/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 96 ms] (2) JBC problem (3) JBCToGraph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, 298 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 0 ms] (6) JBCTerminationSCC (7) SCCToIRSProof [SOUND, 105 ms] (8) IRSwT (9) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 56 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT (15) TempFilterProof [SOUND, 59 ms] (16) IntTRS (17) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (18) AND (19) IntTRS (20) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (21) YES (22) IntTRS (23) RankingReductionPairProof [EQUIVALENT, 0 ms] (24) 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 PastaC3 { public static void main(String[] args) { Random.args = args; int x = Random.random(); int y = Random.random(); int z = Random.random(); while (x < y) { if (x < z) { x++; } else { z++; } } } } 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 PastaC3 { public static void main(String[] args) { Random.args = args; int x = Random.random(); int y = Random.random(); int z = Random.random(); while (x < y) { if (x < z) { x++; } else { z++; } } } } 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: PastaC3.main([Ljava/lang/String;)V: Graph of 250 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: PastaC3.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: f508_0_main_Load(EOS(STATIC_508), i19, i77, i78, i19) -> f511_0_main_GE(EOS(STATIC_511), i19, i77, i78, i19, i77) :|: TRUE f511_0_main_GE(EOS(STATIC_511), i19, i77, i78, i19, i77) -> f516_0_main_GE(EOS(STATIC_516), i19, i77, i78, i19, i77) :|: i19 < i77 f516_0_main_GE(EOS(STATIC_516), i19, i77, i78, i19, i77) -> f520_0_main_Load(EOS(STATIC_520), i19, i77, i78) :|: i19 < i77 f520_0_main_Load(EOS(STATIC_520), i19, i77, i78) -> f523_0_main_Load(EOS(STATIC_523), i19, i77, i78, i19) :|: TRUE f523_0_main_Load(EOS(STATIC_523), i19, i77, i78, i19) -> f525_0_main_GE(EOS(STATIC_525), i19, i77, i78, i19, i78) :|: TRUE f525_0_main_GE(EOS(STATIC_525), i19, i77, i78, i19, i78) -> f530_0_main_GE(EOS(STATIC_530), i19, i77, i78, i19, i78) :|: i19 >= i78 f525_0_main_GE(EOS(STATIC_525), i19, i77, i78, i19, i78) -> f531_0_main_GE(EOS(STATIC_531), i19, i77, i78, i19, i78) :|: i19 < i78 f530_0_main_GE(EOS(STATIC_530), i19, i77, i78, i19, i78) -> f532_0_main_Inc(EOS(STATIC_532), i19, i77, i78) :|: i19 >= i78 f532_0_main_Inc(EOS(STATIC_532), i19, i77, i78) -> f548_0_main_JMP(EOS(STATIC_548), i19, i77, i78 + 1) :|: TRUE f548_0_main_JMP(EOS(STATIC_548), i19, i77, i85) -> f559_0_main_Load(EOS(STATIC_559), i19, i77, i85) :|: TRUE f559_0_main_Load(EOS(STATIC_559), i19, i77, i85) -> f505_0_main_Load(EOS(STATIC_505), i19, i77, i85) :|: TRUE f505_0_main_Load(EOS(STATIC_505), i19, i77, i78) -> f508_0_main_Load(EOS(STATIC_508), i19, i77, i78, i19) :|: TRUE f531_0_main_GE(EOS(STATIC_531), i19, i77, i78, i19, i78) -> f545_0_main_Inc(EOS(STATIC_545), i19, i77, i78) :|: i19 < i78 f545_0_main_Inc(EOS(STATIC_545), i19, i77, i78) -> f552_0_main_JMP(EOS(STATIC_552), i19 + 1, i77, i78) :|: TRUE f552_0_main_JMP(EOS(STATIC_552), i86, i77, i78) -> f562_0_main_Load(EOS(STATIC_562), i86, i77, i78) :|: TRUE f562_0_main_Load(EOS(STATIC_562), i86, i77, i78) -> f505_0_main_Load(EOS(STATIC_505), i86, i77, i78) :|: TRUE Combined rules. Obtained 2 IRulesP rules: f508_0_main_Load(EOS(STATIC_508), i19:0, i77:0, i78:0, i19:0) -> f508_0_main_Load(EOS(STATIC_508), i19:0, i77:0, i78:0 + 1, i19:0) :|: i77:0 > i19:0 && i78:0 <= i19:0 f508_0_main_Load(EOS(STATIC_508), i19:0, i77:0, i78:0, i19:0) -> f508_0_main_Load(EOS(STATIC_508), i19:0 + 1, i77:0, i78:0, i19:0 + 1) :|: i77:0 > i19:0 && i78:0 > i19:0 Filtered constant ground arguments: f508_0_main_Load(x1, x2, x3, x4, x5) -> f508_0_main_Load(x2, x3, x4, x5) EOS(x1) -> EOS Filtered duplicate arguments: f508_0_main_Load(x1, x2, x3, x4) -> f508_0_main_Load(x2, x3, x4) Finished conversion. Obtained 2 rules.P rules: f508_0_main_Load(i77:0, i78:0, i19:0) -> f508_0_main_Load(i77:0, i78:0 + 1, i19:0) :|: i77:0 > i19:0 && i78:0 <= i19:0 f508_0_main_Load(i77:0, i78:0, i19:0) -> f508_0_main_Load(i77:0, i78:0, i19:0 + 1) :|: i77:0 > i19:0 && i78:0 > i19:0 ---------------------------------------- (8) Obligation: Rules: f508_0_main_Load(i77:0, i78:0, i19:0) -> f508_0_main_Load(i77:0, i78:0 + 1, i19:0) :|: i77:0 > i19:0 && i78:0 <= i19:0 f508_0_main_Load(x, x1, x2) -> f508_0_main_Load(x, x1, x2 + 1) :|: x > x2 && x1 > x2 ---------------------------------------- (9) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (10) Obligation: Rules: f508_0_main_Load(i77:0, i78:0, i19:0) -> f508_0_main_Load(i77:0, arith, i19:0) :|: i77:0 > i19:0 && i78:0 <= i19:0 && arith = i78:0 + 1 f508_0_main_Load(x3, x4, x5) -> f508_0_main_Load(x3, x4, x6) :|: x3 > x5 && x4 > x5 && x6 = x5 + 1 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f508_0_main_Load(i77:0, i78:0, i19:0) -> f508_0_main_Load(i77:0, arith, i19:0) :|: i77:0 > i19:0 && i78:0 <= i19:0 && arith = i78:0 + 1 (2) f508_0_main_Load(x3, x4, x5) -> f508_0_main_Load(x3, x4, x6) :|: x3 > x5 && x4 > x5 && x6 = x5 + 1 Arcs: (1) -> (1), (2) (2) -> (1), (2) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) f508_0_main_Load(i77:0, i78:0, i19:0) -> f508_0_main_Load(i77:0, arith, i19:0) :|: i77:0 > i19:0 && i78:0 <= i19:0 && arith = i78:0 + 1 (2) f508_0_main_Load(x3, x4, x5) -> f508_0_main_Load(x3, x4, x6) :|: x3 > x5 && x4 > x5 && x6 = x5 + 1 Arcs: (1) -> (1), (2) (2) -> (1), (2) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: f508_0_main_Load(i77:0:0, i78:0:0, i19:0:0) -> f508_0_main_Load(i77:0:0, i78:0:0 + 1, i19:0:0) :|: i77:0:0 > i19:0:0 && i78:0:0 <= i19:0:0 f508_0_main_Load(x3:0, x4:0, x5:0) -> f508_0_main_Load(x3:0, x4:0, x5:0 + 1) :|: x5:0 < x3:0 && x5:0 < x4:0 ---------------------------------------- (15) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f508_0_main_Load(INTEGER, INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (16) Obligation: Rules: f508_0_main_Load(i77:0:0, i78:0:0, i19:0:0) -> f508_0_main_Load(i77:0:0, c, i19:0:0) :|: c = i78:0:0 + 1 && (i77:0:0 > i19:0:0 && i78:0:0 <= i19:0:0) f508_0_main_Load(x3:0, x4:0, x5:0) -> f508_0_main_Load(x3:0, x4:0, c1) :|: c1 = x5:0 + 1 && (x5:0 < x3:0 && x5:0 < x4:0) ---------------------------------------- (17) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f508_0_main_Load(x, x1, x2)] = x - x2 The following rules are decreasing: f508_0_main_Load(x3:0, x4:0, x5:0) -> f508_0_main_Load(x3:0, x4:0, c1) :|: c1 = x5:0 + 1 && (x5:0 < x3:0 && x5:0 < x4:0) The following rules are bounded: f508_0_main_Load(i77:0:0, i78:0:0, i19:0:0) -> f508_0_main_Load(i77:0:0, c, i19:0:0) :|: c = i78:0:0 + 1 && (i77:0:0 > i19:0:0 && i78:0:0 <= i19:0:0) ---------------------------------------- (18) Complex Obligation (AND) ---------------------------------------- (19) Obligation: Rules: f508_0_main_Load(i77:0:0, i78:0:0, i19:0:0) -> f508_0_main_Load(i77:0:0, c, i19:0:0) :|: c = i78:0:0 + 1 && (i77:0:0 > i19:0:0 && i78:0:0 <= i19:0:0) ---------------------------------------- (20) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f508_0_main_Load(x, x1, x2)] = -x1 + x2 The following rules are decreasing: f508_0_main_Load(i77:0:0, i78:0:0, i19:0:0) -> f508_0_main_Load(i77:0:0, c, i19:0:0) :|: c = i78:0:0 + 1 && (i77:0:0 > i19:0:0 && i78:0:0 <= i19:0:0) The following rules are bounded: f508_0_main_Load(i77:0:0, i78:0:0, i19:0:0) -> f508_0_main_Load(i77:0:0, c, i19:0:0) :|: c = i78:0:0 + 1 && (i77:0:0 > i19:0:0 && i78:0:0 <= i19:0:0) ---------------------------------------- (21) YES ---------------------------------------- (22) Obligation: Rules: f508_0_main_Load(x3:0, x4:0, x5:0) -> f508_0_main_Load(x3:0, x4:0, c1) :|: c1 = x5:0 + 1 && (x5:0 < x3:0 && x5:0 < x4:0) ---------------------------------------- (23) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f508_0_main_Load ] = -1*f508_0_main_Load_3 + f508_0_main_Load_2 The following rules are decreasing: f508_0_main_Load(x3:0, x4:0, x5:0) -> f508_0_main_Load(x3:0, x4:0, c1) :|: c1 = x5:0 + 1 && (x5:0 < x3:0 && x5:0 < x4:0) The following rules are bounded: f508_0_main_Load(x3:0, x4:0, x5:0) -> f508_0_main_Load(x3:0, x4:0, c1) :|: c1 = x5:0 + 1 && (x5:0 < x3:0 && x5:0 < x4:0) ---------------------------------------- (24) YES