0] + [-1]x104[0] ≥ 0∧x102[0] + [-1] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD(&&(&&(&&(<=(x104[0], x103[0]), >(x102[0], 0)), >(100, +(x102[0], 1))), <(0, +(x102[0], 1))), 1729_0_sort_GE(x102[0], x103[0], x104[0]))), ≥)∧[(-1)Bound*bni_38] + [(-1)bni_38]x102[0] ≥ 0∧[(-1)bso_39] ≥ 0)



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

    (5)    (x102[0] ≥ 0∧[98] + [-1]x102[0] ≥ 0∧x103[0] + [-1]x104[0] ≥ 0∧x102[0] + [-1] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD(&&(&&(&&(<=(x104[0], x103[0]), >(x102[0], 0)), >(100, +(x102[0], 1))), <(0, +(x102[0], 1))), 1729_0_sort_GE(x102[0], x103[0], x104[0]))), ≥)∧[(-1)Bound*bni_38] + [(-1)bni_38]x102[0] ≥ 0∧[(-1)bso_39] ≥ 0)



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

    (6)    ([1] + x102[0] ≥ 0∧[97] + [-1]x102[0] ≥ 0∧x103[0] + [-1]x104[0] ≥ 0∧x102[0] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD(&&(&&(&&(<=(x104[0], x103[0]), >(x102[0], 0)), >(100, +(x102[0], 1))), <(0, +(x102[0], 1))), 1729_0_sort_GE(x102[0], x103[0], x104[0]))), ≥)∧[(-1)Bound*bni_38 + (-1)bni_38] + [(-1)bni_38]x102[0] ≥ 0∧[(-1)bso_39] ≥ 0)



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

    (7)    ([1] + x102[0] ≥ 0∧[97] + [-1]x102[0] ≥ 0∧x103[0] ≥ 0∧x102[0] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD(&&(&&(&&(<=(x104[0], x103[0]), >(x102[0], 0)), >(100, +(x102[0], 1))), <(0, +(x102[0], 1))), 1729_0_sort_GE(x102[0], x103[0], x104[0]))), ≥)∧[(-1)Bound*bni_38 + (-1)bni_38] + [(-1)bni_38]x102[0] ≥ 0∧[(-1)bso_39] ≥ 0)



    We simplified constraint (7) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

    (8)    ([1] + x102[0] ≥ 0∧[97] + [-1]x102[0] ≥ 0∧x103[0] ≥ 0∧x102[0] ≥ 0∧x104[0] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD(&&(&&(&&(<=(x104[0], x103[0]), >(x102[0], 0)), >(100, +(x102[0], 1))), <(0, +(x102[0], 1))), 1729_0_sort_GE(x102[0], x103[0], x104[0]))), ≥)∧[(-1)Bound*bni_38 + (-1)bni_38] + [(-1)bni_38]x102[0] ≥ 0∧[(-1)bso_39] ≥ 0)


    (9)    ([1] + x102[0] ≥ 0∧[97] + [-1]x102[0] ≥ 0∧x103[0] ≥ 0∧x102[0] ≥ 0∧x104[0] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD(&&(&&(&&(<=(x104[0], x103[0]), >(x102[0], 0)), >(100, +(x102[0], 1))), <(0, +(x102[0], 1))), 1729_0_sort_GE(x102[0], x103[0], x104[0]))), ≥)∧[(-1)Bound*bni_38 + (-1)bni_38] + [(-1)bni_38]x102[0] ≥ 0∧[(-1)bso_39] ≥ 0)







For Pair COND_1729_1_MAIN_INVOKEMETHOD(TRUE, 1729_0_sort_GE(x102, x103, x104)) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(+(x102, 1), 0, -(100, +(x102, 1)))) the following chains were created:
  • We consider the chain COND_1729_1_MAIN_INVOKEMETHOD(TRUE, 1729_0_sort_GE(x102[1], x103[1], x104[1])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(+(x102[1], 1), 0, -(100, +(x102[1], 1)))) which results in the following constraint:

    (10)    (COND_1729_1_MAIN_INVOKEMETHOD(TRUE, 1729_0_sort_GE(x102[1], x103[1], x104[1]))≥NonInfC∧COND_1729_1_MAIN_INVOKEMETHOD(TRUE, 1729_0_sort_GE(x102[1], x103[1], x104[1]))≥1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(+(x102[1], 1), 0, -(100, +(x102[1], 1))))∧(UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(+(x102[1], 1), 0, -(100, +(x102[1], 1))))), ≥))



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

    (11)    ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(+(x102[1], 1), 0, -(100, +(x102[1], 1))))), ≥)∧[1 + (-1)bso_41] ≥ 0)



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

    (12)    ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(+(x102[1], 1), 0, -(100, +(x102[1], 1))))), ≥)∧[1 + (-1)bso_41] ≥ 0)



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

    (13)    ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(+(x102[1], 1), 0, -(100, +(x102[1], 1))))), ≥)∧[1 + (-1)bso_41] ≥ 0)



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

    (14)    ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(+(x102[1], 1), 0, -(100, +(x102[1], 1))))), ≥)∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_41] ≥ 0)







For Pair 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102, x103, x104)) → COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104, x103), >=(x103, 0)), <=(x103, 99)), >=(99, +(x103, 1))), <=(1, +(x103, 1))), 1729_0_sort_GE(x102, x103, x104)) the following chains were created:
  • We consider the chain 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2])) → COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2])), COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3])) → 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3])) which results in the following constraint:

    (15)    (&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1)))=TRUE∧1729_0_sort_GE(x102[2], x103[2], x104[2])=1729_0_sort_GE(x102[3], x103[3], x104[3]) ⇒ 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2]))≥NonInfC∧1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2]))≥COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))∧(UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))), ≥))



    We simplified constraint (15) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (16)    (<=(1, +(x103[2], 1))=TRUE∧>=(99, +(x103[2], 1))=TRUE∧<=(x103[2], 99)=TRUE∧>(x104[2], x103[2])=TRUE∧>=(x103[2], 0)=TRUE ⇒ 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2]))≥NonInfC∧1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2]))≥COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))∧(UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))), ≥))



    We simplified constraint (16) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (17)    (x103[2] ≥ 0∧[98] + [-1]x103[2] ≥ 0∧[99] + [-1]x103[2] ≥ 0∧x104[2] + [-1] + [-1]x103[2] ≥ 0∧x103[2] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))), ≥)∧[(-1)Bound*bni_42] + [(-1)bni_42]x102[2] ≥ 0∧[(-1)bso_43] ≥ 0)



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

    (18)    (x103[2] ≥ 0∧[98] + [-1]x103[2] ≥ 0∧[99] + [-1]x103[2] ≥ 0∧x104[2] + [-1] + [-1]x103[2] ≥ 0∧x103[2] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))), ≥)∧[(-1)Bound*bni_42] + [(-1)bni_42]x102[2] ≥ 0∧[(-1)bso_43] ≥ 0)



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

    (19)    (x103[2] ≥ 0∧[98] + [-1]x103[2] ≥ 0∧[99] + [-1]x103[2] ≥ 0∧x104[2] + [-1] + [-1]x103[2] ≥ 0∧x103[2] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))), ≥)∧[(-1)Bound*bni_42] + [(-1)bni_42]x102[2] ≥ 0∧[(-1)bso_43] ≥ 0)



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

    (20)    (x103[2] ≥ 0∧[98] + [-1]x103[2] ≥ 0∧[99] + [-1]x103[2] ≥ 0∧x104[2] + [-1] + [-1]x103[2] ≥ 0∧x103[2] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))), ≥)∧[(-1)bni_42] = 0∧[(-1)Bound*bni_42] ≥ 0∧0 = 0∧[(-1)bso_43] ≥ 0)



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

    (21)    (x103[2] ≥ 0∧[98] + [-1]x103[2] ≥ 0∧[99] + [-1]x103[2] ≥ 0∧x104[2] ≥ 0∧x103[2] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))), ≥)∧[(-1)bni_42] = 0∧[(-1)Bound*bni_42] ≥ 0∧0 = 0∧[(-1)bso_43] ≥ 0)







For Pair COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102, x103, x104)) → 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102, x103, x206, x207)) the following chains were created:
  • We consider the chain COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3])) → 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3])) which results in the following constraint:

    (22)    (COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3]))≥NonInfC∧COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3]))≥1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))∧(UIncreasing(1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))), ≥))



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

    (23)    ((UIncreasing(1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))), ≥)∧[(-1)bso_45] ≥ 0)



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

    (24)    ((UIncreasing(1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))), ≥)∧[(-1)bso_45] ≥ 0)



    We simplified constraint (24) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (25)    ((UIncreasing(1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))), ≥)∧[(-1)bso_45] ≥ 0)



    We simplified constraint (25) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (26)    ((UIncreasing(1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_45] ≥ 0)







For Pair 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102, x103, x104)) → COND_1729_1_MAIN_INVOKEMETHOD2(&&(&&(&&(&&(>(x104, x103), >=(x103, 0)), <=(x103, 99)), >=(99, +(x103, 1))), <=(1, +(x103, 1))), 1729_0_sort_GE(x102, x103, x104)) the following chains were created:
  • We consider the chain 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[4], x103[4], x104[4])) → COND_1729_1_MAIN_INVOKEMETHOD2(&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1))), 1729_0_sort_GE(x102[4], x103[4], x104[4])), COND_1729_1_MAIN_INVOKEMETHOD2(TRUE, 1729_0_sort_GE(x102[5], x103[5], x104[5])) → 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5])) which results in the following constraint:

    (27)    (&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1)))=TRUE∧1729_0_sort_GE(x102[4], x103[4], x104[4])=1729_0_sort_GE(x102[5], x103[5], x104[5]) ⇒ 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[4], x103[4], x104[4]))≥NonInfC∧1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[4], x103[4], x104[4]))≥COND_1729_1_MAIN_INVOKEMETHOD2(&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1))), 1729_0_sort_GE(x102[4], x103[4], x104[4]))∧(UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD2(&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1))), 1729_0_sort_GE(x102[4], x103[4], x104[4]))), ≥))



    We simplified constraint (27) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (28)    (<=(1, +(x103[4], 1))=TRUE∧>=(99, +(x103[4], 1))=TRUE∧<=(x103[4], 99)=TRUE∧>(x104[4], x103[4])=TRUE∧>=(x103[4], 0)=TRUE ⇒ 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[4], x103[4], x104[4]))≥NonInfC∧1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[4], x103[4], x104[4]))≥COND_1729_1_MAIN_INVOKEMETHOD2(&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1))), 1729_0_sort_GE(x102[4], x103[4], x104[4]))∧(UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD2(&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1))), 1729_0_sort_GE(x102[4], x103[4], x104[4]))), ≥))



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

    (29)    (x103[4] ≥ 0∧[98] + [-1]x103[4] ≥ 0∧[99] + [-1]x103[4] ≥ 0∧x104[4] + [-1] + [-1]x103[4] ≥ 0∧x103[4] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD2(&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1))), 1729_0_sort_GE(x102[4], x103[4], x104[4]))), ≥)∧[(-1)Bound*bni_46] + [(-1)bni_46]x102[4] ≥ 0∧[(-1)bso_47] ≥ 0)



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

    (30)    (x103[4] ≥ 0∧[98] + [-1]x103[4] ≥ 0∧[99] + [-1]x103[4] ≥ 0∧x104[4] + [-1] + [-1]x103[4] ≥ 0∧x103[4] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD2(&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1))), 1729_0_sort_GE(x102[4], x103[4], x104[4]))), ≥)∧[(-1)Bound*bni_46] + [(-1)bni_46]x102[4] ≥ 0∧[(-1)bso_47] ≥ 0)



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

    (31)    (x103[4] ≥ 0∧[98] + [-1]x103[4] ≥ 0∧[99] + [-1]x103[4] ≥ 0∧x104[4] + [-1] + [-1]x103[4] ≥ 0∧x103[4] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD2(&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1))), 1729_0_sort_GE(x102[4], x103[4], x104[4]))), ≥)∧[(-1)Bound*bni_46] + [(-1)bni_46]x102[4] ≥ 0∧[(-1)bso_47] ≥ 0)



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

    (32)    (x103[4] ≥ 0∧[98] + [-1]x103[4] ≥ 0∧[99] + [-1]x103[4] ≥ 0∧x104[4] + [-1] + [-1]x103[4] ≥ 0∧x103[4] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD2(&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1))), 1729_0_sort_GE(x102[4], x103[4], x104[4]))), ≥)∧[(-1)bni_46] = 0∧[(-1)Bound*bni_46] ≥ 0∧0 = 0∧[(-1)bso_47] ≥ 0)



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

    (33)    (x103[4] ≥ 0∧[98] + [-1]x103[4] ≥ 0∧[99] + [-1]x103[4] ≥ 0∧x104[4] ≥ 0∧x103[4] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD2(&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1))), 1729_0_sort_GE(x102[4], x103[4], x104[4]))), ≥)∧[(-1)bni_46] = 0∧[(-1)Bound*bni_46] ≥ 0∧0 = 0∧[(-1)bso_47] ≥ 0)







For Pair COND_1729_1_MAIN_INVOKEMETHOD2(TRUE, 1729_0_sort_GE(x102, x103, x104)) → 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102, x103, x206, x207)) the following chains were created:
  • We consider the chain COND_1729_1_MAIN_INVOKEMETHOD2(TRUE, 1729_0_sort_GE(x102[5], x103[5], x104[5])) → 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5])) which results in the following constraint:

    (34)    (COND_1729_1_MAIN_INVOKEMETHOD2(TRUE, 1729_0_sort_GE(x102[5], x103[5], x104[5]))≥NonInfC∧COND_1729_1_MAIN_INVOKEMETHOD2(TRUE, 1729_0_sort_GE(x102[5], x103[5], x104[5]))≥1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5]))∧(UIncreasing(1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5]))), ≥))



    We simplified constraint (34) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (35)    ((UIncreasing(1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5]))), ≥)∧[(-1)bso_49] ≥ 0)



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

    (36)    ((UIncreasing(1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5]))), ≥)∧[(-1)bso_49] ≥ 0)



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

    (37)    ((UIncreasing(1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5]))), ≥)∧[(-1)bso_49] ≥ 0)



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

    (38)    ((UIncreasing(1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5]))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_49] ≥ 0)







For Pair 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102, x103, x104, x105)) → COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105, x104), >=(x103, 0)), >(x102, 0)), 1809_0_sort_LE(x102, x103, x104, x105)) the following chains were created:
  • We consider the chain 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])) → COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])), COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7]))) which results in the following constraint:

    (39)    (&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0))=TRUE∧1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])=1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7]) ⇒ 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))≥NonInfC∧1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))≥COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))∧(UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥))



    We simplified constraint (39) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (40)    (>(x102[6], 0)=TRUE∧>=(x105[6], x104[6])=TRUE∧>=(x103[6], 0)=TRUE ⇒ 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))≥NonInfC∧1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))≥COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))∧(UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥))



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

    (41)    (x102[6] + [-1] ≥ 0∧x105[6] + [-1]x104[6] ≥ 0∧x103[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[(-1)Bound*bni_50] + [(-1)bni_50]x102[6] ≥ 0∧[(-1)bso_51] ≥ 0)



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

    (42)    (x102[6] + [-1] ≥ 0∧x105[6] + [-1]x104[6] ≥ 0∧x103[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[(-1)Bound*bni_50] + [(-1)bni_50]x102[6] ≥ 0∧[(-1)bso_51] ≥ 0)



    We simplified constraint (42) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (43)    (x102[6] + [-1] ≥ 0∧x105[6] + [-1]x104[6] ≥ 0∧x103[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[(-1)Bound*bni_50] + [(-1)bni_50]x102[6] ≥ 0∧[(-1)bso_51] ≥ 0)



    We simplified constraint (43) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (44)    (x102[6] ≥ 0∧x105[6] + [-1]x104[6] ≥ 0∧x103[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[(-1)Bound*bni_50 + (-1)bni_50] + [(-1)bni_50]x102[6] ≥ 0∧[(-1)bso_51] ≥ 0)



    We simplified constraint (44) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (45)    (x102[6] ≥ 0∧x105[6] ≥ 0∧x103[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[(-1)Bound*bni_50 + (-1)bni_50] + [(-1)bni_50]x102[6] ≥ 0∧[(-1)bso_51] ≥ 0)



    We simplified constraint (45) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

    (46)    (x102[6] ≥ 0∧x105[6] ≥ 0∧x103[6] ≥ 0∧x104[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[(-1)Bound*bni_50 + (-1)bni_50] + [(-1)bni_50]x102[6] ≥ 0∧[(-1)bso_51] ≥ 0)


    (47)    (x102[6] ≥ 0∧x105[6] ≥ 0∧x103[6] ≥ 0∧x104[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[(-1)Bound*bni_50 + (-1)bni_50] + [(-1)bni_50]x102[6] ≥ 0∧[(-1)bso_51] ≥ 0)







