/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 96 ms] (2) JBC problem (3) JBCToGraph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, 339 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 1 ms] (6) JBCTerminationSCC (7) SCCToIRSProof [SOUND, 67 ms] (8) IRSwT (9) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 40 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT (15) TempFilterProof [SOUND, 53 ms] (16) IntTRS (17) PolynomialOrderProcessor [EQUIVALENT, 8 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: f743_0_main_LT(EOS(STATIC_743), i81, i81) -> f747_0_main_LT(EOS(STATIC_747), i81, i81) :|: TRUE f747_0_main_LT(EOS(STATIC_747), i81, i81) -> f752_0_main_ConstantStackPush(EOS(STATIC_752), i81) :|: i81 >= 0 f752_0_main_ConstantStackPush(EOS(STATIC_752), i81) -> f757_0_main_Store(EOS(STATIC_757), i81, 1) :|: TRUE f757_0_main_Store(EOS(STATIC_757), i81, matching1) -> f759_0_main_Load(EOS(STATIC_759), i81, 1) :|: TRUE && matching1 = 1 f759_0_main_Load(EOS(STATIC_759), i81, matching1) -> f810_0_main_Load(EOS(STATIC_810), i81, 1) :|: TRUE && matching1 = 1 f810_0_main_Load(EOS(STATIC_810), i89, i90) -> f865_0_main_Load(EOS(STATIC_865), i89, i90) :|: TRUE f865_0_main_Load(EOS(STATIC_865), i99, i100) -> f933_0_main_Load(EOS(STATIC_933), i99, i100) :|: TRUE f933_0_main_Load(EOS(STATIC_933), i109, i110) -> f934_0_main_Load(EOS(STATIC_934), i109, i110, i109) :|: TRUE f934_0_main_Load(EOS(STATIC_934), i109, i110, i109) -> f935_0_main_LE(EOS(STATIC_935), i109, i110, i109, i110) :|: TRUE f935_0_main_LE(EOS(STATIC_935), i109, i110, i109, i110) -> f940_0_main_LE(EOS(STATIC_940), i109, i110, i109, i110) :|: i109 <= i110 f935_0_main_LE(EOS(STATIC_935), i109, i110, i109, i110) -> f941_0_main_LE(EOS(STATIC_941), i109, i110, i109, i110) :|: i109 > i110 f940_0_main_LE(EOS(STATIC_940), i109, i110, i109, i110) -> f945_0_main_Inc(EOS(STATIC_945), i109) :|: i109 <= i110 f945_0_main_Inc(EOS(STATIC_945), i109) -> f952_0_main_JMP(EOS(STATIC_952), i109 + -1) :|: TRUE f952_0_main_JMP(EOS(STATIC_952), i114) -> f960_0_main_Load(EOS(STATIC_960), i114) :|: TRUE f960_0_main_Load(EOS(STATIC_960), i114) -> f739_0_main_Load(EOS(STATIC_739), i114) :|: TRUE f739_0_main_Load(EOS(STATIC_739), i77) -> f743_0_main_LT(EOS(STATIC_743), i77, i77) :|: TRUE f941_0_main_LE(EOS(STATIC_941), i109, i110, i109, i110) -> f950_0_main_ConstantStackPush(EOS(STATIC_950), i109, i110) :|: i109 > i110 f950_0_main_ConstantStackPush(EOS(STATIC_950), i109, i110) -> f955_0_main_Load(EOS(STATIC_955), i109, i110, 2) :|: TRUE f955_0_main_Load(EOS(STATIC_955), i109, i110, matching1) -> f961_0_main_IntArithmetic(EOS(STATIC_961), i109, 2, i110) :|: TRUE && matching1 = 2 f961_0_main_IntArithmetic(EOS(STATIC_961), i109, matching1, i110) -> f962_0_main_Store(EOS(STATIC_962), i109, 2 * i110) :|: i110 >= 1 && matching1 = 2 f962_0_main_Store(EOS(STATIC_962), i109, i117) -> f964_0_main_JMP(EOS(STATIC_964), i109, i117) :|: TRUE f964_0_main_JMP(EOS(STATIC_964), i109, i117) -> f970_0_main_Load(EOS(STATIC_970), i109, i117) :|: TRUE f970_0_main_Load(EOS(STATIC_970), i109, i117) -> f933_0_main_Load(EOS(STATIC_933), i109, i117) :|: TRUE Combined rules. Obtained 2 IRulesP rules: f935_0_main_LE(EOS(STATIC_935), i109:0, i110:0, i109:0, i110:0) -> f935_0_main_LE(EOS(STATIC_935), i109:0 - 1, 1, i109:0 - 1, 1) :|: i109:0 > 0 && i110:0 >= i109:0 