/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 96 ms] (2) JBC problem (3) JBCToGraph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, 355 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 0 ms] (6) JBCTerminationSCC (7) SCCToIRSProof [SOUND, 83 ms] (8) IRSwT (9) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 44 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT (15) TempFilterProof [SOUND, 54 ms] (16) IntTRS (17) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (18) IntTRS (19) RankingReductionPairProof [EQUIVALENT, 0 ms] (20) 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 PastaC1 { public static void main(String[] args) { Random.args = args; int x = Random.random(); while (x >= 0) { int y = 1; while (x > y) { y = 2*y; } 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 PastaC1 { public static void main(String[] args) { Random.args = args; int x = Random.random(); while (x >= 0) { int y = 1; while (x > y) { y = 2*y; } 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: PastaC1.main([Ljava/lang/String;)V: Graph of 124 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: PastaC1.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 23 IRulesP rules: f949_0_main_LT(EOS(STATIC_949), i90, i90) -> f951_0_main_LT(EOS(STATIC_951), i90, i90) :|: TRUE f951_0_main_LT(EOS(STATIC_951), i90, i90) -> f953_0_main_ConstantStackPush(EOS(STATIC_953), i90) :|: i90 >= 0 f953_0_main_ConstantStackPush(EOS(STATIC_953), i90) -> f956_0_main_Store(EOS(STATIC_956), i90, 1) :|: TRUE f956_0_main_Store(EOS(STATIC_956), i90, matching1) -> f957_0_main_Load(EOS(STATIC_957), i90, 1) :|: TRUE && matching1 = 1 f957_0_main_Load(EOS(STATIC_957), i90, matching1) -> f1034_0_main_Load(EOS(STATIC_1034), i90, 1) :|: TRUE && matching1 = 1 f1034_0_main_Load(EOS(STATIC_1034), i98, i99) -> f1092_0_main_Load(EOS(STATIC_1092), i98, i99) :|: TRUE f1092_0_main_Load(EOS(STATIC_1092), i106, i107) -> f1143_0_main_Load(EOS(STATIC_1143), i106, i107) :|: TRUE f1143_0_main_Load(EOS(STATIC_1143), i117, i118) -> f1147_0_main_Load(EOS(STATIC_1147), i117, i118, i117) :|: TRUE f1147_0_main_Load(EOS(STATIC_1147), i117, i118, i117) -> f1149_0_main_LE(EOS(STATIC_1149), i117, i118, i117, i118) :|: TRUE f1149_0_main_LE(EOS(STATIC_1149), i117, i118, i117, i118) -> f1165_0_main_LE(EOS(STATIC_1165), i117, i118, i117, i118) :|: i117 <= i118 f1149_0_main_LE(EOS(STATIC_1149), i117, i118, i117, i118) -> f1166_0_main_LE(EOS(STATIC_1166), i117, i118, i117, i118) :|: i117 > i118 f1165_0_main_LE(EOS(STATIC_1165), i117, i118, i117, i118) -> f1175_0_main_Inc(EOS(STATIC_1175), i117) :|: i117 <= i118 f1175_0_main_Inc(EOS(STATIC_1175), i117) -> f1185_0_main_JMP(EOS(STATIC_1185), i117 + -1) :|: TRUE f1185_0_main_JMP(EOS(STATIC_1185), i124) -> f1194_0_main_Load(EOS(STATIC_1194), i124) :|: TRUE f1194_0_main_Load(EOS(STATIC_1194), i124) -> f948_0_main_Load(EOS(STATIC_948), i124) :|: TRUE f948_0_main_Load(EOS(STATIC_948), i87) -> f949_0_main_LT(EOS(STATIC_949), i87, i87) :|: TRUE f1166_0_main_LE(EOS(STATIC_1166), i117, i118, i117, i118) -> f1182_0_main_ConstantStackPush(EOS(STATIC_1182), i117, i118) :|: i117 > i118 f1182_0_main_ConstantStackPush(EOS(STATIC_1182), i117, i118) -> f1187_0_main_Load(EOS(STATIC_1187), i117, i118, 2) :|: TRUE f1187_0_main_Load(EOS(STATIC_1187), i117, i118, matching1) -> f1196_0_main_IntArithmetic(EOS(STATIC_1196), i117, 2, i118) :|: TRUE && matching1 = 2 f1196_0_main_IntArithmetic(EOS(STATIC_1196), i117, matching1, i118) -> f1197_0_main_Store(EOS(STATIC_1197), i117, 2 * i118) :|: i118 >= 1 && matching1 = 2 f1197_0_main_Store(EOS(STATIC_1197), i117, i126) -> f1198_0_main_JMP(EOS(STATIC_1198), i117, i126) :|: TRUE f1198_0_main_JMP(EOS(STATIC_1198), i117, i126) -> f1201_0_main_Load(EOS(STATIC_1201), i117, i126) :|: TRUE f1201_0_main_Load(EOS(STATIC_1201), i117, i126) -> f1143_0_main_Load(EOS(STATIC_1143), i117, i126) :|: TRUE Combined rules. Obtained 2 IRulesP