For Pair COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102, x103, x104, x105)) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102, +(x103, 1), -(100, x102))) the following chains were created:
  • We consider the chain COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7]))) which results in the following constraint:

    (48)    (COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7]))≥NonInfC∧COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7]))≥1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))∧(UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))), ≥))



    We simplified constraint (48) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (49)    ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))), ≥)∧[(-1)bso_53] ≥ 0)



    We simplified constraint (49) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (50)    ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))), ≥)∧[(-1)bso_53] ≥ 0)



    We simplified constraint (50) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (51)    ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))), ≥)∧[(-1)bso_53] ≥ 0)



    We simplified constraint (51) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (52)    ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_53] ≥ 0)







For Pair 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x0, x1, x2, x3)) → COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3, x2), >=(x1, 0)), <=(x1, 99)), >(x0, 0)), >=(99, +(x1, 1))), <=(1, +(x1, 1))), 1810_0_sort_LE(x0, x1, x2, x3)) the following chains were created:
  • We consider the chain 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8])) → COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8])), COND_1810_1_MAIN_INVOKEMETHOD(TRUE, 1810_0_sort_LE(x0[9], x1[9], x2[9], x3[9])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0[9], +(x1[9], 1), -(100, x0[9]))) which results in the following constraint:

    (53)    (&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1)))=TRUE∧1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8])=1810_0_sort_LE(x0[9], x1[9], x2[9], x3[9]) ⇒ 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))≥NonInfC∧1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))≥COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))∧(UIncreasing(COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))), ≥))



    We simplified constraint (53) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (54)    (<=(1, +(x1[8], 1))=TRUE∧>=(99, +(x1[8], 1))=TRUE∧>(x0[8], 0)=TRUE∧<=(x1[8], 99)=TRUE∧<(x3[8], x2[8])=TRUE∧>=(x1[8], 0)=TRUE ⇒ 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))≥NonInfC∧1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))≥COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))∧(UIncreasing(COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))), ≥))



    We simplified constraint (54) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (55)    (x1[8] ≥ 0∧[98] + [-1]x1[8] ≥ 0∧x0[8] + [-1] ≥ 0∧[99] + [-1]x1[8] ≥ 0∧x2[8] + [-1] + [-1]x3[8] ≥ 0∧x1[8] ≥ 0 ⇒ (UIncreasing(COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))), ≥)∧[(-1)Bound*bni_54] + [(-1)bni_54]x0[8] ≥ 0∧[(-1)bso_55] ≥ 0)



    We simplified constraint (55) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (56)    (x1[8] ≥ 0∧[98] + [-1]x1[8] ≥ 0∧x0[8] + [-1] ≥ 0∧[99] + [-1]x1[8] ≥ 0∧x2[8] + [-1] + [-1]x3[8] ≥ 0∧x1[8] ≥ 0 ⇒ (UIncreasing(COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))), ≥)∧[(-1)Bound*bni_54] + [(-1)bni_54]x0[8] ≥ 0∧[(-1)bso_55] ≥ 0)



    We simplified constraint (56) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (57)    (x1[8] ≥ 0∧[98] + [-1]x1[8] ≥ 0∧x0[8] + [-1] ≥ 0∧[99] + [-1]x1[8] ≥ 0∧x2[8] + [-1] + [-1]x3[8] ≥ 0∧x1[8] ≥ 0 ⇒ (UIncreasing(COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))), ≥)∧[(-1)Bound*bni_54] + [(-1)bni_54]x0[8] ≥ 0∧[(-1)bso_55] ≥ 0)



    We simplified constraint (57) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (58)    (x1[8] ≥ 0∧[98] + [-1]x1[8] ≥ 0∧x0[8] ≥ 0∧[99] + [-1]x1[8] ≥ 0∧x2[8] + [-1] + [-1]x3[8] ≥ 0∧x1[8] ≥ 0 ⇒ (UIncreasing(COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))), ≥)∧[(-1)Bound*bni_54 + (-1)bni_54] + [(-1)bni_54]x0[8] ≥ 0∧[(-1)bso_55] ≥ 0)



    We simplified constraint (58) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (59)    (x1[8] ≥ 0∧[98] + [-1]x1[8] ≥ 0∧x0[8] ≥ 0∧[99] + [-1]x1[8] ≥ 0∧x2[8] ≥ 0∧x1[8] ≥ 0 ⇒ (UIncreasing(COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))), ≥)∧[(-1)Bound*bni_54 + (-1)bni_54] + [(-1)bni_54]x0[8] ≥ 0∧[(-1)bso_55] ≥ 0)



    We simplified constraint (59) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

    (60)    (x1[8] ≥ 0∧[98] + [-1]x1[8] ≥ 0∧x0[8] ≥ 0∧[99] + [-1]x1[8] ≥ 0∧x2[8] ≥ 0∧x1[8] ≥ 0∧x3[8] ≥ 0 ⇒ (UIncreasing(COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))), ≥)∧[(-1)Bound*bni_54 + (-1)bni_54] + [(-1)bni_54]x0[8] ≥ 0∧[(-1)bso_55] ≥ 0)


    (61)    (x1[8] ≥ 0∧[98] + [-1]x1[8] ≥ 0∧x0[8] ≥ 0∧[99] + [-1]x1[8] ≥ 0∧x2[8] ≥ 0∧x1[8] ≥ 0∧x3[8] ≥ 0 ⇒ (UIncreasing(COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))), ≥)∧[(-1)Bound*bni_54 + (-1)bni_54] + [(-1)bni_54]x0[8] ≥ 0∧[(-1)bso_55] ≥ 0)







For Pair COND_1810_1_MAIN_INVOKEMETHOD(TRUE, 1810_0_sort_LE(x0, x1, x2, x3)) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0, +(x1, 1), -(100, x0))) the following chains were created:
  • We consider the chain COND_1810_1_MAIN_INVOKEMETHOD(TRUE, 1810_0_sort_LE(x0[9], x1[9], x2[9], x3[9])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0[9], +(x1[9], 1), -(100, x0[9]))) which results in the following constraint:

    (62)    (COND_1810_1_MAIN_INVOKEMETHOD(TRUE, 1810_0_sort_LE(x0[9], x1[9], x2[9], x3[9]))≥NonInfC∧COND_1810_1_MAIN_INVOKEMETHOD(TRUE, 1810_0_sort_LE(x0[9], x1[9], x2[9], x3[9]))≥1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0[9], +(x1[9], 1), -(100, x0[9])))∧(UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0[9], +(x1[9], 1), -(100, x0[9])))), ≥))



    We simplified constraint (62) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (63)    ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0[9], +(x1[9], 1), -(100, x0[9])))), ≥)∧[(-1)bso_57] ≥ 0)



    We simplified constraint (63) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (64)    ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0[9], +(x1[9], 1), -(100, x0[9])))), ≥)∧[(-1)bso_57] ≥ 0)



    We simplified constraint (64) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (65)    ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0[9], +(x1[9], 1), -(100, x0[9])))), ≥)∧[(-1)bso_57] ≥ 0)



    We simplified constraint (65) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (66)    ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0[9], +(x1[9], 1), -(100, x0[9])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_57] ≥ 0)







To summarize, we get the following constraints P≥ for the following pairs.
  • 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102, x103, x104)) → COND_1729_1_MAIN_INVOKEMETHOD(&&(&&(&&(<=(x104, x103), >(x102, 0)), >(100, +(x102, 1))), <(0, +(x102, 1))), 1729_0_sort_GE(x102, x103, x104))
    • ([1] + x102[0] ≥ 0∧[97] + [-1]x102[0] ≥ 0∧x103[0] ≥ 0∧x102[0] ≥ 0∧x104[0] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD(&&(&&(&&(<=(x104[0], x103[0]), >(x102[0], 0)), >(100, +(x102[0], 1))), <(0, +(x102[0], 1))), 1729_0_sort_GE(x102[0], x103[0], x104[0]))), ≥)∧[(-1)Bound*bni_38 + (-1)bni_38] + [(-1)bni_38]x102[0] ≥ 0∧[(-1)bso_39] ≥ 0)
    • ([1] + x102[0] ≥ 0∧[97] + [-1]x102[0] ≥ 0∧x103[0] ≥ 0∧x102[0] ≥ 0∧x104[0] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD(&&(&&(&&(<=(x104[0], x103[0]), >(x102[0], 0)), >(100, +(x102[0], 1))), <(0, +(x102[0], 1))), 1729_0_sort_GE(x102[0], x103[0], x104[0]))), ≥)∧[(-1)Bound*bni_38 + (-1)bni_38] + [(-1)bni_38]x102[0] ≥ 0∧[(-1)bso_39] ≥ 0)

  • COND_1729_1_MAIN_INVOKEMETHOD(TRUE, 1729_0_sort_GE(x102, x103, x104)) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(+(x102, 1), 0, -(100, +(x102, 1))))
    • ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(+(x102[1], 1), 0, -(100, +(x102[1], 1))))), ≥)∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_41] ≥ 0)

  • 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102, x103, x104)) → COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104, x103), >=(x103, 0)), <=(x103, 99)), >=(99, +(x103, 1))), <=(1, +(x103, 1))), 1729_0_sort_GE(x102, x103, x104))
    • (x103[2] ≥ 0∧[98] + [-1]x103[2] ≥ 0∧[99] + [-1]x103[2] ≥ 0∧x104[2] ≥ 0∧x103[2] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))), ≥)∧[(-1)bni_42] = 0∧[(-1)Bound*bni_42] ≥ 0∧0 = 0∧[(-1)bso_43] ≥ 0)

  • COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102, x103, x104)) → 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102, x103, x206, x207))
    • ((UIncreasing(1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_45] ≥ 0)

  • 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102, x103, x104)) → COND_1729_1_MAIN_INVOKEMETHOD2(&&(&&(&&(&&(>(x104, x103), >=(x103, 0)), <=(x103, 99)), >=(99, +(x103, 1))), <=(1, +(x103, 1))), 1729_0_sort_GE(x102, x103, x104))
    • (x103[4] ≥ 0∧[98] + [-1]x103[4] ≥ 0∧[99] + [-1]x103[4] ≥ 0∧x104[4] ≥ 0∧x103[4] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD2(&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1))), 1729_0_sort_GE(x102[4], x103[4], x104[4]))), ≥)∧[(-1)bni_46] = 0∧[(-1)Bound*bni_46] ≥ 0∧0 = 0∧[(-1)bso_47] ≥ 0)

  • COND_1729_1_MAIN_INVOKEMETHOD2(TRUE, 1729_0_sort_GE(x102, x103, x104)) → 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102, x103, x206, x207))
    • ((UIncreasing(1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5]))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_49] ≥ 0)

  • 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102, x103, x104, x105)) → COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105, x104), >=(x103, 0)), >(x102, 0)), 1809_0_sort_LE(x102, x103, x104, x105))
    • (x102[6] ≥ 0∧x105[6] ≥ 0∧x103[6] ≥ 0∧x104[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[(-1)Bound*bni_50 + (-1)bni_50] + [(-1)bni_50]x102[6] ≥ 0∧[(-1)bso_51] ≥ 0)
    • (x102[6] ≥ 0∧x105[6] ≥ 0∧x103[6] ≥ 0∧x104[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[(-1)Bound*bni_50 + (-1)bni_50] + [(-1)bni_50]x102[6] ≥ 0∧[(-1)bso_51] ≥ 0)

  • COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102, x103, x104, x105)) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102, +(x103, 1), -(100, x102)))
    • ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_53] ≥ 0)

  • 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x0, x1, x2, x3)) → COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3, x2), >=(x1, 0)), <=(x1, 99)), >(x0, 0)), >=(99, +(x1, 1))), <=(1, +(x1, 1))), 1810_0_sort_LE(x0, x1, x2, x3))
    • (x1[8] ≥ 0∧[98] + [-1]x1[8] ≥ 0∧x0[8] ≥ 0∧[99] + [-1]x1[8] ≥ 0∧x2[8] ≥ 0∧x1[8] ≥ 0∧x3[8] ≥ 0 ⇒ (UIncreasing(COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))), ≥)∧[(-1)Bound*bni_54 + (-1)bni_54] + [(-1)bni_54]x0[8] ≥ 0∧[(-1)bso_55] ≥ 0)
    • (x1[8] ≥ 0∧[98] + [-1]x1[8] ≥ 0∧x0[8] ≥ 0∧[99] + [-1]x1[8] ≥ 0∧x2[8] ≥ 0∧x1[8] ≥ 0∧x3[8] ≥ 0 ⇒ (UIncreasing(COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))), ≥)∧[(-1)Bound*bni_54 + (-1)bni_54] + [(-1)bni_54]x0[8] ≥ 0∧[(-1)bso_55] ≥ 0)

  • COND_1810_1_MAIN_INVOKEMETHOD(TRUE, 1810_0_sort_LE(x0, x1, x2, x3)) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0, +(x1, 1), -(100, x0)))
    • ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0[9], +(x1[9], 1), -(100, x0[9])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_57] ≥ 0)




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

POL(TRUE) = 0   
POL(FALSE) = 0   
POL(1729_1_MAIN_INVOKEMETHOD(x1)) = [-1] + [-1]x1   
POL(1729_0_sort_GE(x1, x2, x3)) = [-1] + x1   
POL(COND_1729_1_MAIN_INVOKEMETHOD(x1, x2)) = [-1] + [-1]x2   
POL(&&(x1, x2)) = [-1]   
POL(<=(x1, x2)) = [-1]   
POL(>(x1, x2)) = [-1]   
POL(0) = 0   
POL(100) = [100]   
POL(+(x1, x2)) = x1 + x2   
POL(1) = [1]   
POL(<(x1, x2)) = [-1]   
POL(-(x1, x2)) = x1 + [-1]x2   
POL(COND_1729_1_MAIN_INVOKEMETHOD1(x1, x2)) = [-1] + [-1]x2   
POL(>=(x1, x2)) = [-1]   
POL(99) = [99]   
POL(1809_1_MAIN_INVOKEMETHOD(x1)) = [-1] + [-1]x1   
POL(1809_0_sort_LE(x1, x2, x3, x4)) = [-1] + x1   
POL(COND_1729_1_MAIN_INVOKEMETHOD2(x1, x2)) = [-1] + [-1]x2   
POL(1810_1_MAIN_INVOKEMETHOD(x1)) = [-1] + [-1]x1   
POL(1810_0_sort_LE(x1, x2, x3, x4)) = [-1] + x1   
POL(COND_1809_1_MAIN_INVOKEMETHOD(x1, x2)) = [-1] + [-1]x2   
POL(COND_1810_1_MAIN_INVOKEMETHOD(x1, x2)) = [-1] + [-1]x2   

The following pairs are in P>:

COND_1729_1_MAIN_INVOKEMETHOD(TRUE, 1729_0_sort_GE(x102[1], x103[1], x104[1])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(+(x102[1], 1), 0, -(100, +(x102[1], 1))))

The following pairs are in Pbound:

1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[0], x103[0], x104[0])) → COND_1729_1_MAIN_INVOKEMETHOD(&&(&&(&&(<=(x104[0], x103[0]), >(x102[0], 0)), >(100, +(x102[0], 1))), <(0, +(x102[0], 1))), 1729_0_sort_GE(x102[0], x103[0], x104[0]))

The following pairs are in P≥:

1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[0], x103[0], x104[0])) → COND_1729_1_MAIN_INVOKEMETHOD(&&(&&(&&(<=(x104[0], x103[0]), >(x102[0], 0)), >(100, +(x102[0], 1))), <(0, +(x102[0], 1))), 1729_0_sort_GE(x102[0], x103[0], x104[0]))
1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2])) → COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))
COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3])) → 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))
1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[4], x103[4], x104[4])) → COND_1729_1_MAIN_INVOKEMETHOD2(&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1))), 1729_0_sort_GE(x102[4], x103[4], x104[4]))
COND_1729_1_MAIN_INVOKEMETHOD2(TRUE, 1729_0_sort_GE(x102[5], x103[5], x104[5])) → 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5]))
1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])) → COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))
COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))
1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8])) → COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))
COND_1810_1_MAIN_INVOKEMETHOD(TRUE, 1810_0_sort_LE(x0[9], x1[9], x2[9], x3[9])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0[9], +(x1[9], 1), -(100, x0[9])))

There are no usable rules.

