/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.jar /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.jar # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 96 ms] (2) JBC problem (3) JBCToGraph [EQUIVALENT, 865 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 0 ms] (6) AND (7) JBCTerminationSCC (8) SCCToIRSProof [SOUND, 160 ms] (9) IRSwT (10) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (11) IRSwT (12) IRSwTTerminationDigraphProof [EQUIVALENT, 26 ms] (13) IRSwT (14) TempFilterProof [SOUND, 22 ms] (15) IRSwT (16) IRSwTToQDPProof [SOUND, 0 ms] (17) QDP (18) QDPSizeChangeProof [EQUIVALENT, 0 ms] (19) YES (20) JBCTerminationSCC (21) SCCToIRSProof [SOUND, 77 ms] (22) IRSwT (23) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (24) IRSwT (25) IRSwTTerminationDigraphProof [EQUIVALENT, 30 ms] (26) IRSwT (27) IntTRSCompressionProof [EQUIVALENT, 0 ms] (28) IRSwT (29) TempFilterProof [SOUND, 19 ms] (30) IntTRS (31) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (32) YES ---------------------------------------- (0) Obligation: need to prove termination of the following program: package SearchTreeR; public class Random { static String[] args; static int index = 0; public static int random() { final String string = args[index]; index++; return string.length(); } } package SearchTreeR; public class SearchTreeR { public static void main(final String[] args) { Random.args = args; final Tree t = new Tree(Random.random()); final int numberOfVals = Random.random(); for (int i = 0; i < numberOfVals; i++) { t.insert(Random.random()); } } } package SearchTreeR; public class Tree { Tree left; Tree right; int value; public Tree(final int val) { this.value = val; } public void insert(final int v) { if (v <= this.value) { if (this.left == null) { this.left = new Tree(v); } else { this.left.insert(v); } } else { if (this.right == null) { this.right = new Tree(v); } else { this.right.insert(v); } } } } ---------------------------------------- (1) BareJBCToJBCProof (EQUIVALENT) initialized classpath ---------------------------------------- (2) Obligation: need to prove termination of the following program: package SearchTreeR; public class Random { static String[] args; static int index = 0; public static int random() { final String string = args[index]; index++; return string.length(); } } package SearchTreeR; public class SearchTreeR { public static void main(final String[] args) { Random.args = args; final Tree t = new Tree(Random.random()); final int numberOfVals = Random.random(); for (int i = 0; i < numberOfVals; i++) { t.insert(Random.random()); } } } package SearchTreeR; public class Tree { Tree left; Tree right; int value; public Tree(final int val) { this.value = val; } public void insert(final int v) { if (v <= this.value) { if (this.left == null) { this.left = new Tree(v); } else { this.left.insert(v); } } else { if (this.right == null) { this.right = new Tree(v); } else { this.right.insert(v); } } } } ---------------------------------------- (3) JBCToGraph (EQUIVALENT) Constructed TerminationGraph. ---------------------------------------- (4) Obligation: Termination Graph based on JBC Program: SearchTreeR.SearchTreeR.main([Ljava/lang/String;)V: Graph of 292 nodes with 1 SCC. SearchTreeR.Tree.insert(I)V: Graph of 72 nodes with 0 SCCs. ---------------------------------------- (5) TerminationGraphToSCCProof (SOUND) Splitted TerminationGraph to 2 SCCss. ---------------------------------------- (6) Complex Obligation (AND) ---------------------------------------- (7) Obligation: SCC of termination graph based on JBC Program. SCC contains nodes from the following methods: SearchTreeR.Tree.insert(I)V SCC calls the following helper methods: SearchTreeR.Tree.insert(I)V Performed SCC analyses: *Used field analysis yielded the following read fields: *SearchTreeR.Tree: [value, right, left] *Marker field analysis yielded the following relations that could be markers: ---------------------------------------- (8) SCCToIRSProof (SOUND) Transformed FIGraph SCCs to intTRSs. Log: Generated rules. Obtained 30 IRulesP rules: f2900_0_insert_Load(EOS(STATIC_2900), java.lang.Object(o725sub), i574, java.lang.Object(o725sub), i574, i574) -> f2904_0_insert_FieldAccess(EOS(STATIC_2904), java.lang.Object(o725sub), i574, java.lang.Object(o725sub), i574, i574, java.lang.Object(o725sub)) :|: TRUE f2904_0_insert_FieldAccess(EOS(STATIC_2904), java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765)), i574, java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765)), i574, i574, java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765))) -> f2908_0_insert_FieldAccess(EOS(STATIC_2908), java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765)), i574, java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765)), i574, i574, java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765))) :|: TRUE