6.86/2.76 YES 6.86/2.78 proof of /export/starexec/sandbox/benchmark/theBenchmark.jar 6.86/2.78 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 6.86/2.78 6.86/2.78 6.86/2.78 termination of the given Bare JBC problem could be proven: 6.86/2.78 6.86/2.78 (0) Bare JBC problem 6.86/2.78 (1) BareJBCToJBCProof [EQUIVALENT, 95 ms] 6.86/2.78 (2) JBC problem 6.86/2.78 (3) JBCToGraph [EQUIVALENT, 273 ms] 6.86/2.78 (4) JBCTerminationGraph 6.86/2.78 (5) TerminationGraphToSCCProof [SOUND, 0 ms] 6.86/2.78 (6) AND 6.86/2.78 (7) JBCTerminationSCC 6.86/2.78 (8) SCCToIRSProof [SOUND, 32 ms] 6.86/2.78 (9) IRSwT 6.86/2.78 (10) IRSFormatTransformerProof [EQUIVALENT, 0 ms] 6.86/2.78 (11) IRSwT 6.86/2.78 (12) IRSwTTerminationDigraphProof [EQUIVALENT, 44 ms] 6.86/2.78 (13) AND 6.86/2.78 (14) IRSwT 6.86/2.78 (15) IntTRSCompressionProof [EQUIVALENT, 0 ms] 6.86/2.78 (16) IRSwT 6.86/2.78 (17) TempFilterProof [SOUND, 8 ms] 6.86/2.78 (18) IntTRS 6.86/2.78 (19) RankingReductionPairProof [EQUIVALENT, 0 ms] 6.86/2.78 (20) YES 6.86/2.78 (21) IRSwT 6.86/2.78 (22) IntTRSCompressionProof [EQUIVALENT, 0 ms] 6.86/2.78 (23) IRSwT 6.86/2.78 (24) TempFilterProof [SOUND, 13 ms] 6.86/2.78 (25) IntTRS 6.86/2.78 (26) RankingReductionPairProof [EQUIVALENT, 7 ms] 6.86/2.78 (27) YES 6.86/2.78 (28) JBCTerminationSCC 6.86/2.78 (29) SCCToIRSProof [SOUND, 63 ms] 6.86/2.78 (30) IRSwT 6.86/2.78 (31) IRSFormatTransformerProof [EQUIVALENT, 0 ms] 6.86/2.78 (32) IRSwT 6.86/2.78 (33) IRSwTTerminationDigraphProof [EQUIVALENT, 19 ms] 6.86/2.78 (34) IRSwT 6.86/2.78 (35) IntTRSCompressionProof [EQUIVALENT, 0 ms] 6.86/2.78 (36) IRSwT 6.86/2.78 (37) TempFilterProof [SOUND, 37 ms] 6.86/2.78 (38) IntTRS 6.86/2.78 (39) PolynomialOrderProcessor [EQUIVALENT, 13 ms] 6.86/2.78 (40) YES 6.86/2.78 6.86/2.78 6.86/2.78 ---------------------------------------- 6.86/2.78 6.86/2.78 (0) 6.86/2.78 Obligation: 6.86/2.78 need to prove termination of the following program: 6.86/2.78 /** 6.86/2.78 * This class represents a list. The function get(n) can be used to access 6.86/2.78 * the n-th element. 6.86/2.78 * @author Marc Brockschmidt 6.86/2.78 */ 6.86/2.78 public class CyclicList { 6.86/2.78 /** 6.86/2.78 * A reference to the next list element. 6.86/2.78 */ 6.86/2.78 private CyclicList next; 6.86/2.78 6.86/2.78 public static void main(String[] args) { 6.86/2.78 CyclicList list = CyclicList.create(args.length); 6.86/2.78 list.get(args[0].length()); 6.86/2.78 } 6.86/2.78 6.86/2.78 /** 6.86/2.78 * Create a new list element. 6.86/2.78 * @param n a reference to the next element. 