(6) Complex Obligation (AND)

(7) 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): 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[0], x103[0], x104[0])) → COND_1729_1_MAIN_INVOKEMETHOD(x104[0] <= x103[0] && x102[0] > 0 && 100 > x102[0] + 1 && 0 < x102[0] + 1, 1729_0_sort_GE(x102[0], x103[0], x104[0]))
(2): 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2])) → COND_1729_1_MAIN_INVOKEMETHOD1(x104[2] > x103[2] && x103[2] >= 0 && x103[2] <= 99 && 99 >= x103[2] + 1 && 1 <= x103[2] + 1, 1729_0_sort_GE(x102[2], x103[2], x104[2]))
(3): COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3])) → 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))
(4): 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[4], x103[4], x104[4])) → COND_1729_1_MAIN_INVOKEMETHOD2(x104[4] > x103[4] && x103[4] >= 0 && x103[4] <= 99 && 99 >= x103[4] + 1 && 1 <= x103[4] + 1, 1729_0_sort_GE(x102[4], x103[4], x104[4]))
(5): COND_1729_1_MAIN_INVOKEMETHOD2(TRUE, 1729_0_sort_GE(x102[5], x103[5], x104[5])) → 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5]))
(6): 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])) → COND_1809_1_MAIN_INVOKEMETHOD(x105[6] >= x104[6] && x103[6] >= 0 && x102[6] > 0, 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))
(7): COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], x103[7] + 1, 100 - x102[7]))
(8): 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8])) → COND_1810_1_MAIN_INVOKEMETHOD(x3[8] < x2[8] && x1[8] >= 0 && x1[8] <= 99 && x0[8] > 0 && 99 >= x1[8] + 1 && 1 <= x1[8] + 1, 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))
(9): COND_1810_1_MAIN_INVOKEMETHOD(TRUE, 1810_0_sort_LE(x0[9], x1[9], x2[9], x3[9])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0[9], x1[9] + 1, 100 - x0[9]))

(7) -> (0), if ((1729_0_sort_GE(x102[7], x103[7] + 1, 100 - x102[7]) →* 1729_0_sort_GE(x102[0], x103[0], x104[0])))


(9) -> (0), if ((1729_0_sort_GE(x0[9], x1[9] + 1, 100 - x0[9]) →* 1729_0_sort_GE(x102[0], x103[0], x104[0])))


(7) -> (2), if ((1729_0_sort_GE(x102[7], x103[7] + 1, 100 - x102[7]) →* 1729_0_sort_GE(x102[2], x103[2], x104[2])))


(9) -> (2), if ((1729_0_sort_GE(x0[9], x1[9] + 1, 100 - x0[9]) →* 1729_0_sort_GE(x102[2], x103[2], x104[2])))


(2) -> (3), if ((x104[2] > x103[2] && x103[2] >= 0 && x103[2] <= 99 && 99 >= x103[2] + 1 && 1 <= x103[2] + 1 →* TRUE)∧(1729_0_sort_GE(x102[2], x103[2], x104[2]) →* 1729_0_sort_GE(x102[3], x103[3], x104[3])))


(7) -> (4), if ((1729_0_sort_GE(x102[7], x103[7] + 1, 100 - x102[7]) →* 1729_0_sort_GE(x102[4], x103[4], x104[4])))


(9) -> (4), if ((1729_0_sort_GE(x0[9], x1[9] + 1, 100 - x0[9]) →* 1729_0_sort_GE(x102[4], x103[4], x104[4])))


(4) -> (5), if ((x104[4] > x103[4] && x103[4] >= 0 && x103[4] <= 99 && 99 >= x103[4] + 1 && 1 <= x103[4] + 1 →* TRUE)∧(1729_0_sort_GE(x102[4], x103[4], x104[4]) →* 1729_0_sort_GE(x102[5], x103[5], x104[5])))


(3) -> (6), if ((1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]) →* 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])))


(6) -> (7), if ((x105[6] >= x104[6] && x103[6] >= 0 && x102[6] > 0 →* TRUE)∧(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]) →* 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])))


(5) -> (8), if ((1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5]) →* 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8])))


(8) -> (9), if ((x3[8] < x2[8] && x1[8] >= 0 && x1[8] <= 99 && x0[8] > 0 && 99 >= x1[8] + 1 && 1 <= x1[8] + 1 →* TRUE)∧(1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]) →* 1810_0_sort_LE(x0[9], x1[9], x2[9], x3[9])))



The set Q is empty.

(8) IDependencyGraphProof (EQUIVALENT transformation)

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

(9) 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:
(9): COND_1810_1_MAIN_INVOKEMETHOD(TRUE, 1810_0_sort_LE(x0[9], x1[9], x2[9], x3[9])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0[9], x1[9] + 1, 100 - x0[9]))
(8): 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8])) → COND_1810_1_MAIN_INVOKEMETHOD(x3[8] < x2[8] && x1[8] >= 0 && x1[8] <= 99 && x0[8] > 0 && 99 >= x1[8] + 1 && 1 <= x1[8] + 1, 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))
(5): COND_1729_1_MAIN_INVOKEMETHOD2(TRUE, 1729_0_sort_GE(x102[5], x103[5], x104[5])) → 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5]))
(4): 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[4], x103[4], x104[4])) → COND_1729_1_MAIN_INVOKEMETHOD2(x104[4] > x103[4] && x103[4] >= 0 && x103[4] <= 99 && 99 >= x103[4] + 1 && 1 <= x103[4] + 1, 1729_0_sort_GE(x102[4], x103[4], x104[4]))
(7): COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], x103[7] + 1, 100 - x102[7]))
(6): 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])) → COND_1809_1_MAIN_INVOKEMETHOD(x105[6] >= x104[6] && x103[6] >= 0 && x102[6] > 0, 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))
(3): COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3])) → 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))
(2): 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2])) → COND_1729_1_MAIN_INVOKEMETHOD1(x104[2] > x103[2] && x103[2] >= 0 && x103[2] <= 99 && 99 >= x103[2] + 1 && 1 <= x103[2] + 1, 1729_0_sort_GE(x102[2], x103[2], x104[2]))

(7) -> (2), if ((1729_0_sort_GE(x102[7], x103[7] + 1, 100 - x102[7]) →* 1729_0_sort_GE(x102[2], x103[2], x104[2])))


(9) -> (2), if ((1729_0_sort_GE(x0[9], x1[9] + 1, 100 - x0[9]) →* 1729_0_sort_GE(x102[2], x103[2], x104[2])))


(2) -> (3), if ((x104[2] > x103[2] && x103[2] >= 0 && x103[2] <= 99 && 99 >= x103[2] + 1 && 1 <= x103[2] + 1 →* TRUE)∧(1729_0_sort_GE(x102[2], x103[2], x104[2]) →* 1729_0_sort_GE(x102[3], x103[3], x104[3])))


(7) -> (4), if ((1729_0_sort_GE(x102[7], x103[7] + 1, 100 - x102[7]) →* 1729_0_sort_GE(x102[4], x103[4], x104[4])))


(9) -> (4), if ((1729_0_sort_GE(x0[9], x1[9] + 1, 100 - x0[9]) →* 1729_0_sort_GE(x102[4], x103[4], x104[4])))


(4) -> (5), if ((x104[4] > x103[4] && x103[4] >= 0 && x103[4] <= 99 && 99 >= x103[4] + 1 && 1 <= x103[4] + 1 →* TRUE)∧(1729_0_sort_GE(x102[4], x103[4], x104[4]) →* 1729_0_sort_GE(x102[5], x103[5], x104[5])))


(3) -> (6), if ((1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]) →* 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])))


(6) -> (7), if ((x105[6] >= x104[6] && x103[6] >= 0 && x102[6] > 0 →* TRUE)∧(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]) →* 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])))


(5) -> (8), if ((1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5]) →* 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8])))


(8) -> (9), if ((x3[8] < x2[8] && x1[8] >= 0 && x1[8] <= 99 && x0[8] > 0 && 99 >= x1[8] + 1 && 1 <= x1[8] + 1 →* TRUE)∧(1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]) →* 1810_0_sort_LE(x0[9], x1[9], x2[9], x3[9])))



The set Q is empty.

(10) 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_1810_1_MAIN_INVOKEMETHOD(TRUE, 1810_0_sort_LE(x0[9], x1[9], x2[9], x3[9])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0[9], +(x1[9], 1), -(100, x0[9]))) the following chains were created:
  • We consider the chain COND_1810_1_MAIN_INVOKEMETHOD(TRUE, 1810_0_sort_LE(x0[9], x1[9], x2[9], x3[9])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0[9], +(x1[9], 1), -(100, x0[9]))) which results in the following constraint:

    (1)    (COND_1810_1_MAIN_INVOKEMETHOD(TRUE, 1810_0_sort_LE(x0[9], x1[9], x2[9], x3[9]))≥NonInfC∧COND_1810_1_MAIN_INVOKEMETHOD(TRUE, 1810_0_sort_LE(x0[9], x1[9], x2[9], x3[9]))≥1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0[9], +(x1[9], 1), -(100, x0[9])))∧(UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0[9], +(x1[9], 1), -(100, x0[9])))), ≥))



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

    (2)    ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0[9], +(x1[9], 1), -(100, x0[9])))), ≥)∧[(-1)bso_19] ≥ 0)



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

    (3)    ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0[9], +(x1[9], 1), -(100, x0[9])))), ≥)∧[(-1)bso_19] ≥ 0)



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

    (4)    ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0[9], +(x1[9], 1), -(100, x0[9])))), ≥)∧[(-1)bso_19] ≥ 0)



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

    (5)    ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0[9], +(x1[9], 1), -(100, x0[9])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_19] ≥ 0)







For Pair 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8])) → COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8])) the following chains were created:
  • We consider the chain 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8])) → COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8])), COND_1810_1_MAIN_INVOKEMETHOD(TRUE, 1810_0_sort_LE(x0[9], x1[9], x2[9], x3[9])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0[9], +(x1[9], 1), -(100, x0[9]))) which results in the following constraint:

    (6)    (&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1)))=TRUE∧1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8])=1810_0_sort_LE(x0[9], x1[9], x2[9], x3[9]) ⇒ 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))≥NonInfC∧1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))≥COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))∧(UIncreasing(COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))), ≥))



    We simplified constraint (6) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (7)    (<=(1, +(x1[8], 1))=TRUE∧>=(99, +(x1[8], 1))=TRUE∧>(x0[8], 0)=TRUE∧<=(x1[8], 99)=TRUE∧<(x3[8], x2[8])=TRUE∧>=(x1[8], 0)=TRUE ⇒ 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))≥NonInfC∧1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))≥COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))∧(UIncreasing(COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))), ≥))



    We simplified constraint (7) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (8)    (x1[8] ≥ 0∧[98] + [-1]x1[8] ≥ 0∧x0[8] + [-1] ≥ 0∧[99] + [-1]x1[8] ≥ 0∧x2[8] + [-1] + [-1]x3[8] ≥ 0∧x1[8] ≥ 0 ⇒ (UIncreasing(COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))), ≥)∧[(2)bni_20 + (-1)Bound*bni_20] + [(-1)bni_20]x1[8] + [bni_20]x0[8] ≥ 0∧[1 + (-1)bso_21] ≥ 0)



    We simplified constraint (8) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (9)    (x1[8] ≥ 0∧[98] + [-1]x1[8] ≥ 0∧x0[8] + [-1] ≥ 0∧[99] + [-1]x1[8] ≥ 0∧x2[8] + [-1] + [-1]x3[8] ≥ 0∧x1[8] ≥ 0 ⇒ (UIncreasing(COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))), ≥)∧[(2)bni_20 + (-1)Bound*bni_20] + [(-1)bni_20]x1[8] + [bni_20]x0[8] ≥ 0∧[1 + (-1)bso_21] ≥ 0)



    We simplified constraint (9) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (10)    (x1[8] ≥ 0∧[98] + [-1]x1[8] ≥ 0∧x0[8] + [-1] ≥ 0∧[99] + [-1]x1[8] ≥ 0∧x2[8] + [-1] + [-1]x3[8] ≥ 0∧x1[8] ≥ 0 ⇒ (UIncreasing(COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))), ≥)∧[(2)bni_20 + (-1)Bound*bni_20] + [(-1)bni_20]x1[8] + [bni_20]x0[8] ≥ 0∧[1 + (-1)bso_21] ≥ 0)



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

    (11)    (x1[8] ≥ 0∧[98] + [-1]x1[8] ≥ 0∧x0[8] ≥ 0∧[99] + [-1]x1[8] ≥ 0∧x2[8] + [-1] + [-1]x3[8] ≥ 0∧x1[8] ≥ 0 ⇒ (UIncreasing(COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))), ≥)∧[(3)bni_20 + (-1)Bound*bni_20] + [(-1)bni_20]x1[8] + [bni_20]x0[8] ≥ 0∧[1 + (-1)bso_21] ≥ 0)



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

    (12)    (x1[8] ≥ 0∧[98] + [-1]x1[8] ≥ 0∧x0[8] ≥ 0∧[99] + [-1]x1[8] ≥ 0∧x2[8] ≥ 0∧x1[8] ≥ 0 ⇒ (UIncreasing(COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))), ≥)∧[(3)bni_20 + (-1)Bound*bni_20] + [(-1)bni_20]x1[8] + [bni_20]x0[8] ≥ 0∧[1 + (-1)bso_21] ≥ 0)



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

    (13)    (x1[8] ≥ 0∧[98] + [-1]x1[8] ≥ 0∧x0[8] ≥ 0∧[99] + [-1]x1[8] ≥ 0∧x2[8] ≥ 0∧x1[8] ≥ 0∧x3[8] ≥ 0 ⇒ (UIncreasing(COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))), ≥)∧[(3)bni_20 + (-1)Bound*bni_20] + [(-1)bni_20]x1[8] + [bni_20]x0[8] ≥ 0∧[1 + (-1)bso_21] ≥ 0)


    (14)    (x1[8] ≥ 0∧[98] + [-1]x1[8] ≥ 0∧x0[8] ≥ 0∧[99] + [-1]x1[8] ≥ 0∧x2[8] ≥ 0∧x1[8] ≥ 0∧x3[8] ≥ 0 ⇒ (UIncreasing(COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))), ≥)∧[(3)bni_20 + (-1)Bound*bni_20] + [(-1)bni_20]x1[8] + [bni_20]x0[8] ≥ 0∧[1 + (-1)bso_21] ≥ 0)







For Pair COND_1729_1_MAIN_INVOKEMETHOD2(TRUE, 1729_0_sort_GE(x102[5], x103[5], x104[5])) → 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5])) the following chains were created:
  • We consider the chain COND_1729_1_MAIN_INVOKEMETHOD2(TRUE, 1729_0_sort_GE(x102[5], x103[5], x104[5])) → 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5])) which results in the following constraint:

    (15)    (COND_1729_1_MAIN_INVOKEMETHOD2(TRUE, 1729_0_sort_GE(x102[5], x103[5], x104[5]))≥NonInfC∧COND_1729_1_MAIN_INVOKEMETHOD2(TRUE, 1729_0_sort_GE(x102[5], x103[5], x104[5]))≥1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5]))∧(UIncreasing(1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5]))), ≥))



    We simplified constraint (15) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (16)    ((UIncreasing(1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5]))), ≥)∧[(-1)bso_23] ≥ 0)



    We simplified constraint (16) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (17)    ((UIncreasing(1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5]))), ≥)∧[(-1)bso_23] ≥ 0)



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

    (18)    ((UIncreasing(1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5]))), ≥)∧[(-1)bso_23] ≥ 0)



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

    (19)    ((UIncreasing(1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5]))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_23] ≥ 0)







For Pair 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[4], x103[4], x104[4])) → COND_1729_1_MAIN_INVOKEMETHOD2(&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1))), 1729_0_sort_GE(x102[4], x103[4], x104[4])) the following chains were created:
  • We consider the chain 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[4], x103[4], x104[4])) → COND_1729_1_MAIN_INVOKEMETHOD2(&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1))), 1729_0_sort_GE(x102[4], x103[4], x104[4])), COND_1729_1_MAIN_INVOKEMETHOD2(TRUE, 1729_0_sort_GE(x102[5], x103[5], x104[5])) → 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5])) which results in the following constraint:

    (20)    (&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1)))=TRUE∧1729_0_sort_GE(x102[4], x103[4], x104[4])=1729_0_sort_GE(x102[5], x103[5], x104[5]) ⇒ 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[4], x103[4], x104[4]))≥NonInfC∧1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[4], x103[4], x104[4]))≥COND_1729_1_MAIN_INVOKEMETHOD2(&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1))), 1729_0_sort_GE(x102[4], x103[4], x104[4]))∧(UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD2(&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1))), 1729_0_sort_GE(x102[4], x103[4], x104[4]))), ≥))



    We simplified constraint (20) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (21)    (<=(1, +(x103[4], 1))=TRUE∧>=(99, +(x103[4], 1))=TRUE∧<=(x103[4], 99)=TRUE∧>(x104[4], x103[4])=TRUE∧>=(x103[4], 0)=TRUE ⇒ 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[4], x103[4], x104[4]))≥NonInfC∧1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[4], x103[4], x104[4]))≥COND_1729_1_MAIN_INVOKEMETHOD2(&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1))), 1729_0_sort_GE(x102[4], x103[4], x104[4]))∧(UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD2(&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1))), 1729_0_sort_GE(x102[4], x103[4], x104[4]))), ≥))



