/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.jar /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.jar # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 96 ms] (2) JBC problem (3) JBCToGraph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, 553 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 0 ms] (6) JBCTerminationSCC (7) SCCToIRSProof [SOUND, 34 ms] (8) IRSwT (9) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 14 ms] (12) AND (13) IRSwT (14) IntTRSCompressionProof [EQUIVALENT, 0 ms] (15) IRSwT (16) TempFilterProof [SOUND, 21 ms] (17) IntTRS (18) PolynomialOrderProcessor [EQUIVALENT, 8 ms] (19) YES (20) IRSwT (21) IntTRSCompressionProof [EQUIVALENT, 0 ms] (22) IRSwT (23) TempFilterProof [SOUND, 14 ms] (24) IntTRS (25) RankingReductionPairProof [EQUIVALENT, 1 ms] (26) YES ---------------------------------------- (0) Obligation: need to prove termination of the following program: /** * Example taken from "A Term Rewriting Approach to the Automated Termination * Analysis of Imperative Programs" (http://www.cs.unm.edu/~spf/papers/2009-02.pdf) * and converted to Java. */ public class PastaA10 { public static void main(String[] args) { Random.args = args; int x = Random.random(); int y = Random.random(); while (x != y) { if (x > y) { y++; } else { x++; } } } } public class Random { static String[] args; static int index = 0; public static int random() { String string = args[index]; index++; return string.length(); } } ---------------------------------------- (1) BareJBCToJBCProof (EQUIVALENT) initialized classpath ---------------------------------------- (2) Obligation: need to prove termination of the following program: /** * Example taken from "A Term Rewriting Approach to the Automated Termination * Analysis of Imperative Programs" (http://www.cs.unm.edu/~spf/papers/2009-02.pdf) * and converted to Java. */ public class PastaA10 { public static void main(String[] args) { Random.args = args; int x = Random.random(); int y = Random.random(); while (x != y) { if (x > y) { y++; } else { x++; } } } } public class Random { static String[] args; static int index = 0; public static int random() { String string = args[index]; index++; return string.length(); } } ---------------------------------------- (3) JBCToGraph (EQUIVALENT) Constructed TerminationGraph. ---------------------------------------- (4) Obligation: Termination Graph based on JBC Program: PastaA10.main([Ljava/lang/String;)V: Graph of 183 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: PastaA10.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 16 IRulesP rules: f375_0_main_Load(EOS(STATIC_375), i48, i49, i48) -> f378_0_main_EQ(EOS(STATIC_378), i48, i49, i48, i49) :|: TRUE f378_0_main_EQ(EOS(STATIC_378), i48, i49, i48, i49) -> f383_0_main_EQ(EOS(STATIC_383), i48, i49, i48, i49) :|: !(i48 = i49) f383_0_main_EQ(EOS(STATIC_383), i48, i49, i48, i49) -> f388_0_main_Load(EOS(STATIC_388), i48, i49) :|: !(i48 = i49) f388_0_main_Load(EOS(STATIC_388), i48, i49) -> f393_0_main_Load(EOS(STATIC_393), i48, i49, i48) :|: TRUE f393_0_main_Load(EOS(STATIC_393), i48, i49, i48) -> f399_0_main_LE(EOS(STATIC_399), i48, i49, i48, i49) :|: TRUE f399_0_main_LE(EOS(STATIC_399), i48, i49, i48, i49) -> f404_0_main_LE(EOS(STATIC_404), i48, i49, i48, i49) :|: i48 <= i49 f399_0_main_LE(EOS(STATIC_399), i48, i49, i48, i49) -> f405_0_main_LE(EOS(STATIC_405), i48, i49, i48, i49) :|: i48 > i49 f404_0_main_LE(EOS(STATIC_404), i48, i49, i48, i49) -> f408_0_main_Inc(EOS(STATIC_408), i48, i49) :|: i48 < i49 f408_0_main_Inc(EOS(STATIC_408), i48, i49) -> f410_0_main_JMP(EOS(STATIC_410), i48 + 1, i49) :|: TRUE f410_0_main_JMP(EOS(STATIC_410), i54, i49) -> f425_0_main_Load(EOS(STATIC_425), i54, i49) :|: TRUE f425_0_main_Load(EOS(STATIC_425), i54, i49) -> f367_0_main_Load(EOS(STATIC_367), i54, i49) :|: TRUE f367_0_main_Load(EOS(STATIC_367), i48, i49) -> f375_0_main_Load(EOS(STATIC_375), i48, i49, i48) :|: TRUE f405_0_main_LE(EOS(STATIC_405), i48, i49, i48, i49) -> f409_0_main_Inc(EOS(STATIC_409), i48, i49) :|: i48 > i49 f409_0_main_Inc(EOS(STATIC_409), i48, i49) -> f411_0_main_JMP(EOS(STATIC_411), i48, i49 + 1) :|: TRUE