/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 97 ms] (2) JBC problem (3) JBCToGraph [EQUIVALENT, 331 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 0 ms] (6) JBCTerminationSCC (7) SCCToIRSProof [SOUND, 62 ms] (8) IRSwT (9) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 48 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT (15) TempFilterProof [SOUND, 53 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 PastaC2 { public static void main(String[] args) { Random.args = args; int x = Random.random(); while (x >= 0) { x = x+1; int y = 1; while (x >= y) { y++; } x = x-2; } } } 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 PastaC2 { public static void main(String[] args) { Random.args = args; int x = Random.random(); while (x >= 0) { x = x+1; int y = 1; while (x >= y) { y++; } x = x-2; } } } 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: PastaC2.main([Ljava/lang/String;)V: Graph of 127 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: PastaC2.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 27 IRulesP rules: f680_0_main_LT(EOS(STATIC_680), i48, i48) -> f684_0_main_LT(EOS(STATIC_684), i48, i48) :|: TRUE f684_0_main_LT(EOS(STATIC_684), i48, i48) -> f689_0_main_Load(EOS(STATIC_689), i48) :|: i48 >= 0 f689_0_main_Load(EOS(STATIC_689), i48) -> f704_0_main_ConstantStackPush(EOS(STATIC_704), i48) :|: TRUE f704_0_main_ConstantStackPush(EOS(STATIC_704), i48) -> f705_0_main_IntArithmetic(EOS(STATIC_705), i48, 1) :|: TRUE f705_0_main_IntArithmetic(EOS(STATIC_705), i48, matching1) -> f707_0_main_Store(EOS(STATIC_707), i48 + 1) :|: i48 >= 0 && matching1 = 1 f707_0_main_Store(EOS(STATIC_707), i49) -> f725_0_main_ConstantStackPush(EOS(STATIC_725), i49) :|: TRUE f725_0_main_ConstantStackPush(EOS(STATIC_725), i49) -> f726_0_main_Store(EOS(STATIC_726), i49, 1) :|: TRUE f726_0_main_Store(EOS(STATIC_726), i49, matching1) -> f728_0_main_Load(EOS(STATIC_728), i49, 1) :|: TRUE && matching1 = 1 f728_0_main_Load(EOS(STATIC_728), i49, matching1) -> f766_0_main_Load(EOS(STATIC_766), i49, 1) :|: TRUE && matching1 = 1 f766_0_main_Load(EOS(STATIC_766), i49, i51) -> f819_0_main_Load(EOS(STATIC_819), i49, i51) :|: TRUE f819_0_main_Load(EOS(STATIC_819), i49, i55) -> f843_0_main_Load(EOS(STATIC_843), i49, i55) :|: TRUE f843_0_main_Load(EOS(STATIC_843), i49, i58) -> f847_0_main_Load(EOS(STATIC_847), i49, i58, i49) :|: TRUE f847_0_main_Load(EOS(STATIC_847), i49, i58, i49) -> f850_0_main_LT(EOS(STATIC_850), i49, i58, i49, i58) :|: TRUE f850_0_main_LT(EOS(STATIC_850), i49, i58, i49, i58) -> f877_0_main_LT(EOS(STATIC_877), i49, i58, i49, i58) :|: i49 < i58 f850_0_main_LT(EOS(STATIC_850), i49, i58, i49, i58) -> f879_0_main_LT(EOS(STATIC_879), i49, i58, i49, i58) :|: i49 >= i58 f877_0_main_LT(EOS(STATIC_877), i49, i58, i49, i58) -> f882_0_main_Load(EOS(STATIC_882), i49) :|: i49 < i58 f882_0_main_Load(EOS(STATIC_882), i49) -> f890_0_main_ConstantStackPush(EOS(STATIC_890), i49) :|: TRUE f890_0_main_ConstantStackPush(EOS(STATIC_890), i49) -> f892_0_main_IntArithmetic(EOS(STATIC_892), i49, 2) :|: TRUE f892_0_main_IntArithmetic(EOS(STATIC_892), i49, matching1) -> f903_0_main_Store(EOS(STATIC_903), i49 - 2) :|: i49 > 0 && matching1 = 2 f903_0_main_Store(EOS(STATIC_903), i63) -> f905_0_main_JMP(EOS(STATIC_905), i63) :|: TRUE f905_0_main_JMP(EOS(STATIC_905), i63) -> f910_0_main_Load(EOS(STATIC_910), i63) :|: TRUE f910_0_main_Load(EOS(STATIC_910), i63) -> f675_0_main_Load(EOS(STATIC_675), i63) :|: TRUE f675_0_main_Load(EOS(STATIC_675), i46) -> f680_0_main_LT(EOS(STATIC_680), i46, i46) :|: TRUE f879_0_main_LT(EOS(STATIC_879), i49, i58, i49, i58) -> f889_0_main_Inc(EOS(STATIC_889), i49, i58) :|: i49 >= i58 f889_0_main_Inc(EOS(STATIC_889), i49, i58) -> f891_0_main_JMP(EOS(STATIC_891), i49, i58 + 1) :|: TRUE f891_0_main_JMP(EOS(STATIC_891), i49, i60) -> f900_0_main_Load(EOS(STATIC_900), i49, i60) :|: TRUE f900_0_main_Load(EOS(STATIC_900), i49, i60) -> f843_0_main_Load(EOS(STATIC_843), i49, i60) :|: TRUE Combined rules. Obtained 2 IRulesP rules: f850_0_main_LT(EOS(STATIC_850), i49:0, i58:0, i49:0, i58:0) -> f850_0_main_LT(EOS(STATIC_850), i49:0, i58:0 + 1, i49:0, i58:0 + 1) :|: i58:0 <= i49:0 f850_0_main_LT(EOS(STATIC_850), i49:0, i58:0, i49:0, i58:0) -> f850_0_main_LT(EOS(STATIC_850), i49:0 - 1, 1, i49:0 - 1, 1) :|: i49:0 > 1 && i58:0 > i49:0 Filtered constant ground arguments: f850_0_main_LT(x1, x2, x3, x4, x5) -> f850_0_main_LT(x2, x3, x4, x5) EOS(x1) -> EOS Filtered duplicate arguments: f850_0_main_LT(x1, x2, x3, x4) -> f850_0_main_LT(x3, x4) Finished conversion. Obtained 2 rules.P rules: f850_0_main_LT(i49:0, i58:0) -> f850_0_main_LT(i49:0, i58:0 + 1) :|: i58:0 <= i49:0 f850_0_main_LT(i49:0, i58:0) -> f850_0_main_LT(i49:0 - 1, 1) :|: i49:0 > 1 && i58:0 > i49:0 ---------------------------------------- (8) Obligation: Rules: f850_0_main_LT(i49:0, i58:0) -> f850_0_main_LT(i49:0, i58:0 + 1) :|: i58:0 <= i49:0 f850_0_main_LT(x, x1) -> f850_0_main_LT(x - 1, 1) :|: x > 1 && x1 > x ---------------------------------------- (9) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (10) Obligation: Rules: f850_0_main_LT(i49:0, i58:0) -> f850_0_main_LT(i49:0, arith) :|: i58:0 <= i49:0 && arith = i58:0 + 1 f850_0_main_LT(x2, x3) -> f850_0_main_LT(x4, 1) :|: x2 > 1 && x3 > x2 && x4 = x2 - 1 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f850_0_main_LT(i49:0, i58:0) -> f850_0_main_LT(i49:0, arith) :|: i58:0 <= i49:0 && arith = i58:0 + 1 (2) f850_0_main_LT(x2, x3) -> f850_0_main_LT(x4, 1) :|: x2 > 1 && x3 > x2 && x4 = x2 - 1 Arcs: (1) -> (1), (2) (2) -> (1) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) f850_0_main_LT(i49:0, i58:0) -> f850_0_main_LT(i49:0, arith) :|: i58:0 <= i49:0 && arith = i58:0 + 1 (2) f850_0_main_LT(x2, x3) -> f850_0_main_LT(x4, 1) :|: x2 > 1 && x3 > x2 && x4 = x2 - 1 Arcs: (1) -> (1), (2) (2) -> (1) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: f850_0_main_LT(i49:0:0, i58:0:0) -> f850_0_main_LT(i49:0:0, i58:0:0 + 1) :|: i58:0:0 <= i49:0:0 f850_0_main_LT(x2:0, x3:0) -> f850_0_main_LT(x2:0 - 1, 1) :|: x2:0 > 1 && x3:0 > x2:0 ---------------------------------------- (15) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f850_0_main_LT(INTEGER, VARIABLE) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (16) Obligation: Rules: f850_0_main_LT(i49:0:0, i58:0:0) -> f850_0_main_LT(i49:0:0, c) :|: c = i58:0:0 + 1 && i58:0:0 <= i49:0:0 f850_0_main_LT(x2:0, x3:0) -> f850_0_main_LT(c1, c2) :|: c2 = 1 && c1 = x2:0 - 1 && (x2:0 > 1 && x3:0 > x2:0) ---------------------------------------- (17) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f850_0_main_LT(x, x1)] = -1 + x The following rules are decreasing: f850_0_main_LT(x2:0, x3:0) -> f850_0_main_LT(c1, c2) :|: c2 = 1 && c1 = x2:0 - 1 && (x2:0 > 1 && x3:0 > x2:0) The following rules are bounded: f850_0_main_LT(x2:0, x3:0) -> f850_0_main_LT(c1, c2) :|: c2 = 1 && c1 = x2:0 - 1 && (x2:0 > 1 && x3:0 > x2:0) ---------------------------------------- (18) Obligation: Rules: f850_0_main_LT(i49:0:0, i58:0:0) -> f850_0_main_LT(i49:0:0, c) :|: c = i58:0:0 + 1 && i58:0:0 <= i49:0:0 ---------------------------------------- (19) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f850_0_main_LT(x, x1)] = x - x1 The following rules are decreasing: f850_0_main_LT(i49:0:0, i58:0:0) -> f850_0_main_LT(i49:0:0, c) :|: c = i58:0:0 + 1 && i58:0:0 <= i49:0:0 The following rules are bounded: f850_0_main_LT(i49:0:0, i58:0:0) -> f850_0_main_LT(i49:0:0, c) :|: c = i58:0:0 + 1 && i58:0:0 <= i49:0:0 ---------------------------------------- (20) YES