Termination proof of /tmp/tmpJwfw5e/PastaC7.jar

Termination of the given JBC could be proven:

0 JBC

↳1 JBCToGraph (⇒, 230 ms)

↳2 JBCTerminationGraph

↳3 TerminationGraphToSCCProof (⇒, 0 ms)

↳4 JBCTerminationSCC

↳5 SCCToIDPv1Proof (⇒, 100 ms)

↳6 IDP

↳7 IDPNonInfProof (⇒, 580 ms)

↳8 IDP

↳9 IDependencyGraphProof (⇔, 0 ms)

↳10 TRUE

(0) Obligation:

JBC Problem based on JBC Program:
Manifest-Version: 1.0 Created-By: 1.6.0_16 (Sun Microsystems Inc.) Main-Class: PastaC7

/**
 * Example taken from "A Term Rewriting Approach to the Automated Termination
 * Analysis of Imperative Programs" (http://www.cs.unm.edu/~spf/papers/2009-02.pdf)
 * and converted to Java.
 */

public class PastaC7 {
    public static void main(String[] args) {
        Random.args = args;
        int i = Random.random();
        int j = Random.random();
        int k = Random.random();

        while (i <= 100 && j <= k) {
            int t = i;
            i = j;
            j = i + 1;
            k--;
        }
    }
}


public class Random {
  static String[] args;
  static int index = 0;

  public static int random() {
    String string = args[index];
    index++;
    return string.length();
  }
}

(1) JBCToGraph (SOUND transformation)

Constructed TerminationGraph.

(2) Obligation:

Termination Graph based on JBC Program:
PastaC7.main([Ljava/lang/String;)V: Graph of 260 nodes with 1 SCC.

(3) TerminationGraphToSCCProof (SOUND transformation)

Splitted TerminationGraph to 1 SCCs.

(4) Obligation:

SCC of termination graph based on JBC Program.
SCC contains nodes from the following methods: PastaC7.main([Ljava/lang/String;)V
SCC calls the following helper methods:
Performed SCC analyses: UsedFieldsAnalysis

(5) SCCToIDPv1Proof (SOUND transformation)

Transformed FIGraph SCCs to IDPs. Log:

Generated 19 rules for P and 0 rules for R.

P rules:
911_0_main_ConstantStackPush(EOS(STATIC_911), i200, i201, i202, i200) → 914_0_main_GT(EOS(STATIC_914), i200, i201, i202, i200, 100)
914_0_main_GT(EOS(STATIC_914), i210, i201, i202, i210, matching1) → 916_0_main_GT(EOS(STATIC_916), i210, i201, i202, i210, 100) | =(matching1, 100)
916_0_main_GT(EOS(STATIC_916), i210, i201, i202, i210, matching1) → 919_0_main_Load(EOS(STATIC_919), i210, i201, i202) | &&(<=(i210, 100), =(matching1, 100))
919_0_main_Load(EOS(STATIC_919), i210, i201, i202) → 923_0_main_Load(EOS(STATIC_923), i210, i201, i202, i201)
923_0_main_Load(EOS(STATIC_923), i210, i201, i202, i201) → 927_0_main_GT(EOS(STATIC_927), i210, i201, i202, i201, i202)
927_0_main_GT(EOS(STATIC_927), i210, i201, i202, i201, i202) → 930_0_main_GT(EOS(STATIC_930), i210, i201, i202, i201, i202)
930_0_main_GT(EOS(STATIC_930), i210, i201, i202, i201, i202) → 937_0_main_Load(EOS(STATIC_937), i210, i201, i202) | <=(i201, i202)
937_0_main_Load(EOS(STATIC_937), i210, i201, i202) → 940_0_main_Store(EOS(STATIC_940), i201, i202, i210)
940_0_main_Store(EOS(STATIC_940), i201, i202, i210) → 942_0_main_Load(EOS(STATIC_942), i201, i202)
942_0_main_Load(EOS(STATIC_942), i201, i202) → 944_0_main_Store(EOS(STATIC_944), i202, i201)
944_0_main_Store(EOS(STATIC_944), i202, i201) → 946_0_main_Load(EOS(STATIC_946), i201, i202)
946_0_main_Load(EOS(STATIC_946), i201, i202) → 948_0_main_ConstantStackPush(EOS(STATIC_948), i201, i202, i201)
948_0_main_ConstantStackPush(EOS(STATIC_948), i201, i202, i201) → 950_0_main_IntArithmetic(EOS(STATIC_950), i201, i202, i201, 1)
950_0_main_IntArithmetic(EOS(STATIC_950), i201, i202, i201, matching1) → 952_0_main_Store(EOS(STATIC_952), i201, i202, +(i201, 1)) | =(matching1, 1)
952_0_main_Store(EOS(STATIC_952), i201, i202, i216) → 954_0_main_Inc(EOS(STATIC_954), i201, i216, i202)
954_0_main_Inc(EOS(STATIC_954), i201, i216, i202) → 956_0_main_JMP(EOS(STATIC_956), i201, i216, +(i202, -1))
956_0_main_JMP(EOS(STATIC_956), i201, i216, i217) → 961_0_main_Load(EOS(STATIC_961), i201, i216, i217)
961_0_main_Load(EOS(STATIC_961), i201, i216, i217) → 908_0_main_Load(EOS(STATIC_908), i201, i216, i217)
908_0_main_Load(EOS(STATIC_908), i200, i201, i202) → 911_0_main_ConstantStackPush(EOS(STATIC_911), i200, i201, i202, i200)
R rules:

