Termination proof of /tmp/tmpxJhPRx/SharingAnalysis.jar

Termination of the given JBC could be proven:

0 JBC

↳1 JBCToGraph (⇒, 470 ms)

↳2 JBCTerminationGraph

↳3 TerminationGraphToSCCProof (⇒, 0 ms)

↳4 AND

    ↳5 JBCTerminationSCC

        ↳6 SCCToIDPv1Proof (⇒, 500 ms)

        ↳7 IDP

        ↳8 IDPtoQDPProof (⇒, 0 ms)

        ↳9 QDP

        ↳10 QDPSizeChangeProof (⇔, 0 ms)

        ↳11 YES

    ↳12 JBCTerminationSCC

        ↳13 SCCToIDPv1Proof (⇒, 80 ms)

        ↳14 IDP

        ↳15 IDPNonInfProof (⇒, 120 ms)

        ↳16 AND

            ↳17 IDP

                ↳18 IDependencyGraphProof (⇔, 0 ms)

                ↳19 TRUE

            ↳20 IDP

                ↳21 IDependencyGraphProof (⇔, 0 ms)

                ↳22 TRUE

(0) Obligation:

JBC Problem based on JBC Program:
Manifest-Version: 1.0 Created-By: 1.6.0_25 (Sun Microsystems Inc.) Main-Class: SharingAnalysis/SharingAnalysis

package SharingAnalysis;

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

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


package SharingAnalysis;

public class SharingAnalysis {
	int val;
	SharingAnalysis field;

	public static void main(String[] args) {
		Random.args = args;
		SharingAnalysis t1 = new SharingAnalysis();
		SharingAnalysis t2 = t1.appendNewList(1);
		SharingAnalysis t3 = t2.appendNewList(Random.random());
		t2.field = null;
		copy(t1, t3);
	}

	public static void copy(SharingAnalysis source, SharingAnalysis target) {
		while (source != null) {
			SharingAnalysis newEle = new SharingAnalysis();
			newEle.val = source.val;
			target.field = newEle;
			source = source.field;
			target = target.field;
		}
	}

	/**
 	 * @param i number of elements to append
 	 * @return the last list element appended
 	 */
	private SharingAnalysis appendNewList(int i) {
		this.field = new SharingAnalysis();
		SharingAnalysis cur = this.field;
		while (i > 1) {
			i--;
			cur = cur.field = new SharingAnalysis();
		}
		return cur;
	}
}

(1) JBCToGraph (SOUND transformation)

Constructed TerminationGraph.

(2) Obligation:

Termination Graph based on JBC Program:
SharingAnalysis.SharingAnalysis.main([Ljava/lang/String;)V: Graph of 259 nodes with 2 SCCs.

(3) TerminationGraphToSCCProof (SOUND transformation)

Splitted TerminationGraph to 2 SCCss.

(4) Complex Obligation (AND)

(5) Obligation:

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

(6) SCCToIDPv1Proof (SOUND transformation)

Transformed FIGraph SCCs to IDPs. Log:

Generated 88 rules for P and 0 rules for R.