f2908_0_insert_FieldAccess(EOS(STATIC_2908), java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765)), i574, java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765)), i574, i574, java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765))) -> f2912_0_insert_GT(EOS(STATIC_2912), java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765)), i574, java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765)), i574, i574, i654) :|: TRUE f2912_0_insert_GT(EOS(STATIC_2912), java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765)), i574, java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765)), i574, i574, i654) -> f2920_0_insert_GT(EOS(STATIC_2920), java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765)), i574, java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765)), i574, i574, i654) :|: i574 > i654 f2912_0_insert_GT(EOS(STATIC_2912), java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765)), i574, java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765)), i574, i574, i654) -> f2921_0_insert_GT(EOS(STATIC_2921), java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765)), i574, java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765)), i574, i574, i654) :|: i574 <= i654 f2920_0_insert_GT(EOS(STATIC_2920), java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765)), i574, java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765)), i574, i574, i654) -> f2942_0_insert_Load(EOS(STATIC_2942), java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765)), i574, java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765)), i574) :|: i574 > i654 f2942_0_insert_Load(EOS(STATIC_2942), java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765)), i574, java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765)), i574) -> f2962_0_insert_FieldAccess(EOS(STATIC_2962), java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765)), i574, java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765)), i574, java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765))) :|: TRUE f2962_0_insert_FieldAccess(EOS(STATIC_2962), java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765)), i574, java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765)), i574, java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765))) -> f2973_0_insert_NONNULL(EOS(STATIC_2973), java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765)), i574, java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765)), i574, o766) :|: TRUE f2973_0_insert_NONNULL(EOS(STATIC_2973), java.lang.Object(SearchTreeR.Tree(EOC, i654, java.lang.Object(o795sub), o765)), i574, java.lang.Object(SearchTreeR.Tree(EOC, i654, java.lang.Object(o795sub), o765)), i574, java.lang.Object(o795sub)) -> f2985_0_insert_NONNULL(EOS(STATIC_2985), java.lang.Object(SearchTreeR.Tree(EOC, i654, java.lang.Object(o795sub), o765)), i574, java.lang.Object(SearchTreeR.Tree(EOC, i654, java.lang.Object(o795sub), o765)), i574, java.lang.Object(o795sub)) :|: TRUE f2985_0_insert_NONNULL(EOS(STATIC_2985), java.lang.Object(SearchTreeR.Tree(EOC, i654, java.lang.Object(o795sub), o765)), i574, java.lang.Object(SearchTreeR.Tree(EOC, i654, java.lang.Object(o795sub), o765)), i574, java.lang.Object(o795sub)) -> f2996_0_insert_Load(EOS(STATIC_2996), java.lang.Object(SearchTreeR.Tree(EOC, i654, java.lang.Object(o795sub), o765)), i574, java.lang.Object(SearchTreeR.Tree(EOC, i654, java.lang.Object(o795sub), o765)), i574) :|: TRUE f2996_0_insert_Load(EOS(STATIC_2996), java.lang.Object(SearchTreeR.Tree(EOC, i654, java.lang.Object(o795sub), o765)), i574, java.lang.Object(SearchTreeR.Tree(EOC, i654, java.lang.Object(o795sub), o765)), i574) -> f3006_0_insert_FieldAccess(EOS(STATIC_3006), java.lang.Object(SearchTreeR.Tree(EOC, i654, java.lang.Object(o795sub), o765)), i574, i574, java.lang.Object(SearchTreeR.Tree(EOC, i654, java.lang.Object(o795sub), o765))) :|: TRUE f3006_0_insert_FieldAccess(EOS(STATIC_3006), java.lang.Object(SearchTreeR.Tree(EOC, i654, java.lang.Object(o795sub), o765)), i574, i574, java.lang.Object(SearchTreeR.Tree(EOC, i654, java.lang.Object(o795sub), o765))) -> f3011_0_insert_Load(EOS(STATIC_3011), java.lang.Object(SearchTreeR.Tree(EOC, i654, java.lang.Object(o795sub), o765)), i574, i574, java.lang.Object(o795sub)) :|: TRUE f3011_0_insert_Load(EOS(STATIC_3011), java.lang.Object(SearchTreeR.Tree(EOC, i654, java.lang.Object(o795sub), o765)), i574, i574, java.lang.Object(o795sub)) -> f3021_0_insert_InvokeMethod(EOS(STATIC_3021), java.lang.Object(SearchTreeR.Tree(EOC, i654, java.lang.Object(o795sub), o765)), i574, java.lang.Object(o795sub), i574) :|: TRUE f3021_0_insert_InvokeMethod(EOS(STATIC_3021), java.lang.Object(SearchTreeR.Tree(EOC, i654, java.lang.Object(o795sub), o765)), i574, java.lang.Object(o795sub), i574) -> f3030_0_insert_Load(EOS(STATIC_3030), java.lang.Object(o795sub), i574, java.lang.Object(o795sub), i574) :|: i573 >= 1 && i574 > i654 