Combined rules. Obtained 1 conditional rules for P and 0 conditional rules for R.

P rules:
911_0_main_ConstantStackPush(EOS(STATIC_911), x0, x1, x2, x0) → 911_0_main_ConstantStackPush(EOS(STATIC_911), x1, +(x1, 1), +(x2, -1), x1) | &&(>=(x2, x1), <=(x0, 100))
R rules:

Filtered ground terms:

911_0_main_ConstantStackPush(x1, x2, x3, x4, x5) → 911_0_main_ConstantStackPush(x2, x3, x4, x5)
EOS(x1) → EOS
Cond_911_0_main_ConstantStackPush(x1, x2, x3, x4, x5, x6) → Cond_911_0_main_ConstantStackPush(x1, x3, x4, x5, x6)

Filtered duplicate args:

911_0_main_ConstantStackPush(x1, x2, x3, x4) → 911_0_main_ConstantStackPush(x2, x3, x4)
Cond_911_0_main_ConstantStackPush(x1, x2, x3, x4, x5) → Cond_911_0_main_ConstantStackPush(x1, x3, x4, x5)

Filtered unneeded arguments:

Cond_911_0_main_ConstantStackPush(x1, x2, x3, x4) → Cond_911_0_main_ConstantStackPush(x1, x2, x3)

Combined rules. Obtained 1 conditional rules for P and 0 conditional rules for R.

P rules:
911_0_main_ConstantStackPush(x1, x2, x0) → 911_0_main_ConstantStackPush(+(x1, 1), +(x2, -1), x1) | &&(>=(x2, x1), <=(x0, 100))
R rules:

Finished conversion. Obtained 2 rules for P and 0 rules for R. System has predefined symbols.

P rules:
911_0_MAIN_CONSTANTSTACKPUSH(x1, x2, x0) → COND_911_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2, x1), <=(x0, 100)), x1, x2, x0)
COND_911_0_MAIN_CONSTANTSTACKPUSH(TRUE, x1, x2, x0) → 911_0_MAIN_CONSTANTSTACKPUSH(+(x1, 1), +(x2, -1), x1)
R rules:

(6) Obligation:

IDP problem:
The following function symbols are pre-defined:

!=	~	Neq: (Integer, Integer) -> Boolean
*	~	Mul: (Integer, Integer) -> Integer
>=	~	Ge: (Integer, Integer) -> Boolean
-1	~	UnaryMinus: (Integer) -> Integer
\|	~	Bwor: (Integer, Integer) -> Integer
/	~	Div: (Integer, Integer) -> Integer
=	~	Eq: (Integer, Integer) -> Boolean
	~	Bwxor: (Integer, Integer) -> Integer
\|\|	~	Lor: (Boolean, Boolean) -> Boolean
!	~	Lnot: (Boolean) -> Boolean
<	~	Lt: (Integer, Integer) -> Boolean
-	~	Sub: (Integer, Integer) -> Integer
<=	~	Le: (Integer, Integer) -> Boolean
>	~	Gt: (Integer, Integer) -> Boolean
~	~	Bwnot: (Integer) -> Integer
%	~	Mod: (Integer, Integer) -> Integer
&	~	Bwand: (Integer, Integer) -> Integer
+	~	Add: (Integer, Integer) -> Integer
&&	~	Land: (Boolean, Boolean) -> Boolean