P rules:
1086_0_copy_NULL(EOS(STATIC_1086), java.lang.Object(o1173sub), java.lang.Object(o1183sub), java.lang.Object(o1183sub)) → 1089_0_copy_NULL(EOS(STATIC_1089), java.lang.Object(o1173sub), java.lang.Object(o1183sub), java.lang.Object(o1183sub))
1089_0_copy_NULL(EOS(STATIC_1089), java.lang.Object(o1173sub), java.lang.Object(o1183sub), java.lang.Object(o1183sub)) → 1092_0_copy_New(EOS(STATIC_1092), java.lang.Object(o1173sub), java.lang.Object(o1183sub))
1092_0_copy_New(EOS(STATIC_1092), java.lang.Object(o1173sub), java.lang.Object(o1183sub)) → 1095_0_copy_Duplicate(EOS(STATIC_1095), java.lang.Object(o1173sub), java.lang.Object(o1183sub))
1095_0_copy_Duplicate(EOS(STATIC_1095), java.lang.Object(o1173sub), java.lang.Object(o1183sub)) → 1099_0_copy_InvokeMethod(EOS(STATIC_1099), java.lang.Object(o1173sub), java.lang.Object(o1183sub))
1099_0_copy_InvokeMethod(EOS(STATIC_1099), java.lang.Object(o1173sub), java.lang.Object(o1183sub)) → 1101_0_<init>_Load(EOS(STATIC_1101), java.lang.Object(o1173sub), java.lang.Object(o1183sub))
1101_0_<init>_Load(EOS(STATIC_1101), java.lang.Object(o1173sub), java.lang.Object(o1183sub)) → 1105_0_<init>_InvokeMethod(EOS(STATIC_1105), java.lang.Object(o1173sub), java.lang.Object(o1183sub))
1105_0_<init>_InvokeMethod(EOS(STATIC_1105), java.lang.Object(o1173sub), java.lang.Object(o1183sub)) → 1108_0_<init>_Return(EOS(STATIC_1108), java.lang.Object(o1173sub), java.lang.Object(o1183sub))
1108_0_<init>_Return(EOS(STATIC_1108), java.lang.Object(o1173sub), java.lang.Object(o1183sub)) → 1110_0_copy_Store(EOS(STATIC_1110), java.lang.Object(o1173sub), java.lang.Object(o1183sub))
1110_0_copy_Store(EOS(STATIC_1110), java.lang.Object(o1173sub), java.lang.Object(o1183sub)) → 1111_0_copy_Load(EOS(STATIC_1111), java.lang.Object(o1173sub), java.lang.Object(o1183sub))
1111_0_copy_Load(EOS(STATIC_1111), java.lang.Object(o1173sub), java.lang.Object(o1183sub)) → 1112_0_copy_Load(EOS(STATIC_1112), java.lang.Object(o1173sub), java.lang.Object(o1183sub))
1112_0_copy_Load(EOS(STATIC_1112), java.lang.Object(o1173sub), java.lang.Object(o1183sub)) → 1113_0_copy_FieldAccess(EOS(STATIC_1113), java.lang.Object(o1173sub), java.lang.Object(o1183sub), java.lang.Object(o1183sub))
1113_0_copy_FieldAccess(EOS(STATIC_1113), java.lang.Object(o1173sub), java.lang.Object(o1183sub), java.lang.Object(o1183sub)) → 1114_0_copy_FieldAccess(EOS(STATIC_1114), java.lang.Object(o1173sub), java.lang.Object(o1183sub), java.lang.Object(o1183sub))
1113_0_copy_FieldAccess(EOS(STATIC_1113), java.lang.Object(o1173sub), java.lang.Object(o1173sub), java.lang.Object(o1173sub)) → 1115_0_copy_FieldAccess(EOS(STATIC_1115), java.lang.Object(o1173sub), java.lang.Object(o1173sub), java.lang.Object(o1173sub))
1114_0_copy_FieldAccess(EOS(STATIC_1114), java.lang.Object(o1173sub), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i165, o1192)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i165, o1192))) → 1117_0_copy_FieldAccess(EOS(STATIC_1117), java.lang.Object(o1173sub), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i165, o1192)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i165, o1192)))
1117_0_copy_FieldAccess(EOS(STATIC_1117), java.lang.Object(o1173sub), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i165, o1192)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i165, o1192))) → 1121_0_copy_FieldAccess(EOS(STATIC_1121), java.lang.Object(o1173sub), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i165, o1192)))
1121_0_copy_FieldAccess(EOS(STATIC_1121), java.lang.Object(o1173sub), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i165, o1192))) → 1127_0_copy_Load(EOS(STATIC_1127), java.lang.Object(o1173sub), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i165, o1192)))
1127_0_copy_Load(EOS(STATIC_1127), java.lang.Object(o1173sub), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i165, o1192))) → 1132_0_copy_Load(EOS(STATIC_1132), java.lang.Object(o1173sub), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i165, o1192)))
1132_0_copy_Load(EOS(STATIC_1132), java.lang.Object(o1173sub), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i165, o1192))) → 1139_0_copy_FieldAccess(EOS(STATIC_1139), java.lang.Object(o1173sub), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i165, o1192)))
1139_0_copy_FieldAccess(EOS(STATIC_1139), java.lang.Object(o1173sub), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i165, o1192))) → 1148_0_copy_FieldAccess(EOS(STATIC_1148), java.lang.Object(o1173sub), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i165, o1192)))
1139_0_copy_FieldAccess(EOS(STATIC_1139), java.lang.Object(o1173sub), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i165, o1192))) → 1149_0_copy_FieldAccess(EOS(STATIC_1149), java.lang.Object(o1173sub), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i165, o1192)))
1148_0_copy_FieldAccess(EOS(STATIC_1148), java.lang.Object(o1173sub), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i165, o1192))) → 1156_0_copy_FieldAccess(EOS(STATIC_1156), java.lang.Object(o1173sub), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i165, o1192)))
1156_0_copy_FieldAccess(EOS(STATIC_1156), java.lang.Object(o1173sub), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i165, o1192))) → 1168_0_copy_FieldAccess(EOS(STATIC_1168), java.lang.Object(o1173sub), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i165, o1192)))
1156_0_copy_FieldAccess(EOS(STATIC_1156), java.lang.Object(o1173sub), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i165, o1192))) → 1170_0_copy_FieldAccess(EOS(STATIC_1170), java.lang.Object(o1173sub), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i165, o1192)))
1168_0_copy_FieldAccess(EOS(STATIC_1168), java.lang.Object(o1173sub), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i165, o1192))) → 1186_0_copy_Load(EOS(STATIC_1186), java.lang.Object(o1173sub), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i165, o1192)))