6.86/2.78 */ 6.86/2.78 public CyclicList(final CyclicList n) { 6.86/2.78 this.next = n; 6.86/2.78 } 6.86/2.78 6.86/2.78 /** 6.86/2.78 * Create a new cyclical list of a length l. 6.86/2.78 * @param l some length 6.86/2.78 * @return cyclical list of length max(1, l) 6.86/2.78 */ 6.86/2.78 public static CyclicList create(int x) { 6.86/2.78 CyclicList last, current; 6.86/2.78 last = current = new CyclicList(null); 6.86/2.78 while (--x > 0) 6.86/2.78 current = new CyclicList(current); 6.86/2.78 return last.next = current; 6.86/2.78 } 6.86/2.78 6.86/2.78 public CyclicList get(int n) { 6.86/2.78 CyclicList cur = this; 6.86/2.78 while (--n > 0) { 6.86/2.78 cur = cur.next; 6.86/2.78 } 6.86/2.78 return cur; 6.86/2.78 } 6.86/2.78 } 6.86/2.78 6.86/2.78 6.86/2.78 6.86/2.78 6.86/2.78 ---------------------------------------- 6.86/2.78 6.86/2.78 (1) BareJBCToJBCProof (EQUIVALENT) 6.86/2.78 initialized classpath 6.86/2.78 ---------------------------------------- 6.86/2.78 6.86/2.78 (2) 6.86/2.78 Obligation: 6.86/2.78 need to prove termination of the following program: 6.86/2.78 /** 6.86/2.78 * This class represents a list. The function get(n) can be used to access 6.86/2.78 * the n-th element. 6.86/2.78 * @author Marc Brockschmidt 6.86/2.78 */ 6.86/2.78 public class CyclicList { 6.86/2.78 /** 6.86/2.78 * A reference to the next list element. 6.86/2.78 */ 6.86/2.78 private CyclicList next; 6.86/2.78 6.86/2.78 public static void main(String[] args) { 6.86/2.78 CyclicList list = CyclicList.create(args.length); 6.86/2.78 list.get(args[0].length()); 6.86/2.78 } 6.86/2.78 6.86/2.78 /** 6.86/2.78 * Create a new list element. 6.86/2.78 * @param n a reference to the next element. 6.86/2.78 */ 6.86/2.78 public CyclicList(final CyclicList n) { 6.86/2.78 this.next = n; 6.86/2.78 } 6.86/2.78 6.86/2.78 /** 6.86/2.78 * Create a new cyclical list of a length l. 6.86/2.78 * @param l some length 6.86/2.78 * @return cyclical list of length max(1, l) 6.86/2.78 */ 6.86/2.78 public static CyclicList create(int x) { 6.86/2.78 CyclicList last, current; 6.86/2.78 last = current = new CyclicList(null); 6.86/2.78 while (--x > 0) 6.86/2.78 current = new CyclicList(current); 6.86/2.78 return last.next = current; 6.86/2.78 } 6.86/2.78 6.86/2.78 public CyclicList get(int n) { 6.86/2.78 CyclicList cur = this; 6.86/2.78 while (--n > 0) { 6.86/2.78 cur = cur.next; 6.86/2.78 } 6.86/2.78 return cur; 6.86/2.78 } 6.86/2.78 } 6.86/2.78 6.86/2.78 6.86/2.78 6.86/2.78 6.86/2.78 ---------------------------------------- 6.86/2.78 6.86/2.78 (3) JBCToGraph (EQUIVALENT) 6.86/2.78 Constructed TerminationGraph. 6.86/2.78 ---------------------------------------- 6.86/2.78 6.86/2.78 (4) 6.86/2.78 Obligation: 6.86/2.78 Termination Graph based on JBC Program: 6.86/2.78 CyclicList.main([Ljava/lang/String;)V: Graph of 131 nodes with 2 SCCs. 6.86/2.78 6.86/2.78 6.86/2.78 6.86/2.78 6.86/2.78 6.86/2.78 ---------------------------------------- 6.86/2.78 6.86/2.78 (5) TerminationGraphToSCCProof (SOUND) 6.86/2.78 Splitted TerminationGraph to 2 SCCss. 6.86/2.78 ---------------------------------------- 6.86/2.78 6.86/2.78 (6) 6.86/2.78 Complex Obligation (AND) 6.86/2.78 6.86/2.78 ---------------------------------------- 6.86/2.78 6.86/2.78 (7) 6.86/2.78 Obligation: 6.86/2.78 SCC of termination graph based on JBC Program. 