The following domains are used:

Boolean, Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): 911_0_MAIN_CONSTANTSTACKPUSH(x1[0], x2[0], x0[0]) → COND_911_0_MAIN_CONSTANTSTACKPUSH(x2[0] >= x1[0] && x0[0] <= 100, x1[0], x2[0], x0[0])
(1): COND_911_0_MAIN_CONSTANTSTACKPUSH(TRUE, x1[1], x2[1], x0[1]) → 911_0_MAIN_CONSTANTSTACKPUSH(x1[1] + 1, x2[1] + -1, x1[1])

(0) -> (1), if (x2[0] >= x1[0] && x0[0] <= 100 ∧x1[0] →^* x1[1]∧x2[0] →^* x2[1]∧x0[0] →^* x0[1])

(1) -> (0), if (x1[1] + 1 →^* x1[0]∧x2[1] + -1 →^* x2[0]∧x1[1] →^* x0[0])

The set Q is empty.

(7) IDPNonInfProof (SOUND transformation)

Used the following options for this NonInfProof:
IDPGPoloSolver: Range: [(-1,2)] IsNat: false Interpretation Shape Heuristic: aprove.DPFramework.IDPProblem.Processors.nonInf.poly.IdpDefaultShapeHeuristic@535bf497 Constraint Generator: NonInfConstraintGenerator: PathGenerator: MetricPathGenerator: Max Left Steps: 1 Max Right Steps: 1

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 911_0_MAIN_CONSTANTSTACKPUSH(x1, x2, x0) → COND_911_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2, x1), <=(x0, 100)), x1, x2, x0) the following chains were created:

We consider the chain 911_0_MAIN_CONSTANTSTACKPUSH(x1[0], x2[0], x0[0]) → COND_911_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0]), COND_911_0_MAIN_CONSTANTSTACKPUSH(TRUE, x1[1], x2[1], x0[1]) → 911_0_MAIN_CONSTANTSTACKPUSH(+(x1[1], 1), +(x2[1], -1), x1[1]) which results in the following constraint:
(1)    (&&(>=(x2[0], x1[0]), <=(x0[0], 100))=TRUE∧x1[0]=x1[1]∧x2[0]=x2[1]∧x0[0]=x0[1] ⇒ 911_0_MAIN_CONSTANTSTACKPUSH(x1[0], x2[0], x0[0])≥NonInfC∧911_0_MAIN_CONSTANTSTACKPUSH(x1[0], x2[0], x0[0])≥COND_911_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0])∧(U^Increasing(COND_911_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0])), ≥))

We simplified constraint (1) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:
(2)    (>=(x2[0], x1[0])=TRUE∧<=(x0[0], 100)=TRUE ⇒ 911_0_MAIN_CONSTANTSTACKPUSH(x1[0], x2[0], x0[0])≥NonInfC∧911_0_MAIN_CONSTANTSTACKPUSH(x1[0], x2[0], x0[0])≥COND_911_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0])∧(U^Increasing(COND_911_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0])), ≥))

We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(3)    (x2[0] + [-1]x1[0] ≥ 0∧[100] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(COND_911_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0])), ≥)∧[bni_15 + (-1)Bound*bni_15] + [bni_15]x2[0] + [(-1)bni_15]x1[0] ≥ 0∧[(-1)bso_16] ≥ 0)

We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(4)    (x2[0] + [-1]x1[0] ≥ 0∧[100] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(COND_911_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0])), ≥)∧[bni_15 + (-1)Bound*bni_15] + [bni_15]x2[0] + [(-1)bni_15]x1[0] ≥ 0∧[(-1)bso_16] ≥ 0)

We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(5)    (x2[0] + [-1]x1[0] ≥ 0∧[100] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(COND_911_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0])), ≥)∧[bni_15 + (-1)Bound*bni_15] + [bni_15]x2[0] + [(-1)bni_15]x1[0] ≥ 0∧[(-1)bso_16] ≥ 0)