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

    (22)    (x103[4] ≥ 0∧[98] + [-1]x103[4] ≥ 0∧[99] + [-1]x103[4] ≥ 0∧x104[4] + [-1] + [-1]x103[4] ≥ 0∧x103[4] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD2(&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1))), 1729_0_sort_GE(x102[4], x103[4], x104[4]))), ≥)∧[(2)bni_24 + (-1)Bound*bni_24] + [(-1)bni_24]x103[4] + [bni_24]x102[4] ≥ 0∧[(-1)bso_25] ≥ 0)



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

    (23)    (x103[4] ≥ 0∧[98] + [-1]x103[4] ≥ 0∧[99] + [-1]x103[4] ≥ 0∧x104[4] + [-1] + [-1]x103[4] ≥ 0∧x103[4] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD2(&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1))), 1729_0_sort_GE(x102[4], x103[4], x104[4]))), ≥)∧[(2)bni_24 + (-1)Bound*bni_24] + [(-1)bni_24]x103[4] + [bni_24]x102[4] ≥ 0∧[(-1)bso_25] ≥ 0)



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

    (24)    (x103[4] ≥ 0∧[98] + [-1]x103[4] ≥ 0∧[99] + [-1]x103[4] ≥ 0∧x104[4] + [-1] + [-1]x103[4] ≥ 0∧x103[4] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD2(&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1))), 1729_0_sort_GE(x102[4], x103[4], x104[4]))), ≥)∧[(2)bni_24 + (-1)Bound*bni_24] + [(-1)bni_24]x103[4] + [bni_24]x102[4] ≥ 0∧[(-1)bso_25] ≥ 0)



    We simplified constraint (24) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (25)    (x103[4] ≥ 0∧[98] + [-1]x103[4] ≥ 0∧[99] + [-1]x103[4] ≥ 0∧x104[4] + [-1] + [-1]x103[4] ≥ 0∧x103[4] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD2(&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1))), 1729_0_sort_GE(x102[4], x103[4], x104[4]))), ≥)∧[bni_24] = 0∧[(2)bni_24 + (-1)Bound*bni_24] + [(-1)bni_24]x103[4] ≥ 0∧0 = 0∧[(-1)bso_25] ≥ 0)



    We simplified constraint (25) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (26)    (x103[4] ≥ 0∧[98] + [-1]x103[4] ≥ 0∧[99] + [-1]x103[4] ≥ 0∧x104[4] ≥ 0∧x103[4] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD2(&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1))), 1729_0_sort_GE(x102[4], x103[4], x104[4]))), ≥)∧[bni_24] = 0∧[(2)bni_24 + (-1)Bound*bni_24] + [(-1)bni_24]x103[4] ≥ 0∧0 = 0∧[(-1)bso_25] ≥ 0)







For Pair COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7]))) the following chains were created:
  • We consider the chain COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7]))) which results in the following constraint:

    (27)    (COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7]))≥NonInfC∧COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7]))≥1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))∧(UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))), ≥))



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

    (28)    ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))), ≥)∧[(-1)bso_27] ≥ 0)



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

    (29)    ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))), ≥)∧[(-1)bso_27] ≥ 0)



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

    (30)    ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))), ≥)∧[(-1)bso_27] ≥ 0)



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

    (31)    ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_27] ≥ 0)







For Pair 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])) → COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])) the following chains were created:
  • We consider the chain 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])) → COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])), COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7]))) which results in the following constraint:

    (32)    (&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0))=TRUE∧1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])=1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7]) ⇒ 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))≥NonInfC∧1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))≥COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))∧(UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥))



    We simplified constraint (32) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (33)    (>(x102[6], 0)=TRUE∧>=(x105[6], x104[6])=TRUE∧>=(x103[6], 0)=TRUE ⇒ 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))≥NonInfC∧1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))≥COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))∧(UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥))



    We simplified constraint (33) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (34)    (x102[6] + [-1] ≥ 0∧x105[6] + [-1]x104[6] ≥ 0∧x103[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[bni_28 + (-1)Bound*bni_28] + [(-1)bni_28]x103[6] + [bni_28]x102[6] ≥ 0∧[(-1)bso_29] ≥ 0)



    We simplified constraint (34) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (35)    (x102[6] + [-1] ≥ 0∧x105[6] + [-1]x104[6] ≥ 0∧x103[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[bni_28 + (-1)Bound*bni_28] + [(-1)bni_28]x103[6] + [bni_28]x102[6] ≥ 0∧[(-1)bso_29] ≥ 0)



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

    (36)    (x102[6] + [-1] ≥ 0∧x105[6] + [-1]x104[6] ≥ 0∧x103[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[bni_28 + (-1)Bound*bni_28] + [(-1)bni_28]x103[6] + [bni_28]x102[6] ≥ 0∧[(-1)bso_29] ≥ 0)



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

    (37)    (x102[6] ≥ 0∧x105[6] + [-1]x104[6] ≥ 0∧x103[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[(2)bni_28 + (-1)Bound*bni_28] + [(-1)bni_28]x103[6] + [bni_28]x102[6] ≥ 0∧[(-1)bso_29] ≥ 0)



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

    (38)    (x102[6] ≥ 0∧x105[6] ≥ 0∧x103[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[(2)bni_28 + (-1)Bound*bni_28] + [(-1)bni_28]x103[6] + [bni_28]x102[6] ≥ 0∧[(-1)bso_29] ≥ 0)



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

    (39)    (x102[6] ≥ 0∧x105[6] ≥ 0∧x103[6] ≥ 0∧x104[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[(2)bni_28 + (-1)Bound*bni_28] + [(-1)bni_28]x103[6] + [bni_28]x102[6] ≥ 0∧[(-1)bso_29] ≥ 0)


    (40)    (x102[6] ≥ 0∧x105[6] ≥ 0∧x103[6] ≥ 0∧x104[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[(2)bni_28 + (-1)Bound*bni_28] + [(-1)bni_28]x103[6] + [bni_28]x102[6] ≥ 0∧[(-1)bso_29] ≥ 0)







For Pair COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3])) → 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3])) the following chains were created:
  • We consider the chain COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3])) → 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3])) which results in the following constraint:

    (41)    (COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3]))≥NonInfC∧COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3]))≥1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))∧(UIncreasing(1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))), ≥))



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

    (42)    ((UIncreasing(1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))), ≥)∧[(-1)bso_31] ≥ 0)



    We simplified constraint (42) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (43)    ((UIncreasing(1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))), ≥)∧[(-1)bso_31] ≥ 0)



    We simplified constraint (43) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (44)    ((UIncreasing(1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))), ≥)∧[(-1)bso_31] ≥ 0)



    We simplified constraint (44) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (45)    ((UIncreasing(1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_31] ≥ 0)







For Pair 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2])) → COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2])) the following chains were created:
  • We consider the chain 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2])) → COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2])), COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3])) → 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3])) which results in the following constraint:

    (46)    (&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1)))=TRUE∧1729_0_sort_GE(x102[2], x103[2], x104[2])=1729_0_sort_GE(x102[3], x103[3], x104[3]) ⇒ 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2]))≥NonInfC∧1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2]))≥COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))∧(UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))), ≥))



    We simplified constraint (46) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (47)    (<=(1, +(x103[2], 1))=TRUE∧>=(99, +(x103[2], 1))=TRUE∧<=(x103[2], 99)=TRUE∧>(x104[2], x103[2])=TRUE∧>=(x103[2], 0)=TRUE ⇒ 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2]))≥NonInfC∧1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2]))≥COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))∧(UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))), ≥))



    We simplified constraint (47) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (48)    (x103[2] ≥ 0∧[98] + [-1]x103[2] ≥ 0∧[99] + [-1]x103[2] ≥ 0∧x104[2] + [-1] + [-1]x103[2] ≥ 0∧x103[2] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))), ≥)∧[(2)bni_32 + (-1)Bound*bni_32] + [(-1)bni_32]x103[2] + [bni_32]x102[2] ≥ 0∧[1 + (-1)bso_33] ≥ 0)



    We simplified constraint (48) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (49)    (x103[2] ≥ 0∧[98] + [-1]x103[2] ≥ 0∧[99] + [-1]x103[2] ≥ 0∧x104[2] + [-1] + [-1]x103[2] ≥ 0∧x103[2] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))), ≥)∧[(2)bni_32 + (-1)Bound*bni_32] + [(-1)bni_32]x103[2] + [bni_32]x102[2] ≥ 0∧[1 + (-1)bso_33] ≥ 0)



    We simplified constraint (49) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (50)    (x103[2] ≥ 0∧[98] + [-1]x103[2] ≥ 0∧[99] + [-1]x103[2] ≥ 0∧x104[2] + [-1] + [-1]x103[2] ≥ 0∧x103[2] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))), ≥)∧[(2)bni_32 + (-1)Bound*bni_32] + [(-1)bni_32]x103[2] + [bni_32]x102[2] ≥ 0∧[1 + (-1)bso_33] ≥ 0)



    We simplified constraint (50) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (51)    (x103[2] ≥ 0∧[98] + [-1]x103[2] ≥ 0∧[99] + [-1]x103[2] ≥ 0∧x104[2] + [-1] + [-1]x103[2] ≥ 0∧x103[2] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))), ≥)∧[bni_32] = 0∧[(2)bni_32 + (-1)Bound*bni_32] + [(-1)bni_32]x103[2] ≥ 0∧0 = 0∧[1 + (-1)bso_33] ≥ 0)



    We simplified constraint (51) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (52)    (x103[2] ≥ 0∧[98] + [-1]x103[2] ≥ 0∧[99] + [-1]x103[2] ≥ 0∧x104[2] ≥ 0∧x103[2] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))), ≥)∧[bni_32] = 0∧[(2)bni_32 + (-1)Bound*bni_32] + [(-1)bni_32]x103[2] ≥ 0∧0 = 0∧[1 + (-1)bso_33] ≥ 0)







To summarize, we get the following constraints P≥ for the following pairs.
  • COND_1810_1_MAIN_INVOKEMETHOD(TRUE, 1810_0_sort_LE(x0[9], x1[9], x2[9], x3[9])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0[9], +(x1[9], 1), -(100, x0[9])))
    • ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0[9], +(x1[9], 1), -(100, x0[9])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_19] ≥ 0)

  • 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8])) → COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))
    • (x1[8] ≥ 0∧[98] + [-1]x1[8] ≥ 0∧x0[8] ≥ 0∧[99] + [-1]x1[8] ≥ 0∧x2[8] ≥ 0∧x1[8] ≥ 0∧x3[8] ≥ 0 ⇒ (UIncreasing(COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))), ≥)∧[(3)bni_20 + (-1)Bound*bni_20] + [(-1)bni_20]x1[8] + [bni_20]x0[8] ≥ 0∧[1 + (-1)bso_21] ≥ 0)
    • (x1[8] ≥ 0∧[98] + [-1]x1[8] ≥ 0∧x0[8] ≥ 0∧[99] + [-1]x1[8] ≥ 0∧x2[8] ≥ 0∧x1[8] ≥ 0∧x3[8] ≥ 0 ⇒ (UIncreasing(COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))), ≥)∧[(3)bni_20 + (-1)Bound*bni_20] + [(-1)bni_20]x1[8] + [bni_20]x0[8] ≥ 0∧[1 + (-1)bso_21] ≥ 0)

  • COND_1729_1_MAIN_INVOKEMETHOD2(TRUE, 1729_0_sort_GE(x102[5], x103[5], x104[5])) → 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5]))
    • ((UIncreasing(1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5]))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_23] ≥ 0)

  • 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[4], x103[4], x104[4])) → COND_1729_1_MAIN_INVOKEMETHOD2(&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1))), 1729_0_sort_GE(x102[4], x103[4], x104[4]))
    • (x103[4] ≥ 0∧[98] + [-1]x103[4] ≥ 0∧[99] + [-1]x103[4] ≥ 0∧x104[4] ≥ 0∧x103[4] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD2(&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1))), 1729_0_sort_GE(x102[4], x103[4], x104[4]))), ≥)∧[bni_24] = 0∧[(2)bni_24 + (-1)Bound*bni_24] + [(-1)bni_24]x103[4] ≥ 0∧0 = 0∧[(-1)bso_25] ≥ 0)

  • COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))
    • ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_27] ≥ 0)

  • 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])) → COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))
    • (x102[6] ≥ 0∧x105[6] ≥ 0∧x103[6] ≥ 0∧x104[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[(2)bni_28 + (-1)Bound*bni_28] + [(-1)bni_28]x103[6] + [bni_28]x102[6] ≥ 0∧[(-1)bso_29] ≥ 0)
    • (x102[6] ≥ 0∧x105[6] ≥ 0∧x103[6] ≥ 0∧x104[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[(2)bni_28 + (-1)Bound*bni_28] + [(-1)bni_28]x103[6] + [bni_28]x102[6] ≥ 0∧[(-1)bso_29] ≥ 0)

  • COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3])) → 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))
    • ((UIncreasing(1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_31] ≥ 0)

  • 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2])) → COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))
    • (x103[2] ≥ 0∧[98] + [-1]x103[2] ≥ 0∧[99] + [-1]x103[2] ≥ 0∧x104[2] ≥ 0∧x103[2] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))), ≥)∧[bni_32] = 0∧[(2)bni_32 + (-1)Bound*bni_32] + [(-1)bni_32]x103[2] ≥ 0∧0 = 0∧[1 + (-1)bso_33] ≥ 0)




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

POL(TRUE) = 0   
POL(FALSE) = 0   
POL(COND_1810_1_MAIN_INVOKEMETHOD(x1, x2)) = [-1]x2   
POL(1810_0_sort_LE(x1, x2, x3, x4)) = [-1] + x2 + [-1]x1   
POL(1729_1_MAIN_INVOKEMETHOD(x1)) = [2] + [-1]x1   
POL(1729_0_sort_GE(x1, x2, x3)) = x2 + [-1]x1   
POL(+(x1, x2)) = x1 + x2   
POL(1) = [1]   
POL(-(x1, x2)) = x1 + [-1]x2   
POL(100) = [100]   
POL(1810_1_MAIN_INVOKEMETHOD(x1)) = [1] + [-1]x1   
POL(&&(x1, x2)) = [-1]   
POL(<(x1, x2)) = [-1]   
POL(>=(x1, x2)) = [-1]   
POL(0) = 0   
POL(<=(x1, x2)) = [-1]   
POL(99) = [99]   
POL(>(x1, x2)) = [-1]   
POL(COND_1729_1_MAIN_INVOKEMETHOD2(x1, x2)) = [2] + [-1]x2   
POL(COND_1809_1_MAIN_INVOKEMETHOD(x1, x2)) = [-1] + x2   
POL(1809_0_sort_LE(x1, x2, x3, x4)) = [2] + [-1]x2 + x1   
POL(1809_1_MAIN_INVOKEMETHOD(x1)) = [-1] + x1   
POL(COND_1729_1_MAIN_INVOKEMETHOD1(x1, x2)) = [1] + [-1]x2   

The following pairs are in P>:

1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8])) → COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))
1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2])) → COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))

The following pairs are in Pbound:

1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8])) → COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))

The following pairs are in P≥:

COND_1810_1_MAIN_INVOKEMETHOD(TRUE, 1810_0_sort_LE(x0[9], x1[9], x2[9], x3[9])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0[9], +(x1[9], 1), -(100, x0[9])))
COND_1729_1_MAIN_INVOKEMETHOD2(TRUE, 1729_0_sort_GE(x102[5], x103[5], x104[5])) → 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5]))
1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[4], x103[4], x104[4])) → COND_1729_1_MAIN_INVOKEMETHOD2(&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1))), 1729_0_sort_GE(x102[4], x103[4], x104[4]))
COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))
1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])) → COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))
COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3])) → 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))

There are no usable rules.