f935_0_main_LE(EOS(STATIC_935), i109:0, i110:0, i109:0, i110:0) -> f935_0_main_LE(EOS(STATIC_935), i109:0, 2 * i110:0, i109:0, 2 * i110:0) :|: i110:0 < i109:0 && i110:0 > 0 Filtered constant ground arguments: f935_0_main_LE(x1, x2, x3, x4, x5) -> f935_0_main_LE(x2, x3, x4, x5) EOS(x1) -> EOS Filtered duplicate arguments: f935_0_main_LE(x1, x2, x3, x4) -> f935_0_main_LE(x3, x4) Finished conversion. Obtained 2 rules.P rules: f935_0_main_LE(i109:0, i110:0) -> f935_0_main_LE(i109:0 - 1, 1) :|: i109:0 > 0 && i110:0 >= i109:0 f935_0_main_LE(i109:0, i110:0) -> f935_0_main_LE(i109:0, 2 * i110:0) :|: i110:0 < i109:0 && i110:0 > 0 ---------------------------------------- (8) Obligation: Rules: f935_0_main_LE(i109:0, i110:0) -> f935_0_main_LE(i109:0 - 1, 1) :|: i109:0 > 0 && i110:0 >= i109:0 f935_0_main_LE(x, x1) -> f935_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: f935_0_main_LE(i109:0, i110:0) -> f935_0_main_LE(arith, 1) :|: i109:0 > 0 && i110:0 >= i109:0 && arith = i109:0 - 1 f935_0_main_LE(x2, x3) -> f935_0_main_LE(x2, x4) :|: x3 < x2 && x3 > 0 && x4 = 2 * x3 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f935_0_main_LE(i109:0, i110:0) -> f935_0_main_LE(arith, 1) :|: i109:0 > 0 && i110:0 >= i109:0 && arith = i109:0 - 1 (2) f935_0_main_LE(x2, x3) -> f935_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) f935_0_main_LE(i109:0, i110:0) -> f935_0_main_LE(arith, 1) :|: i109:0 > 0 && i110:0 >= i109:0 && arith = i109:0 - 1 (2) f935_0_main_LE(x2, x3) -> f935_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: f935_0_main_LE(i109:0:0, i110:0:0) -> f935_0_main_LE(i109:0:0 - 1, 1) :|: i109:0:0 > 0 && i110:0:0 >= i109:0:0 f935_0_main_LE(x2:0, x3:0) -> f935_0_main_LE(x2:0, 2 * x3:0) :|: x3:0 < x2:0 && x3:0 > 0 ---------------------------------------- (15) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f935_0_main_LE(INTEGER, VARIABLE) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (16) Obligation: Rules: f935_0_main_LE(i109:0:0, i110:0:0) -> f935_0_main_LE(c, c1) :|: c1 = 1 && c = i109:0:0 - 1 && (i109:0:0 > 0 && i110:0:0 >= i109:0:0) f935_0_main_LE(x2:0, x3:0) -> f935_0_main_LE(x2:0, c2) :|: c2 = 2 * x3:0 && (x3:0 < x2:0 && x3:0 > 0) ---------------------------------------- (17) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f935_0_main_LE(x, x1)] = x The following rules are decreasing: f935_0_main_LE(i109:0:0, i110:0:0) -> f935_0_main_LE(c, c1) :|: c1 = 1 && c = i109:0:0 - 1 && (i109:0:0 > 0 && i110:0:0 >= i109:0:0) The following rules are bounded: f935_0_main_LE(i109:0:0, i110:0:0) -> f935_0_main_LE(c, c1) :|: c1 = 1 && c = i109:0:0 - 1 && (i109:0:0 > 0 && i110:0:0 >= i109:0:0) f935_0_main_LE(x2:0, x3:0) -> f935_0_main_LE(x2:0, c2) :|: c2 = 2 * x3:0 && (x3:0 < x2:0 && x3:0 > 0) ---------------------------------------- (18) Obligation: Rules: f935_0_main_LE(x2:0, x3:0) -> f935_0_main_LE(x2:0, c2) :|: c2 = 2 * x3:0 && (x3:0 < x2:0 && x3:0 > 0) ---------------------------------------- (19) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f935_0_main_LE ] = -1*f935_0_main_LE_2 + f935_0_main_LE_1 The following rules are decreasing: f935_0_main_LE(x2:0, x3:0) -> f935_0_main_LE(x2:0, c2) :|: c2 = 2 * x3:0 && (x3:0 < x2:0 && x3:0 > 0) The following rules are bounded: f935_0_main_LE(x2:0, x3:0) -> f935_0_main_LE(x2:0, c2) :|: c2 = 2 * x3:0 && (x3:0 < x2:0 && x3:0 > 0) ---------------------------------------- (20) YES