6.86/2.78 SCC contains nodes from the following methods: CyclicList.main([Ljava/lang/String;)V 6.86/2.78 SCC calls the following helper methods: 6.86/2.78 Performed SCC analyses: 6.86/2.78 *Used field analysis yielded the following read fields: 6.86/2.78 *CyclicList: [next] 6.86/2.78 *Marker field analysis yielded the following relations that could be markers: 6.86/2.78 6.86/2.78 ---------------------------------------- 6.86/2.78 6.86/2.78 (8) SCCToIRSProof (SOUND) 6.86/2.78 Transformed FIGraph SCCs to intTRSs. Log: 6.86/2.78 Generated rules. Obtained 16 IRulesP rules: 6.86/2.78 f916_0_get_Load(EOS(STATIC_916), i141, o29[CyclicList.next]o29) -> f921_0_get_LE(EOS(STATIC_921), i141, i141, o29[CyclicList.next]o29) :|: TRUE 6.86/2.78 f921_0_get_LE(EOS(STATIC_921), i145, i145, o29[CyclicList.next]o29) -> f930_0_get_LE(EOS(STATIC_930), i145, i145, o29[CyclicList.next]o29) :|: TRUE 6.86/2.78 f930_0_get_LE(EOS(STATIC_930), i145, i145, o29[CyclicList.next]o29) -> f1001_0_get_Load(EOS(STATIC_1001), i145, o29[CyclicList.next]o29) :|: i145 > 0 6.86/2.78 f1001_0_get_Load(EOS(STATIC_1001), i145, o29[CyclicList.next]o29) -> f1005_0_get_FieldAccess(EOS(STATIC_1005), i145, o29[CyclicList.next]o29) :|: TRUE 6.86/2.78 f1005_0_get_FieldAccess(EOS(STATIC_1005), i145, o89[CyclicList.next]o89) -> f1019_0_get_FieldAccess(EOS(STATIC_1019), i145, o90[CyclicList.next]o89) :|: o90[CyclicList.next]o89 < o89[CyclicList.next]o89 && o89[CyclicList.next]o89 >= 0 6.86/2.78 f1019_0_get_FieldAccess(EOS(STATIC_1019), i145, o90[CyclicList.next]o89) -> f1041_0_get_FieldAccess(EOS(STATIC_1041), i145, o90[CyclicList.next]o89) :|: o90[CyclicList.next]o89 > 0 6.86/2.78 f1019_0_get_FieldAccess(EOS(STATIC_1019), i145, o90[CyclicList.next]o93) -> f1042_0_get_FieldAccess(EOS(STATIC_1042), i145) :|: TRUE 6.86/2.78 f1041_0_get_FieldAccess(EOS(STATIC_1041), i145, o90[CyclicList.next]o89) -> f1053_0_get_Store(EOS(STATIC_1053), i145, o90[CyclicList.next]o90) :|: o90[CyclicList.next]o90 > o90[CyclicList.next]o89 && o90[CyclicList.next]o89 >= 0 6.86/2.78 f1053_0_get_Store(EOS(STATIC_1053), i145, o90[CyclicList.next]o90) -> f1059_0_get_JMP(EOS(STATIC_1059), i145, o90[CyclicList.next]o90) :|: TRUE 6.86/2.78 f1059_0_get_JMP(EOS(STATIC_1059), i145, o90[CyclicList.next]o90) -> f1076_0_get_Inc(EOS(STATIC_1076), i145, o90[CyclicList.next]o90) :|: TRUE 6.86/2.78 f1076_0_get_Inc(EOS(STATIC_1076), i145, o90[CyclicList.next]o90) -> f913_0_get_Inc(EOS(STATIC_913), i145, o90[CyclicList.next]o90) :|: TRUE 6.86/2.78 f913_0_get_Inc(EOS(STATIC_913), i139, o29[CyclicList.next]o29) -> f916_0_get_Load(EOS(STATIC_916), i139 + -1, o29[CyclicList.next]o29) :|: TRUE 6.86/2.78 f1042_0_get_FieldAccess(EOS(STATIC_1042), i145) -> f1055_0_get_Store(EOS(STATIC_1055), i145) :|: TRUE 6.86/2.78 f1055_0_get_Store(EOS(STATIC_1055), i145) -> f1061_0_get_JMP(EOS(STATIC_1061), i145) :|: TRUE 6.86/2.78 f1061_0_get_JMP(EOS(STATIC_1061), i145) -> f1088_0_get_Inc(EOS(STATIC_1088), i145) :|: TRUE 6.86/2.79 