/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 96 ms] (2) JBC problem (3) JBCToGraph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, 245 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 0 ms] (6) JBCTerminationSCC (7) SCCToIRSProof [SOUND, 61 ms] (8) IRSwT (9) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 34 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT (15) FilterProof [EQUIVALENT, 0 ms] (16) IntTRS (17) IntTRSCompressionProof [EQUIVALENT, 0 ms] (18) IntTRS (19) RankingReductionPairProof [EQUIVALENT, 3 ms] (20) YES ---------------------------------------- (0) Obligation: need to prove termination of the following program: package example_2; public class Test { public static int divBy(int x){ int r = 0; int y; while (x > 0) { y = 2; x = x/y; r = r + x; } return r; } public static void main(String[] args) { if (args.length > 0) { int x = args[0].length(); int r = divBy(x); // System.out.println("Result: " + r); } // else System.out.println("Error: Incorrect call"); } } ---------------------------------------- (1) BareJBCToJBCProof (EQUIVALENT) initialized classpath ---------------------------------------- (2) Obligation: need to prove termination of the following program: package example_2; public class Test { public static int divBy(int x){ int r = 0; int y; while (x > 0) { y = 2; x = x/y; r = r + x; } return r; } public static void main(String[] args) { if (args.length > 0) { int x = args[0].length(); int r = divBy(x); // System.out.println("Result: " + r); } // else System.out.println("Error: Incorrect call"); } } ---------------------------------------- (3) JBCToGraph (EQUIVALENT) Constructed TerminationGraph. ---------------------------------------- (4) Obligation: Termination Graph based on JBC Program: example_2.Test.main([Ljava/lang/String;)V: Graph of 67 nodes with 1 SCC. ---------------------------------------- (5) TerminationGraphToSCCProof (SOUND) Splitted TerminationGraph to 1 SCCs. ---------------------------------------- (6) Obligation: SCC of termination graph based on JBC Program. SCC contains nodes from the following methods: example_2.Test.main([Ljava/lang/String;)V SCC calls the following helper methods: Performed SCC analyses: *Used field analysis yielded the following read fields: *Marker field analysis yielded the following relations that could be markers: ---------------------------------------- (7) SCCToIRSProof (SOUND) Transformed FIGraph SCCs to intTRSs. Log: Generated rules. Obtained 15 IRulesP rules: f852_0_divBy_LE(EOS(STATIC_852), i141, i141) -> f856_0_divBy_LE(EOS(STATIC_856), i141, i141) :|: TRUE f856_0_divBy_LE(EOS(STATIC_856), i141, i141) -> f861_0_divBy_ConstantStackPush(EOS(STATIC_861), i141) :|: i141 > 0 f861_0_divBy_ConstantStackPush(EOS(STATIC_861), i141) -> f865_0_divBy_Store(EOS(STATIC_865), i141, 2) :|: TRUE f865_0_divBy_Store(EOS(STATIC_865), i141, matching1) -> f870_0_divBy_Load(EOS(STATIC_870), i141, 2) :|: TRUE && matching1 = 2 f870_0_divBy_Load(EOS(STATIC_870), i141, matching1) -> f876_0_divBy_Load(EOS(STATIC_876), 2, i141) :|: TRUE && matching1 = 2 f876_0_divBy_Load(EOS(STATIC_876), matching1, i141) -> f880_0_divBy_IntArithmetic(EOS(STATIC_880), i141, 2) :|: TRUE && matching1 = 2 f880_0_divBy_IntArithmetic(EOS(STATIC_880), i141, matching1) -> f883_0_divBy_Store(EOS(STATIC_883), i144) :|: i144 = i141 / 2 && i141 >= 1 && i144 < i141 && matching1 = 2 f883_0_divBy_Store(EOS(STATIC_883), i144) -> f885_0_divBy_Load(EOS(STATIC_885), i144) :|: TRUE f885_0_divBy_Load(EOS(STATIC_885), i144) -> f887_0_divBy_Load(EOS(STATIC_887), i144) :|: TRUE f887_0_divBy_Load(EOS(STATIC_887), i144) -> f890_0_divBy_IntArithmetic(EOS(STATIC_890), i144, i144) :|: TRUE f890_0_divBy_IntArithmetic(EOS(STATIC_890), i144, i144) -> f891_0_divBy_Store(EOS(STATIC_891), i144) :|: i144 >= 0 f891_0_divBy_Store(EOS(STATIC_891), i144) -> f894_0_divBy_JMP(EOS(STATIC_894), i144) :|: TRUE f894_0_divBy_JMP(EOS(STATIC_894), i144) -> f915_0_divBy_Load(EOS(STATIC_915), i144) :|: TRUE f915_0_divBy_Load(EOS(STATIC_915), i144) -> f846_0_divBy_Load(EOS(STATIC_846), i144) :|: TRUE f846_0_divBy_Load(EOS(STATIC_846), i129) -> f852_0_divBy_LE(EOS(STATIC_852), i129, i129) :|: TRUE Combined rules. Obtained 2 IRulesP rules: f852_0_divBy_LE(EOS(STATIC_852), i141:0, i141:0) -> f852_0_divBy_LE'(EOS(STATIC_852), i141:0, i141:0) :|: i141:0 > 0 && div > -1 && i141:0 > div f852_0_divBy_LE'(EOS(STATIC_852), i141:0, i141:0) -> f852_0_divBy_LE(EOS(STATIC_852), div, div) :|: i141:0 > 0 && i141:0 > div && div > -1 && i141:0 - 2 * div < 2 && i141:0 - 2 * div > -2 Filtered constant ground arguments: f852_0_divBy_LE(x1, x2, x3) -> f852_0_divBy_LE(x2, x3) f852_0_divBy_LE'(x1, x2, x3) -> f852_0_divBy_LE'(x2, x3) EOS(x1) -> EOS Filtered duplicate arguments: f852_0_divBy_LE(x1, x2) -> f852_0_divBy_LE(x2) f852_0_divBy_LE'(x1, x2) -> f852_0_divBy_LE'(x2) Finished conversion. Obtained 2 rules.P rules: f852_0_divBy_LE(i141:0) -> f852_0_divBy_LE'(i141:0) :|: div > -1 && i141:0 > div && i141:0 > 0 f852_0_divBy_LE'(i141:0) -> f852_0_divBy_LE(div) :|: i141:0 > div && i141:0 > 0 && div > -1 && i141:0 - 2 * div > -2 && i141:0 - 2 * div < 2 ---------------------------------------- (8) Obligation: Rules: f852_0_divBy_LE(x) -> f852_0_divBy_LE'(x) :|: x1 > -1 && x > x1 && x > 0 f852_0_divBy_LE'(x2) -> f852_0_divBy_LE(x3) :|: x2 > x3 && x2 > 0 && x3 > -1 && x2 - 2 * x3 > -2 && x2 - 2 * x3 < 2 ---------------------------------------- (9) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (10) Obligation: Rules: f852_0_divBy_LE(x) -> f852_0_divBy_LE'(x) :|: x1 > -1 && x > x1 && x > 0 f852_0_divBy_LE'(x2) -> f852_0_divBy_LE(x3) :|: x2 > x3 && x2 > 0 && x3 > -1 && x2 - 2 * x3 > -2 && x2 - 2 * x3 < 2 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f852_0_divBy_LE(x) -> f852_0_divBy_LE'(x) :|: x1 > -1 && x > x1 && x > 0 (2) f852_0_divBy_LE'(x2) -> f852_0_divBy_LE(x3) :|: x2 > x3 && x2 > 0 && x3 > -1 && x2 - 2 * x3 > -2 && x2 - 2 * x3 < 2 Arcs: (1) -> (2) (2) -> (1) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) f852_0_divBy_LE(x) -> f852_0_divBy_LE'(x) :|: x1 > -1 && x > x1 && x > 0 (2) f852_0_divBy_LE'(x2) -> f852_0_divBy_LE(x3) :|: x2 > x3 && x2 > 0 && x3 > -1 && x2 - 2 * x3 > -2 && x2 - 2 * x3 < 2 Arcs: (1) -> (2) (2) -> (1) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: f852_0_divBy_LE(x:0) -> f852_0_divBy_LE(x3:0) :|: x:0 - 2 * x3:0 < 2 && x1:0 > -1 && x:0 > x1:0 && x:0 - 2 * x3:0 > -2 && x3:0 > -1 && x:0 > 0 && x:0 > x3:0 ---------------------------------------- (15) FilterProof (EQUIVALENT) Used the following sort dictionary for filtering: f852_0_divBy_LE(INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (16) Obligation: Rules: f852_0_divBy_LE(x:0) -> f852_0_divBy_LE(x3:0) :|: x:0 - 2 * x3:0 < 2 && x1:0 > -1 && x:0 > x1:0 && x:0 - 2 * x3:0 > -2 && x3:0 > -1 && x:0 > 0 && x:0 > x3:0 ---------------------------------------- (17) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (18) Obligation: Rules: f852_0_divBy_LE(x:0:0) -> f852_0_divBy_LE(x3:0:0) :|: x:0:0 > 0 && x:0:0 > x3:0:0 && x3:0:0 > -1 && x:0:0 - 2 * x3:0:0 > -2 && x:0:0 > x1:0:0 && x1:0:0 > -1 && x:0:0 - 2 * x3:0:0 < 2 ---------------------------------------- (19) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f852_0_divBy_LE ] = f852_0_divBy_LE_1 The following rules are decreasing: f852_0_divBy_LE(x:0:0) -> f852_0_divBy_LE(x3:0:0) :|: x:0:0 > 0 && x:0:0 > x3:0:0 && x3:0:0 > -1 && x:0:0 - 2 * x3:0:0 > -2 && x:0:0 > x1:0:0 && x1:0:0 > -1 && x:0:0 - 2 * x3:0:0 < 2 The following rules are bounded: f852_0_divBy_LE(x:0:0) -> f852_0_divBy_LE(x3:0:0) :|: x:0:0 > 0 && x:0:0 > x3:0:0 && x3:0:0 > -1 && x:0:0 - 2 * x3:0:0 > -2 && x:0:0 > x1:0:0 && x1:0:0 > -1 && x:0:0 - 2 * x3:0:0 < 2 ---------------------------------------- (20) YES