(11) 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:
(9): COND_1810_1_MAIN_INVOKEMETHOD(TRUE, 1810_0_sort_LE(x0[9], x1[9], x2[9], x3[9])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0[9], x1[9] + 1, 100 - x0[9]))
(5): COND_1729_1_MAIN_INVOKEMETHOD2(TRUE, 1729_0_sort_GE(x102[5], x103[5], x104[5])) → 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5]))
(4): 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[4], x103[4], x104[4])) → COND_1729_1_MAIN_INVOKEMETHOD2(x104[4] > x103[4] && x103[4] >= 0 && x103[4] <= 99 && 99 >= x103[4] + 1 && 1 <= x103[4] + 1, 1729_0_sort_GE(x102[4], x103[4], x104[4]))
(7): COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], x103[7] + 1, 100 - x102[7]))
(6): 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])) → COND_1809_1_MAIN_INVOKEMETHOD(x105[6] >= x104[6] && x103[6] >= 0 && x102[6] > 0, 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))
(3): COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3])) → 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))
(2): 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2])) → COND_1729_1_MAIN_INVOKEMETHOD1(x104[2] > x103[2] && x103[2] >= 0 && x103[2] <= 99 && 99 >= x103[2] + 1 && 1 <= x103[2] + 1, 1729_0_sort_GE(x102[2], x103[2], x104[2]))

(7) -> (2), if ((1729_0_sort_GE(x102[7], x103[7] + 1, 100 - x102[7]) →* 1729_0_sort_GE(x102[2], x103[2], x104[2])))


(9) -> (2), if ((1729_0_sort_GE(x0[9], x1[9] + 1, 100 - x0[9]) →* 1729_0_sort_GE(x102[2], x103[2], x104[2])))


(2) -> (3), if ((x104[2] > x103[2] && x103[2] >= 0 && x103[2] <= 99 && 99 >= x103[2] + 1 && 1 <= x103[2] + 1 →* TRUE)∧(1729_0_sort_GE(x102[2], x103[2], x104[2]) →* 1729_0_sort_GE(x102[3], x103[3], x104[3])))


(7) -> (4), if ((1729_0_sort_GE(x102[7], x103[7] + 1, 100 - x102[7]) →* 1729_0_sort_GE(x102[4], x103[4], x104[4])))


(9) -> (4), if ((1729_0_sort_GE(x0[9], x1[9] + 1, 100 - x0[9]) →* 1729_0_sort_GE(x102[4], x103[4], x104[4])))


(4) -> (5), if ((x104[4] > x103[4] && x103[4] >= 0 && x103[4] <= 99 && 99 >= x103[4] + 1 && 1 <= x103[4] + 1 →* TRUE)∧(1729_0_sort_GE(x102[4], x103[4], x104[4]) →* 1729_0_sort_GE(x102[5], x103[5], x104[5])))


(3) -> (6), if ((1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]) →* 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])))


(6) -> (7), if ((x105[6] >= x104[6] && x103[6] >= 0 && x102[6] > 0 →* TRUE)∧(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]) →* 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])))



The set Q is empty.

(12) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes.

(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:

Integer, Boolean


R is empty.

The integer pair graph contains the following rules and edges:
(7): COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], x103[7] + 1, 100 - x102[7]))
(6): 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])) → COND_1809_1_MAIN_INVOKEMETHOD(x105[6] >= x104[6] && x103[6] >= 0 && x102[6] > 0, 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))
(3): COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3])) → 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))
(2): 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2])) → COND_1729_1_MAIN_INVOKEMETHOD1(x104[2] > x103[2] && x103[2] >= 0 && x103[2] <= 99 && 99 >= x103[2] + 1 && 1 <= x103[2] + 1, 1729_0_sort_GE(x102[2], x103[2], x104[2]))

(7) -> (2), if ((1729_0_sort_GE(x102[7], x103[7] + 1, 100 - x102[7]) →* 1729_0_sort_GE(x102[2], x103[2], x104[2])))


(2) -> (3), if ((x104[2] > x103[2] && x103[2] >= 0 && x103[2] <= 99 && 99 >= x103[2] + 1 && 1 <= x103[2] + 1 →* TRUE)∧(1729_0_sort_GE(x102[2], x103[2], x104[2]) →* 1729_0_sort_GE(x102[3], x103[3], x104[3])))


(3) -> (6), if ((1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]) →* 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])))


(6) -> (7), if ((x105[6] >= x104[6] && x103[6] >= 0 && x102[6] > 0 →* TRUE)∧(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]) →* 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])))



The set Q is empty.

(14) 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_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7]))) the following chains were created:
  • We consider the chain COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7]))) which results in the following constraint:

    (1)    (COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7]))≥NonInfC∧COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7]))≥1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))∧(UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))), ≥))



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

    (2)    ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))), ≥)∧[(-1)bso_14] ≥ 0)



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

    (3)    ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))), ≥)∧[(-1)bso_14] ≥ 0)



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

    (4)    ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))), ≥)∧[(-1)bso_14] ≥ 0)



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

    (5)    ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_14] ≥ 0)







For Pair 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])) → COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])) the following chains were created:
  • We consider the chain 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])) → COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])), COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7]))) which results in the following constraint:

    (6)    (&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0))=TRUE∧1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])=1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7]) ⇒ 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))≥NonInfC∧1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))≥COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))∧(UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥))



    We simplified constraint (6) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (7)    (>(x102[6], 0)=TRUE∧>=(x105[6], x104[6])=TRUE∧>=(x103[6], 0)=TRUE ⇒ 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))≥NonInfC∧1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))≥COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))∧(UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥))



    We simplified constraint (7) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (8)    (x102[6] + [-1] ≥ 0∧x105[6] + [-1]x104[6] ≥ 0∧x103[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[(2)bni_15 + (-1)Bound*bni_15] + [(-1)bni_15]x103[6] ≥ 0∧[1 + (-1)bso_16] ≥ 0)



    We simplified constraint (8) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (9)    (x102[6] + [-1] ≥ 0∧x105[6] + [-1]x104[6] ≥ 0∧x103[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[(2)bni_15 + (-1)Bound*bni_15] + [(-1)bni_15]x103[6] ≥ 0∧[1 + (-1)bso_16] ≥ 0)



    We simplified constraint (9) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (10)    (x102[6] + [-1] ≥ 0∧x105[6] + [-1]x104[6] ≥ 0∧x103[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[(2)bni_15 + (-1)Bound*bni_15] + [(-1)bni_15]x103[6] ≥ 0∧[1 + (-1)bso_16] ≥ 0)



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

    (11)    (x102[6] ≥ 0∧x105[6] + [-1]x104[6] ≥ 0∧x103[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[(2)bni_15 + (-1)Bound*bni_15] + [(-1)bni_15]x103[6] ≥ 0∧[1 + (-1)bso_16] ≥ 0)



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

    (12)    (x102[6] ≥ 0∧x105[6] ≥ 0∧x103[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[(2)bni_15 + (-1)Bound*bni_15] + [(-1)bni_15]x103[6] ≥ 0∧[1 + (-1)bso_16] ≥ 0)



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

    (13)    (x102[6] ≥ 0∧x105[6] ≥ 0∧x103[6] ≥ 0∧x104[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[(2)bni_15 + (-1)Bound*bni_15] + [(-1)bni_15]x103[6] ≥ 0∧[1 + (-1)bso_16] ≥ 0)


    (14)    (x102[6] ≥ 0∧x105[6] ≥ 0∧x103[6] ≥ 0∧x104[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[(2)bni_15 + (-1)Bound*bni_15] + [(-1)bni_15]x103[6] ≥ 0∧[1 + (-1)bso_16] ≥ 0)







For Pair COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3])) → 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3])) the following chains were created:
  • We consider the chain COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3])) → 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3])) which results in the following constraint:

    (15)    (COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3]))≥NonInfC∧COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3]))≥1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))∧(UIncreasing(1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))), ≥))



    We simplified constraint (15) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (16)    ((UIncreasing(1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))), ≥)∧[(-1)bso_18] ≥ 0)



    We simplified constraint (16) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (17)    ((UIncreasing(1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))), ≥)∧[(-1)bso_18] ≥ 0)



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

    (18)    ((UIncreasing(1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))), ≥)∧[(-1)bso_18] ≥ 0)



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

    (19)    ((UIncreasing(1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_18] ≥ 0)







For Pair 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2])) → COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2])) the following chains were created:
  • We consider the chain 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2])) → COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2])), COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3])) → 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3])) which results in the following constraint:

    (20)    (&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1)))=TRUE∧1729_0_sort_GE(x102[2], x103[2], x104[2])=1729_0_sort_GE(x102[3], x103[3], x104[3]) ⇒ 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2]))≥NonInfC∧1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2]))≥COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))∧(UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))), ≥))



    We simplified constraint (20) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (21)    (<=(1, +(x103[2], 1))=TRUE∧>=(99, +(x103[2], 1))=TRUE∧<=(x103[2], 99)=TRUE∧>(x104[2], x103[2])=TRUE∧>=(x103[2], 0)=TRUE ⇒ 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2]))≥NonInfC∧1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2]))≥COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))∧(UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))), ≥))



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

    (22)    (x103[2] ≥ 0∧[98] + [-1]x103[2] ≥ 0∧[99] + [-1]x103[2] ≥ 0∧x104[2] + [-1] + [-1]x103[2] ≥ 0∧x103[2] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))), ≥)∧[(2)bni_19 + (-1)Bound*bni_19] + [(-1)bni_19]x103[2] ≥ 0∧[(-1)bso_20] ≥ 0)



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

    (23)    (x103[2] ≥ 0∧[98] + [-1]x103[2] ≥ 0∧[99] + [-1]x103[2] ≥ 0∧x104[2] + [-1] + [-1]x103[2] ≥ 0∧x103[2] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))), ≥)∧[(2)bni_19 + (-1)Bound*bni_19] + [(-1)bni_19]x103[2] ≥ 0∧[(-1)bso_20] ≥ 0)



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

    (24)    (x103[2] ≥ 0∧[98] + [-1]x103[2] ≥ 0∧[99] + [-1]x103[2] ≥ 0∧x104[2] + [-1] + [-1]x103[2] ≥ 0∧x103[2] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))), ≥)∧[(2)bni_19 + (-1)Bound*bni_19] + [(-1)bni_19]x103[2] ≥ 0∧[(-1)bso_20] ≥ 0)



    We simplified constraint (24) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (25)    (x103[2] ≥ 0∧[98] + [-1]x103[2] ≥ 0∧[99] + [-1]x103[2] ≥ 0∧x104[2] + [-1] + [-1]x103[2] ≥ 0∧x103[2] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))), ≥)∧0 = 0∧[(2)bni_19 + (-1)Bound*bni_19] + [(-1)bni_19]x103[2] ≥ 0∧0 = 0∧[(-1)bso_20] ≥ 0)



    We simplified constraint (25) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (26)    (x103[2] ≥ 0∧[98] + [-1]x103[2] ≥ 0∧[99] + [-1]x103[2] ≥ 0∧x104[2] ≥ 0∧x103[2] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))), ≥)∧0 = 0∧[(2)bni_19 + (-1)Bound*bni_19] + [(-1)bni_19]x103[2] ≥ 0∧0 = 0∧[(-1)bso_20] ≥ 0)







To summarize, we get the following constraints P≥ for the following pairs.
  • COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))
    • ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_14] ≥ 0)

  • 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])) → COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))
    • (x102[6] ≥ 0∧x105[6] ≥ 0∧x103[6] ≥ 0∧x104[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[(2)bni_15 + (-1)Bound*bni_15] + [(-1)bni_15]x103[6] ≥ 0∧[1 + (-1)bso_16] ≥ 0)
    • (x102[6] ≥ 0∧x105[6] ≥ 0∧x103[6] ≥ 0∧x104[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[(2)bni_15 + (-1)Bound*bni_15] + [(-1)bni_15]x103[6] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

  • COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3])) → 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))
    • ((UIncreasing(1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_18] ≥ 0)

  • 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2])) → COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))
    • (x103[2] ≥ 0∧[98] + [-1]x103[2] ≥ 0∧[99] + [-1]x103[2] ≥ 0∧x104[2] ≥ 0∧x103[2] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))), ≥)∧0 = 0∧[(2)bni_19 + (-1)Bound*bni_19] + [(-1)bni_19]x103[2] ≥ 0∧0 = 0∧[(-1)bso_20] ≥ 0)




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

POL(TRUE) = 0   
POL(FALSE) = 0   
POL(COND_1809_1_MAIN_INVOKEMETHOD(x1, x2)) = [-1]x2   
POL(1809_0_sort_LE(x1, x2, x3, x4)) = [-1] + x2   
POL(1729_1_MAIN_INVOKEMETHOD(x1)) = [2] + [-1]x1   
POL(1729_0_sort_GE(x1, x2, x3)) = x2   
POL(+(x1, x2)) = x1 + x2   
POL(1) = [1]   
POL(-(x1, x2)) = x1 + [-1]x2   
POL(100) = [100]   
POL(1809_1_MAIN_INVOKEMETHOD(x1)) = [1] + [-1]x1   
POL(&&(x1, x2)) = 0   
POL(>=(x1, x2)) = [-1]   
POL(0) = 0   
POL(>(x1, x2)) = [-1]   
POL(COND_1729_1_MAIN_INVOKEMETHOD1(x1, x2)) = [2] + [-1]x2   
POL(<=(x1, x2)) = [-1]   
POL(99) = [99]   

The following pairs are in P>:

1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])) → COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))

The following pairs are in Pbound:

1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2])) → COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))

The following pairs are in P≥:

COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))
COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3])) → 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))
1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2])) → COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))

There are no usable rules.

(15) Complex Obligation (AND)

(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, Boolean


R is empty.

The integer pair graph contains the following rules and edges:
(7): COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], x103[7] + 1, 100 - x102[7]))
(3): COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3])) → 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))
(2): 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2])) → COND_1729_1_MAIN_INVOKEMETHOD1(x104[2] > x103[2] && x103[2] >= 0 && x103[2] <= 99 && 99 >= x103[2] + 1 && 1 <= x103[2] + 1, 1729_0_sort_GE(x102[2], x103[2], x104[2]))

(7) -> (2), if ((1729_0_sort_GE(x102[7], x103[7] + 1, 100 - x102[7]) →* 1729_0_sort_GE(x102[2], x103[2], x104[2])))


(2) -> (3), if ((x104[2] > x103[2] && x103[2] >= 0 && x103[2] <= 99 && 99 >= x103[2] + 1 && 1 <= x103[2] + 1 →* TRUE)∧(1729_0_sort_GE(x102[2], x103[2], x104[2]) →* 1729_0_sort_GE(x102[3], x103[3], x104[3])))



The set Q is empty.

(17) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 3 less nodes.

(18) TRUE

(19) 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:
(7): COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], x103[7] + 1, 100 - x102[7]))
(6): 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])) → COND_1809_1_MAIN_INVOKEMETHOD(x105[6] >= x104[6] && x103[6] >= 0 && x102[6] > 0, 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))
(3): COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3])) → 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))

(3) -> (6), if ((1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]) →* 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])))


(6) -> (7), if ((x105[6] >= x104[6] && x103[6] >= 0 && x102[6] > 0 →* TRUE)∧(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]) →* 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])))



The set Q is empty.

(20) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 3 less nodes.

(21) TRUE

(22) Obligation:

IDP problem:
The following function symbols are pre-defined:
!=~Neq: (Integer, Integer) -> Boolean
*~Mul: (Integer, Integer) -> Integer
>=~Ge: (Integer, Integer) -> Boolean
-1~UnaryMinus: (Integer) -> Integer
|~Bwor: (Integer, Integer) -> Integer
/~Div: (Integer, Integer) -> Integer
=~Eq: (Integer, Integer) -> Boolean
~Bwxor: (Integer, Integer) -> Integer
||~Lor: (Boolean, Boolean) -> Boolean
!~Lnot: (Boolean) -> Boolean
<~Lt: (Integer, Integer) -> Boolean
-~Sub: (Integer, Integer) -> Integer
<=~Le: (Integer, Integer) -> Boolean
>~Gt: (Integer, Integer) -> Boolean
~~Bwnot: (Integer) -> Integer
%~Mod: (Integer, Integer) -> Integer
&~Bwand: (Integer, Integer) -> Integer
+~Add: (Integer, Integer) -> Integer
&&~Land: (Boolean, Boolean) -> Boolean


The following domains are used:

Integer, Boolean


R is empty.

