/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 96 ms] (2) JBC problem (3) JBCToGraph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, 398 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 0 ms] (6) JBCTerminationSCC (7) SCCToIRSProof [SOUND, 150 ms] (8) IRSwT (9) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 67 ms] (12) AND (13) IRSwT (14) IntTRSCompressionProof [EQUIVALENT, 0 ms] (15) IRSwT (16) TempFilterProof [SOUND, 31 ms] (17) IntTRS (18) RankingReductionPairProof [EQUIVALENT, 0 ms] (19) YES (20) IRSwT (21) IntTRSCompressionProof [EQUIVALENT, 0 ms] (22) IRSwT (23) TempFilterProof [SOUND, 7 ms] (24) IntTRS (25) PolynomialOrderProcessor [EQUIVALENT, 0 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 PastaB11 { public static void main(String[] args) { Random.args = args; int x = Random.random(); int y = Random.random(); while (x + y > 0) { if (x > y) { x--; } else if (x == y) { x--; } else { y--; } } } } 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 PastaB11 { public static void main(String[] args) { Random.args = args; int x = Random.random(); int y = Random.random(); while (x + y > 0) { if (x > y) { x--; } else if (x == y) { x--; } else { y--; } } } } 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: PastaB11.main([Ljava/lang/String;)V: Graph of 197 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: PastaB11.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 26 IRulesP rules: f881_0_main_Load(EOS(STATIC_881), i176, i157, i176) -> f882_0_main_IntArithmetic(EOS(STATIC_882), i176, i157, i176, i157) :|: TRUE f882_0_main_IntArithmetic(EOS(STATIC_882), i176, i157, i176, i157) -> f883_0_main_LE(EOS(STATIC_883), i176, i157, i176 + i157) :|: TRUE f883_0_main_LE(EOS(STATIC_883), i176, i157, i184) -> f886_0_main_LE(EOS(STATIC_886), i176, i157, i184) :|: TRUE f886_0_main_LE(EOS(STATIC_886), i176, i157, i184) -> f888_0_main_Load(EOS(STATIC_888), i176, i157) :|: i184 > 0 f888_0_main_Load(EOS(STATIC_888), i176, i157) -> f890_0_main_Load(EOS(STATIC_890), i176, i157, i176) :|: TRUE f890_0_main_Load(EOS(STATIC_890), i176, i157, i176) -> f891_0_main_LE(EOS(STATIC_891), i176, i157, i176, i157) :|: TRUE f891_0_main_LE(EOS(STATIC_891), i176, i157, i176, i157) -> f940_0_main_LE(EOS(STATIC_940), i176, i157, i176, i157) :|: i176 <= i157 f891_0_main_LE(EOS(STATIC_891), i176, i157, i176, i157) -> f942_0_main_LE(EOS(STATIC_942), i176, i157, i176, i157) :|: i176 > i157 f940_0_main_LE(EOS(STATIC_940), i176, i157, i176, i157) -> f945_0_main_Load(EOS(STATIC_945), i176, i157) :|: i176 <= i157 f945_0_main_Load(EOS(STATIC_945), i176, i157) -> f947_0_main_Load(EOS(STATIC_947), i176, i157, i176) :|: TRUE f947_0_main_Load(EOS(STATIC_947), i176, i157, i176) -> f949_0_main_NE(EOS(STATIC_949), i176, i157, i176, i157) :|: TRUE f949_0_main_NE(EOS(STATIC_949), i176, i157, i176, i157) -> f969_0_main_NE(EOS(STATIC_969), i176, i157, i176, i157) :|: !