/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 96 ms] (2) JBC problem (3) JBCToGraph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, 311 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 0 ms] (6) JBCTerminationSCC (7) SCCToIRSProof [SOUND, 90 ms] (8) IRSwT (9) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 35 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT (15) TempFilterProof [SOUND, 45 ms] (16) IntTRS (17) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (18) IntTRS (19) PolynomialOrderProcessor [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 PastaA1 { public static void main(String[] args) { Random.args = args; int x = Random.random(); while (x > 0) { int y = 0; while (y < x) { 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 PastaA1 { public static void main(String[] args) { Random.args = args; int x = Random.random(); while (x > 0) { int y = 0; while (y < x) { 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: PastaA1.main([Ljava/lang/String;)V: Graph of 119 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: PastaA1.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 20 IRulesP rules: f124_0_main_LE(EOS(STATIC_124), i21, i21) -> f131_0_main_LE(EOS(STATIC_131), i21, i21) :|: TRUE f131_0_main_LE(EOS(STATIC_131), i21, i21) -> f138_0_main_ConstantStackPush(EOS(STATIC_138), i21) :|: i21 > 0 f138_0_main_ConstantStackPush(EOS(STATIC_138), i21) -> f147_0_main_Store(EOS(STATIC_147), i21, 0) :|: TRUE f147_0_main_Store(EOS(STATIC_147), i21, matching1) -> f159_0_main_Load(EOS(STATIC_159), i21, 0) :|: TRUE && matching1 = 0 f159_0_main_Load(EOS(STATIC_159), i21, matching1) -> f247_0_main_Load(EOS(STATIC_247), i21, 0) :|: TRUE && matching1 = 0 f247_0_main_Load(EOS(STATIC_247), i21, i24) -> f375_0_main_Load(EOS(STATIC_375), i21, i24) :|: TRUE f375_0_main_Load(EOS(STATIC_375), i21, i34) -> f4731_0_main_Load(EOS(STATIC_4731), i21, i34) :|: TRUE f4731_0_main_Load(EOS(STATIC_4731), i21, i75) -> f4732_0_main_Load(EOS(STATIC_4732), i21, i75, i75) :|: TRUE f4732_0_main_Load(EOS(STATIC_4732), i21, i75, i75) -> f4733_0_main_GE(EOS(STATIC_4733), i21, i75, i75, i21) :|: TRUE f4733_0_main_GE(EOS(STATIC_4733), i21, i75, i75, i21) -> f4734_0_main_GE(EOS(STATIC_4734), i21, i75, i75, i21) :|: i75 >= i21 f4733_0_main_GE(EOS(STATIC_4733), i21, i75, i75, i21) -> f4735_0_main_GE(EOS(STATIC_4735), i21, i75, i75, i21) :|: i75 < i21 f4734_0_main_GE(EOS(STATIC_4734), i21, i75, i75, i21) -> f4736_0_main_Inc(EOS(STATIC_4736), i21) :|: i75 >= i21 f4736_0_main_Inc(EOS(STATIC_4736), i21) -> f4738_0_main_JMP(EOS(STATIC_4738), i21 + -1) :|: TRUE f4738_0_main_JMP(EOS(STATIC_4738), i77) -> f4740_0_main_Load(EOS(STATIC_4740), i77) :|: TRUE f4740_0_main_Load(EOS(STATIC_4740), i77) -> f115_0_main_Load(EOS(STATIC_115), i77) :|: TRUE f115_0_main_Load(EOS(STATIC_115), i17) -> f124_0_main_LE(EOS(STATIC_124), i17, i17) :|: TRUE f4735_0_main_GE(EOS(STATIC_4735), i21, i75, i75, i21) -> f4737_0_main_Inc(EOS(STATIC_4737), i21, i75) :|: i75 < i21 f4737_0_main_Inc(EOS(STATIC_4737), i21, i75) -> f4739_0_main_JMP(EOS(STATIC_4739), i21, i75 + 1) :|: TRUE f4739_0_main_JMP(EOS(STATIC_4739), i21, i78) -> f4741_0_main_Load(EOS(STATIC_4741), i21, i78) :|: TRUE f4741_0_main_Load(EOS(STATIC_4741), i21, i78) -> f4731_0_main_Load(EOS(STATIC_4731), i21, i78) :|: TRUE Combined rules. Obtained 2 IRulesP rules: f4733_0_main_GE(EOS(STATIC_4733), i21:0, i75:0, i75:0, i21:0) -> f4733_0_main_GE(EOS(STATIC_4733), i21:0 - 1, 0, 0, i21:0 - 1) :|: i21:0 > 1 && i75:0 >= i21:0 f4733_0_main_GE(EOS(STATIC_4733), i21:0, i75:0, i75:0, i21:0) -> f4733_0_main_GE(EOS(STATIC_4733), i21:0, i75:0 + 1, i75:0 + 1, i21:0) :|: i75:0 < i21:0 Filtered constant ground arguments: f4733_0_main_GE(x1, x2, x3, x4, x5) -> f4733_0_main_GE(x2, x3, x4, x5) EOS(x1) -> EOS Filtered duplicate arguments: f4733_0_main_GE(x1, x2, x3, x4) -> f4733_0_main_GE(x3, x4) Finished conversion. Obtained 2 rules.P rules: f4733_0_main_GE(i75:0, i21:0) -> f4733_0_main_GE(0, i21:0 - 1) :|: i21:0 > 1 && i75:0 >= i21:0 f4733_0_main_GE(i75:0, i21:0) -> f4733_0_main_GE(i75:0 + 1, i21:0) :|: i75:0 < i21:0 ---------------------------------------- (8) Obligation: Rules: f4733_0_main_GE(i75:0, i21:0) -> f4733_0_main_GE(0, i21:0 - 1) :|: i21:0 > 1 && i75:0 >= i21:0 f4733_0_main_GE(x, x1) -> f4733_0_main_GE(x + 1, x1) :|: x < x1 ---------------------------------------- (9) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (10) Obligation: Rules: f4733_0_main_GE(i75:0, i21:0) -> f4733_0_main_GE(0, arith) :|: i21:0 > 1 && i75:0 >= i21:0 && arith = i21:0 - 1 f4733_0_main_GE(x2, x3) -> f4733_0_main_GE(x4, x3) :|: x2 < x3 && x4 = x2 + 1 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f4733_0_main_GE(i75:0, i21:0) -> f4733_0_main_GE(0, arith) :|: i21:0 > 1 && i75:0 >= i21:0 && arith = i21:0 - 1 (2) f4733_0_main_GE(x2, x3) -> f4733_0_main_GE(x4, x3) :|: x2 < x3 && x4 = x2 + 1 Arcs: (1) -> (2) (2) -> (1), (2) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) f4733_0_main_GE(i75:0, i21:0) -> f4733_0_main_GE(0, arith) :|: i21:0 > 1 && i75:0 >= i21:0 && arith = i21:0 - 1 (2) f4733_0_main_GE(x2, x3) -> f4733_0_main_GE(x4, x3) :|: x2 < x3 && x4 = x2 + 1 Arcs: (1) -> (2) (2) -> (1), (2) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: f4733_0_main_GE(x2:0, x3:0) -> f4733_0_main_GE(x2:0 + 1, x3:0) :|: x3:0 > x2:0 f4733_0_main_GE(i75:0:0, i21:0:0) -> f4733_0_main_GE(0, i21:0:0 - 1) :|: i21:0:0 > 1 && i75:0:0 >= i21:0:0 ---------------------------------------- (15) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f4733_0_main_GE(VARIABLE, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (16) Obligation: Rules: f4733_0_main_GE(x2:0, x3:0) -> f4733_0_main_GE(c, x3:0) :|: c = x2:0 + 1 && x3:0 > x2:0 f4733_0_main_GE(i75:0:0, i21:0:0) -> f4733_0_main_GE(c1, c2) :|: c2 = i21:0:0 - 1 && c1 = 0 && (i21:0:0 > 1 && i75:0:0 >= i21:0:0) ---------------------------------------- (17) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f4733_0_main_GE(x, x1)] = -2 + x1 The following rules are decreasing: f4733_0_main_GE(i75:0:0, i21:0:0) -> f4733_0_main_GE(c1, c2) :|: c2 = i21:0:0 - 1 && c1 = 0 && (i21:0:0 > 1 && i75:0:0 >= i21:0:0) The following rules are bounded: f4733_0_main_GE(i75:0:0, i21:0:0) -> f4733_0_main_GE(c1, c2) :|: c2 = i21:0:0 - 1 && c1 = 0 && (i21:0:0 > 1 && i75:0:0 >= i21:0:0) ---------------------------------------- (18) Obligation: Rules: f4733_0_main_GE(x2:0, x3:0) -> f4733_0_main_GE(c, x3:0) :|: c = x2:0 + 1 && x3:0 > x2:0 ---------------------------------------- (19) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f4733_0_main_GE(x, x1)] = -x + x1 The following rules are decreasing: f4733_0_main_GE(x2:0, x3:0) -> f4733_0_main_GE(c, x3:0) :|: c = x2:0 + 1 && x3:0 > x2:0 The following rules are bounded: f4733_0_main_GE(x2:0, x3:0) -> f4733_0_main_GE(c, x3:0) :|: c = x2:0 + 1 && x3:0 > x2:0 ---------------------------------------- (20) YES