1186_0_copy_Load(EOS(STATIC_1186), java.lang.Object(o1173sub), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i165, o1192))) → 1223_0_copy_FieldAccess(EOS(STATIC_1223), java.lang.Object(o1173sub), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i165, o1192)))
1223_0_copy_FieldAccess(EOS(STATIC_1223), java.lang.Object(o1173sub), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i165, o1192))) → 1248_0_copy_Store(EOS(STATIC_1248), java.lang.Object(o1173sub), o1192)
1248_0_copy_Store(EOS(STATIC_1248), java.lang.Object(o1173sub), o1192) → 1273_0_copy_Load(EOS(STATIC_1273), java.lang.Object(o1173sub), o1192)
1273_0_copy_Load(EOS(STATIC_1273), java.lang.Object(o1173sub), o1192) → 1299_0_copy_FieldAccess(EOS(STATIC_1299), java.lang.Object(o1173sub), o1192)
1299_0_copy_FieldAccess(EOS(STATIC_1299), java.lang.Object(o1173sub), o1192) → 1324_0_copy_Store(EOS(STATIC_1324), java.lang.Object(o1173sub), o1192)
1324_0_copy_Store(EOS(STATIC_1324), java.lang.Object(o1173sub), o1192) → 1344_0_copy_JMP(EOS(STATIC_1344), java.lang.Object(o1173sub), o1192)
1344_0_copy_JMP(EOS(STATIC_1344), java.lang.Object(o1173sub), o1192) → 1362_0_copy_Load(EOS(STATIC_1362), java.lang.Object(o1173sub), o1192)
1362_0_copy_Load(EOS(STATIC_1362), java.lang.Object(o1173sub), o1192) → 1082_0_copy_Load(EOS(STATIC_1082), java.lang.Object(o1173sub), o1192)
1082_0_copy_Load(EOS(STATIC_1082), java.lang.Object(o1173sub), o1170) → 1086_0_copy_NULL(EOS(STATIC_1086), java.lang.Object(o1173sub), o1170, o1170)
1170_0_copy_FieldAccess(EOS(STATIC_1170), java.lang.Object(o1173sub), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i165, o1192))) → 1193_0_copy_Load(EOS(STATIC_1193), java.lang.Object(o1173sub), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i165, o1192)))
1193_0_copy_Load(EOS(STATIC_1193), java.lang.Object(o1173sub), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i165, o1192))) → 1224_0_copy_FieldAccess(EOS(STATIC_1224), java.lang.Object(o1173sub), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i165, o1192)))
1224_0_copy_FieldAccess(EOS(STATIC_1224), java.lang.Object(o1173sub), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i165, o1192))) → 1252_0_copy_Store(EOS(STATIC_1252), java.lang.Object(o1173sub), o1192)
1252_0_copy_Store(EOS(STATIC_1252), java.lang.Object(o1173sub), o1192) → 1278_0_copy_Load(EOS(STATIC_1278), java.lang.Object(o1173sub), o1192)
1278_0_copy_Load(EOS(STATIC_1278), java.lang.Object(o1173sub), o1192) → 1303_0_copy_FieldAccess(EOS(STATIC_1303), java.lang.Object(o1173sub), o1192)
1303_0_copy_FieldAccess(EOS(STATIC_1303), java.lang.Object(o1173sub), o1192) → 1325_0_copy_Store(EOS(STATIC_1325), java.lang.Object(o1173sub), o1192)
1325_0_copy_Store(EOS(STATIC_1325), java.lang.Object(o1173sub), o1192) → 1349_0_copy_JMP(EOS(STATIC_1349), java.lang.Object(o1173sub), o1192)
1349_0_copy_JMP(EOS(STATIC_1349), java.lang.Object(o1173sub), o1192) → 1366_0_copy_Load(EOS(STATIC_1366), java.lang.Object(o1173sub), o1192)
1366_0_copy_Load(EOS(STATIC_1366), java.lang.Object(o1173sub), o1192) → 1082_0_copy_Load(EOS(STATIC_1082), java.lang.Object(o1173sub), o1192)
1149_0_copy_FieldAccess(EOS(STATIC_1149), java.lang.Object(o1173sub), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i165, o1192))) → 1159_0_copy_Load(EOS(STATIC_1159), java.lang.Object(o1173sub), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i165, o1192)))
1159_0_copy_Load(EOS(STATIC_1159), java.lang.Object(o1173sub), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i165, o1192))) → 1171_0_copy_FieldAccess(EOS(STATIC_1171), java.lang.Object(o1173sub), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i165, o1192)))
1171_0_copy_FieldAccess(EOS(STATIC_1171), java.lang.Object(o1173sub), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i165, o1192))) → 1195_0_copy_Store(EOS(STATIC_1195), java.lang.Object(o1173sub), o1192)
1195_0_copy_Store(EOS(STATIC_1195), java.lang.Object(o1173sub), o1192) → 1225_0_copy_Load(EOS(STATIC_1225), java.lang.Object(o1173sub), o1192)
1225_0_copy_Load(EOS(STATIC_1225), java.lang.Object(o1173sub), o1192) → 1254_0_copy_FieldAccess(EOS(STATIC_1254), java.lang.Object(o1173sub), o1192)
1254_0_copy_FieldAccess(EOS(STATIC_1254), java.lang.Object(o1173sub), o1192) → 1280_0_copy_Store(EOS(STATIC_1280), java.lang.Object(o1173sub), o1192)
1280_0_copy_Store(EOS(STATIC_1280), java.lang.Object(o1173sub), o1192) → 1304_0_copy_JMP(EOS(STATIC_1304), java.lang.Object(o1173sub), o1192)
1304_0_copy_JMP(EOS(STATIC_1304), java.lang.Object(o1173sub), o1192) → 1326_0_copy_Load(EOS(STATIC_1326), java.lang.Object(o1173sub), o1192)
1326_0_copy_Load(EOS(STATIC_1326), java.lang.Object(o1173sub), o1192) → 1082_0_copy_Load(EOS(STATIC_1082), java.lang.Object(o1173sub), o1192)
1115_0_copy_FieldAccess(EOS(STATIC_1115), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194))) → 1119_0_copy_FieldAccess(EOS(STATIC_1119), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)))
1119_0_copy_FieldAccess(EOS(STATIC_1119), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194))) → 1124_0_copy_FieldAccess(EOS(STATIC_1124), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)))
1124_0_copy_FieldAccess(EOS(STATIC_1124), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194))) → 1130_0_copy_Load(EOS(STATIC_1130), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)))
1130_0_copy_Load(EOS(STATIC_1130), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194))) → 1136_0_copy_Load(EOS(STATIC_1136), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)))
1136_0_copy_Load(EOS(STATIC_1136), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194))) → 1146_0_copy_FieldAccess(EOS(STATIC_1146), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)))
1146_0_copy_FieldAccess(EOS(STATIC_1146), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194))) → 1152_0_copy_FieldAccess(EOS(STATIC_1152), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)))
1146_0_copy_FieldAccess(EOS(STATIC_1146), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194))) → 1154_0_copy_FieldAccess(EOS(STATIC_1154), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)))