The integer pair graph contains the following rules and edges:
(1): COND_1729_1_MAIN_INVOKEMETHOD(TRUE, 1729_0_sort_GE(x102[1], x103[1], x104[1])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[1] + 1, 0, 100 - x102[1] + 1))
(2): 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2])) → COND_1729_1_MAIN_INVOKEMETHOD1(x104[2] > x103[2] && x103[2] >= 0 && x103[2] <= 99 && 99 >= x103[2] + 1 && 1 <= x103[2] + 1, 1729_0_sort_GE(x102[2], x103[2], x104[2]))
(3): COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3])) → 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))
(4): 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[4], x103[4], x104[4])) → COND_1729_1_MAIN_INVOKEMETHOD2(x104[4] > x103[4] && x103[4] >= 0 && x103[4] <= 99 && 99 >= x103[4] + 1 && 1 <= x103[4] + 1, 1729_0_sort_GE(x102[4], x103[4], x104[4]))
(5): COND_1729_1_MAIN_INVOKEMETHOD2(TRUE, 1729_0_sort_GE(x102[5], x103[5], x104[5])) → 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5]))
(6): 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])) → COND_1809_1_MAIN_INVOKEMETHOD(x105[6] >= x104[6] && x103[6] >= 0 && x102[6] > 0, 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))
(7): COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], x103[7] + 1, 100 - x102[7]))
(8): 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8])) → COND_1810_1_MAIN_INVOKEMETHOD(x3[8] < x2[8] && x1[8] >= 0 && x1[8] <= 99 && x0[8] > 0 && 99 >= x1[8] + 1 && 1 <= x1[8] + 1, 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))
(9): COND_1810_1_MAIN_INVOKEMETHOD(TRUE, 1810_0_sort_LE(x0[9], x1[9], x2[9], x3[9])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0[9], x1[9] + 1, 100 - x0[9]))

(1) -> (2), if ((1729_0_sort_GE(x102[1] + 1, 0, 100 - x102[1] + 1) →* 1729_0_sort_GE(x102[2], x103[2], x104[2])))


(7) -> (2), if ((1729_0_sort_GE(x102[7], x103[7] + 1, 100 - x102[7]) →* 1729_0_sort_GE(x102[2], x103[2], x104[2])))


(9) -> (2), if ((1729_0_sort_GE(x0[9], x1[9] + 1, 100 - x0[9]) →* 1729_0_sort_GE(x102[2], x103[2], x104[2])))


(2) -> (3), if ((x104[2] > x103[2] && x103[2] >= 0 && x103[2] <= 99 && 99 >= x103[2] + 1 && 1 <= x103[2] + 1 →* TRUE)∧(1729_0_sort_GE(x102[2], x103[2], x104[2]) →* 1729_0_sort_GE(x102[3], x103[3], x104[3])))


(1) -> (4), if ((1729_0_sort_GE(x102[1] + 1, 0, 100 - x102[1] + 1) →* 1729_0_sort_GE(x102[4], x103[4], x104[4])))


(7) -> (4), if ((1729_0_sort_GE(x102[7], x103[7] + 1, 100 - x102[7]) →* 1729_0_sort_GE(x102[4], x103[4], x104[4])))


(9) -> (4), if ((1729_0_sort_GE(x0[9], x1[9] + 1, 100 - x0[9]) →* 1729_0_sort_GE(x102[4], x103[4], x104[4])))


(4) -> (5), if ((x104[4] > x103[4] && x103[4] >= 0 && x103[4] <= 99 && 99 >= x103[4] + 1 && 1 <= x103[4] + 1 →* TRUE)∧(1729_0_sort_GE(x102[4], x103[4], x104[4]) →* 1729_0_sort_GE(x102[5], x103[5], x104[5])))


(3) -> (6), if ((1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]) →* 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])))


(6) -> (7), if ((x105[6] >= x104[6] && x103[6] >= 0 && x102[6] > 0 →* TRUE)∧(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]) →* 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])))


(5) -> (8), if ((1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5]) →* 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8])))


(8) -> (9), if ((x3[8] < x2[8] && x1[8] >= 0 && x1[8] <= 99 && x0[8] > 0 && 99 >= x1[8] + 1 && 1 <= x1[8] + 1 →* TRUE)∧(1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]) →* 1810_0_sort_LE(x0[9], x1[9], x2[9], x3[9])))



The set Q is empty.

(23) IDependencyGraphProof (EQUIVALENT transformation)

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

(24) 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:
(9): COND_1810_1_MAIN_INVOKEMETHOD(TRUE, 1810_0_sort_LE(x0[9], x1[9], x2[9], x3[9])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0[9], x1[9] + 1, 100 - x0[9]))
(8): 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8])) → COND_1810_1_MAIN_INVOKEMETHOD(x3[8] < x2[8] && x1[8] >= 0 && x1[8] <= 99 && x0[8] > 0 && 99 >= x1[8] + 1 && 1 <= x1[8] + 1, 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))
(5): COND_1729_1_MAIN_INVOKEMETHOD2(TRUE, 1729_0_sort_GE(x102[5], x103[5], x104[5])) → 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5]))
(4): 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[4], x103[4], x104[4])) → COND_1729_1_MAIN_INVOKEMETHOD2(x104[4] > x103[4] && x103[4] >= 0 && x103[4] <= 99 && 99 >= x103[4] + 1 && 1 <= x103[4] + 1, 1729_0_sort_GE(x102[4], x103[4], x104[4]))
(7): COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], x103[7] + 1, 100 - x102[7]))
(6): 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])) → COND_1809_1_MAIN_INVOKEMETHOD(x105[6] >= x104[6] && x103[6] >= 0 && x102[6] > 0, 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))
(3): COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3])) → 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))
(2): 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2])) → COND_1729_1_MAIN_INVOKEMETHOD1(x104[2] > x103[2] && x103[2] >= 0 && x103[2] <= 99 && 99 >= x103[2] + 1 && 1 <= x103[2] + 1, 1729_0_sort_GE(x102[2], x103[2], x104[2]))

(7) -> (2), if ((1729_0_sort_GE(x102[7], x103[7] + 1, 100 - x102[7]) →* 1729_0_sort_GE(x102[2], x103[2], x104[2])))


(9) -> (2), if ((1729_0_sort_GE(x0[9], x1[9] + 1, 100 - x0[9]) →* 1729_0_sort_GE(x102[2], x103[2], x104[2])))


(2) -> (3), if ((x104[2] > x103[2] && x103[2] >= 0 && x103[2] <= 99 && 99 >= x103[2] + 1 && 1 <= x103[2] + 1 →* TRUE)∧(1729_0_sort_GE(x102[2], x103[2], x104[2]) →* 1729_0_sort_GE(x102[3], x103[3], x104[3])))


(7) -> (4), if ((1729_0_sort_GE(x102[7], x103[7] + 1, 100 - x102[7]) →* 1729_0_sort_GE(x102[4], x103[4], x104[4])))


(9) -> (4), if ((1729_0_sort_GE(x0[9], x1[9] + 1, 100 - x0[9]) →* 1729_0_sort_GE(x102[4], x103[4], x104[4])))


(4) -> (5), if ((x104[4] > x103[4] && x103[4] >= 0 && x103[4] <= 99 && 99 >= x103[4] + 1 && 1 <= x103[4] + 1 →* TRUE)∧(1729_0_sort_GE(x102[4], x103[4], x104[4]) →* 1729_0_sort_GE(x102[5], x103[5], x104[5])))


(3) -> (6), if ((1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]) →* 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])))


(6) -> (7), if ((x105[6] >= x104[6] && x103[6] >= 0 && x102[6] > 0 →* TRUE)∧(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]) →* 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])))


(5) -> (8), if ((1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5]) →* 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8])))


(8) -> (9), if ((x3[8] < x2[8] && x1[8] >= 0 && x1[8] <= 99 && x0[8] > 0 && 99 >= x1[8] + 1 && 1 <= x1[8] + 1 →* TRUE)∧(1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]) →* 1810_0_sort_LE(x0[9], x1[9], x2[9], x3[9])))



The set Q is empty.

(25) 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_1810_1_MAIN_INVOKEMETHOD(TRUE, 1810_0_sort_LE(x0[9], x1[9], x2[9], x3[9])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0[9], +(x1[9], 1), -(100, x0[9]))) the following chains were created:
  • We consider the chain COND_1810_1_MAIN_INVOKEMETHOD(TRUE, 1810_0_sort_LE(x0[9], x1[9], x2[9], x3[9])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0[9], +(x1[9], 1), -(100, x0[9]))) which results in the following constraint:

    (1)    (COND_1810_1_MAIN_INVOKEMETHOD(TRUE, 1810_0_sort_LE(x0[9], x1[9], x2[9], x3[9]))≥NonInfC∧COND_1810_1_MAIN_INVOKEMETHOD(TRUE, 1810_0_sort_LE(x0[9], x1[9], x2[9], x3[9]))≥1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0[9], +(x1[9], 1), -(100, x0[9])))∧(UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0[9], +(x1[9], 1), -(100, x0[9])))), ≥))



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

    (2)    ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0[9], +(x1[9], 1), -(100, x0[9])))), ≥)∧[(-1)bso_19] ≥ 0)



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

    (3)    ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0[9], +(x1[9], 1), -(100, x0[9])))), ≥)∧[(-1)bso_19] ≥ 0)



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

    (4)    ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0[9], +(x1[9], 1), -(100, x0[9])))), ≥)∧[(-1)bso_19] ≥ 0)



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

    (5)    ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0[9], +(x1[9], 1), -(100, x0[9])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_19] ≥ 0)







For Pair 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8])) → COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8])) the following chains were created:
  • We consider the chain 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8])) → COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8])), COND_1810_1_MAIN_INVOKEMETHOD(TRUE, 1810_0_sort_LE(x0[9], x1[9], x2[9], x3[9])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0[9], +(x1[9], 1), -(100, x0[9]))) which results in the following constraint:

    (6)    (&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1)))=TRUE∧1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8])=1810_0_sort_LE(x0[9], x1[9], x2[9], x3[9]) ⇒ 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))≥NonInfC∧1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))≥COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))∧(UIncreasing(COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))), ≥))



    We simplified constraint (6) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (7)    (<=(1, +(x1[8], 1))=TRUE∧>=(99, +(x1[8], 1))=TRUE∧>(x0[8], 0)=TRUE∧<=(x1[8], 99)=TRUE∧<(x3[8], x2[8])=TRUE∧>=(x1[8], 0)=TRUE ⇒ 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))≥NonInfC∧1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))≥COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))∧(UIncreasing(COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))), ≥))



    We simplified constraint (7) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (8)    (x1[8] ≥ 0∧[98] + [-1]x1[8] ≥ 0∧x0[8] + [-1] ≥ 0∧[99] + [-1]x1[8] ≥ 0∧x2[8] + [-1] + [-1]x3[8] ≥ 0∧x1[8] ≥ 0 ⇒ (UIncreasing(COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))), ≥)∧[(-1)Bound*bni_20] + [(-1)bni_20]x1[8] + [bni_20]x0[8] ≥ 0∧[(-1)bso_21] ≥ 0)



    We simplified constraint (8) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (9)    (x1[8] ≥ 0∧[98] + [-1]x1[8] ≥ 0∧x0[8] + [-1] ≥ 0∧[99] + [-1]x1[8] ≥ 0∧x2[8] + [-1] + [-1]x3[8] ≥ 0∧x1[8] ≥ 0 ⇒ (UIncreasing(COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))), ≥)∧[(-1)Bound*bni_20] + [(-1)bni_20]x1[8] + [bni_20]x0[8] ≥ 0∧[(-1)bso_21] ≥ 0)



    We simplified constraint (9) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (10)    (x1[8] ≥ 0∧[98] + [-1]x1[8] ≥ 0∧x0[8] + [-1] ≥ 0∧[99] + [-1]x1[8] ≥ 0∧x2[8] + [-1] + [-1]x3[8] ≥ 0∧x1[8] ≥ 0 ⇒ (UIncreasing(COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))), ≥)∧[(-1)Bound*bni_20] + [(-1)bni_20]x1[8] + [bni_20]x0[8] ≥ 0∧[(-1)bso_21] ≥ 0)



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

    (11)    (x1[8] ≥ 0∧[98] + [-1]x1[8] ≥ 0∧x0[8] ≥ 0∧[99] + [-1]x1[8] ≥ 0∧x2[8] + [-1] + [-1]x3[8] ≥ 0∧x1[8] ≥ 0 ⇒ (UIncreasing(COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))), ≥)∧[(-1)Bound*bni_20 + bni_20] + [(-1)bni_20]x1[8] + [bni_20]x0[8] ≥ 0∧[(-1)bso_21] ≥ 0)



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

    (12)    (x1[8] ≥ 0∧[98] + [-1]x1[8] ≥ 0∧x0[8] ≥ 0∧[99] + [-1]x1[8] ≥ 0∧x2[8] ≥ 0∧x1[8] ≥ 0 ⇒ (UIncreasing(COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))), ≥)∧[(-1)Bound*bni_20 + bni_20] + [(-1)bni_20]x1[8] + [bni_20]x0[8] ≥ 0∧[(-1)bso_21] ≥ 0)



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

    (13)    (x1[8] ≥ 0∧[98] + [-1]x1[8] ≥ 0∧x0[8] ≥ 0∧[99] + [-1]x1[8] ≥ 0∧x2[8] ≥ 0∧x1[8] ≥ 0∧x3[8] ≥ 0 ⇒ (UIncreasing(COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))), ≥)∧[(-1)Bound*bni_20 + bni_20] + [(-1)bni_20]x1[8] + [bni_20]x0[8] ≥ 0∧[(-1)bso_21] ≥ 0)


    (14)    (x1[8] ≥ 0∧[98] + [-1]x1[8] ≥ 0∧x0[8] ≥ 0∧[99] + [-1]x1[8] ≥ 0∧x2[8] ≥ 0∧x1[8] ≥ 0∧x3[8] ≥ 0 ⇒ (UIncreasing(COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))), ≥)∧[(-1)Bound*bni_20 + bni_20] + [(-1)bni_20]x1[8] + [bni_20]x0[8] ≥ 0∧[(-1)bso_21] ≥ 0)







For Pair COND_1729_1_MAIN_INVOKEMETHOD2(TRUE, 1729_0_sort_GE(x102[5], x103[5], x104[5])) → 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5])) the following chains were created:
  • We consider the chain COND_1729_1_MAIN_INVOKEMETHOD2(TRUE, 1729_0_sort_GE(x102[5], x103[5], x104[5])) → 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5])) which results in the following constraint:

    (15)    (COND_1729_1_MAIN_INVOKEMETHOD2(TRUE, 1729_0_sort_GE(x102[5], x103[5], x104[5]))≥NonInfC∧COND_1729_1_MAIN_INVOKEMETHOD2(TRUE, 1729_0_sort_GE(x102[5], x103[5], x104[5]))≥1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5]))∧(UIncreasing(1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5]))), ≥))



    We simplified constraint (15) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (16)    ((UIncreasing(1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5]))), ≥)∧[(-1)bso_23] ≥ 0)



    We simplified constraint (16) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (17)    ((UIncreasing(1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5]))), ≥)∧[(-1)bso_23] ≥ 0)



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

    (18)    ((UIncreasing(1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5]))), ≥)∧[(-1)bso_23] ≥ 0)



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

    (19)    ((UIncreasing(1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5]))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_23] ≥ 0)







For Pair 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[4], x103[4], x104[4])) → COND_1729_1_MAIN_INVOKEMETHOD2(&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1))), 1729_0_sort_GE(x102[4], x103[4], x104[4])) the following chains were created:
  • We consider the chain 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[4], x103[4], x104[4])) → COND_1729_1_MAIN_INVOKEMETHOD2(&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1))), 1729_0_sort_GE(x102[4], x103[4], x104[4])), COND_1729_1_MAIN_INVOKEMETHOD2(TRUE, 1729_0_sort_GE(x102[5], x103[5], x104[5])) → 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5])) which results in the following constraint:

    (20)    (&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1)))=TRUE∧1729_0_sort_GE(x102[4], x103[4], x104[4])=1729_0_sort_GE(x102[5], x103[5], x104[5]) ⇒ 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[4], x103[4], x104[4]))≥NonInfC∧1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[4], x103[4], x104[4]))≥COND_1729_1_MAIN_INVOKEMETHOD2(&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1))), 1729_0_sort_GE(x102[4], x103[4], x104[4]))∧(UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD2(&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1))), 1729_0_sort_GE(x102[4], x103[4], x104[4]))), ≥))



    We simplified constraint (20) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (21)    (<=(1, +(x103[4], 1))=TRUE∧>=(99, +(x103[4], 1))=TRUE∧<=(x103[4], 99)=TRUE∧>(x104[4], x103[4])=TRUE∧>=(x103[4], 0)=TRUE ⇒ 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[4], x103[4], x104[4]))≥NonInfC∧1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[4], x103[4], x104[4]))≥COND_1729_1_MAIN_INVOKEMETHOD2(&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1))), 1729_0_sort_GE(x102[4], x103[4], x104[4]))∧(UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD2(&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1))), 1729_0_sort_GE(x102[4], x103[4], x104[4]))), ≥))



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

    (22)    (x103[4] ≥ 0∧[98] + [-1]x103[4] ≥ 0∧[99] + [-1]x103[4] ≥ 0∧x104[4] + [-1] + [-1]x103[4] ≥ 0∧x103[4] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD2(&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1))), 1729_0_sort_GE(x102[4], x103[4], x104[4]))), ≥)∧[bni_24 + (-1)Bound*bni_24] + [(-1)bni_24]x103[4] + [bni_24]x102[4] ≥ 0∧[1 + (-1)bso_25] ≥ 0)



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

    (23)    (x103[4] ≥ 0∧[98] + [-1]x103[4] ≥ 0∧[99] + [-1]x103[4] ≥ 0∧x104[4] + [-1] + [-1]x103[4] ≥ 0∧x103[4] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD2(&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1))), 1729_0_sort_GE(x102[4], x103[4], x104[4]))), ≥)∧[bni_24 + (-1)Bound*bni_24] + [(-1)bni_24]x103[4] + [bni_24]x102[4] ≥ 0∧[1 + (-1)bso_25] ≥ 0)