We simplified constraint (5) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(6)    (x2[0] ≥ 0∧[100] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(COND_911_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0])), ≥)∧[bni_15 + (-1)Bound*bni_15] + [bni_15]x2[0] ≥ 0∧[(-1)bso_16] ≥ 0)

We simplified constraint (6) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(7)    (x2[0] ≥ 0∧[100] + [-1]x0[0] ≥ 0∧x1[0] ≥ 0 ⇒ (U^Increasing(COND_911_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0])), ≥)∧[bni_15 + (-1)Bound*bni_15] + [bni_15]x2[0] ≥ 0∧[(-1)bso_16] ≥ 0)

(8)    (x2[0] ≥ 0∧[100] + [-1]x0[0] ≥ 0∧x1[0] ≥ 0 ⇒ (U^Increasing(COND_911_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0])), ≥)∧[bni_15 + (-1)Bound*bni_15] + [bni_15]x2[0] ≥ 0∧[(-1)bso_16] ≥ 0)

We simplified constraint (7) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(9)    (x2[0] ≥ 0∧[100] + [-1]x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_911_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0])), ≥)∧[bni_15 + (-1)Bound*bni_15] + [bni_15]x2[0] ≥ 0∧[(-1)bso_16] ≥ 0)

(10)    (x2[0] ≥ 0∧[100] + x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_911_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0])), ≥)∧[bni_15 + (-1)Bound*bni_15] + [bni_15]x2[0] ≥ 0∧[(-1)bso_16] ≥ 0)

We simplified constraint (8) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(11)    (x2[0] ≥ 0∧[100] + [-1]x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_911_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0])), ≥)∧[bni_15 + (-1)Bound*bni_15] + [bni_15]x2[0] ≥ 0∧[(-1)bso_16] ≥ 0)

(12)    (x2[0] ≥ 0∧[100] + x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_911_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0])), ≥)∧[bni_15 + (-1)Bound*bni_15] + [bni_15]x2[0] ≥ 0∧[(-1)bso_16] ≥ 0)

For Pair COND_911_0_MAIN_CONSTANTSTACKPUSH(TRUE, x1, x2, x0) → 911_0_MAIN_CONSTANTSTACKPUSH(+(x1, 1), +(x2, -1), x1) the following chains were created:

We consider the chain 911_0_MAIN_CONSTANTSTACKPUSH(x1[0], x2[0], x0[0]) → COND_911_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0]), COND_911_0_MAIN_CONSTANTSTACKPUSH(TRUE, x1[1], x2[1], x0[1]) → 911_0_MAIN_CONSTANTSTACKPUSH(+(x1[1], 1), +(x2[1], -1), x1[1]), 911_0_MAIN_CONSTANTSTACKPUSH(x1[0], x2[0], x0[0]) → COND_911_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0]) which results in the following constraint:
(13)    (&&(>=(x2[0], x1[0]), <=(x0[0], 100))=TRUE∧x1[0]=x1[1]∧x2[0]=x2[1]∧x0[0]=x0[1]∧+(x1[1], 1)=x1[0]1∧+(x2[1], -1)=x2[0]1∧x1[1]=x0[0]1 ⇒ COND_911_0_MAIN_CONSTANTSTACKPUSH(TRUE, x1[1], x2[1], x0[1])≥NonInfC∧COND_911_0_MAIN_CONSTANTSTACKPUSH(TRUE, x1[1], x2[1], x0[1])≥911_0_MAIN_CONSTANTSTACKPUSH(+(x1[1], 1), +(x2[1], -1), x1[1])∧(U^Increasing(911_0_MAIN_CONSTANTSTACKPUSH(+(x1[1], 1), +(x2[1], -1), x1[1])), ≥))

We simplified constraint (13) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(14)    (>=(x2[0], x1[0])=TRUE∧<=(x0[0], 100)=TRUE ⇒ COND_911_0_MAIN_CONSTANTSTACKPUSH(TRUE, x1[0], x2[0], x0[0])≥NonInfC∧COND_911_0_MAIN_CONSTANTSTACKPUSH(TRUE, x1[0], x2[0], x0[0])≥911_0_MAIN_CONSTANTSTACKPUSH(+(x1[0], 1), +(x2[0], -1), x1[0])∧(U^Increasing(911_0_MAIN_CONSTANTSTACKPUSH(+(x1[1], 1), +(x2[1], -1), x1[1])), ≥))

