/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 96 ms] (2) JBC problem (3) JBCToGraph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, 322 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 0 ms] (6) JBCTerminationSCC (7) SCCToIRSProof [SOUND, 36 ms] (8) IRSwT (9) IRSFormatTransformerProof [EQUIVALENT, 1 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 32 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT (15) TempFilterProof [SOUND, 59 ms] (16) IntTRS (17) RankingReductionPairProof [EQUIVALENT, 25 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 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 120 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: f338_0_main_LE(EOS(STATIC_338), i35, i35) -> f341_0_main_LE(EOS(STATIC_341), i35, i35) :|: TRUE f341_0_main_LE(EOS(STATIC_341), i35, i35) -> f343_0_main_ConstantStackPush(EOS(STATIC_343), i35) :|: i35 > 0 f343_0_main_ConstantStackPush(EOS(STATIC_343), i35) -> f346_0_main_Store(EOS(STATIC_346), i35, 0) :|: TRUE f346_0_main_Store(EOS(STATIC_346), i35, matching1) -> f347_0_main_Load(EOS(STATIC_347), i35, 0) :|: TRUE && matching1 = 0 f347_0_main_Load(EOS(STATIC_347), i35, matching1) -> f381_0_main_Load(EOS(STATIC_381), i35, 0) :|: TRUE && matching1 = 0 f381_0_main_Load(EOS(STATIC_381), i35, i36) -> f452_0_main_Load(EOS(STATIC_452), i35, i36) :|: TRUE f452_0_main_Load(EOS(STATIC_452), i35, i43) -> f754_0_main_Load(EOS(STATIC_754), i35, i43) :|: TRUE f754_0_main_Load(EOS(STATIC_754), i35, i53) -> f758_0_main_Load(EOS(STATIC_758), i35, i53, i53) :|: TRUE f758_0_main_Load(EOS(STATIC_758), i35, i53, i53) -> f759_0_main_GE(EOS(STATIC_759), i35, i53, i53, i35) :|: TRUE f759_0_main_GE(EOS(STATIC_759), i35, i53, i53, i35) -> f772_0_main_GE(EOS(STATIC_772), i35, i53, i53, i35) :|: i53 >= i35 f759_0_main_GE(EOS(STATIC_759), i35, i53, i53, i35) -> f773_0_main_GE(EOS(STATIC_773), i35, i53, i53, i35) :|: i53 < i35 f772_0_main_GE(EOS(STATIC_772), i35, i53, i53, i35) -> f775_0_main_Inc(EOS(STATIC_775), i35) :|: i53 >= i35 f775_0_main_Inc(EOS(STATIC_775), i35) -> f780_0_main_JMP(EOS(STATIC_780), i35 + -1) :|: TRUE f780_0_main_JMP(EOS(STATIC_780), i56) -> f788_0_main_Load(EOS(STATIC_788), i56) :|: TRUE f788_0_main_Load(EOS(STATIC_788), i56) -> f336_0_main_Load(EOS(STATIC_336), i56) :|: TRUE f336_0_main_Load(EOS(STATIC_336), i32) -> f338_0_main_LE(EOS(STATIC_338), i32, i32) :|: TRUE f773_0_main_GE(EOS(STATIC_773), i35, i53, i53, i35) -> f777_0_main_Inc(EOS(STATIC_777), i35, i53) :|: i53 < i35 f777_0_main_Inc(EOS(STATIC_777), i35, i53) -> f782_0_main_JMP(EOS(STATIC_782), i35, i53 + 1) :|: TRUE f782_0_main_JMP(EOS(STATIC_782), i35, i57) -> f801_0_main_Load(EOS(STATIC_801), i35, i57) :|: TRUE f801_0_main_Load(EOS(STATIC_801), i35, i57) -> f754_0_main_Load(EOS(STATIC_754), i35, i57) :|: TRUE Combined rules. Obtained 2 IRulesP rules: f759_0_main_GE(EOS(STATIC_759), i35:0, i53:0, i53:0, i35:0) -> f759_0_main_GE(EOS(STATIC_759), i35:0, i53:0 + 1, i53:0 + 1, i35:0) :|: i53:0 < i35:0 f759_0_main_GE(EOS(STATIC_759), i35:0, i53:0, i53:0, i35:0) -> f759_0_main_GE(EOS(STATIC_759), i35:0 - 1, 0, 0, i35:0 - 1) :|: i35:0 > 1 && i53:0 >= i35:0 Filtered constant ground arguments: f759_0_main_GE(x1, x2, x3, x4, x5) -> f759_0_main_GE(x2, x3, x4, x5) EOS(x1) -> EOS Filtered duplicate arguments: f759_0_main_GE(x1, x2, x3, x4) -> f759_0_main_GE(x3, x4) Finished conversion. Obtained 2 rules.P rules: f759_0_main_GE(i53:0, i35:0) -> f759_0_main_GE(i53:0 + 1, i35:0) :|: i53:0 < i35:0 f759_0_main_GE(i53:0, i35:0) -> f759_0_main_GE(0, i35:0 - 1) :|: i35:0 > 1 && i53:0 >= i35:0 ---------------------------------------- (8) Obligation: Rules: f759_0_main_GE(i53:0, i35:0) -> f759_0_main_GE(i53:0 + 1, i35:0) :|: i53:0 < i35:0 f759_0_main_GE(x, x1) -> f759_0_main_GE(0, x1 - 1) :|: x1 > 1 && x >= x1 ---------------------------------------- (9) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (10) Obligation: Rules: f759_0_main_GE(i53:0, i35:0) -> f759_0_main_GE(arith, i35:0) :|: i53:0 < i35:0 && arith = i53:0 + 1 f759_0_main_GE(x2, x3) -> f759_0_main_GE(0, x4) :|: x3 > 1 && x2 >= x3 && x4 = x3 - 1 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f759_0_main_GE(i53:0, i35:0) -> f759_0_main_GE(arith, i35:0) :|: i53:0 < i35:0 && arith = i53:0 + 1 (2) f759_0_main_GE(x2, x3) -> f759_0_main_GE(0, x4) :|: x3 > 1 && x2 >= x3 && x4 = x3 - 1 Arcs: (1) -> (1), (2) (2) -> (1) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) f759_0_main_GE(i53:0, i35:0) -> f759_0_main_GE(arith, i35:0) :|: i53:0 < i35:0 && arith = i53:0 + 1 (2) f759_0_main_GE(x2, x3) -> f759_0_main_GE(0, x4) :|: x3 > 1 && x2 >= x3 && x4 = x3 - 1 Arcs: (1) -> (1), (2) (2) -> (1) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: f759_0_main_GE(i53:0:0, i35:0:0) -> f759_0_main_GE(i53:0:0 + 1, i35:0:0) :|: i53:0:0 < i35:0:0 f759_0_main_GE(x2:0, x3:0) -> f759_0_main_GE(0, x3:0 - 1) :|: x3:0 > 1 && x3:0 <= x2:0 ---------------------------------------- (15) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f759_0_main_GE(VARIABLE, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (16) Obligation: Rules: f759_0_main_GE(i53:0:0, i35:0:0) -> f759_0_main_GE(c, i35:0:0) :|: c = i53:0:0 + 1 && i53:0:0 < i35:0:0 f759_0_main_GE(x2:0, x3:0) -> f759_0_main_GE(c1, c2) :|: c2 = x3:0 - 1 && c1 = 0 && (x3:0 > 1 && x3:0 <= x2:0) ---------------------------------------- (17) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f759_0_main_GE ] = 4*f759_0_main_GE_2 The following rules are decreasing: f759_0_main_GE(x2:0, x3:0) -> f759_0_main_GE(c1, c2) :|: c2 = x3:0 - 1 && c1 = 0 && (x3:0 > 1 && x3:0 <= x2:0) The following rules are bounded: f759_0_main_GE(x2:0, x3:0) -> f759_0_main_GE(c1, c2) :|: c2 = x3:0 - 1 && c1 = 0 && (x3:0 > 1 && x3:0 <= x2:0) ---------------------------------------- (18) Obligation: Rules: f759_0_main_GE(i53:0:0, i35:0:0) -> f759_0_main_GE(c, i35:0:0) :|: c = i53:0:0 + 1 && i53:0:0 < i35:0:0 ---------------------------------------- (19) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f759_0_main_GE ] = -1*f759_0_main_GE_1 + f759_0_main_GE_2 The following rules are decreasing: f759_0_main_GE(i53:0:0, i35:0:0) -> f759_0_main_GE(c, i35:0:0) :|: c = i53:0:0 + 1 && i53:0:0 < i35:0:0 The following rules are bounded: f759_0_main_GE(i53:0:0, i35:0:0) -> f759_0_main_GE(c, i35:0:0) :|: c = i53:0:0 + 1 && i53:0:0 < i35:0:0 ---------------------------------------- (20) YES