f1088_0_get_Inc(EOS(STATIC_1088), i145) -> f913_0_get_Inc(EOS(STATIC_913), i145, o93[CyclicList.next]o93) :|: o93[CyclicList.next]o93 = 1 6.86/2.79 Combined rules. Obtained 2 IRulesP rules: 6.86/2.79 f916_0_get_Load(EOS(STATIC_916), i141:0, o29[CyclicList.next]o29:0) -> f916_0_get_Load(EOS(STATIC_916), i141:0 - 1, 1) :|: i141:0 > 0 && o90[CyclicList.next]o89:0 < o29[CyclicList.next]o29:0 && o29[CyclicList.next]o29:0 > -1 6.86/2.79 f916_0_get_Load(EOS(STATIC_916), i141:0, o29[CyclicList.next]o29:0) -> f916_0_get_Load(EOS(STATIC_916), i141:0 - 1, o90[CyclicList.next]o90:0) :|: o90[CyclicList.next]o89:0 > 0 && i141:0 > 0 && o29[CyclicList.next]o29:0 > -1 && o90[CyclicList.next]o90:0 > o90[CyclicList.next]o89:0 && o90[CyclicList.next]o89:0 < o29[CyclicList.next]o29:0 6.86/2.79 Filtered constant ground arguments: 6.86/2.79 f916_0_get_Load(x1, x2, x3) -> f916_0_get_Load(x2, x3) 6.86/2.79 EOS(x1) -> EOS 6.86/2.79 Finished conversion. Obtained 2 rules.P rules: 6.86/2.79 f916_0_get_Load(i141:0, o29[CyclicList.next]o29:0) -> f916_0_get_Load(i141:0 - 1, 1) :|: o90[CyclicList.next]o89:0 < o29[CyclicList.next]o29:0 && o29[CyclicList.next]o29:0 > -1 && i141:0 > 0 6.86/2.79 f916_0_get_Load(i141:0, o29[CyclicList.next]o29:0) -> f916_0_get_Load(i141:0 - 1, o90[CyclicList.next]o90:0) :|: i141:0 > 0 && o90[CyclicList.next]o89:0 > 0 && o29[CyclicList.next]o29:0 > -1 && o90[CyclicList.next]o89:0 < o29[CyclicList.next]o29:0 && o90[CyclicList.next]o90:0 > o90[CyclicList.next]o89:0 6.86/2.79 6.86/2.79 ---------------------------------------- 6.86/2.79 6.86/2.79 (9) 6.86/2.79 Obligation: 6.86/2.79 Rules: 6.86/2.79 f916_0_get_Load(i141:0, o29[CyclicList.next]o29:0) -> f916_0_get_Load(i141:0 - 1, 1) :|: o90[CyclicList.next]o89:0 < o29[CyclicList.next]o29:0 && o29[CyclicList.next]o29:0 > -1 && i141:0 > 0 6.86/2.79 f916_0_get_Load(x, x1) -> f916_0_get_Load(x - 1, x2) :|: x > 0 && x3 > 0 && x1 > -1 && x3 < x1 && x2 > x3 6.86/2.79 6.86/2.79 ---------------------------------------- 6.86/2.79 6.86/2.79 (10) IRSFormatTransformerProof (EQUIVALENT) 6.86/2.79 Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). 6.86/2.79 ---------------------------------------- 6.86/2.79 6.86/2.79 (11) 6.86/2.79 Obligation: 6.86/2.79 Rules: 6.86/2.79 f916_0_get_Load(i141:0, o29[CyclicList.next]o29:0) -> f916_0_get_Load(arith, 1) :|: o90[CyclicList.next]o89:0 < o29[CyclicList.next]o29:0 && o29[CyclicList.next]o29:0 > -1 && i141:0 > 0 && arith = i141:0 - 1 6.86/2.79 f916_0_get_Load(x4, x5) -> f916_0_get_Load(x6, x7) :|: x4 > 0 && x8 > 0 && x5 > -1 && x8 < x5 && x7 > x8 && x6 = x4 - 1 6.86/2.79 6.86/2.79 ---------------------------------------- 6.86/2.79 6.86/2.79 (12) IRSwTTerminationDigraphProof (EQUIVALENT) 6.86/2.79 Constructed termination digraph! 