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

    (24)    (x103[4] ≥ 0∧[98] + [-1]x103[4] ≥ 0∧[99] + [-1]x103[4] ≥ 0∧x104[4] + [-1] + [-1]x103[4] ≥ 0∧x103[4] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD2(&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1))), 1729_0_sort_GE(x102[4], x103[4], x104[4]))), ≥)∧[bni_24 + (-1)Bound*bni_24] + [(-1)bni_24]x103[4] + [bni_24]x102[4] ≥ 0∧[1 + (-1)bso_25] ≥ 0)



    We simplified constraint (24) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (25)    (x103[4] ≥ 0∧[98] + [-1]x103[4] ≥ 0∧[99] + [-1]x103[4] ≥ 0∧x104[4] + [-1] + [-1]x103[4] ≥ 0∧x103[4] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD2(&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1))), 1729_0_sort_GE(x102[4], x103[4], x104[4]))), ≥)∧[bni_24] = 0∧[bni_24 + (-1)Bound*bni_24] + [(-1)bni_24]x103[4] ≥ 0∧0 = 0∧[1 + (-1)bso_25] ≥ 0)



    We simplified constraint (25) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (26)    (x103[4] ≥ 0∧[98] + [-1]x103[4] ≥ 0∧[99] + [-1]x103[4] ≥ 0∧x104[4] ≥ 0∧x103[4] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD2(&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1))), 1729_0_sort_GE(x102[4], x103[4], x104[4]))), ≥)∧[bni_24] = 0∧[bni_24 + (-1)Bound*bni_24] + [(-1)bni_24]x103[4] ≥ 0∧0 = 0∧[1 + (-1)bso_25] ≥ 0)







For Pair COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7]))) the following chains were created:
  • We consider the chain COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7]))) which results in the following constraint:

    (27)    (COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7]))≥NonInfC∧COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7]))≥1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))∧(UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))), ≥))



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

    (28)    ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))), ≥)∧[(-1)bso_27] ≥ 0)



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

    (29)    ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))), ≥)∧[(-1)bso_27] ≥ 0)



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

    (30)    ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))), ≥)∧[(-1)bso_27] ≥ 0)



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

    (31)    ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_27] ≥ 0)







For Pair 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])) → COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])) the following chains were created:
  • We consider the chain 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])) → COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])), COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7]))) which results in the following constraint:

    (32)    (&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0))=TRUE∧1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])=1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7]) ⇒ 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))≥NonInfC∧1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))≥COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))∧(UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥))



    We simplified constraint (32) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (33)    (>(x102[6], 0)=TRUE∧>=(x105[6], x104[6])=TRUE∧>=(x103[6], 0)=TRUE ⇒ 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))≥NonInfC∧1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))≥COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))∧(UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥))



    We simplified constraint (33) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (34)    (x102[6] + [-1] ≥ 0∧x105[6] + [-1]x104[6] ≥ 0∧x103[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[(-1)Bound*bni_28] + [(-1)bni_28]x103[6] + [bni_28]x102[6] ≥ 0∧[(-1)bso_29] ≥ 0)



    We simplified constraint (34) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (35)    (x102[6] + [-1] ≥ 0∧x105[6] + [-1]x104[6] ≥ 0∧x103[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[(-1)Bound*bni_28] + [(-1)bni_28]x103[6] + [bni_28]x102[6] ≥ 0∧[(-1)bso_29] ≥ 0)



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

    (36)    (x102[6] + [-1] ≥ 0∧x105[6] + [-1]x104[6] ≥ 0∧x103[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[(-1)Bound*bni_28] + [(-1)bni_28]x103[6] + [bni_28]x102[6] ≥ 0∧[(-1)bso_29] ≥ 0)



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

    (37)    (x102[6] ≥ 0∧x105[6] + [-1]x104[6] ≥ 0∧x103[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[(-1)Bound*bni_28 + bni_28] + [(-1)bni_28]x103[6] + [bni_28]x102[6] ≥ 0∧[(-1)bso_29] ≥ 0)



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

    (38)    (x102[6] ≥ 0∧x105[6] ≥ 0∧x103[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[(-1)Bound*bni_28 + bni_28] + [(-1)bni_28]x103[6] + [bni_28]x102[6] ≥ 0∧[(-1)bso_29] ≥ 0)



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

    (39)    (x102[6] ≥ 0∧x105[6] ≥ 0∧x103[6] ≥ 0∧x104[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[(-1)Bound*bni_28 + bni_28] + [(-1)bni_28]x103[6] + [bni_28]x102[6] ≥ 0∧[(-1)bso_29] ≥ 0)


    (40)    (x102[6] ≥ 0∧x105[6] ≥ 0∧x103[6] ≥ 0∧x104[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[(-1)Bound*bni_28 + bni_28] + [(-1)bni_28]x103[6] + [bni_28]x102[6] ≥ 0∧[(-1)bso_29] ≥ 0)







For Pair COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3])) → 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3])) the following chains were created:
  • We consider the chain COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3])) → 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3])) which results in the following constraint:

    (41)    (COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3]))≥NonInfC∧COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3]))≥1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))∧(UIncreasing(1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))), ≥))



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

    (42)    ((UIncreasing(1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))), ≥)∧[1 + (-1)bso_31] ≥ 0)



    We simplified constraint (42) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (43)    ((UIncreasing(1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))), ≥)∧[1 + (-1)bso_31] ≥ 0)



    We simplified constraint (43) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (44)    ((UIncreasing(1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))), ≥)∧[1 + (-1)bso_31] ≥ 0)



    We simplified constraint (44) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (45)    ((UIncreasing(1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_31] ≥ 0)







For Pair 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2])) → COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2])) the following chains were created:
  • We consider the chain 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2])) → COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2])), COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3])) → 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3])) which results in the following constraint:

    (46)    (&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1)))=TRUE∧1729_0_sort_GE(x102[2], x103[2], x104[2])=1729_0_sort_GE(x102[3], x103[3], x104[3]) ⇒ 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2]))≥NonInfC∧1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2]))≥COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))∧(UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))), ≥))



    We simplified constraint (46) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (47)    (<=(1, +(x103[2], 1))=TRUE∧>=(99, +(x103[2], 1))=TRUE∧<=(x103[2], 99)=TRUE∧>(x104[2], x103[2])=TRUE∧>=(x103[2], 0)=TRUE ⇒ 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2]))≥NonInfC∧1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2]))≥COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))∧(UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))), ≥))



    We simplified constraint (47) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (48)    (x103[2] ≥ 0∧[98] + [-1]x103[2] ≥ 0∧[99] + [-1]x103[2] ≥ 0∧x104[2] + [-1] + [-1]x103[2] ≥ 0∧x103[2] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))), ≥)∧[bni_32 + (-1)Bound*bni_32] + [(-1)bni_32]x103[2] + [bni_32]x102[2] ≥ 0∧[(-1)bso_33] ≥ 0)



    We simplified constraint (48) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (49)    (x103[2] ≥ 0∧[98] + [-1]x103[2] ≥ 0∧[99] + [-1]x103[2] ≥ 0∧x104[2] + [-1] + [-1]x103[2] ≥ 0∧x103[2] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))), ≥)∧[bni_32 + (-1)Bound*bni_32] + [(-1)bni_32]x103[2] + [bni_32]x102[2] ≥ 0∧[(-1)bso_33] ≥ 0)



    We simplified constraint (49) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (50)    (x103[2] ≥ 0∧[98] + [-1]x103[2] ≥ 0∧[99] + [-1]x103[2] ≥ 0∧x104[2] + [-1] + [-1]x103[2] ≥ 0∧x103[2] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))), ≥)∧[bni_32 + (-1)Bound*bni_32] + [(-1)bni_32]x103[2] + [bni_32]x102[2] ≥ 0∧[(-1)bso_33] ≥ 0)



    We simplified constraint (50) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (51)    (x103[2] ≥ 0∧[98] + [-1]x103[2] ≥ 0∧[99] + [-1]x103[2] ≥ 0∧x104[2] + [-1] + [-1]x103[2] ≥ 0∧x103[2] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))), ≥)∧[bni_32] = 0∧[bni_32 + (-1)Bound*bni_32] + [(-1)bni_32]x103[2] ≥ 0∧0 = 0∧[(-1)bso_33] ≥ 0)



    We simplified constraint (51) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (52)    (x103[2] ≥ 0∧[98] + [-1]x103[2] ≥ 0∧[99] + [-1]x103[2] ≥ 0∧x104[2] ≥ 0∧x103[2] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))), ≥)∧[bni_32] = 0∧[bni_32 + (-1)Bound*bni_32] + [(-1)bni_32]x103[2] ≥ 0∧0 = 0∧[(-1)bso_33] ≥ 0)







To summarize, we get the following constraints P≥ for the following pairs.
  • COND_1810_1_MAIN_INVOKEMETHOD(TRUE, 1810_0_sort_LE(x0[9], x1[9], x2[9], x3[9])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0[9], +(x1[9], 1), -(100, x0[9])))
    • ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0[9], +(x1[9], 1), -(100, x0[9])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_19] ≥ 0)

  • 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8])) → COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))
    • (x1[8] ≥ 0∧[98] + [-1]x1[8] ≥ 0∧x0[8] ≥ 0∧[99] + [-1]x1[8] ≥ 0∧x2[8] ≥ 0∧x1[8] ≥ 0∧x3[8] ≥ 0 ⇒ (UIncreasing(COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))), ≥)∧[(-1)Bound*bni_20 + bni_20] + [(-1)bni_20]x1[8] + [bni_20]x0[8] ≥ 0∧[(-1)bso_21] ≥ 0)
    • (x1[8] ≥ 0∧[98] + [-1]x1[8] ≥ 0∧x0[8] ≥ 0∧[99] + [-1]x1[8] ≥ 0∧x2[8] ≥ 0∧x1[8] ≥ 0∧x3[8] ≥ 0 ⇒ (UIncreasing(COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))), ≥)∧[(-1)Bound*bni_20 + bni_20] + [(-1)bni_20]x1[8] + [bni_20]x0[8] ≥ 0∧[(-1)bso_21] ≥ 0)

  • COND_1729_1_MAIN_INVOKEMETHOD2(TRUE, 1729_0_sort_GE(x102[5], x103[5], x104[5])) → 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5]))
    • ((UIncreasing(1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5]))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_23] ≥ 0)

  • 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[4], x103[4], x104[4])) → COND_1729_1_MAIN_INVOKEMETHOD2(&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1))), 1729_0_sort_GE(x102[4], x103[4], x104[4]))
    • (x103[4] ≥ 0∧[98] + [-1]x103[4] ≥ 0∧[99] + [-1]x103[4] ≥ 0∧x104[4] ≥ 0∧x103[4] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD2(&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1))), 1729_0_sort_GE(x102[4], x103[4], x104[4]))), ≥)∧[bni_24] = 0∧[bni_24 + (-1)Bound*bni_24] + [(-1)bni_24]x103[4] ≥ 0∧0 = 0∧[1 + (-1)bso_25] ≥ 0)

  • COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))
    • ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_27] ≥ 0)

  • 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])) → COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))
    • (x102[6] ≥ 0∧x105[6] ≥ 0∧x103[6] ≥ 0∧x104[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[(-1)Bound*bni_28 + bni_28] + [(-1)bni_28]x103[6] + [bni_28]x102[6] ≥ 0∧[(-1)bso_29] ≥ 0)
    • (x102[6] ≥ 0∧x105[6] ≥ 0∧x103[6] ≥ 0∧x104[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[(-1)Bound*bni_28 + bni_28] + [(-1)bni_28]x103[6] + [bni_28]x102[6] ≥ 0∧[(-1)bso_29] ≥ 0)

  • COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3])) → 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))
    • ((UIncreasing(1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_31] ≥ 0)

  • 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2])) → COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))
    • (x103[2] ≥ 0∧[98] + [-1]x103[2] ≥ 0∧[99] + [-1]x103[2] ≥ 0∧x104[2] ≥ 0∧x103[2] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))), ≥)∧[bni_32] = 0∧[bni_32 + (-1)Bound*bni_32] + [(-1)bni_32]x103[2] ≥ 0∧0 = 0∧[(-1)bso_33] ≥ 0)




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

POL(TRUE) = 0   
POL(FALSE) = 0   
POL(COND_1810_1_MAIN_INVOKEMETHOD(x1, x2)) = [1] + x2   
POL(1810_0_sort_LE(x1, x2, x3, x4)) = [-1] + [-1]x2 + x1   
POL(1729_1_MAIN_INVOKEMETHOD(x1)) = [1] + [-1]x1   
POL(1729_0_sort_GE(x1, x2, x3)) = x2 + [-1]x1   
POL(+(x1, x2)) = x1 + x2   
POL(1) = [1]   
POL(-(x1, x2)) = x1 + [-1]x2   
POL(100) = [100]   
POL(1810_1_MAIN_INVOKEMETHOD(x1)) = [1] + x1   
POL(&&(x1, x2)) = [-1]   
POL(<(x1, x2)) = [-1]   
POL(>=(x1, x2)) = [-1]   
POL(0) = 0   
POL(<=(x1, x2)) = [-1]   
POL(99) = [99]   
POL(>(x1, x2)) = [-1]   
POL(COND_1729_1_MAIN_INVOKEMETHOD2(x1, x2)) = [-1]x2   
POL(COND_1809_1_MAIN_INVOKEMETHOD(x1, x2)) = [-1] + [-1]x2   
POL(1809_0_sort_LE(x1, x2, x3, x4)) = [-1] + x2 + [-1]x1   
POL(1809_1_MAIN_INVOKEMETHOD(x1)) = [-1] + [-1]x1   
POL(COND_1729_1_MAIN_INVOKEMETHOD1(x1, x2)) = [1] + [-1]x2   

The following pairs are in P>:

1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[4], x103[4], x104[4])) → COND_1729_1_MAIN_INVOKEMETHOD2(&&(&&(&&(&&(>(x104[4], x103[4]), >=(x103[4], 0)), <=(x103[4], 99)), >=(99, +(x103[4], 1))), <=(1, +(x103[4], 1))), 1729_0_sort_GE(x102[4], x103[4], x104[4]))
COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3])) → 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))

The following pairs are in Pbound:

1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8])) → COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))

The following pairs are in P≥:

COND_1810_1_MAIN_INVOKEMETHOD(TRUE, 1810_0_sort_LE(x0[9], x1[9], x2[9], x3[9])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0[9], +(x1[9], 1), -(100, x0[9])))
1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8])) → COND_1810_1_MAIN_INVOKEMETHOD(&&(&&(&&(&&(&&(<(x3[8], x2[8]), >=(x1[8], 0)), <=(x1[8], 99)), >(x0[8], 0)), >=(99, +(x1[8], 1))), <=(1, +(x1[8], 1))), 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))
COND_1729_1_MAIN_INVOKEMETHOD2(TRUE, 1729_0_sort_GE(x102[5], x103[5], x104[5])) → 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5]))
COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))
1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])) → COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))
1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2])) → COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))

There are no usable rules.

(26) Complex Obligation (AND)

(27) 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:
(9): COND_1810_1_MAIN_INVOKEMETHOD(TRUE, 1810_0_sort_LE(x0[9], x1[9], x2[9], x3[9])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0[9], x1[9] + 1, 100 - x0[9]))
(8): 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8])) → COND_1810_1_MAIN_INVOKEMETHOD(x3[8] < x2[8] && x1[8] >= 0 && x1[8] <= 99 && x0[8] > 0 && 99 >= x1[8] + 1 && 1 <= x1[8] + 1, 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]))
(5): COND_1729_1_MAIN_INVOKEMETHOD2(TRUE, 1729_0_sort_GE(x102[5], x103[5], x104[5])) → 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5]))
(7): COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], x103[7] + 1, 100 - x102[7]))
(6): 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])) → COND_1809_1_MAIN_INVOKEMETHOD(x105[6] >= x104[6] && x103[6] >= 0 && x102[6] > 0, 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))
(2): 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2])) → COND_1729_1_MAIN_INVOKEMETHOD1(x104[2] > x103[2] && x103[2] >= 0 && x103[2] <= 99 && 99 >= x103[2] + 1 && 1 <= x103[2] + 1, 1729_0_sort_GE(x102[2], x103[2], x104[2]))

(7) -> (2), if ((1729_0_sort_GE(x102[7], x103[7] + 1, 100 - x102[7]) →* 1729_0_sort_GE(x102[2], x103[2], x104[2])))


(9) -> (2), if ((1729_0_sort_GE(x0[9], x1[9] + 1, 100 - x0[9]) →* 1729_0_sort_GE(x102[2], x103[2], x104[2])))


(6) -> (7), if ((x105[6] >= x104[6] && x103[6] >= 0 && x102[6] > 0 →* TRUE)∧(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]) →* 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])))


(5) -> (8), if ((1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5]) →* 1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8])))


(8) -> (9), if ((x3[8] < x2[8] && x1[8] >= 0 && x1[8] <= 99 && x0[8] > 0 && 99 >= x1[8] + 1 && 1 <= x1[8] + 1 →* TRUE)∧(1810_0_sort_LE(x0[8], x1[8], x2[8], x3[8]) →* 1810_0_sort_LE(x0[9], x1[9], x2[9], x3[9])))



The set Q is empty.