rules: f1149_0_main_LE(EOS(STATIC_1149), i117:0, i118:0, i117:0, i118:0) -> f1149_0_main_LE(EOS(STATIC_1149), i117:0 - 1, 1, i117:0 - 1, 1) :|: i117:0 > 0 && i118:0 >= i117:0 f1149_0_main_LE(EOS(STATIC_1149), i117:0, i118:0, i117:0, i118:0) -> f1149_0_main_LE(EOS(STATIC_1149), i117:0, 2 * i118:0, i117:0, 2 * i118:0) :|: i118:0 < i117:0 && i118:0 > 0 Filtered constant ground arguments: f1149_0_main_LE(x1, x2, x3, x4, x5) -> f1149_0_main_LE(x2, x3, x4, x5) EOS(x1) -> EOS Filtered duplicate arguments: f1149_0_main_LE(x1, x2, x3, x4) -> f1149_0_main_LE(x3, x4) Finished conversion. Obtained 2 rules.P rules: f1149_0_main_LE(i117:0, i118:0) -> f1149_0_main_LE(i117:0 - 1, 1) :|: i117:0 > 0 && i118:0 >= i117:0 f1149_0_main_LE(i117:0, i118:0) -> f1149_0_main_LE(i117:0, 2 * i118:0) :|: i118:0 < i117:0 && i118:0 > 0 ---------------------------------------- (8) Obligation: Rules: f1149_0_main_LE(i117:0, i118:0) -> f1149_0_main_LE(i117:0 - 1, 1) :|: i117:0 > 0 && i118:0 >= i117:0 f1149_0_main_LE(x, x1) -> f1149_0_main_LE(x, 2 * x1) :|: x1 < x && x1 > 0 ---------------------------------------- (9) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (10) Obligation: Rules: f1149_0_main_LE(i117:0, i118:0) -> f1149_0_main_LE(arith, 1) :|: i117:0 > 0 && i118:0 >= i117:0 && arith = i117:0 - 1 f1149_0_main_LE(x2, x3) -> f1149_0_main_LE(x2, x4) :|: x3 < x2 && x3 > 0 && x4 = 2 * x3 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f1149_0_main_LE(i117:0, i118:0) -> f1149_0_main_LE(arith, 1) :|: i117:0 > 0 && i118:0 >= i117:0 && arith = i117:0 - 1 (2) f1149_0_main_LE(x2, x3) -> f1149_0_main_LE(x2, x4) :|: x3 < x2 && x3 > 0 && x4 = 2 * x3 Arcs: (1) -> (1), (2) (2) -> (1), (2) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) f1149_0_main_LE(i117:0, i118:0) -> f1149_0_main_LE(arith, 1) :|: i117:0 > 0 && i118:0 >= i117:0 && arith = i117:0 - 1 (2) f1149_0_main_LE(x2, x3) -> f1149_0_main_LE(x2, x4) :|: x3 < x2 && x3 > 0 && x4 = 2 * x3 Arcs: (1) -> (1), (2) (2) -> (1), (2) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: f1149_0_main_LE(x2:0, x3:0) -> f1149_0_main_LE(x2:0, 2 * x3:0) :|: x3:0 < x2:0 && x3:0 > 0 f1149_0_main_LE(i117:0:0, i118:0:0) -> f1149_0_main_LE(i117:0:0 - 1, 1) :|: i117:0:0 > 0 && i118:0:0 >= i117:0:0 ---------------------------------------- (15) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f1149_0_main_LE(INTEGER, VARIABLE) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (16) Obligation: Rules: f1149_0_main_LE(x2:0, x3:0) -> f1149_0_main_LE(x2:0, c) :|: c = 2 * x3:0 && (x3:0 < x2:0 && x3:0 > 0) f1149_0_main_LE(i117:0:0, i118:0:0) -> f1149_0_main_LE(c1, c2) :|: c2 = 1 && c1 = i117:0:0 - 1 && (i117:0:0 > 0 && i118:0:0 >= i117:0:0) ---------------------------------------- (17) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f1149_0_main_LE(x, x1)] = x The following rules are decreasing: f1149_0_main_LE(i117:0:0, i118:0:0) -> f1149_0_main_LE(c1, c2) :|: c2 = 1 && c1 = i117:0:0 - 1 && (i117:0:0 > 0 && i118:0:0 >= i117:0:0) The following rules are bounded: f1149_0_main_LE(x2:0, x3:0) -> f1149_0_main_LE(x2:0, c) :|: c = 2 * x3:0 && (x3:0 < x2:0 && x3:0 > 0) f1149_0_main_LE(i117:0:0, i118:0:0) -> f1149_0_main_LE(c1, c2) :|: c2 = 1 && c1 = i117:0:0 - 1 && (i117:0:0 > 0 && i118:0:0 >= i117:0:0) ---------------------------------------- (18) Obligation: Rules: f1149_0_main_LE(x2:0, x3:0) -> f1149_0_main_LE(x2:0, c) :|: c = 2 * x3:0 && (x3:0 < x2:0 && x3:0 > 0) ---------------------------------------- (19) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f1149_0_main_LE ] = -1*f1149_0_main_LE_2 + f1149_0_main_LE_1 The following rules are decreasing: f1149_0_main_LE(x2:0, x3:0) -> f1149_0_main_LE(x2:0, c) :|: c = 2 * x3:0 && (x3:0 < x2:0 && x3:0 > 0) The following rules are bounded: f1149_0_main_LE(x2:0, x3:0) -> f1149_0_main_LE(x2:0, c) :|: c = 2 * x3:0 && (x3:0 < x2:0 && x3:0 > 0) ---------------------------------------- (20) YES