6.86/2.79 Nodes: 6.86/2.79 (1) f916_0_get_Load(i141:0, o29[CyclicList.next]o29:0) -> f916_0_get_Load(arith, 1) :|: o90[CyclicList.next]o89:0 < o29[CyclicList.next]o29:0 && o29[CyclicList.next]o29:0 > -1 && i141:0 > 0 && arith = i141:0 - 1 6.86/2.79 (2) f916_0_get_Load(x4, x5) -> f916_0_get_Load(x6, x7) :|: x4 > 0 && x8 > 0 && x5 > -1 && x8 < x5 && x7 > x8 && x6 = x4 - 1 6.86/2.79 6.86/2.79 Arcs: 6.86/2.79 (1) -> (1) 6.86/2.79 (2) -> (1), (2) 6.86/2.79 6.86/2.79 This digraph is fully evaluated! 6.86/2.79 ---------------------------------------- 6.86/2.79 6.86/2.79 (13) 6.86/2.79 Complex Obligation (AND) 6.86/2.79 6.86/2.79 ---------------------------------------- 6.86/2.79 6.86/2.79 (14) 6.86/2.79 Obligation: 6.86/2.79 6.86/2.79 Termination digraph: 6.86/2.79 Nodes: 6.86/2.79 (1) f916_0_get_Load(x4, x5) -> f916_0_get_Load(x6, x7) :|: x4 > 0 && x8 > 0 && x5 > -1 && x8 < x5 && x7 > x8 && x6 = x4 - 1 6.86/2.79 6.86/2.79 Arcs: 6.86/2.79 (1) -> (1) 6.86/2.79 6.86/2.79 This digraph is fully evaluated! 6.86/2.79 6.86/2.79 ---------------------------------------- 6.86/2.79 6.86/2.79 (15) IntTRSCompressionProof (EQUIVALENT) 6.86/2.79 Compressed rules. 6.86/2.79 ---------------------------------------- 6.86/2.79 6.86/2.79 (16) 6.86/2.79 Obligation: 6.86/2.79 Rules: 6.86/2.79 f916_0_get_Load(x4:0, x5:0) -> f916_0_get_Load(x4:0 - 1, x7:0) :|: x8:0 < x5:0 && x8:0 < x7:0 && x5:0 > -1 && x8:0 > 0 && x4:0 > 0 6.86/2.79 6.86/2.79 ---------------------------------------- 6.86/2.79 6.86/2.79 (17) TempFilterProof (SOUND) 6.86/2.79 Used the following sort dictionary for filtering: 6.86/2.79 f916_0_get_Load(INTEGER, INTEGER) 6.86/2.79 Replaced non-predefined constructor symbols by 0. 6.86/2.79 ---------------------------------------- 6.86/2.79 6.86/2.79 (18) 6.86/2.79 Obligation: 6.86/2.79 Rules: 6.86/2.79 f916_0_get_Load(x4:0, x5:0) -> f916_0_get_Load(c, x7:0) :|: c = x4:0 - 1 && (x8:0 < x5:0 && x8:0 < x7:0 && x5:0 > -1 && x8:0 > 0 && x4:0 > 0) 6.86/2.79 6.86/2.79 ---------------------------------------- 6.86/2.79 6.86/2.79 (19) RankingReductionPairProof (EQUIVALENT) 6.86/2.79 Interpretation: 6.86/2.79 [ f916_0_get_Load ] = f916_0_get_Load_1 6.86/2.79 6.86/2.79 The following rules are decreasing: 6.86/2.79 f916_0_get_Load(x4:0, x5:0) -> f916_0_get_Load(c, x7:0) :|: c = x4:0 - 1 && (x8:0 < x5:0 && x8:0 < x7:0 && x5:0 > -1 && x8:0 > 0 && x4:0 > 0) 6.86/2.79 6.86/2.79 The following rules are bounded: 6.86/2.79 f916_0_get_Load(x4:0, x5:0) -> f916_0_get_Load(c, x7:0) :|: c = x4:0 - 1 && (x8:0 < x5:0 && x8:0 < x7:0 && x5:0 > -1 && x8:0 > 0 && x4:0 > 0) 6.86/2.79 6.86/2.79 6.86/2.79 ---------------------------------------- 6.86/2.79 6.86/2.79 (20) 6.86/2.79 YES 6.86/2.79 6.86/2.79 ---------------------------------------- 6.86/2.79 6.86/2.79 (21) 6.86/2.79 Obligation: 6.86/2.79 6.86/2.79 Termination digraph: 6.86/2.79 Nodes: 6.86/2.79 (1) f916_0_get_Load(i141:0, o29[CyclicList.next]o29:0) -> f916_0_get_Load(arith, 1) :|: o90[CyclicList.next]o89:0 < o29[CyclicList.next]o29:0 && o29[CyclicList.next]o29:0 > -1 && i141:0 > 0 && arith = i141:0 - 1 6.86/2.79 6.86/2.79 Arcs: 6.86/2.79 (1) -> (1) 6.86/2.79 6.86/2.79 This digraph is fully evaluated! 