1152_0_copy_FieldAccess(EOS(STATIC_1152), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194))) → 1161_0_copy_FieldAccess(EOS(STATIC_1161), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)))
1161_0_copy_FieldAccess(EOS(STATIC_1161), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194))) → 1175_0_copy_FieldAccess(EOS(STATIC_1175), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)))
1161_0_copy_FieldAccess(EOS(STATIC_1161), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194))) → 1176_0_copy_FieldAccess(EOS(STATIC_1176), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)))
1175_0_copy_FieldAccess(EOS(STATIC_1175), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194))) → 1204_0_copy_Load(EOS(STATIC_1204), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)))
1204_0_copy_Load(EOS(STATIC_1204), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194))) → 1233_0_copy_FieldAccess(EOS(STATIC_1233), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)))
1233_0_copy_FieldAccess(EOS(STATIC_1233), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194))) → 1260_0_copy_Store(EOS(STATIC_1260), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), o1194)
1260_0_copy_Store(EOS(STATIC_1260), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), o1194) → 1286_0_copy_Load(EOS(STATIC_1286), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), o1194)
1286_0_copy_Load(EOS(STATIC_1286), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), o1194) → 1310_0_copy_FieldAccess(EOS(STATIC_1310), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), o1194)
1310_0_copy_FieldAccess(EOS(STATIC_1310), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), o1194) → 1331_0_copy_Store(EOS(STATIC_1331), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), o1194)
1331_0_copy_Store(EOS(STATIC_1331), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), o1194) → 1353_0_copy_JMP(EOS(STATIC_1353), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), o1194)
1353_0_copy_JMP(EOS(STATIC_1353), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), o1194) → 1369_0_copy_Load(EOS(STATIC_1369), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), o1194)
1369_0_copy_Load(EOS(STATIC_1369), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), o1194) → 1082_0_copy_Load(EOS(STATIC_1082), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), o1194)
1176_0_copy_FieldAccess(EOS(STATIC_1176), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194))) → 1215_0_copy_Load(EOS(STATIC_1215), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)))
1215_0_copy_Load(EOS(STATIC_1215), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194))) → 1241_0_copy_FieldAccess(EOS(STATIC_1241), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)))
1241_0_copy_FieldAccess(EOS(STATIC_1241), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194))) → 1267_0_copy_Store(EOS(STATIC_1267), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), o1194)
1267_0_copy_Store(EOS(STATIC_1267), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), o1194) → 1293_0_copy_Load(EOS(STATIC_1293), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), o1194)
1293_0_copy_Load(EOS(STATIC_1293), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), o1194) → 1317_0_copy_FieldAccess(EOS(STATIC_1317), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), o1194)
1317_0_copy_FieldAccess(EOS(STATIC_1317), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), o1194) → 1337_0_copy_Store(EOS(STATIC_1337), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), o1194)
1337_0_copy_Store(EOS(STATIC_1337), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), o1194) → 1359_0_copy_JMP(EOS(STATIC_1359), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), o1194)
1359_0_copy_JMP(EOS(STATIC_1359), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), o1194) → 1373_0_copy_Load(EOS(STATIC_1373), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), o1194)
1373_0_copy_Load(EOS(STATIC_1373), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), o1194) → 1082_0_copy_Load(EOS(STATIC_1082), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), o1194)
1154_0_copy_FieldAccess(EOS(STATIC_1154), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194))) → 1165_0_copy_Load(EOS(STATIC_1165), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)))
1165_0_copy_Load(EOS(STATIC_1165), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194))) → 1179_0_copy_FieldAccess(EOS(STATIC_1179), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)))
1179_0_copy_FieldAccess(EOS(STATIC_1179), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194))) → 1218_0_copy_Store(EOS(STATIC_1218), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), o1194)
1218_0_copy_Store(EOS(STATIC_1218), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), o1194) → 1244_0_copy_Load(EOS(STATIC_1244), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), o1194)
1244_0_copy_Load(EOS(STATIC_1244), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), o1194) → 1269_0_copy_FieldAccess(EOS(STATIC_1269), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), o1194)
1269_0_copy_FieldAccess(EOS(STATIC_1269), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), o1194) → 1295_0_copy_Store(EOS(STATIC_1295), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), o1194)
1295_0_copy_Store(EOS(STATIC_1295), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), o1194) → 1320_0_copy_JMP(EOS(STATIC_1320), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), o1194)
1320_0_copy_JMP(EOS(STATIC_1320), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), o1194) → 1340_0_copy_Load(EOS(STATIC_1340), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), o1194)
1340_0_copy_Load(EOS(STATIC_1340), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), o1194) → 1082_0_copy_Load(EOS(STATIC_1082), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, i166, o1194)), o1194)
R rules:

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

P rules:
1086_0_copy_NULL(EOS(STATIC_1086), java.lang.Object(x0), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, x1, x2)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, x1, x2))) → 1086_0_copy_NULL(EOS(STATIC_1086), java.lang.Object(x0), x2, x2)
1086_0_copy_NULL(EOS(STATIC_1086), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, x0, x1)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, x0, x1)), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, x0, x1))) → 1086_0_copy_NULL(EOS(STATIC_1086), java.lang.Object(SharingAnalysis.SharingAnalysis(EOC, x0, x1)), x1, x1)
R rules:

Filtered ground terms:

1086_0_copy_NULL(x1, x2, x3, x4) → 1086_0_copy_NULL(x2, x3, x4)
SharingAnalysis.SharingAnalysis(x1, x2, x3) → SharingAnalysis.SharingAnalysis(x2, x3)
EOS(x1) → EOS

Filtered duplicate args:

1086_0_copy_NULL(x1, x2, x3) → 1086_0_copy_NULL(x1, x3)

Filtered unneeded arguments:

SharingAnalysis.SharingAnalysis(x1, x2) → SharingAnalysis.SharingAnalysis(x2)

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

P rules:
1086_0_copy_NULL(java.lang.Object(x0), java.lang.Object(SharingAnalysis.SharingAnalysis(x2))) → 1086_0_copy_NULL(java.lang.Object(x0), x2)
1086_0_copy_NULL(java.lang.Object(SharingAnalysis.SharingAnalysis(x1)), java.lang.Object(SharingAnalysis.SharingAnalysis(x1))) → 1086_0_copy_NULL(java.lang.Object(SharingAnalysis.SharingAnalysis(x1)), x1)
R rules:

Finished conversion. Obtained 2 rules for P and 0 rules for R. System has no predefined symbols.

P rules:
1086_0_COPY_NULL(java.lang.Object(x0), java.lang.Object(SharingAnalysis.SharingAnalysis(x2))) → 1086_0_COPY_NULL(java.lang.Object(x0), x2)
1086_0_COPY_NULL(java.lang.Object(SharingAnalysis.SharingAnalysis(x1)), java.lang.Object(SharingAnalysis.SharingAnalysis(x1))) → 1086_0_COPY_NULL(java.lang.Object(SharingAnalysis.SharingAnalysis(x1)), x1)
R rules:

(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:
none

R is empty.