f3021_0_insert_InvokeMethod(EOS(STATIC_3021), java.lang.Object(SearchTreeR.Tree(EOC, i654, java.lang.Object(o795sub), o765)), i574, java.lang.Object(o795sub), i574) -> f3030_1_insert_Load(EOS(STATIC_3030), java.lang.Object(SearchTreeR.Tree(EOC, i654, java.lang.Object(o795sub), o765)), i574, java.lang.Object(o795sub), i574) :|: i573 >= 1 && i574 > i654 f3030_0_insert_Load(EOS(STATIC_3030), java.lang.Object(o795sub), i574, java.lang.Object(o795sub), i574) -> f3041_0_insert_Load(EOS(STATIC_3041), java.lang.Object(o795sub), i574, java.lang.Object(o795sub), i574) :|: TRUE f3041_0_insert_Load(EOS(STATIC_3041), java.lang.Object(o795sub), i574, java.lang.Object(o795sub), i574) -> f2790_0_insert_Load(EOS(STATIC_2790), java.lang.Object(o795sub), i574, java.lang.Object(o795sub), i574) :|: TRUE f2790_0_insert_Load(EOS(STATIC_2790), java.lang.Object(o725sub), i574, java.lang.Object(o725sub), i574) -> f2900_0_insert_Load(EOS(STATIC_2900), java.lang.Object(o725sub), i574, java.lang.Object(o725sub), i574, i574) :|: TRUE f2921_0_insert_GT(EOS(STATIC_2921), java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765)), i574, java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765)), i574, i574, i654) -> f2948_0_insert_Load(EOS(STATIC_2948), java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765)), i574, java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765)), i574) :|: i574 <= i654 f2948_0_insert_Load(EOS(STATIC_2948), java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765)), i574, java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765)), i574) -> f2964_0_insert_FieldAccess(EOS(STATIC_2964), java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765)), i574, java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765)), i574, java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765))) :|: TRUE f2964_0_insert_FieldAccess(EOS(STATIC_2964), java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765)), i574, java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765)), i574, java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765))) -> f2975_0_insert_NONNULL(EOS(STATIC_2975), java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765)), i574, java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, o765)), i574, o765) :|: TRUE f2975_0_insert_NONNULL(EOS(STATIC_2975), java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, java.lang.Object(o796sub))), i574, java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, java.lang.Object(o796sub))), i574, java.lang.Object(o796sub)) -> f2989_0_insert_NONNULL(EOS(STATIC_2989), java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, java.lang.Object(o796sub))), i574, java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, java.lang.Object(o796sub))), i574, java.lang.Object(o796sub)) :|: TRUE f2989_0_insert_NONNULL(EOS(STATIC_2989), java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, java.lang.Object(o796sub))), i574, java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, java.lang.Object(o796sub))), i574, java.lang.Object(o796sub)) -> f2999_0_insert_Load(EOS(STATIC_2999), java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, java.lang.Object(o796sub))), i574, java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, java.lang.Object(o796sub))), i574) :|: TRUE f2999_0_insert_Load(EOS(STATIC_2999), java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, java.lang.Object(o796sub))), i574, java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, java.lang.Object(o796sub))), i574) -> f3008_0_insert_FieldAccess(EOS(STATIC_3008), java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, java.lang.Object(o796sub))), i574, i574, java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, java.lang.Object(o796sub)))) :|: TRUE f3008_0_insert_FieldAccess(EOS(STATIC_3008), java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, java.lang.Object(o796sub))), i574, i574, java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, java.lang.Object(o796sub)))) -> f3015_0_insert_Load(EOS(STATIC_3015), java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, java.lang.Object(o796sub))), i574, i574, java.lang.Object(o796sub)) :|: TRUE f3015_0_insert_Load(EOS(STATIC_3015), java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, java.lang.Object(o796sub))), i574, i574, java.lang.Object(o796sub)) -> f3025_0_insert_InvokeMethod(EOS(STATIC_3025), java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, java.lang.Object(o796sub))), i574, java.lang.Object(o796sub), i574) :|: TRUE f3025_0_insert_InvokeMethod(EOS(STATIC_3025), java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, java.lang.Object(o796sub))), i574, java.lang.Object(o796sub), i574) -> f3034_0_insert_Load(EOS(STATIC_3034), java.lang.Object(o796sub), i574, java.lang.Object(o796sub), i574) :|: i573 >= 1 && i574 <= i654 