6.86/2.79 6.86/2.79 ---------------------------------------- 6.86/2.79 6.86/2.79 (22) IntTRSCompressionProof (EQUIVALENT) 6.86/2.79 Compressed rules. 6.86/2.79 ---------------------------------------- 6.86/2.79 6.86/2.79 (23) 6.86/2.79 Obligation: 6.86/2.79 Rules: 6.86/2.79 f916_0_get_Load(i141:0:0, o29[CyclicList.next]o29:0:0) -> f916_0_get_Load(i141:0:0 - 1, 1) :|: o90[CyclicList.next]o89:0:0 < o29[CyclicList.next]o29:0:0 && o29[CyclicList.next]o29:0:0 > -1 && i141:0:0 > 0 6.86/2.79 6.86/2.79 ---------------------------------------- 6.86/2.79 6.86/2.79 (24) TempFilterProof (SOUND) 6.86/2.79 Used the following sort dictionary for filtering: 6.86/2.79 f916_0_get_Load(INTEGER, VARIABLE) 6.86/2.79 Replaced non-predefined constructor symbols by 0. 6.86/2.79 ---------------------------------------- 6.86/2.79 6.86/2.79 (25) 6.86/2.79 Obligation: 6.86/2.79 Rules: 6.86/2.79 f916_0_get_Load(i141:0:0, o29[CyclicList.next]o29:0:0) -> f916_0_get_Load(c, c1) :|: c1 = 1 && c = i141:0:0 - 1 && (o90[CyclicList.next]o89:0:0 < o29[CyclicList.next]o29:0:0 && o29[CyclicList.next]o29:0:0 > -1 && i141:0:0 > 0) 6.86/2.79 6.86/2.79 ---------------------------------------- 6.86/2.79 6.86/2.79 (26) RankingReductionPairProof (EQUIVALENT) 6.86/2.79 Interpretation: 6.86/2.79 [ f916_0_get_Load ] = f916_0_get_Load_1 6.86/2.79 6.86/2.79 The following rules are decreasing: 6.86/2.79 f916_0_get_Load(i141:0:0, o29[CyclicList.next]o29:0:0) -> f916_0_get_Load(c, c1) :|: c1 = 1 && c = i141:0:0 - 1 && (o90[CyclicList.next]o89:0:0 < o29[CyclicList.next]o29:0:0 && o29[CyclicList.next]o29:0:0 > -1 && i141:0:0 > 0) 6.86/2.79 6.86/2.79 The following rules are bounded: 6.86/2.79 f916_0_get_Load(i141:0:0, o29[CyclicList.next]o29:0:0) -> f916_0_get_Load(c, c1) :|: c1 = 1 && c = i141:0:0 - 1 && (o90[CyclicList.next]o89:0:0 < o29[CyclicList.next]o29:0:0 && o29[CyclicList.next]o29:0:0 > -1 && i141:0:0 > 0) 6.86/2.79 6.86/2.79 6.86/2.79 ---------------------------------------- 6.86/2.79 6.86/2.79 (27) 6.86/2.79 YES 6.86/2.79 6.86/2.79 ---------------------------------------- 6.86/2.79 6.86/2.79 (28) 6.86/2.79 Obligation: 6.86/2.79 SCC of termination graph based on JBC Program. 6.86/2.79 SCC contains nodes from the following methods: CyclicList.main([Ljava/lang/String;)V 6.86/2.79 SCC calls the following helper methods: 6.86/2.79 Performed SCC analyses: 6.86/2.79 *Used field analysis yielded the following read fields: 6.86/2.79 6.86/2.79 *Marker field analysis yielded the following relations that could be markers: 6.86/2.79 6.86/2.79 ---------------------------------------- 6.86/2.79 6.86/2.79 (29) SCCToIRSProof (SOUND) 6.86/2.79 Transformed FIGraph SCCs to intTRSs. Log: 6.86/2.79 Generated rules. Obtained 17 IRulesP rules: 6.86/2.79 f482_0_create_Load(EOS(STATIC_482), i76, o29[CyclicList.next]o28) -> f485_0_create_LE(EOS(STATIC_485), i76, i76, o29[CyclicList.next]o28) :|: TRUE 6.86/2.79 