The integer pair graph contains the following rules and edges:
(0): 1086_0_COPY_NULL(java.lang.Object(x0[0]), java.lang.Object(SharingAnalysis.SharingAnalysis(x2[0]))) → 1086_0_COPY_NULL(java.lang.Object(x0[0]), x2[0])
(1): 1086_0_COPY_NULL(java.lang.Object(SharingAnalysis.SharingAnalysis(x1[1])), java.lang.Object(SharingAnalysis.SharingAnalysis(x1[1]))) → 1086_0_COPY_NULL(java.lang.Object(SharingAnalysis.SharingAnalysis(x1[1])), x1[1])

(0) -> (0), if (java.lang.Object(x0[0]) →^* java.lang.Object(x0[0]')∧x2[0] →^* java.lang.Object(SharingAnalysis.SharingAnalysis(x2[0]')))

(0) -> (1), if (java.lang.Object(x0[0]) →^* java.lang.Object(SharingAnalysis.SharingAnalysis(x1[1]))∧x2[0] →^* java.lang.Object(SharingAnalysis.SharingAnalysis(x1[1])))

(1) -> (0), if (java.lang.Object(SharingAnalysis.SharingAnalysis(x1[1])) →^* java.lang.Object(x0[0])∧x1[1] →^* java.lang.Object(SharingAnalysis.SharingAnalysis(x2[0])))

(1) -> (1), if (java.lang.Object(SharingAnalysis.SharingAnalysis(x1[1])) →^* java.lang.Object(SharingAnalysis.SharingAnalysis(x1[1]'))∧x1[1] →^* java.lang.Object(SharingAnalysis.SharingAnalysis(x1[1]')))

The set Q is empty.

(8) IDPtoQDPProof (SOUND transformation)

Represented integers and predefined function symbols by Terms

(9) Obligation:

Q DP problem:
The TRS P consists of the following rules:

1086_0_COPY_NULL(java.lang.Object(x0[0]), java.lang.Object(SharingAnalysis.SharingAnalysis(x2[0]))) → 1086_0_COPY_NULL(java.lang.Object(x0[0]), x2[0])
1086_0_COPY_NULL(java.lang.Object(SharingAnalysis.SharingAnalysis(x1[1])), java.lang.Object(SharingAnalysis.SharingAnalysis(x1[1]))) → 1086_0_COPY_NULL(java.lang.Object(SharingAnalysis.SharingAnalysis(x1[1])), x1[1])

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(10) QDPSizeChangeProof (EQUIVALENT transformation)

By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs:

1086_0_COPY_NULL(java.lang.Object(x0[0]), java.lang.Object(SharingAnalysis.SharingAnalysis(x2[0]))) → 1086_0_COPY_NULL(java.lang.Object(x0[0]), x2[0])
The graph contains the following edges 1 >= 1, 2 > 2
1086_0_COPY_NULL(java.lang.Object(SharingAnalysis.SharingAnalysis(x1[1])), java.lang.Object(SharingAnalysis.SharingAnalysis(x1[1]))) → 1086_0_COPY_NULL(java.lang.Object(SharingAnalysis.SharingAnalysis(x1[1])), x1[1])
The graph contains the following edges 1 >= 1, 2 >= 1, 1 > 2, 2 > 2

(11) YES

(12) Obligation:

(13) SCCToIDPv1Proof (SOUND transformation)

Transformed FIGraph SCCs to IDPs. Log:

Generated 23 rules for P and 0 rules for R.

P rules:
424_0_appendNewList_ConstantStackPush(EOS(STATIC_424), i35, i35) → 428_0_appendNewList_LE(EOS(STATIC_428), i35, i35, 1)
428_0_appendNewList_LE(EOS(STATIC_428), i47, i47, matching1) → 432_0_appendNewList_LE(EOS(STATIC_432), i47, i47, 1) | =(matching1, 1)
432_0_appendNewList_LE(EOS(STATIC_432), i47, i47, matching1) → 435_0_appendNewList_Inc(EOS(STATIC_435), i47) | &&(>(i47, 1), =(matching1, 1))
435_0_appendNewList_Inc(EOS(STATIC_435), i47) → 439_0_appendNewList_Load(EOS(STATIC_439), +(i47, -1)) | >(i47, 0)
439_0_appendNewList_Load(EOS(STATIC_439), i48) → 443_0_appendNewList_New(EOS(STATIC_443), i48)
443_0_appendNewList_New(EOS(STATIC_443), i48) → 446_0_appendNewList_Duplicate(EOS(STATIC_446), i48)
446_0_appendNewList_Duplicate(EOS(STATIC_446), i48) → 450_0_appendNewList_InvokeMethod(EOS(STATIC_450), i48)
450_0_appendNewList_InvokeMethod(EOS(STATIC_450), i48) → 454_0_<init>_Load(EOS(STATIC_454), i48)
454_0_<init>_Load(EOS(STATIC_454), i48) → 462_0_<init>_InvokeMethod(EOS(STATIC_462), i48)
462_0_<init>_InvokeMethod(EOS(STATIC_462), i48) → 467_0_<init>_Return(EOS(STATIC_467), i48)
467_0_<init>_Return(EOS(STATIC_467), i48) → 471_0_appendNewList_Duplicate(EOS(STATIC_471), i48)
471_0_appendNewList_Duplicate(EOS(STATIC_471), i48) → 477_0_appendNewList_FieldAccess(EOS(STATIC_477), i48)
477_0_appendNewList_FieldAccess(EOS(STATIC_477), i48) → 481_0_appendNewList_FieldAccess(EOS(STATIC_481), i48)
477_0_appendNewList_FieldAccess(EOS(STATIC_477), i48) → 482_0_appendNewList_FieldAccess(EOS(STATIC_482), i48)
481_0_appendNewList_FieldAccess(EOS(STATIC_481), i48) → 489_0_appendNewList_Store(EOS(STATIC_489), i48)
489_0_appendNewList_Store(EOS(STATIC_489), i48) → 498_0_appendNewList_JMP(EOS(STATIC_498), i48)
498_0_appendNewList_JMP(EOS(STATIC_498), i48) → 513_0_appendNewList_Load(EOS(STATIC_513), i48)
513_0_appendNewList_Load(EOS(STATIC_513), i48) → 417_0_appendNewList_Load(EOS(STATIC_417), i48)
417_0_appendNewList_Load(EOS(STATIC_417), i35) → 424_0_appendNewList_ConstantStackPush(EOS(STATIC_424), i35, i35)
482_0_appendNewList_FieldAccess(EOS(STATIC_482), i48) → 494_0_appendNewList_Store(EOS(STATIC_494), i48)
494_0_appendNewList_Store(EOS(STATIC_494), i48) → 502_0_appendNewList_JMP(EOS(STATIC_502), i48)
502_0_appendNewList_JMP(EOS(STATIC_502), i48) → 523_0_appendNewList_Load(EOS(STATIC_523), i48)
523_0_appendNewList_Load(EOS(STATIC_523), i48) → 417_0_appendNewList_Load(EOS(STATIC_417), i48)
R rules:

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

P rules:
424_0_appendNewList_ConstantStackPush(EOS(STATIC_424), x0, x0) → 424_0_appendNewList_ConstantStackPush(EOS(STATIC_424), +(x0, -1), +(x0, -1)) | >(x0, 1)
R rules:

Filtered ground terms:

424_0_appendNewList_ConstantStackPush(x1, x2, x3) → 424_0_appendNewList_ConstantStackPush(x2, x3)
EOS(x1) → EOS
Cond_424_0_appendNewList_ConstantStackPush(x1, x2, x3, x4) → Cond_424_0_appendNewList_ConstantStackPush(x1, x3, x4)

Filtered duplicate args:

424_0_appendNewList_ConstantStackPush(x1, x2) → 424_0_appendNewList_ConstantStackPush(x2)
Cond_424_0_appendNewList_ConstantStackPush(x1, x2, x3) → Cond_424_0_appendNewList_ConstantStackPush(x1, x3)

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

P rules:
424_0_appendNewList_ConstantStackPush(x0) → 424_0_appendNewList_ConstantStackPush(+(x0, -1)) | >(x0, 1)
R rules:

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

P rules:
424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(x0) → COND_424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(>(x0, 1), x0)
COND_424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(TRUE, x0) → 424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(+(x0, -1))
R rules:

(14) Obligation:

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

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

The following domains are used:

Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): 424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(x0[0]) → COND_424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(x0[0] > 1, x0[0])
(1): COND_424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(TRUE, x0[1]) → 424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(x0[1] + -1)

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

(1) -> (0), if (x0[1] + -1 →^* x0[0])

The set Q is empty.

(15) 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.IdpCand1ShapeHeuristic@14c8cdca Constraint Generator: NonInfConstraintGenerator: PathGenerator: MetricPathGenerator: Max Left Steps: 0 Max Right Steps: 0

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 424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(x0) → COND_424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(>(x0, 1), x0) the following chains were created:

We consider the chain 424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(x0[0]) → COND_424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(>(x0[0], 1), x0[0]), COND_424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(TRUE, x0[1]) → 424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(+(x0[1], -1)) which results in the following constraint:
(1)    (>(x0[0], 1)=TRUE∧x0[0]=x0[1] ⇒ 424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(x0[0])≥NonInfC∧424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(x0[0])≥COND_424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(>(x0[0], 1), x0[0])∧(U^Increasing(COND_424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(>(x0[0], 1), x0[0])), ≥))

We simplified constraint (1) using rule (IV) which results in the following new constraint:
(2)    (>(x0[0], 1)=TRUE ⇒ 424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(x0[0])≥NonInfC∧424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(x0[0])≥COND_424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(>(x0[0], 1), x0[0])∧(U^Increasing(COND_424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(>(x0[0], 1), x0[0])), ≥))

We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(3)    (x0[0] + [-2] ≥ 0 ⇒ (U^Increasing(COND_424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(>(x0[0], 1), x0[0])), ≥)∧[(-1)Bound*bni_8] + [(2)bni_8]x0[0] ≥ 0∧[(-1)bso_9] ≥ 0)