f411_0_main_JMP(EOS(STATIC_411), i48, i55) -> f427_0_main_Load(EOS(STATIC_427), i48, i55) :|: TRUE f427_0_main_Load(EOS(STATIC_427), i48, i55) -> f367_0_main_Load(EOS(STATIC_367), i48, i55) :|: TRUE Combined rules. Obtained 2 IRulesP rules: f375_0_main_Load(EOS(STATIC_375), i48:0, i49:0, i48:0) -> f375_0_main_Load(EOS(STATIC_375), i48:0, i49:0 + 1, i48:0) :|: i49:0 < i48:0 f375_0_main_Load(EOS(STATIC_375), i48:0, i49:0, i48:0) -> f375_0_main_Load(EOS(STATIC_375), i48:0 + 1, i49:0, i48:0 + 1) :|: i49:0 > i48:0 Filtered constant ground arguments: f375_0_main_Load(x1, x2, x3, x4) -> f375_0_main_Load(x2, x3, x4) EOS(x1) -> EOS Filtered duplicate arguments: f375_0_main_Load(x1, x2, x3) -> f375_0_main_Load(x2, x3) Finished conversion. Obtained 2 rules.P rules: f375_0_main_Load(i49:0, i48:0) -> f375_0_main_Load(i49:0 + 1, i48:0) :|: i49:0 < i48:0 f375_0_main_Load(i49:0, i48:0) -> f375_0_main_Load(i49:0, i48:0 + 1) :|: i49:0 > i48:0 ---------------------------------------- (8) Obligation: Rules: f375_0_main_Load(i49:0, i48:0) -> f375_0_main_Load(i49:0 + 1, i48:0) :|: i49:0 < i48:0 f375_0_main_Load(x, x1) -> f375_0_main_Load(x, x1 + 1) :|: x > x1 ---------------------------------------- (9) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (10) Obligation: Rules: f375_0_main_Load(i49:0, i48:0) -> f375_0_main_Load(arith, i48:0) :|: i49:0 < i48:0 && arith = i49:0 + 1 f375_0_main_Load(x2, x3) -> f375_0_main_Load(x2, x4) :|: x2 > x3 && x4 = x3 + 1 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f375_0_main_Load(i49:0, i48:0) -> f375_0_main_Load(arith, i48:0) :|: i49:0 < i48:0 && arith = i49:0 + 1 (2) f375_0_main_Load(x2, x3) -> f375_0_main_Load(x2, x4) :|: x2 > x3 && x4 = x3 + 1 Arcs: (1) -> (1) (2) -> (2) This digraph is fully evaluated! ---------------------------------------- (12) Complex Obligation (AND) ---------------------------------------- (13) Obligation: Termination digraph: Nodes: (1) f375_0_main_Load(x2, x3) -> f375_0_main_Load(x2, x4) :|: x2 > x3 && x4 = x3 + 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (14) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (15) Obligation: Rules: f375_0_main_Load(x2:0, x3:0) -> f375_0_main_Load(x2:0, x3:0 + 1) :|: x3:0 < x2:0 ---------------------------------------- (16) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f375_0_main_Load(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (17) Obligation: Rules: f375_0_main_Load(x2:0, x3:0) -> f375_0_main_Load(x2:0, c) :|: c = x3:0 + 1 && x3:0 < x2:0 ---------------------------------------- (18) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f375_0_main_Load(x, x1)] = x - x1 The following rules are decreasing: f375_0_main_Load(x2:0, x3:0) -> f375_0_main_Load(x2:0, c) :|: c = x3:0 + 1 && x3:0 < x2:0 The following rules are bounded: f375_0_main_Load(x2:0, x3:0) -> f375_0_main_Load(x2:0, c) :|: c = x3:0 + 1 && x3:0 < x2:0 ---------------------------------------- (19) YES ---------------------------------------- (20) Obligation: Termination digraph: Nodes: (1) f375_0_main_Load(i49:0, i48:0) -> f375_0_main_Load(arith, i48:0) :|: i49:0 < i48:0 && arith = i49:0 + 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (21) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (22) Obligation: Rules: f375_0_main_Load(i49:0:0, i48:0:0) -> f375_0_main_Load(i49:0:0 + 1, i48:0:0) :|: i49:0:0 < i48:0:0 ---------------------------------------- (23) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f375_0_main_Load(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (24) Obligation: Rules: f375_0_main_Load(i49:0:0, i48:0:0) -> f375_0_main_Load(c, i48:0:0) :|: c = i49:0:0 + 1 && i49:0:0 < i48:0:0 ---------------------------------------- (25) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f375_0_main_Load ] = -1*f375_0_main_Load_1 + f375_0_main_Load_2 The following rules are decreasing: f375_0_main_Load(i49:0:0, i48:0:0) -> f375_0_main_Load(c, i48:0:0) :|: c = i49:0:0 + 1 && i49:0:0 < i48:0:0 The following rules are bounded: f375_0_main_Load(i49:0:0, i48:0:0) -> f375_0_main_Load(c, i48:0:0) :|: c = i49:0:0 + 1 && i49:0:0 < i48:0:0 ---------------------------------------- (26) YES