f485_0_create_LE(EOS(STATIC_485), i78, i78, o29[CyclicList.next]o28) -> f490_0_create_LE(EOS(STATIC_490), i78, i78, o29[CyclicList.next]o28) :|: TRUE 6.86/2.79 f490_0_create_LE(EOS(STATIC_490), i78, i78, o29[CyclicList.next]o28) -> f495_0_create_New(EOS(STATIC_495), i78, o29[CyclicList.next]o28) :|: i78 > 0 6.86/2.79 f495_0_create_New(EOS(STATIC_495), i78, o29[CyclicList.next]o28) -> f501_0_create_Duplicate(EOS(STATIC_501), i78, o29[CyclicList.next]o28) :|: TRUE 6.86/2.79 f501_0_create_Duplicate(EOS(STATIC_501), i78, o29[CyclicList.next]o28) -> f514_0_create_Load(EOS(STATIC_514), i78, o29[CyclicList.next]o28) :|: TRUE 6.86/2.79 f514_0_create_Load(EOS(STATIC_514), i78, o29[CyclicList.next]o28) -> f519_0_create_InvokeMethod(EOS(STATIC_519), i78, o29[CyclicList.next]o28) :|: TRUE 6.86/2.79 f519_0_create_InvokeMethod(EOS(STATIC_519), i78, o29[CyclicList.next]o28) -> f555_0__init__Load(EOS(STATIC_555), i78, o29[CyclicList.next]o28) :|: TRUE 6.86/2.79 f555_0__init__Load(EOS(STATIC_555), i78, o29[CyclicList.next]o28) -> f580_0__init__InvokeMethod(EOS(STATIC_580), i78, o29[CyclicList.next]o28) :|: TRUE 6.86/2.79 f580_0__init__InvokeMethod(EOS(STATIC_580), i78, o29[CyclicList.next]o28) -> f587_0__init__Load(EOS(STATIC_587), i78, o29[CyclicList.next]o28) :|: TRUE 6.86/2.79 f587_0__init__Load(EOS(STATIC_587), i78, o29[CyclicList.next]o28) -> f596_0__init__Load(EOS(STATIC_596), i78, o29[CyclicList.next]o28) :|: TRUE 6.86/2.79 f596_0__init__Load(EOS(STATIC_596), i78, o29[CyclicList.next]o28) -> f606_0__init__FieldAccess(EOS(STATIC_606), i78, o29[CyclicList.next]o28) :|: TRUE 6.86/2.79 f606_0__init__FieldAccess(EOS(STATIC_606), i78, o29[CyclicList.next]o28) -> f631_0__init__Return(EOS(STATIC_631), i78, o29[CyclicList.next]o28) :|: TRUE 6.86/2.79 f631_0__init__Return(EOS(STATIC_631), i78, o29[CyclicList.next]o28) -> f637_0_create_Store(EOS(STATIC_637), i78, o29[CyclicList.next]o28) :|: TRUE 6.86/2.79 f637_0_create_Store(EOS(STATIC_637), i78, o29[CyclicList.next]o28) -> f646_0_create_JMP(EOS(STATIC_646), i78, o29[CyclicList.next]o28) :|: TRUE 6.86/2.79 f646_0_create_JMP(EOS(STATIC_646), i78, o29[CyclicList.next]o28) -> f848_0_create_Inc(EOS(STATIC_848), i78, o29[CyclicList.next]o28) :|: TRUE 6.86/2.79 f848_0_create_Inc(EOS(STATIC_848), i78, o29[CyclicList.next]o28) -> f466_0_create_Inc(EOS(STATIC_466), i78, o55[CyclicList.next]o28) :|: TRUE 6.86/2.79 f466_0_create_Inc(EOS(STATIC_466), i22, o29[CyclicList.next]o28) -> f482_0_create_Load(EOS(STATIC_482), i22 + -1, o29[CyclicList.next]o28) :|: TRUE 6.86/2.79 Combined rules. Obtained 1 IRulesP rules: 6.86/2.79 f482_0_create_Load(EOS(STATIC_482), i76:0, o29[CyclicList.next]o28:0) -> f482_0_create_Load(EOS(STATIC_482), i76:0 - 1, o55[CyclicList.next]o28:0) :|: i76:0 > 0 6.86/2.79 Filtered constant ground arguments: 6.86/2.79 f482_0_create_Load(x1, x2, x3) -> f482_0_create_Load(x2, x3) 6.86/2.79 EOS(x1) -> EOS 6.86/2.79 Filtered unneeded arguments: 6.86/2.79 f482_0_create_Load(x1, x2) -> f482_0_create_Load(x1) 6.86/2.79 Finished