(i176 = i157) f949_0_main_NE(EOS(STATIC_949), i157, i157, i157, i157) -> f970_0_main_NE(EOS(STATIC_970), i157, i157, i157, i157) :|: i176 = i157 f969_0_main_NE(EOS(STATIC_969), i176, i157, i176, i157) -> f972_0_main_Inc(EOS(STATIC_972), i176, i157) :|: i176 < i157 f972_0_main_Inc(EOS(STATIC_972), i176, i157) -> f974_0_main_JMP(EOS(STATIC_974), i176, i157 + -1) :|: TRUE f974_0_main_JMP(EOS(STATIC_974), i176, i215) -> f977_0_main_Load(EOS(STATIC_977), i176, i215) :|: TRUE f977_0_main_Load(EOS(STATIC_977), i176, i215) -> f880_0_main_Load(EOS(STATIC_880), i176, i215) :|: TRUE f880_0_main_Load(EOS(STATIC_880), i176, i157) -> f881_0_main_Load(EOS(STATIC_881), i176, i157, i176) :|: TRUE f970_0_main_NE(EOS(STATIC_970), i157, i157, i157, i157) -> f973_0_main_Inc(EOS(STATIC_973), i157, i157) :|: TRUE f973_0_main_Inc(EOS(STATIC_973), i157, i157) -> f975_0_main_JMP(EOS(STATIC_975), i157 + -1, i157) :|: TRUE f975_0_main_JMP(EOS(STATIC_975), i216, i157) -> f983_0_main_Load(EOS(STATIC_983), i216, i157) :|: TRUE f983_0_main_Load(EOS(STATIC_983), i216, i157) -> f880_0_main_Load(EOS(STATIC_880), i216, i157) :|: TRUE f942_0_main_LE(EOS(STATIC_942), i176, i157, i176, i157) -> f946_0_main_Inc(EOS(STATIC_946), i176, i157) :|: i176 > i157 f946_0_main_Inc(EOS(STATIC_946), i176, i157) -> f948_0_main_JMP(EOS(STATIC_948), i176 + -1, i157) :|: TRUE f948_0_main_JMP(EOS(STATIC_948), i197, i157) -> f962_0_main_Load(EOS(STATIC_962), i197, i157) :|: TRUE f962_0_main_Load(EOS(STATIC_962), i197, i157) -> f880_0_main_Load(EOS(STATIC_880), i197, i157) :|: TRUE Combined rules. Obtained 3 IRulesP rules: f881_0_main_Load(EOS(STATIC_881), i176:0, i157:0, i176:0) -> f881_0_main_Load(EOS(STATIC_881), i176:0, i157:0 - 1, i176:0) :|: i176:0 < i157:0 && i176:0 + i157:0 > 0 f881_0_main_Load(EOS(STATIC_881), i176:0, i176:0, i176:0) -> f881_0_main_Load(EOS(STATIC_881), i176:0 - 1, i176:0, i176:0 - 1) :|: i176:0 + i176:0 > 0 f881_0_main_Load(EOS(STATIC_881), i176:0, i157:0, i176:0) -> f881_0_main_Load(EOS(STATIC_881), i176:0 - 1, i157:0, i176:0 - 1) :|: i176:0 + i157:0 > 0 && i176:0 > i157:0 Filtered constant ground arguments: f881_0_main_Load(x1, x2, x3, x4) -> f881_0_main_Load(x2, x3, x4) EOS(x1) -> EOS Filtered duplicate arguments: f881_0_main_Load(x1, x2, x3) -> f881_0_main_Load(x2, x3) Finished conversion. Obtained 3 rules.P rules: f881_0_main_Load(i157:0, i176:0) -> f881_0_main_Load(i157:0 - 1, i176:0) :|: i176:0 < i157:0 && i176:0 + i157:0 > 0 f881_0_main_Load(i176:0, i176:0) -> f881_0_main_Load(i176:0, i176:0 - 1) :|: i176:0 + i176:0 > 0 f881_0_main_Load(i157:0, i176:0) -> f881_0_main_Load(i157:0, i176:0 - 1) :|: i176:0 + i157:0 > 0 && i176:0 > i157:0 ---------------------------------------- (8) Obligation: Rules: f881_0_main_Load(i157:0, i176:0) -> f881_0_main_Load(i157:0 - 1, i176:0) :|: i176:0 < i157:0 && i176:0 + i157:0 > 0 f881_0_main_Load(x, x) -> f881_0_main_Load(x, x - 1) :|: x + x > 0 f881_0_main_Load(x1, x2) -> f881_0_main_Load(x1, x2 - 1) :|: x2 + x1 > 0 && x2 > x1 ---------------------------------------- (9) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (10) Obligation: Rules: f881_0_main_Load(i157:0, i176:0) -> f881_0_main_Load(arith, i176:0) :|: i176:0 < i157:0 && i176:0 + i157:0 > 0 && arith = i157:0 - 1 f881_0_main_Load(x3, x3) -> f881_0_main_Load(x3, x4) :|: x3 + x3 > 0 && x4 = x3 - 1 f881_0_main_Load(x5, x6) -> f881_0_main_Load(x5, x7) :|: x6 + x5 > 0 && x6 > x5 && x7 = x6 - 1 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f881_0_main_Load(i157:0, i176:0) -> f881_0_main_Load(arith, i176:0) :|: i176:0 < i157:0 && i176:0 + i157:0 > 0 && arith = i157:0 - 1 (2) f881_0_main_Load(x3, x3) -> f881_0_main_Load(x3, x4) :|: x3 + x3 > 0 && x4 = x3 - 1 (3) f881_0_main_Load(x5, x6) -> f881_0_main_Load(x5, x7) :|: x6 + x5 > 0 && x6 > x5 && x7 = x6 - 1 Arcs: (1) -> (1), (2) (2) -> (1) (3) -> (2), (3) This digraph is fully evaluated! ---------------------------------------- (12) Complex Obligation (AND) ---------------------------------------- (13) Obligation: Termination digraph: Nodes: (1) f881_0_main_Load(x5, x6) -> f881_0_main_Load(x5, x7) :|: x6 + x5 > 0 && x6 > x5 && x7 = x6 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (14) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (15) Obligation: Rules: f881_0_main_Load(x5:0, x6:0) -> f881_0_main_Load(x5:0, x6:0 - 1) :|: x6:0 + x5:0 > 0 && x6:0 > x5:0 ---------------------------------------- (16) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f881_0_main_Load(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (17) Obligation: Rules: f881_0_main_Load(x5:0, x6:0) -> f881_0_main_Load(x5:0, c) :|: c = x6:0 - 1 && (x6:0 + x5:0 > 0 && x6:0 > x5:0) ---------------------------------------- (18) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f881_0_main_Load ] = f881_0_main_Load_2 + -1*f881_0_main_Load_1 The following rules are decreasing: f881_0_main_Load(x5:0, x6:0) -> f881_0_main_Load(x5:0, c) :|: c = x6:0 - 1 && (x6:0 + x5:0 > 0 && x6:0 > x5:0) The following rules are bounded: f881_0_main_Load(x5:0, x6:0) -> f881_0_main_Load(x5:0, c) :|: c = x6:0 - 1 && (x6:0 + x5:0 > 0 && x6:0 > x5:0) ---------------------------------------- (19) YES ---------------------------------------- (20) Obligation: Termination digraph: Nodes: (1) f881_0_main_Load(i157:0, i176:0) -> f881_0_main_Load(arith, i176:0) :|: i176:0 < i157:0 && i176:0 + i157:0 > 0 && arith = i157:0 - 1 (2) f881_0_main_Load(x3, x3) -> f881_0_main_Load(x3, x4) :|: x3 + x3 > 0 && x4 = x3 - 1 Arcs: (1) -> (1), (2) (2) -> (1) This digraph is fully evaluated! ---------------------------------------- (21) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (22) Obligation: Rules: f881_0_main_Load(x3:0, x3:0) -> f881_0_main_Load(x3:0, x3:0 - 1) :|: x3:0 + x3:0 > 0 f881_0_main_Load(i157:0:0, i176:0:0) -> f881_0_main_Load(i157:0:0 - 1, i176:0:0) :|: i176:0:0 < i157:0:0 && i176:0:0 + i157:0:0 > 0 ---------------------------------------- (23) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f881_0_main_Load(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (24) Obligation: Rules: f881_0_main_Load(x3:0, x3:0) -> f881_0_main_Load(x3:0, c) :|: c = x3:0 - 1 && x3:0 + x3:0 > 0 f881_0_main_Load(i157:0:0, i176:0:0) -> f881_0_main_Load(c1, i176:0:0) :|: c1 = i157:0:0 - 1 && (i176:0:0 < i157:0:0 && i176:0:0 + i157:0:0 > 0) ---------------------------------------- (25) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f881_0_main_Load(x, x1)] = x + x1 The following rules are decreasing: f881_0_main_Load(x3:0, x3:0) -> f881_0_main_Load(x3:0, c) :|: c = x3:0 - 1 && x3:0 + x3:0 > 0 f881_0_main_Load(i157:0:0, i176:0:0) -> f881_0_main_Load(c1, i176:0:0) :|: c1 = i157:0:0 - 1 && (i176:0:0 < i157:0:0 && i176:0:0 + i157:0:0 > 0) The following rules are bounded: f881_0_main_Load(x3:0, x3:0) -> f881_0_main_Load(x3:0, c) :|: c = x3:0 - 1 && x3:0 + x3:0 > 0 f881_0_main_Load(i157:0:0, i176:0:0) -> f881_0_main_Load(c1, i176:0:0) :|: c1 = i157:0:0 - 1 && (i176:0:0 < i157:0:0 && i176:0:0 + i157:0:0 > 0) ---------------------------------------- (26) YES