f3025_0_insert_InvokeMethod(EOS(STATIC_3025), java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, java.lang.Object(o796sub))), i574, java.lang.Object(o796sub), i574) -> f3034_1_insert_Load(EOS(STATIC_3034), java.lang.Object(SearchTreeR.Tree(EOC, i654, o766, java.lang.Object(o796sub))), i574, java.lang.Object(o796sub), i574) :|: i573 >= 1 && i574 <= i654 f3034_0_insert_Load(EOS(STATIC_3034), java.lang.Object(o796sub), i574, java.lang.Object(o796sub), i574) -> f3047_0_insert_Load(EOS(STATIC_3047), java.lang.Object(o796sub), i574, java.lang.Object(o796sub), i574) :|: TRUE f3047_0_insert_Load(EOS(STATIC_3047), java.lang.Object(o796sub), i574, java.lang.Object(o796sub), i574) -> f2790_0_insert_Load(EOS(STATIC_2790), java.lang.Object(o796sub), i574, java.lang.Object(o796sub), i574) :|: TRUE Combined rules. Obtained 4 IRulesP rules: f2900_0_insert_Load(EOS(STATIC_2900), java.lang.Object(SearchTreeR.Tree(EOC, i654:0, java.lang.Object(o795sub:0), o765:0)), i574:0, java.lang.Object(SearchTreeR.Tree(EOC, i654:0, java.lang.Object(o795sub:0), o765:0)), i574:0, i574:0) -> f2900_0_insert_Load(EOS(STATIC_2900), java.lang.Object(o795sub:0), i574:0, java.lang.Object(o795sub:0), i574:0, i574:0) :|: i654:0 < i574:0 && i573:0 > 0 f2900_0_insert_Load(EOS(STATIC_2900), java.lang.Object(SearchTreeR.Tree(EOC, i654:0, o766:0, java.lang.Object(o796sub:0))), i574:0, java.lang.Object(SearchTreeR.Tree(EOC, i654:0, o766:0, java.lang.Object(o796sub:0))), i574:0, i574:0) -> f2900_0_insert_Load(EOS(STATIC_2900), java.lang.Object(o796sub:0), i574:0, java.lang.Object(o796sub:0), i574:0, i574:0) :|: i654:0 >= i574:0 && i573:0 > 0 Removed following non-SCC rules: f2900_0_insert_Load(EOS(STATIC_2900), java.lang.Object(SearchTreeR.Tree(EOC, i654:0, java.lang.Object(o795sub:0), o765:0)), i574:0, java.lang.Object(SearchTreeR.Tree(EOC, i654:0, java.lang.Object(o795sub:0), o765:0)), i574:0, i574:0) -> f3030_1_insert_Load(EOS(STATIC_3030), java.lang.Object(SearchTreeR.Tree(EOC, i654:0, java.lang.Object(o795sub:0), o765:0)), i574:0, java.lang.Object(o795sub:0), i574:0) :|: i654:0 < i574:0 && i573:0 > 0 f2900_0_insert_Load(EOS(STATIC_2900), java.lang.Object(SearchTreeR.Tree(EOC, i654:0, o766:0, java.lang.Object(o796sub:0))), i574:0, java.lang.Object(SearchTreeR.Tree(EOC, i654:0, o766:0, java.lang.Object(o796sub:0))), i574:0, i574:0) -> f3034_1_insert_Load(EOS(STATIC_3034), java.lang.Object(SearchTreeR.Tree(EOC, i654:0, o766:0, java.lang.Object(o796sub:0))), i574:0, java.lang.Object(o796sub:0), i574:0) :|: i654:0 >= i574:0 && i573:0 > 0 Filtered constant ground arguments: f2900_0_insert_Load(x1, x2, x3, x4, x5, x6) -> f2900_0_insert_Load(x2, x3, x4, x5, x6) EOS(x1) -> EOS SearchTreeR.Tree(x1, x2, x3, x4) -> SearchTreeR.Tree(x2, x3, x4) Filtered duplicate arguments: f2900_0_insert_Load(x1, x2, x3, x4, x5) -> f2900_0_insert_Load(x3, x5) Finished conversion. Obtained 2 rules.P rules: f2900_0_insert_Load(java.lang.Object(SearchTreeR.Tree(i654:0, java.lang.Object(o795sub:0), o765:0)), i574:0) -> f2900_0_insert_Load(java.lang.Object(o795sub:0), i574:0) :|: i654:0 < i574:0 && i573:0 > 0 f2900_0_insert_Load(java.lang.Object(SearchTreeR.Tree(i654:0, o766:0, java.lang.Object(o796sub:0))), i574:0) -> f2900_0_insert_Load(java.lang.Object(o796sub:0), i574:0) :|: i654:0 >= i574:0 && i573:0 > 0 ---------------------------------------- (9) Obligation: Rules: f2900_0_insert_Load(java.lang.Object(SearchTreeR.Tree(i654:0, java.lang.Object(o795sub:0), o765:0)), i574:0) -> f2900_0_insert_Load(java.lang.Object(o795sub:0), i574:0) :|: i654:0 < i574:0 && i573:0 > 0 f2900_0_insert_Load(java.lang.Object(SearchTreeR.Tree(x, x1, java.lang.Object(x2))), x3) -> f2900_0_insert_Load(java.lang.Object(x2), x3) :|: x >= x3 && x4 > 0 ---------------------------------------- (10) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (11) Obligation: Rules: f2900_0_insert_Load(java.lang.Object(SearchTreeR.Tree(i654:0, java.lang.Object(o795sub:0), o765:0)), i574:0) -> f2900_0_insert_Load(java.lang.Object(o795sub:0), i574:0) :|: i654:0 < i574:0 && i573:0 > 0 f2900_0_insert_Load(java.lang.Object(SearchTreeR.Tree(x, x1, java.lang.Object(x2))), x3) -> f2900_0_insert_Load(java.lang.Object(x2), x3) :|: x >= x3 && x4 > 0 ---------------------------------------- (12) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f2900_0_insert_Load(java.lang.Object(SearchTreeR.Tree(i654:0, java.lang.Object(o795sub:0), o765:0)), i574:0) -> f2900_0_insert_Load(java.lang.Object(o795sub:0), i574:0) :|: i654:0 < i574:0 && i573:0 > 0 (2) f2900_0_insert_Load(java.lang.Object(SearchTreeR.Tree(x, x1, java.lang.Object(x2))), x3) -> f2900_0_insert_Load(java.lang.Object(x2), x3) :|: x >= x3 && x4 > 0 Arcs: (1) -> (1), (2) (2) -> (1), (2) This digraph is fully evaluated! ---------------------------------------- (13) Obligation: Termination digraph: Nodes: (1) f2900_0_insert_Load(java.lang.Object(SearchTreeR.Tree(i654:0, java.lang.Object(o795sub:0), o765:0)), i574:0) -> f2900_0_insert_Load(java.lang.Object(o795sub:0), i574:0) :|: i654:0 < i574:0 && i573:0 > 0 (2) f2900_0_insert_Load(java.lang.Object(SearchTreeR.Tree(x, x1, java.lang.Object(x2))), x3) -> f2900_0_insert_Load(java.lang.Object(x2), x3) :|: x >= x3 && x4 > 0 Arcs: (1) -> (1), (2) (2) -> (1), (2) This digraph is fully evaluated! ---------------------------------------- (14) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f2900_0_insert_Load(VARIABLE, INTEGER) java.lang.Object(VARIABLE) SearchTreeR.Tree(INTEGER, VARIABLE, VARIABLE) Removed predefined arithmetic. ---------------------------------------- (15) Obligation: Rules: f2900_0_insert_Load(java.lang.Object(SearchTreeR.Tree(java.lang.Object(o795sub:0), o765:0))) -> f2900_0_insert_Load(java.lang.Object(o795sub:0)) f2900_0_insert_Load(java.lang.Object(SearchTreeR.Tree(x1, java.lang.Object(x2)))) -> f2900_0_insert_Load(java.lang.Object(x2)) ---------------------------------------- (16) IRSwTToQDPProof (SOUND) Removed the integers and created a QDP-Problem. ---------------------------------------- (17) Obligation: Q DP problem: The TRS P consists of the following rules: f2900_0_insert_Load(java.lang.Object(SearchTreeR.Tree(java.lang.Object(o795sub:0), o765:0))) -> f2900_0_insert_Load(java.lang.Object(o795sub:0)) f2900_0_insert_Load(java.lang.Object(SearchTreeR.Tree(x1, java.lang.Object(x2)))) -> f2900_0_insert_Load(java.lang.Object(x2)) R is empty. Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (18) QDPSizeChangeProof (EQUIVALENT) 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: *f2900_0_insert_Load(java.lang.Object(SearchTreeR.Tree(java.lang.Object(o795sub:0), o765:0))) -> f2900_0_insert_Load(java.lang.Object(o795sub:0)) The graph contains the following edges 1 > 1 *f2900_0_insert_Load(java.lang.Object(SearchTreeR.Tree(x1, java.lang.Object(x2)))) -> f2900_0_insert_Load(java.lang.Object(x2)) The graph contains the following edges 1 > 1 ---------------------------------------- (19) YES ---------------------------------------- (20) Obligation: SCC of termination graph based on JBC Program. SCC contains nodes from the following methods: SearchTreeR.SearchTreeR.main([Ljava/lang/String;)V SCC calls the following helper methods: SearchTreeR.Tree.insert(I)V Performed SCC analyses: *Used field analysis yielded the following read fields: *java.lang.String: [count] *Marker field analysis yielded the following relations that could be markers: ---------------------------------------- (21) SCCToIRSProof (SOUND) Transformed FIGraph SCCs to intTRSs. Log: Generated rules. Obtained 40 IRulesP rules: f2611_0_main_Load(EOS(STATIC_2611(java.lang.Object(ARRAY(i4)), i450)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, i453) -> f2612_0_main_GE(EOS(STATIC_2612(java.lang.Object(ARRAY(i4)), i450)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, i453, i452) :|: TRUE f2612_0_main_GE(EOS(STATIC_2612(java.lang.Object(ARRAY(i4)), i450)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, i453, i452) -> f2624_0_main_GE(EOS(STATIC_2624(java.lang.Object(ARRAY(i4)), i450)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, i453, i452) :|: i453 < i452 f2624_0_main_GE(EOS(STATIC_2624(java.lang.Object(ARRAY(i4)), i450)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, i453, i452) -> f2636_0_main_Load(EOS(STATIC_2636(java.lang.Object(ARRAY(i4)), i450)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453) :|: i453 < i452 f2636_0_main_Load(EOS(STATIC_2636(java.lang.Object(ARRAY(i4)), i450)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453) -> f2639_0_main_InvokeMethod(EOS(STATIC_2639(java.lang.Object(ARRAY(i4)), i450)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC))) :|: TRUE f2639_0_main_InvokeMethod(EOS(STATIC_2639(java.lang.Object(ARRAY(i4)), i450)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC))) -> f2640_0_random_FieldAccess(EOS(STATIC_2640(java.lang.Object(ARRAY(i4)), i450)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC))) :|: TRUE f2640_0_random_FieldAccess(EOS(STATIC_2640(java.lang.Object(ARRAY(i4)), i450)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC))) -> f2641_0_random_FieldAccess(EOS(STATIC_2641(java.lang.Object(ARRAY(i4)), i450)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), java.lang.Object(ARRAY(i4))) :|: TRUE f2641_0_random_FieldAccess(EOS(STATIC_2641(java.lang.Object(ARRAY(i4)), i450)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), java.lang.Object(ARRAY(i4))) -> f2644_0_random_ArrayAccess(EOS(STATIC_2644(java.lang.Object(ARRAY(i4)), i450)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), java.lang.Object(ARRAY(i4)), i450) :|: TRUE f2644_0_random_ArrayAccess(EOS(STATIC_2644(java.lang.Object(ARRAY(i4)), i467)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), java.lang.Object(ARRAY(i4)), i467) -> f2646_0_random_ArrayAccess(EOS(STATIC_2646(java.lang.Object(ARRAY(i4)), i467)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), java.lang.Object(ARRAY(i4)), i467) :|: TRUE