conversion. Obtained 1 rules.P rules: 6.86/2.79 f482_0_create_Load(i76:0) -> f482_0_create_Load(i76:0 - 1) :|: i76:0 > 0 6.86/2.79 6.86/2.79 ---------------------------------------- 6.86/2.79 6.86/2.79 (30) 6.86/2.79 Obligation: 6.86/2.79 Rules: 6.86/2.79 f482_0_create_Load(i76:0) -> f482_0_create_Load(i76:0 - 1) :|: i76:0 > 0 6.86/2.79 6.86/2.79 ---------------------------------------- 6.86/2.79 6.86/2.79 (31) IRSFormatTransformerProof (EQUIVALENT) 6.86/2.79 Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). 6.86/2.79 ---------------------------------------- 6.86/2.79 6.86/2.79 (32) 6.86/2.79 Obligation: 6.86/2.79 Rules: 6.86/2.79 f482_0_create_Load(i76:0) -> f482_0_create_Load(arith) :|: i76:0 > 0 && arith = i76:0 - 1 6.86/2.79 6.86/2.79 ---------------------------------------- 6.86/2.79 6.86/2.79 (33) IRSwTTerminationDigraphProof (EQUIVALENT) 6.86/2.79 Constructed termination digraph! 6.86/2.79 Nodes: 6.86/2.79 (1) f482_0_create_Load(i76:0) -> f482_0_create_Load(arith) :|: i76:0 > 0 && arith = i76:0 - 1 6.86/2.79 6.86/2.79 Arcs: 6.86/2.79 (1) -> (1) 6.86/2.79 6.86/2.79 This digraph is fully evaluated! 6.86/2.79 ---------------------------------------- 6.86/2.79 6.86/2.79 (34) 6.86/2.79 Obligation: 6.86/2.79 6.86/2.79 Termination digraph: 6.86/2.79 Nodes: 6.86/2.79 (1) f482_0_create_Load(i76:0) -> f482_0_create_Load(arith) :|: i76:0 > 0 && arith = i76:0 - 1 6.86/2.79 6.86/2.79 Arcs: 6.86/2.79 (1) -> (1) 6.86/2.79 6.86/2.79 This digraph is fully evaluated! 6.86/2.79 6.86/2.79 ---------------------------------------- 6.86/2.79 6.86/2.79 (35) IntTRSCompressionProof (EQUIVALENT) 6.86/2.79 Compressed rules. 6.86/2.79 ---------------------------------------- 6.86/2.79 6.86/2.79 (36) 6.86/2.79 Obligation: 6.86/2.79 Rules: 6.86/2.79 f482_0_create_Load(i76:0:0) -> f482_0_create_Load(i76:0:0 - 1) :|: i76:0:0 > 0 6.86/2.79 6.86/2.79 ---------------------------------------- 6.86/2.79 6.86/2.79 (37) TempFilterProof (SOUND) 6.86/2.79 Used the following sort dictionary for filtering: 6.86/2.79 f482_0_create_Load(INTEGER) 6.86/2.79 Replaced non-predefined constructor symbols by 0. 6.86/2.79 ---------------------------------------- 6.86/2.79 6.86/2.79 (38) 6.86/2.79 Obligation: 6.86/2.79 Rules: 6.86/2.79 f482_0_create_Load(i76:0:0) -> f482_0_create_Load(c) :|: c = i76:0:0 - 1 && i76:0:0 > 0 6.86/2.79 6.86/2.79 ---------------------------------------- 6.86/2.79 6.86/2.79 (39) PolynomialOrderProcessor (EQUIVALENT) 6.86/2.79 Found the following polynomial interpretation: 6.86/2.79 [f482_0_create_Load(x)] = x 6.86/2.79 6.86/2.79 The following rules are decreasing: 6.86/2.79 f482_0_create_Load(i76:0:0) -> f482_0_create_Load(c) :|: c = i76:0:0 - 1 && i76:0:0 > 0 6.86/2.79 The following rules are bounded: 6.86/2.79 f482_0_create_Load(i76:0:0) -> f482_0_create_Load(c) :|: c = i76:0:0 - 1 && i76:0:0 > 0 6.86/2.79 6.86/2.79 ---------------------------------------- 6.86/2.79 6.86/2.79 (40) 6.86/2.79 YES 7.09/2.83 EOF