We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(4)    (x0[0] + [-2] ≥ 0 ⇒ (U^Increasing(COND_424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(>(x0[0], 1), x0[0])), ≥)∧[(-1)Bound*bni_8] + [(2)bni_8]x0[0] ≥ 0∧[(-1)bso_9] ≥ 0)

We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(5)    (x0[0] + [-2] ≥ 0 ⇒ (U^Increasing(COND_424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(>(x0[0], 1), x0[0])), ≥)∧[(-1)Bound*bni_8] + [(2)bni_8]x0[0] ≥ 0∧[(-1)bso_9] ≥ 0)

We simplified constraint (5) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(6)    (x0[0] ≥ 0 ⇒ (U^Increasing(COND_424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(>(x0[0], 1), x0[0])), ≥)∧[(-1)Bound*bni_8 + (4)bni_8] + [(2)bni_8]x0[0] ≥ 0∧[(-1)bso_9] ≥ 0)

For Pair COND_424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(TRUE, x0) → 424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(+(x0, -1)) the following chains were created:

We consider the chain COND_424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(TRUE, x0[1]) → 424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(+(x0[1], -1)) which results in the following constraint:
(7)    (COND_424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(TRUE, x0[1])≥NonInfC∧COND_424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(TRUE, x0[1])≥424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(+(x0[1], -1))∧(U^Increasing(424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(+(x0[1], -1))), ≥))

We simplified constraint (7) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(8)    ((U^Increasing(424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(+(x0[1], -1))), ≥)∧[bni_10] = 0∧[2 + (-1)bso_11] ≥ 0)

We simplified constraint (8) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(9)    ((U^Increasing(424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(+(x0[1], -1))), ≥)∧[bni_10] = 0∧[2 + (-1)bso_11] ≥ 0)

We simplified constraint (9) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(10)    ((U^Increasing(424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(+(x0[1], -1))), ≥)∧[bni_10] = 0∧[2 + (-1)bso_11] ≥ 0)

We simplified constraint (10) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(11)    ((U^Increasing(424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(+(x0[1], -1))), ≥)∧[bni_10] = 0∧0 = 0∧[2 + (-1)bso_11] ≥ 0)

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

424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(x0) → COND_424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(>(x0, 1), x0)
- (x0[0] ≥ 0 ⇒ (U^Increasing(COND_424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(>(x0[0], 1), x0[0])), ≥)∧[(-1)Bound*bni_8 + (4)bni_8] + [(2)bni_8]x0[0] ≥ 0∧[(-1)bso_9] ≥ 0)
COND_424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(TRUE, x0) → 424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(+(x0, -1))
- ((U^Increasing(424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(+(x0[1], -1))), ≥)∧[bni_10] = 0∧0 = 0∧[2 + (-1)bso_11] ≥ 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) = 0
POL(424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(x₁)) = [2]x₁
POL(COND_424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(x₁, x₂)) = [2]x₂
POL(>(x₁, x₂)) = [-1]
POL(1) = [1]
POL(+(x₁, x₂)) = x₁ + x₂
POL(-1) = [-1]

The following pairs are in P_>:

COND_424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(TRUE, x0[1]) → 424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(+(x0[1], -1))

The following pairs are in P_bound:

424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(x0[0]) → COND_424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(>(x0[0], 1), x0[0])

The following pairs are in P_≥:

424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(x0[0]) → COND_424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(>(x0[0], 1), x0[0])

There are no usable rules.

(16) Complex Obligation (AND)

(17) Obligation:

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

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

The following domains are used:

Integer

(18) IDependencyGraphProof (EQUIVALENT transformation)

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

(19) TRUE

(20) Obligation:

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

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

The following domains are used:

Integer

R is empty.

The integer pair graph contains the following rules and edges:
(1): COND_424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(TRUE, x0[1]) → 424_0_APPENDNEWLIST_CONSTANTSTACKPUSH(x0[1] + -1)

The set Q is empty.

(21) IDependencyGraphProof (EQUIVALENT transformation)

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

(0) Obligation:

(1) JBCToGraph (SOUND transformation)

(2) Obligation:

(3) TerminationGraphToSCCProof (SOUND transformation)

(4) Complex Obligation (AND)

(5) Obligation:

(6) SCCToIDPv1Proof (SOUND transformation)

(7) Obligation:

(8) IDPtoQDPProof (SOUND transformation)

(9) Obligation:

(10) QDPSizeChangeProof (EQUIVALENT transformation)

(11) YES

(12) Obligation:

(13) SCCToIDPv1Proof (SOUND transformation)

(14) Obligation:

(15) IDPNonInfProof (SOUND transformation)

(16) Complex Obligation (AND)

(17) Obligation:

(18) IDependencyGraphProof (EQUIVALENT transformation)

(19) TRUE

(20) Obligation:

(21) IDependencyGraphProof (EQUIVALENT transformation)

(22) TRUE