f2646_0_random_ArrayAccess(EOS(STATIC_2646(java.lang.Object(ARRAY(i4)), i467)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), java.lang.Object(ARRAY(i4)), i467) -> f2648_0_random_ArrayAccess(EOS(STATIC_2648(java.lang.Object(ARRAY(i4)), i467)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), java.lang.Object(ARRAY(i4)), i467) :|: TRUE f2648_0_random_ArrayAccess(EOS(STATIC_2648(java.lang.Object(ARRAY(i4)), i467)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), java.lang.Object(ARRAY(i4)), i467) -> f2650_0_random_Store(EOS(STATIC_2650(java.lang.Object(ARRAY(i4)), i467)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), o631) :|: i467 < i4 f2650_0_random_Store(EOS(STATIC_2650(java.lang.Object(ARRAY(i4)), i467)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), o631) -> f2653_0_random_FieldAccess(EOS(STATIC_2653(java.lang.Object(ARRAY(i4)), i467)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), o631) :|: TRUE f2653_0_random_FieldAccess(EOS(STATIC_2653(java.lang.Object(ARRAY(i4)), i467)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), o631) -> f2692_0_random_ConstantStackPush(EOS(STATIC_2692(java.lang.Object(ARRAY(i4)), i467)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), o631, i467) :|: TRUE f2692_0_random_ConstantStackPush(EOS(STATIC_2692(java.lang.Object(ARRAY(i4)), i467)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), o631, i467) -> f2694_0_random_IntArithmetic(EOS(STATIC_2694(java.lang.Object(ARRAY(i4)), i467)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), o631, i467, 1) :|: TRUE f2694_0_random_IntArithmetic(EOS(STATIC_2694(java.lang.Object(ARRAY(i4)), i467)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), o631, i467, matching1) -> f2697_0_random_FieldAccess(EOS(STATIC_2697(java.lang.Object(ARRAY(i4)), i467)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), o631, i467 + 1) :|: i467 >= 0 && matching1 = 1 f2697_0_random_FieldAccess(EOS(STATIC_2697(java.lang.Object(ARRAY(i4)), i467)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), o631, i481) -> f2699_0_random_Load(EOS(STATIC_2699(java.lang.Object(ARRAY(i4)), i481)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), o631) :|: TRUE f2699_0_random_Load(EOS(STATIC_2699(java.lang.Object(ARRAY(i4)), i481)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), o631) -> f2701_0_random_InvokeMethod(EOS(STATIC_2701(java.lang.Object(ARRAY(i4)), i481)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), o631) :|: TRUE f2701_0_random_InvokeMethod(EOS(STATIC_2701(java.lang.Object(ARRAY(i4)), i481)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), java.lang.Object(o667sub)) -> f2704_0_random_InvokeMethod(EOS(STATIC_2704(java.lang.Object(ARRAY(i4)), i481)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), java.lang.Object(o667sub)) :|: TRUE f2704_0_random_InvokeMethod(EOS(STATIC_2704(java.lang.Object(ARRAY(i4)), i481)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), java.lang.Object(o668sub)) -> f2707_0_random_InvokeMethod(EOS(STATIC_2707(java.lang.Object(ARRAY(i4)), i481)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), java.lang.Object(o668sub)) :|: TRUE f2707_0_random_InvokeMethod(EOS(STATIC_2707(java.lang.Object(ARRAY(i4)), i481)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), java.lang.Object(o668sub)) -> f2710_0_length_Load(EOS(STATIC_2710(java.lang.Object(ARRAY(i4)), i481)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), java.lang.Object(o668sub)) :|: TRUE f2710_0_length_Load(EOS(STATIC_2710(java.lang.Object(ARRAY(i4)), i481)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), java.lang.Object(o668sub)) -> f2715_0_length_FieldAccess(EOS(STATIC_2715(java.lang.Object(ARRAY(i4)), i481)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), java.lang.Object(o668sub)) :|: TRUE f2715_0_length_FieldAccess(EOS(STATIC_2715(java.lang.Object(ARRAY(i4)), i481)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), java.lang.Object(java.lang.String(EOC, i520))) -> f2718_0_length_FieldAccess(EOS(STATIC_2718(java.lang.Object(ARRAY(i4)), i481)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), java.lang.Object(java.lang.String(EOC, i520))) :|: i520 >= 0 f2718_0_length_FieldAccess(EOS(STATIC_2718(java.lang.Object(ARRAY(i4)), i481)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), java.lang.Object(java.lang.String(EOC, i520))) -> f2730_0_length_Return(EOS(STATIC_2730(java.lang.Object(ARRAY(i4)), i481)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), i520) :|: TRUE f2730_0_length_Return(EOS(STATIC_2730(java.lang.Object(ARRAY(i4)), i481)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), i520) -> f2733_0_random_Return(EOS(STATIC_2733(java.lang.Object(ARRAY(i4)), i481)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), i520) :|: TRUE f2733_0_random_Return(EOS(STATIC_2733(java.lang.Object(ARRAY(i4)), i481)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), i520) -> f2737_0_main_InvokeMethod(EOS(STATIC_2737(java.lang.Object(ARRAY(i4)), i481)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), i520) :|: TRUE