We simplified constraint (14) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(15)    (x2[0] + [-1]x1[0] ≥ 0∧[100] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(911_0_MAIN_CONSTANTSTACKPUSH(+(x1[1], 1), +(x2[1], -1), x1[1])), ≥)∧[(-1)Bound*bni_17] + [bni_17]x2[0] + [(-1)bni_17]x1[0] ≥ 0∧[1 + (-1)bso_18] ≥ 0)

We simplified constraint (15) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(16)    (x2[0] + [-1]x1[0] ≥ 0∧[100] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(911_0_MAIN_CONSTANTSTACKPUSH(+(x1[1], 1), +(x2[1], -1), x1[1])), ≥)∧[(-1)Bound*bni_17] + [bni_17]x2[0] + [(-1)bni_17]x1[0] ≥ 0∧[1 + (-1)bso_18] ≥ 0)

We simplified constraint (16) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(17)    (x2[0] + [-1]x1[0] ≥ 0∧[100] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(911_0_MAIN_CONSTANTSTACKPUSH(+(x1[1], 1), +(x2[1], -1), x1[1])), ≥)∧[(-1)Bound*bni_17] + [bni_17]x2[0] + [(-1)bni_17]x1[0] ≥ 0∧[1 + (-1)bso_18] ≥ 0)

We simplified constraint (17) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(18)    (x2[0] ≥ 0∧[100] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(911_0_MAIN_CONSTANTSTACKPUSH(+(x1[1], 1), +(x2[1], -1), x1[1])), ≥)∧[(-1)Bound*bni_17] + [bni_17]x2[0] ≥ 0∧[1 + (-1)bso_18] ≥ 0)

We simplified constraint (18) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(19)    (x2[0] ≥ 0∧[100] + [-1]x0[0] ≥ 0∧x1[0] ≥ 0 ⇒ (U^Increasing(911_0_MAIN_CONSTANTSTACKPUSH(+(x1[1], 1), +(x2[1], -1), x1[1])), ≥)∧[(-1)Bound*bni_17] + [bni_17]x2[0] ≥ 0∧[1 + (-1)bso_18] ≥ 0)

(20)    (x2[0] ≥ 0∧[100] + [-1]x0[0] ≥ 0∧x1[0] ≥ 0 ⇒ (U^Increasing(911_0_MAIN_CONSTANTSTACKPUSH(+(x1[1], 1), +(x2[1], -1), x1[1])), ≥)∧[(-1)Bound*bni_17] + [bni_17]x2[0] ≥ 0∧[1 + (-1)bso_18] ≥ 0)

We simplified constraint (19) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(21)    (x2[0] ≥ 0∧[100] + [-1]x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(911_0_MAIN_CONSTANTSTACKPUSH(+(x1[1], 1), +(x2[1], -1), x1[1])), ≥)∧[(-1)Bound*bni_17] + [bni_17]x2[0] ≥ 0∧[1 + (-1)bso_18] ≥ 0)

(22)    (x2[0] ≥ 0∧[100] + x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(911_0_MAIN_CONSTANTSTACKPUSH(+(x1[1], 1), +(x2[1], -1), x1[1])), ≥)∧[(-1)Bound*bni_17] + [bni_17]x2[0] ≥ 0∧[1 + (-1)bso_18] ≥ 0)

We simplified constraint (20) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(23)    (x2[0] ≥ 0∧[100] + x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(911_0_MAIN_CONSTANTSTACKPUSH(+(x1[1], 1), +(x2[1], -1), x1[1])), ≥)∧[(-1)Bound*bni_17] + [bni_17]x2[0] ≥ 0∧[1 + (-1)bso_18] ≥ 0)

(24)    (x2[0] ≥ 0∧[100] + [-1]x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(911_0_MAIN_CONSTANTSTACKPUSH(+(x1[1], 1), +(x2[1], -1), x1[1])), ≥)∧[(-1)Bound*bni_17] + [bni_17]x2[0] ≥ 0∧[1 + (-1)bso_18] ≥ 0)