(28) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 6 less nodes.

(29) TRUE

(30) 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:
(9): COND_1810_1_MAIN_INVOKEMETHOD(TRUE, 1810_0_sort_LE(x0[9], x1[9], x2[9], x3[9])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x0[9], x1[9] + 1, 100 - x0[9]))
(5): COND_1729_1_MAIN_INVOKEMETHOD2(TRUE, 1729_0_sort_GE(x102[5], x103[5], x104[5])) → 1810_1_MAIN_INVOKEMETHOD(1810_0_sort_LE(x102[5], x103[5], x206[5], x207[5]))
(4): 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[4], x103[4], x104[4])) → COND_1729_1_MAIN_INVOKEMETHOD2(x104[4] > x103[4] && x103[4] >= 0 && x103[4] <= 99 && 99 >= x103[4] + 1 && 1 <= x103[4] + 1, 1729_0_sort_GE(x102[4], x103[4], x104[4]))
(7): COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], x103[7] + 1, 100 - x102[7]))
(6): 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])) → COND_1809_1_MAIN_INVOKEMETHOD(x105[6] >= x104[6] && x103[6] >= 0 && x102[6] > 0, 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))
(3): COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3])) → 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))
(2): 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2])) → COND_1729_1_MAIN_INVOKEMETHOD1(x104[2] > x103[2] && x103[2] >= 0 && x103[2] <= 99 && 99 >= x103[2] + 1 && 1 <= x103[2] + 1, 1729_0_sort_GE(x102[2], x103[2], x104[2]))

(7) -> (2), if ((1729_0_sort_GE(x102[7], x103[7] + 1, 100 - x102[7]) →* 1729_0_sort_GE(x102[2], x103[2], x104[2])))


(9) -> (2), if ((1729_0_sort_GE(x0[9], x1[9] + 1, 100 - x0[9]) →* 1729_0_sort_GE(x102[2], x103[2], x104[2])))


(2) -> (3), if ((x104[2] > x103[2] && x103[2] >= 0 && x103[2] <= 99 && 99 >= x103[2] + 1 && 1 <= x103[2] + 1 →* TRUE)∧(1729_0_sort_GE(x102[2], x103[2], x104[2]) →* 1729_0_sort_GE(x102[3], x103[3], x104[3])))


(7) -> (4), if ((1729_0_sort_GE(x102[7], x103[7] + 1, 100 - x102[7]) →* 1729_0_sort_GE(x102[4], x103[4], x104[4])))


(9) -> (4), if ((1729_0_sort_GE(x0[9], x1[9] + 1, 100 - x0[9]) →* 1729_0_sort_GE(x102[4], x103[4], x104[4])))


(4) -> (5), if ((x104[4] > x103[4] && x103[4] >= 0 && x103[4] <= 99 && 99 >= x103[4] + 1 && 1 <= x103[4] + 1 →* TRUE)∧(1729_0_sort_GE(x102[4], x103[4], x104[4]) →* 1729_0_sort_GE(x102[5], x103[5], x104[5])))


(3) -> (6), if ((1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]) →* 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])))


(6) -> (7), if ((x105[6] >= x104[6] && x103[6] >= 0 && x102[6] > 0 →* TRUE)∧(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]) →* 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])))



The set Q is empty.

(31) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes.

(32) 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:
(7): COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], x103[7] + 1, 100 - x102[7]))
(6): 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])) → COND_1809_1_MAIN_INVOKEMETHOD(x105[6] >= x104[6] && x103[6] >= 0 && x102[6] > 0, 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))
(3): COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3])) → 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))
(2): 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2])) → COND_1729_1_MAIN_INVOKEMETHOD1(x104[2] > x103[2] && x103[2] >= 0 && x103[2] <= 99 && 99 >= x103[2] + 1 && 1 <= x103[2] + 1, 1729_0_sort_GE(x102[2], x103[2], x104[2]))

(7) -> (2), if ((1729_0_sort_GE(x102[7], x103[7] + 1, 100 - x102[7]) →* 1729_0_sort_GE(x102[2], x103[2], x104[2])))


(2) -> (3), if ((x104[2] > x103[2] && x103[2] >= 0 && x103[2] <= 99 && 99 >= x103[2] + 1 && 1 <= x103[2] + 1 →* TRUE)∧(1729_0_sort_GE(x102[2], x103[2], x104[2]) →* 1729_0_sort_GE(x102[3], x103[3], x104[3])))


(3) -> (6), if ((1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]) →* 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])))


(6) -> (7), if ((x105[6] >= x104[6] && x103[6] >= 0 && x102[6] > 0 →* TRUE)∧(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]) →* 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])))



The set Q is empty.

(33) 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_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7]))) the following chains were created:
  • We consider the chain COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7]))) which results in the following constraint:

    (1)    (COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7]))≥NonInfC∧COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7]))≥1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))∧(UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))), ≥))



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

    (2)    ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))), ≥)∧[(-1)bso_14] ≥ 0)



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

    (3)    ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))), ≥)∧[(-1)bso_14] ≥ 0)



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

    (4)    ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))), ≥)∧[(-1)bso_14] ≥ 0)



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

    (5)    ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_14] ≥ 0)







For Pair 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])) → COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])) the following chains were created:
  • We consider the chain 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])) → COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])), COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7]))) which results in the following constraint:

    (6)    (&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0))=TRUE∧1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])=1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7]) ⇒ 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))≥NonInfC∧1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))≥COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))∧(UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥))



    We simplified constraint (6) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (7)    (>(x102[6], 0)=TRUE∧>=(x105[6], x104[6])=TRUE∧>=(x103[6], 0)=TRUE ⇒ 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))≥NonInfC∧1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))≥COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))∧(UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥))



    We simplified constraint (7) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (8)    (x102[6] + [-1] ≥ 0∧x105[6] + [-1]x104[6] ≥ 0∧x103[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[(2)bni_15 + (-1)Bound*bni_15] + [(-1)bni_15]x103[6] ≥ 0∧[1 + (-1)bso_16] ≥ 0)



    We simplified constraint (8) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (9)    (x102[6] + [-1] ≥ 0∧x105[6] + [-1]x104[6] ≥ 0∧x103[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[(2)bni_15 + (-1)Bound*bni_15] + [(-1)bni_15]x103[6] ≥ 0∧[1 + (-1)bso_16] ≥ 0)



    We simplified constraint (9) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (10)    (x102[6] + [-1] ≥ 0∧x105[6] + [-1]x104[6] ≥ 0∧x103[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[(2)bni_15 + (-1)Bound*bni_15] + [(-1)bni_15]x103[6] ≥ 0∧[1 + (-1)bso_16] ≥ 0)



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

    (11)    (x102[6] ≥ 0∧x105[6] + [-1]x104[6] ≥ 0∧x103[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[(2)bni_15 + (-1)Bound*bni_15] + [(-1)bni_15]x103[6] ≥ 0∧[1 + (-1)bso_16] ≥ 0)



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

    (12)    (x102[6] ≥ 0∧x105[6] ≥ 0∧x103[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[(2)bni_15 + (-1)Bound*bni_15] + [(-1)bni_15]x103[6] ≥ 0∧[1 + (-1)bso_16] ≥ 0)



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

    (13)    (x102[6] ≥ 0∧x105[6] ≥ 0∧x103[6] ≥ 0∧x104[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[(2)bni_15 + (-1)Bound*bni_15] + [(-1)bni_15]x103[6] ≥ 0∧[1 + (-1)bso_16] ≥ 0)


    (14)    (x102[6] ≥ 0∧x105[6] ≥ 0∧x103[6] ≥ 0∧x104[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[(2)bni_15 + (-1)Bound*bni_15] + [(-1)bni_15]x103[6] ≥ 0∧[1 + (-1)bso_16] ≥ 0)







For Pair COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3])) → 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3])) the following chains were created:
  • We consider the chain COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3])) → 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3])) which results in the following constraint:

    (15)    (COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3]))≥NonInfC∧COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3]))≥1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))∧(UIncreasing(1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))), ≥))



    We simplified constraint (15) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (16)    ((UIncreasing(1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))), ≥)∧[(-1)bso_18] ≥ 0)



    We simplified constraint (16) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (17)    ((UIncreasing(1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))), ≥)∧[(-1)bso_18] ≥ 0)



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

    (18)    ((UIncreasing(1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))), ≥)∧[(-1)bso_18] ≥ 0)



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

    (19)    ((UIncreasing(1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_18] ≥ 0)







For Pair 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2])) → COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2])) the following chains were created:
  • We consider the chain 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2])) → COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2])), COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3])) → 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3])) which results in the following constraint:

    (20)    (&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1)))=TRUE∧1729_0_sort_GE(x102[2], x103[2], x104[2])=1729_0_sort_GE(x102[3], x103[3], x104[3]) ⇒ 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2]))≥NonInfC∧1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2]))≥COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))∧(UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))), ≥))



    We simplified constraint (20) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (21)    (<=(1, +(x103[2], 1))=TRUE∧>=(99, +(x103[2], 1))=TRUE∧<=(x103[2], 99)=TRUE∧>(x104[2], x103[2])=TRUE∧>=(x103[2], 0)=TRUE ⇒ 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2]))≥NonInfC∧1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2]))≥COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))∧(UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))), ≥))



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

    (22)    (x103[2] ≥ 0∧[98] + [-1]x103[2] ≥ 0∧[99] + [-1]x103[2] ≥ 0∧x104[2] + [-1] + [-1]x103[2] ≥ 0∧x103[2] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))), ≥)∧[(2)bni_19 + (-1)Bound*bni_19] + [(-1)bni_19]x103[2] ≥ 0∧[(-1)bso_20] ≥ 0)



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

    (23)    (x103[2] ≥ 0∧[98] + [-1]x103[2] ≥ 0∧[99] + [-1]x103[2] ≥ 0∧x104[2] + [-1] + [-1]x103[2] ≥ 0∧x103[2] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))), ≥)∧[(2)bni_19 + (-1)Bound*bni_19] + [(-1)bni_19]x103[2] ≥ 0∧[(-1)bso_20] ≥ 0)



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

    (24)    (x103[2] ≥ 0∧[98] + [-1]x103[2] ≥ 0∧[99] + [-1]x103[2] ≥ 0∧x104[2] + [-1] + [-1]x103[2] ≥ 0∧x103[2] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))), ≥)∧[(2)bni_19 + (-1)Bound*bni_19] + [(-1)bni_19]x103[2] ≥ 0∧[(-1)bso_20] ≥ 0)



    We simplified constraint (24) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (25)    (x103[2] ≥ 0∧[98] + [-1]x103[2] ≥ 0∧[99] + [-1]x103[2] ≥ 0∧x104[2] + [-1] + [-1]x103[2] ≥ 0∧x103[2] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))), ≥)∧0 = 0∧[(2)bni_19 + (-1)Bound*bni_19] + [(-1)bni_19]x103[2] ≥ 0∧0 = 0∧[(-1)bso_20] ≥ 0)



    We simplified constraint (25) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (26)    (x103[2] ≥ 0∧[98] + [-1]x103[2] ≥ 0∧[99] + [-1]x103[2] ≥ 0∧x104[2] ≥ 0∧x103[2] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))), ≥)∧0 = 0∧[(2)bni_19 + (-1)Bound*bni_19] + [(-1)bni_19]x103[2] ≥ 0∧0 = 0∧[(-1)bso_20] ≥ 0)







To summarize, we get the following constraints P≥ for the following pairs.
  • COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))
    • ((UIncreasing(1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_14] ≥ 0)

  • 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])) → COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))
    • (x102[6] ≥ 0∧x105[6] ≥ 0∧x103[6] ≥ 0∧x104[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[(2)bni_15 + (-1)Bound*bni_15] + [(-1)bni_15]x103[6] ≥ 0∧[1 + (-1)bso_16] ≥ 0)
    • (x102[6] ≥ 0∧x105[6] ≥ 0∧x103[6] ≥ 0∧x104[6] ≥ 0 ⇒ (UIncreasing(COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))), ≥)∧[(2)bni_15 + (-1)Bound*bni_15] + [(-1)bni_15]x103[6] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

  • COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3])) → 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))
    • ((UIncreasing(1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))), ≥)∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_18] ≥ 0)

  • 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2])) → COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))
    • (x103[2] ≥ 0∧[98] + [-1]x103[2] ≥ 0∧[99] + [-1]x103[2] ≥ 0∧x104[2] ≥ 0∧x103[2] ≥ 0 ⇒ (UIncreasing(COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))), ≥)∧0 = 0∧[(2)bni_19 + (-1)Bound*bni_19] + [(-1)bni_19]x103[2] ≥ 0∧0 = 0∧[(-1)bso_20] ≥ 0)




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

POL(TRUE) = 0   
POL(FALSE) = 0   
POL(COND_1809_1_MAIN_INVOKEMETHOD(x1, x2)) = [-1]x2   
POL(1809_0_sort_LE(x1, x2, x3, x4)) = [-1] + x2   
POL(1729_1_MAIN_INVOKEMETHOD(x1)) = [2] + [-1]x1   
POL(1729_0_sort_GE(x1, x2, x3)) = x2   
POL(+(x1, x2)) = x1 + x2   
POL(1) = [1]   
POL(-(x1, x2)) = x1 + [-1]x2   
POL(100) = [100]   
POL(1809_1_MAIN_INVOKEMETHOD(x1)) = [1] + [-1]x1   
POL(&&(x1, x2)) = 0   
POL(>=(x1, x2)) = [-1]   
POL(0) = 0   
POL(>(x1, x2)) = [-1]   
POL(COND_1729_1_MAIN_INVOKEMETHOD1(x1, x2)) = [2] + [-1]x2   
POL(<=(x1, x2)) = [-1]   
POL(99) = [99]   

The following pairs are in P>:

1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])) → COND_1809_1_MAIN_INVOKEMETHOD(&&(&&(>=(x105[6], x104[6]), >=(x103[6], 0)), >(x102[6], 0)), 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))

The following pairs are in Pbound:

1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2])) → COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))

The following pairs are in P≥:

COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], +(x103[7], 1), -(100, x102[7])))
COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3])) → 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))
1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2])) → COND_1729_1_MAIN_INVOKEMETHOD1(&&(&&(&&(&&(>(x104[2], x103[2]), >=(x103[2], 0)), <=(x103[2], 99)), >=(99, +(x103[2], 1))), <=(1, +(x103[2], 1))), 1729_0_sort_GE(x102[2], x103[2], x104[2]))

There are no usable rules.

(34) Complex Obligation (AND)

(35) 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:
(7): COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], x103[7] + 1, 100 - x102[7]))
(3): COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3])) → 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))
(2): 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[2], x103[2], x104[2])) → COND_1729_1_MAIN_INVOKEMETHOD1(x104[2] > x103[2] && x103[2] >= 0 && x103[2] <= 99 && 99 >= x103[2] + 1 && 1 <= x103[2] + 1, 1729_0_sort_GE(x102[2], x103[2], x104[2]))

(7) -> (2), if ((1729_0_sort_GE(x102[7], x103[7] + 1, 100 - x102[7]) →* 1729_0_sort_GE(x102[2], x103[2], x104[2])))


(2) -> (3), if ((x104[2] > x103[2] && x103[2] >= 0 && x103[2] <= 99 && 99 >= x103[2] + 1 && 1 <= x103[2] + 1 →* TRUE)∧(1729_0_sort_GE(x102[2], x103[2], x104[2]) →* 1729_0_sort_GE(x102[3], x103[3], x104[3])))



The set Q is empty.

(36) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 3 less nodes.

(37) TRUE

(38) 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:
(7): COND_1809_1_MAIN_INVOKEMETHOD(TRUE, 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])) → 1729_1_MAIN_INVOKEMETHOD(1729_0_sort_GE(x102[7], x103[7] + 1, 100 - x102[7]))
(6): 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])) → COND_1809_1_MAIN_INVOKEMETHOD(x105[6] >= x104[6] && x103[6] >= 0 && x102[6] > 0, 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]))
(3): COND_1729_1_MAIN_INVOKEMETHOD1(TRUE, 1729_0_sort_GE(x102[3], x103[3], x104[3])) → 1809_1_MAIN_INVOKEMETHOD(1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]))

(3) -> (6), if ((1809_0_sort_LE(x102[3], x103[3], x206[3], x207[3]) →* 1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6])))


(6) -> (7), if ((x105[6] >= x104[6] && x103[6] >= 0 && x102[6] > 0 →* TRUE)∧(1809_0_sort_LE(x102[6], x103[6], x104[6], x105[6]) →* 1809_0_sort_LE(x102[7], x103[7], x104[7], x105[7])))



The set Q is empty.

(39) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 3 less nodes.

(40) TRUE