f2737_0_main_InvokeMethod(EOS(STATIC_2737(java.lang.Object(ARRAY(i4)), i481)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), i520) -> f2740_0_insert_Load(EOS(STATIC_2740(java.lang.Object(ARRAY(i4)), i481)), java.lang.Object(SearchTreeR.Tree(EOC)), i520, java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i520) :|: i452 >= 1 && i481 >= 1 && i453 < i452 && i481 > i453 f2737_0_main_InvokeMethod(EOS(STATIC_2737(java.lang.Object(ARRAY(i4)), i481)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), i520) -> f2740_1_insert_Load(EOS(STATIC_2740(java.lang.Object(ARRAY(i4)), i481)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), i520) :|: i452 >= 1 && i481 >= 1 && i453 < i452 && i481 > i453 f2740_0_insert_Load(EOS(STATIC_2740(java.lang.Object(ARRAY(i4)), i481)), java.lang.Object(SearchTreeR.Tree(EOC)), i520, java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i520) -> f3759_0_insert_Load(EOS(STATIC_3759(java.lang.Object(ARRAY(i4)), i481)), java.lang.Object(SearchTreeR.Tree(EOC)), i520, java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i520) :|: TRUE f3503_0_insert_Return(EOS(STATIC_3503(java.lang.Object(ARRAY(i4)), i714)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453) -> f3507_0_insert_Return(EOS(STATIC_3507(java.lang.Object(ARRAY(i4)), i714)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453) :|: TRUE f3507_0_insert_Return(EOS(STATIC_3507(java.lang.Object(ARRAY(i4)), i753)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453) -> f3512_0_main_Inc(EOS(STATIC_3512(java.lang.Object(ARRAY(i4)), i753)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453) :|: TRUE f3512_0_main_Inc(EOS(STATIC_3512(java.lang.Object(ARRAY(i4)), i753)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453) -> f3515_0_main_JMP(EOS(STATIC_3515(java.lang.Object(ARRAY(i4)), i753)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453 + 1) :|: TRUE f3515_0_main_JMP(EOS(STATIC_3515(java.lang.Object(ARRAY(i4)), i753)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i776) -> f3518_0_main_Load(EOS(STATIC_3518(java.lang.Object(ARRAY(i4)), i753)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i776) :|: TRUE f3518_0_main_Load(EOS(STATIC_3518(java.lang.Object(ARRAY(i4)), i753)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i776) -> f2604_0_main_Load(EOS(STATIC_2604(java.lang.Object(ARRAY(i4)), i753)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i776) :|: TRUE f2604_0_main_Load(EOS(STATIC_2604(java.lang.Object(ARRAY(i4)), i450)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453) -> f2611_0_main_Load(EOS(STATIC_2611(java.lang.Object(ARRAY(i4)), i450)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, i453) :|: TRUE f3506_0_insert_Return(EOS(STATIC_3506(java.lang.Object(ARRAY(i4)), i735)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453) -> f3507_0_insert_Return(EOS(STATIC_3507(java.lang.Object(ARRAY(i4)), i735)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453) :|: TRUE f3520_0_insert_Return(EOS(STATIC_3520(java.lang.Object(ARRAY(i4)), i791)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453) -> f3507_0_insert_Return(EOS(STATIC_3507(java.lang.Object(ARRAY(i4)), i791)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453) :|: TRUE f3523_0_insert_Return(EOS(STATIC_3523(java.lang.Object(ARRAY(i4)), i823)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453) -> f3507_0_insert_Return(EOS(STATIC_3507(java.lang.Object(ARRAY(i4)), i823)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453) :|: TRUE f2740_1_insert_Load(EOS(STATIC_2740(java.lang.Object(ARRAY(i4)), i714)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), i716) -> f3503_0_insert_Return(EOS(STATIC_3503(java.lang.Object(ARRAY(i4)), i714)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453) :|: TRUE f2740_1_insert_Load(EOS(STATIC_2740(java.lang.Object(ARRAY(i4)), i735)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), i737) -> f3506_0_insert_Return(EOS(STATIC_3506(java.lang.Object(ARRAY(i4)), i735)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453) :|: TRUE f2740_1_insert_Load(EOS(STATIC_2740(java.lang.Object(ARRAY(i4)), i791)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), i520) -> f3520_0_insert_Return(EOS(STATIC_3520(java.lang.Object(ARRAY(i4)), i791)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453) :|: TRUE f2740_1_insert_Load(EOS(STATIC_2740(java.lang.Object(ARRAY(i4)), i823)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453, java.lang.Object(SearchTreeR.Tree(EOC)), i520) -> f3523_0_insert_Return(EOS(STATIC_3523(java.lang.Object(ARRAY(i4)), i823)), java.lang.Object(ARRAY(i4)), java.lang.Object(SearchTreeR.Tree(EOC)), i452, i453) :|: TRUE Combined rules. Obtained 2 IRulesP rules: f2611_0_main_Load(EOS(STATIC_2611(java.lang.Object(ARRAY(i4:0)), i450:0)), java.lang.Object(ARRAY(i4:0)), java.lang.Object(SearchTreeR.Tree(EOC)), i452:0, i453:0, i453:0) -> f2611_0_main_Load(EOS(STATIC_2611(java.lang.Object(ARRAY(i4:0)), i450:0 + 1)), java.lang.Object(ARRAY(i4:0)), java.lang.Object(SearchTreeR.Tree(EOC)), i452:0, i453:0 + 1, i453:0 + 1) :|: i453:0 < i452:0 && i4:0 > i450:0 && i450:0 > -1 && i520:0 > -1 && i452:0 > 0 && i453:0 < i450:0 + 1 Removed following non-SCC rules: f2611_0_main_Load(EOS(STATIC_2611(java.lang.Object(ARRAY(i4:0)), i450:0)), java.lang.Object(ARRAY(i4:0)), java.lang.Object(SearchTreeR.Tree(EOC)), i452:0, i453:0, i453:0) -> f3759_0_insert_Load(EOS(STATIC_3759(java.lang.Object(ARRAY(i4:0)), i450:0 + 1)), java.lang.Object(SearchTreeR.Tree(EOC)), i520:0, java.lang.Object(ARRAY(i4:0)), java.lang.Object(SearchTreeR.Tree(EOC)), i520:0) :|: i453:0 < i452:0 && i4:0 > i450:0 && i450:0 > -1 && i520:0 > -1 && i452:0 > 0 && i453:0 < i450:0 + 1 Filtered constant ground arguments: f2611_0_main_Load(x1, x2, x3, x4, x5, x6) -> f2611_0_main_Load(x1, x2, x4, x5, x6) SearchTreeR.Tree(x1) -> SearchTreeR.Tree Filtered duplicate arguments: f2611_0_main_Load(x1, x2, x3, x4, x5) -> f2611_0_main_Load(x1, x2, x3, x5) Finished conversion. Obtained 1 rules.P rules: f2611_0_main_Load(java.lang.Object(ARRAY(i4:0)), i452:0, i453:0, i4:0, i450:0, i4:0) -> f2611_0_main_Load(java.lang.Object(ARRAY(i4:0)), i452:0, i453:0 + 1, i4:0, i450:0 + 1, i4:0) :|: i4:0 > i450:0 && i453:0 < i452:0 && i450:0 > -1 && i520:0 > -1 && i453:0 < i450:0 + 1 && i452:0 > 0 ---------------------------------------- (22) Obligation: Rules: f2611_0_main_Load(java.lang.Object(ARRAY(i4:0)), i452:0, i453:0, i4:0, i450:0, i4:0) -> f2611_0_main_Load(java.lang.Object(ARRAY(i4:0)), i452:0, i453:0 + 1, i4:0, i450:0 + 1, i4:0) :|: i4:0 > i450:0 && i453:0 < i452:0 && i450:0 > -1 && i520:0 > -1 && i453:0 < i450:0 + 1 && i452:0 > 0 ---------------------------------------- (23) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (24) Obligation: Rules: f2611_0_main_Load(java.lang.Object(ARRAY(i4:0)), i452:0, i453:0, i4:0, i450:0, i4:0) -> f2611_0_main_Load(java.lang.Object(ARRAY(i4:0)), i452:0, arith, i4:0, arith1, i4:0) :|: i4:0 > i450:0 && i453:0 < i452:0 && i450:0 > -1 && i520:0 > -1 && i453:0 < i450:0 + 1 && i452:0 > 0 && arith = i453:0 + 1 && arith1 = i450:0 + 1 ---------------------------------------- (25) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f2611_0_main_Load(java.lang.Object(ARRAY(i4:0)), i452:0, i453:0, i4:0, i450:0, i4:0) -> f2611_0_main_Load(java.lang.Object(ARRAY(i4:0)), i452:0, arith, i4:0, arith1, i4:0) :|: i4:0 > i450:0 && i453:0 < i452:0 && i450:0 > -1 && i520:0 > -1 && i453:0 < i450:0 + 1 && i452:0 > 0 && arith = i453:0 + 1 && arith1 = i450:0 + 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (26) Obligation: Termination digraph: Nodes: (1) f2611_0_main_Load(java.lang.Object(ARRAY(i4:0)), i452:0, i453:0, i4:0, i450:0, i4:0) -> f2611_0_main_Load(java.lang.Object(ARRAY(i4:0)), i452:0, arith, i4:0, arith1, i4:0) :|: i4:0 > i450:0 && i453:0 < i452:0 && i450:0 > -1 && i520:0 > -1 && i453:0 < i450:0 + 1 && i452:0 > 0 && arith = i453:0 + 1 && arith1 = i450:0 + 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (27) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (28) Obligation: Rules: f2611_0_main_Load(java.lang.Object(ARRAY(i4:0:0)), i452:0:0, i453:0:0, i4:0:0, i450:0:0, i4:0:0) -> f2611_0_main_Load(java.lang.Object(ARRAY(i4:0:0)), i452:0:0, i453:0:0 + 1, i4:0:0, i450:0:0 + 1, i4:0:0) :|: i453:0:0 < i450:0:0 + 1 && i452:0:0 > 0 && i520:0:0 > -1 && i450:0:0 > -1 && i453:0:0 < i452:0:0 && i4:0:0 > i450:0:0 ---------------------------------------- (29) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f2611_0_main_Load(VARIABLE, INTEGER, INTEGER, INTEGER, INTEGER, INTEGER) java.lang.Object(VARIABLE) ARRAY(INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (30) Obligation: Rules: f2611_0_main_Load(c, i452:0:0, i453:0:0, i4:0:0, i450:0:0, i4:0:0) -> f2611_0_main_Load(c1, i452:0:0, c2, i4:0:0, c3, i4:0:0) :|: c3 = i450:0:0 + 1 && (c2 = i453:0:0 + 1 && (c1 = 0 && c = 0)) && (i453:0:0 < i450:0:0 + 1 && i452:0:0 > 0 && i520:0:0 > -1 && i450:0:0 > -1 && i453:0:0 < i452:0:0 && i4:0:0 > i450:0:0) ---------------------------------------- (31) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f2611_0_main_Load(x, x1, x2, x3, x4, x5)] = c*x + x1 - x2 The following rules are decreasing: f2611_0_main_Load(c, i452:0:0, i453:0:0, i4:0:0, i450:0:0, i4:0:0) -> f2611_0_main_Load(c1, i452:0:0, c2, i4:0:0, c3, i4:0:0) :|: c3 = i450:0:0 + 1 && (c2 = i453:0:0 + 1 && (c1 = 0 && c = 0)) && (i453:0:0 < i450:0:0 + 1 && i452:0:0 > 0 && i520:0:0 > -1 && i450:0:0 > -1 && i453:0:0 < i452:0:0 && i4:0:0 > i450:0:0) The following rules are bounded: f2611_0_main_Load(c, i452:0:0, i453:0:0, i4:0:0, i450:0:0, i4:0:0) -> f2611_0_main_Load(c1, i452:0:0, c2, i4:0:0, c3, i4:0:0) :|: c3 = i450:0:0 + 1 && (c2 = i453:0:0 + 1 && (c1 = 0 && c = 0)) && (i453:0:0 < i450:0:0 + 1 && i452:0:0 > 0 && i520:0:0 > -1 && i450:0:0 > -1 && i453:0:0 < i452:0:0 && i4:0:0 > i450:0:0) ---------------------------------------- (32) YES