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

911_0_MAIN_CONSTANTSTACKPUSH(x1, x2, x0) → COND_911_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2, x1), <=(x0, 100)), x1, x2, x0)
- (x2[0] ≥ 0∧[100] + [-1]x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_911_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0])), ≥)∧[bni_15 + (-1)Bound*bni_15] + [bni_15]x2[0] ≥ 0∧[(-1)bso_16] ≥ 0)
- (x2[0] ≥ 0∧[100] + x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_911_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0])), ≥)∧[bni_15 + (-1)Bound*bni_15] + [bni_15]x2[0] ≥ 0∧[(-1)bso_16] ≥ 0)
- (x2[0] ≥ 0∧[100] + [-1]x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_911_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0])), ≥)∧[bni_15 + (-1)Bound*bni_15] + [bni_15]x2[0] ≥ 0∧[(-1)bso_16] ≥ 0)
- (x2[0] ≥ 0∧[100] + x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_911_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0])), ≥)∧[bni_15 + (-1)Bound*bni_15] + [bni_15]x2[0] ≥ 0∧[(-1)bso_16] ≥ 0)
COND_911_0_MAIN_CONSTANTSTACKPUSH(TRUE, x1, x2, x0) → 911_0_MAIN_CONSTANTSTACKPUSH(+(x1, 1), +(x2, -1), x1)
- (x2[0] ≥ 0∧[100] + [-1]x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(911_0_MAIN_CONSTANTSTACKPUSH(+(x1[1], 1), +(x2[1], -1), x1[1])), ≥)∧[(-1)Bound*bni_17] + [bni_17]x2[0] ≥ 0∧[1 + (-1)bso_18] ≥ 0)
- (x2[0] ≥ 0∧[100] + x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(911_0_MAIN_CONSTANTSTACKPUSH(+(x1[1], 1), +(x2[1], -1), x1[1])), ≥)∧[(-1)Bound*bni_17] + [bni_17]x2[0] ≥ 0∧[1 + (-1)bso_18] ≥ 0)
- (x2[0] ≥ 0∧[100] + x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(911_0_MAIN_CONSTANTSTACKPUSH(+(x1[1], 1), +(x2[1], -1), x1[1])), ≥)∧[(-1)Bound*bni_17] + [bni_17]x2[0] ≥ 0∧[1 + (-1)bso_18] ≥ 0)
- (x2[0] ≥ 0∧[100] + [-1]x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(911_0_MAIN_CONSTANTSTACKPUSH(+(x1[1], 1), +(x2[1], -1), x1[1])), ≥)∧[(-1)Bound*bni_17] + [bni_17]x2[0] ≥ 0∧[1 + (-1)bso_18] ≥ 0)

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

POL(TRUE) = 0
POL(FALSE) = [3]
POL(911_0_MAIN_CONSTANTSTACKPUSH(x₁, x₂, x₃)) = [1] + x₂ + [-1]x₁
POL(COND_911_0_MAIN_CONSTANTSTACKPUSH(x₁, x₂, x₃, x₄)) = x₃ + [-1]x₂ + [-1]x₁
POL(&&(x₁, x₂)) = [-1]
POL(>=(x₁, x₂)) = [-1]
POL(<=(x₁, x₂)) = [-1]
POL(100) = [100]
POL(+(x₁, x₂)) = x₁ + x₂
POL(1) = [1]
POL(-1) = [-1]

The following pairs are in P_>:

COND_911_0_MAIN_CONSTANTSTACKPUSH(TRUE, x1[1], x2[1], x0[1]) → 911_0_MAIN_CONSTANTSTACKPUSH(+(x1[1], 1), +(x2[1], -1), x1[1])

The following pairs are in P_bound:

911_0_MAIN_CONSTANTSTACKPUSH(x1[0], x2[0], x0[0]) → COND_911_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0])
COND_911_0_MAIN_CONSTANTSTACKPUSH(TRUE, x1[1], x2[1], x0[1]) → 911_0_MAIN_CONSTANTSTACKPUSH(+(x1[1], 1), +(x2[1], -1), x1[1])

The following pairs are in P_≥:

911_0_MAIN_CONSTANTSTACKPUSH(x1[0], x2[0], x0[0]) → COND_911_0_MAIN_CONSTANTSTACKPUSH(&&(>=(x2[0], x1[0]), <=(x0[0], 100)), x1[0], x2[0], x0[0])

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

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

(8) Obligation: