/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 95 ms] (2) JBC problem (3) JBCToGraph [EQUIVALENT, 321 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 0 ms] (6) JBCTerminationSCC (7) SCCToIRSProof [SOUND, 147 ms] (8) IRSwT (9) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 59 ms] (12) AND (13) IRSwT (14) IntTRSCompressionProof [EQUIVALENT, 0 ms] (15) IRSwT (16) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (17) IRSwT (18) TempFilterProof [SOUND, 13 ms] (19) IntTRS (20) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (21) YES (22) IRSwT (23) IntTRSCompressionProof [EQUIVALENT, 0 ms] (24) IRSwT (25) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (26) IRSwT (27) TempFilterProof [SOUND, 8 ms] (28) IntTRS (29) RankingReductionPairProof [EQUIVALENT, 0 ms] (30) 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 PastaB18 { public static void main(String[] args) { Random.args = args; int x = Random.random(); int y = Random.random(); while (x > 0 && y > 0) { if (x > y) { while (x > 0) { x--; } } else { while (y > 0) { 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 PastaB18 { public static void main(String[] args) { Random.args = args; int x = Random.random(); int y = Random.random(); while (x > 0 && y > 0) { if (x > y) { while (x > 0) { x--; } } else { while (y > 0) { 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: PastaB18.main([Ljava/lang/String;)V: Graph of 200 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: PastaB18.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 33 IRulesP rules: f579_0_main_LE(EOS(STATIC_579), i96, i85, i96) -> f584_0_main_LE(EOS(STATIC_584), i96, i85, i96) :|: TRUE f584_0_main_LE(EOS(STATIC_584), i96, i85, i96) -> f588_0_main_Load(EOS(STATIC_588), i96, i85) :|: i96 > 0 f588_0_main_Load(EOS(STATIC_588), i96, i85) -> f593_0_main_LE(EOS(STATIC_593), i96, i85, i85) :|: TRUE f593_0_main_LE(EOS(STATIC_593), i96, i99, i99) -> f597_0_main_LE(EOS(STATIC_597), i96, i99, i99) :|: TRUE f597_0_main_LE(EOS(STATIC_597), i96, i99, i99) -> f605_0_main_Load(EOS(STATIC_605), i96, i99) :|: i99 > 0 f605_0_main_Load(EOS(STATIC_605), i96, i99) -> f607_0_main_Load(EOS(STATIC_607), i96, i99, i96) :|: TRUE f607_0_main_Load(EOS(STATIC_607), i96, i99, i96) -> f609_0_main_LE(EOS(STATIC_609), i96, i99, i96, i99) :|: TRUE f609_0_main_LE(EOS(STATIC_609), i96, i99, i96, i99) -> f636_0_main_LE(EOS(STATIC_636), i96, i99, i96, i99) :|: i96 <= i99 f609_0_main_LE(EOS(STATIC_609), i96, i99, i96, i99) -> f637_0_main_LE(EOS(STATIC_637), i96, i99, i96, i99) :|: i96 > i99 f636_0_main_LE(EOS(STATIC_636), i96, i99, i96, i99) -> f648_0_main_Load(EOS(STATIC_648), i96, i99) :|: i96 <= i99 f648_0_main_Load(EOS(STATIC_648), i96, i99) -> f713_0_main_Load(EOS(STATIC_713), i96, i99) :|: TRUE f713_0_main_Load(EOS(STATIC_713), i96, i114) -> f829_0_main_LE(EOS(STATIC_829), i96, i114, i114) :|: TRUE f829_0_main_LE(EOS(STATIC_829), i96, matching1, matching2) -> f833_0_main_LE(EOS(STATIC_833), i96, 0, 0) :|: TRUE && matching1 = 0 && matching2 = 0 f829_0_main_LE(EOS(STATIC_829), i96, i144, i144) -> f834_0_main_LE(EOS(STATIC_834), i96, i144, i144) :|: TRUE f833_0_main_LE(EOS(STATIC_833), i96, matching1, matching2) -> f920_0_main_Load(EOS(STATIC_920), i96, 0) :|: 0 <= 0 && matching1 = 0 && matching2 = 0 f920_0_main_Load(EOS(STATIC_920), i96, matching1) -> f575_0_main_Load(EOS(STATIC_575), i96, 0) :|: TRUE && matching1 = 0 f575_0_main_Load(EOS(STATIC_575), i84, i85) -> f579_0_main_LE(EOS(STATIC_579), i84, i85, i84) :|: TRUE f834_0_main_LE(EOS(STATIC_834), i96, i144, i144) -> f924_0_main_Inc(EOS(STATIC_924), i96, i144) :|: i144 > 0 f924_0_main_Inc(EOS(STATIC_924), i96, i144) -> f929_0_main_JMP(EOS(STATIC_929), i96, i144 + -1) :|: TRUE f929_0_main_JMP(EOS(STATIC_929), i96, i165) -> f977_0_main_Load(EOS(STATIC_977), i96, i165) :|: TRUE f977_0_main_Load(EOS(STATIC_977), i96, i165) -> f713_0_main_Load(EOS(STATIC_713), i96, i165) :|: TRUE f637_0_main_LE(EOS(STATIC_637), i96, i99, i96, i99) -> f658_0_main_Load(EOS(STATIC_658), i96, i99) :|: i96 > i99 f658_0_main_Load(EOS(STATIC_658), i96, i99) -> f826_0_main_Load(EOS(STATIC_826), i96, i99) :|: TRUE f826_0_main_Load(EOS(STATIC_826), i123, i99) -> f961_0_main_Load(EOS(STATIC_961), i123, i99) :|: TRUE f961_0_main_Load(EOS(STATIC_961), i167, i99) -> f980_0_main_LE(EOS(STATIC_980), i167, i99, i167) :|: TRUE f980_0_main_LE(EOS(STATIC_980), matching1, i99, matching2) -> f983_0_main_LE(EOS(STATIC_983), 0, i99, 0) :|: TRUE && matching1 = 0 && matching2 = 0 f980_0_main_LE(EOS(STATIC_980), i178, i99, i178) -> f985_0_main_LE(EOS(STATIC_985), i178, i99, i178) :|: TRUE f983_0_main_LE(EOS(STATIC_983), matching1, i99, matching2) -> f1029_0_main_Load(EOS(STATIC_1029), 0, i99) :|: 0 <= 0 && matching1 = 0 && matching2 = 0 f1029_0_main_Load(EOS(STATIC_1029), matching1, i99) -> f575_0_main_Load(EOS(STATIC_575), 0, i99) :|: TRUE && matching1 = 0 f985_0_main_LE(EOS(STATIC_985), i178, i99, i178) -> f1032_0_main_Inc(EOS(STATIC_1032), i178, i99) :|: i178 > 0 f1032_0_main_Inc(EOS(STATIC_1032), i178, i99) -> f1036_0_main_JMP(EOS(STATIC_1036), i178 + -1, i99) :|: TRUE f1036_0_main_JMP(EOS(STATIC_1036), i189, i99) -> f1049_0_main_Load(EOS(STATIC_1049), i189, i99) :|: TRUE f1049_0_main_Load(EOS(STATIC_1049), i189, i99) -> f961_0_main_Load(EOS(STATIC_961), i189, i99) :|: TRUE Combined rules. Obtained 6 IRulesP rules: f579_0_main_LE(EOS(STATIC_579), i96:0, i85:0, i96:0) -> f829_0_main_LE(EOS(STATIC_829), i96:0, i85:0, i85:0) :|: i96:0 > 0 && i85:0 > 0 && i96:0 <= i85:0 f829_0_main_LE(EOS(STATIC_829), i96:0, i144:0, i144:0) -> f829_0_main_LE(EOS(STATIC_829), i96:0, i144:0 - 1, i144:0 - 1) :|: i144:0 > 0 f579_0_main_LE(EOS(STATIC_579), i96:0, i85:0, i96:0) -> f980_0_main_LE(EOS(STATIC_980), i96:0, i85:0, i96:0) :|: i96:0 > 0 && i85:0 > 0 && i96:0 > i85:0 f980_0_main_LE(EOS(STATIC_980), i178:0, i99:0, i178:0) -> f980_0_main_LE(EOS(STATIC_980), i178:0 - 1, i99:0, i178:0 - 1) :|: i178:0 > 0 f829_0_main_LE(EOS(STATIC_829), i96:0, 0, 0) -> f579_0_main_LE(EOS(STATIC_579), i96:0, 0, i96:0) :|: TRUE f980_0_main_LE(EOS(STATIC_980), 0, i99:0, 0) -> f579_0_main_LE(EOS(STATIC_579), 0, i99:0, 0) :|: TRUE Filtered constant ground arguments: f579_0_main_LE(x1, x2, x3, x4) -> f579_0_main_LE(x2, x3, x4) f829_0_main_LE(x1, x2, x3, x4) -> f829_0_main_LE(x2, x3, x4) f980_0_main_LE(x1, x2, x3, x4) -> f980_0_main_LE(x2, x3, x4) Filtered duplicate arguments: f579_0_main_LE(x1, x2, x3) -> f579_0_main_LE(x2, x3) f829_0_main_LE(x1, x2, x3) -> f829_0_main_LE(x1, x3) f980_0_main_LE(x1, x2, x3) -> f980_0_main_LE(x2, x3) Finished conversion. Obtained 6 rules.P rules: f579_0_main_LE(i85:0, i96:0) -> f829_0_main_LE(i96:0, i85:0) :|: i85:0 > 0 && i96:0 <= i85:0 && i96:0 > 0 f829_0_main_LE(i96:0, i144:0) -> f829_0_main_LE(i96:0, i144:0 - 1) :|: i144:0 > 0 f579_0_main_LE(i85:0, i96:0) -> f980_0_main_LE(i85:0, i96:0) :|: i85:0 > 0 && i96:0 > i85:0 && i96:0 > 0 f980_0_main_LE(i99:0, i178:0) -> f980_0_main_LE(i99:0, i178:0 - 1) :|: i178:0 > 0 f829_0_main_LE(i96:0, cons_0) -> f579_0_main_LE(0, i96:0) :|: TRUE && cons_0 = 0 f980_0_main_LE(i99:0, cons_0) -> f579_0_main_LE(i99:0, 0) :|: TRUE && cons_0 = 0 ---------------------------------------- (8) Obligation: Rules: f579_0_main_LE(i85:0, i96:0) -> f829_0_main_LE(i96:0, i85:0) :|: i85:0 > 0 && i96:0 <= i85:0 && i96:0 > 0 f829_0_main_LE(x, x1) -> f829_0_main_LE(x, x1 - 1) :|: x1 > 0 f579_0_main_LE(x2, x3) -> f980_0_main_LE(x2, x3) :|: x2 > 0 && x3 > x2 && x3 > 0 f980_0_main_LE(i99:0, i178:0) -> f980_0_main_LE(i99:0, i178:0 - 1) :|: i178:0 > 0 f829_0_main_LE(x4, x5) -> f579_0_main_LE(0, x4) :|: TRUE && x5 = 0 f980_0_main_LE(x6, x7) -> f579_0_main_LE(x6, 0) :|: TRUE && x7 = 0 ---------------------------------------- (9) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (10) Obligation: Rules: f579_0_main_LE(i85:0, i96:0) -> f829_0_main_LE(i96:0, i85:0) :|: i85:0 > 0 && i96:0 <= i85:0 && i96:0 > 0 f829_0_main_LE(x, x1) -> f829_0_main_LE(x, arith) :|: x1 > 0 && arith = x1 - 1 f579_0_main_LE(x2, x3) -> f980_0_main_LE(x2, x3) :|: x2 > 0 && x3 > x2 && x3 > 0 f980_0_main_LE(x8, x9) -> f980_0_main_LE(x8, x10) :|: x9 > 0 && x10 = x9 - 1 f829_0_main_LE(x4, x5) -> f579_0_main_LE(0, x4) :|: TRUE && x5 = 0 f980_0_main_LE(x6, x7) -> f579_0_main_LE(x6, 0) :|: TRUE && x7 = 0 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f579_0_main_LE(i85:0, i96:0) -> f829_0_main_LE(i96:0, i85:0) :|: i85:0 > 0 && i96:0 <= i85:0 && i96:0 > 0 (2) f829_0_main_LE(x, x1) -> f829_0_main_LE(x, arith) :|: x1 > 0 && arith = x1 - 1 (3) f579_0_main_LE(x2, x3) -> f980_0_main_LE(x2, x3) :|: x2 > 0 && x3 > x2 && x3 > 0 (4) f980_0_main_LE(x8, x9) -> f980_0_main_LE(x8, x10) :|: x9 > 0 && x10 = x9 - 1 (5) f829_0_main_LE(x4, x5) -> f579_0_main_LE(0, x4) :|: TRUE && x5 = 0 (6) f980_0_main_LE(x6, x7) -> f579_0_main_LE(x6, 0) :|: TRUE && x7 = 0 Arcs: (1) -> (2) (2) -> (2), (5) (3) -> (4) (4) -> (4), (6) This digraph is fully evaluated! ---------------------------------------- (12) Complex Obligation (AND) ---------------------------------------- (13) Obligation: Termination digraph: Nodes: (1) f980_0_main_LE(x8, x9) -> f980_0_main_LE(x8, x10) :|: x9 > 0 && x10 = x9 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (14) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (15) Obligation: Rules: f980_0_main_LE(x8:0, x9:0) -> f980_0_main_LE(x8:0, x9:0 - 1) :|: x9:0 > 0 ---------------------------------------- (16) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f980_0_main_LE(x1, x2) -> f980_0_main_LE(x2) ---------------------------------------- (17) Obligation: Rules: f980_0_main_LE(x9:0) -> f980_0_main_LE(x9:0 - 1) :|: x9:0 > 0 ---------------------------------------- (18) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f980_0_main_LE(INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (19) Obligation: Rules: f980_0_main_LE(x9:0) -> f980_0_main_LE(c) :|: c = x9:0 - 1 && x9:0 > 0 ---------------------------------------- (20) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f980_0_main_LE(x)] = x The following rules are decreasing: f980_0_main_LE(x9:0) -> f980_0_main_LE(c) :|: c = x9:0 - 1 && x9:0 > 0 The following rules are bounded: f980_0_main_LE(x9:0) -> f980_0_main_LE(c) :|: c = x9:0 - 1 && x9:0 > 0 ---------------------------------------- (21) YES ---------------------------------------- (22) Obligation: Termination digraph: Nodes: (1) f829_0_main_LE(x, x1) -> f829_0_main_LE(x, arith) :|: x1 > 0 && arith = x1 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (23) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (24) Obligation: Rules: f829_0_main_LE(x:0, x1:0) -> f829_0_main_LE(x:0, x1:0 - 1) :|: x1:0 > 0 ---------------------------------------- (25) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f829_0_main_LE(x1, x2) -> f829_0_main_LE(x2) ---------------------------------------- (26) Obligation: Rules: f829_0_main_LE(x1:0) -> f829_0_main_LE(x1:0 - 1) :|: x1:0 > 0 ---------------------------------------- (27) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f829_0_main_LE(INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (28) Obligation: Rules: f829_0_main_LE(x1:0) -> f829_0_main_LE(c) :|: c = x1:0 - 1 && x1:0 > 0 ---------------------------------------- (29) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f829_0_main_LE ] = f829_0_main_LE_1 The following rules are decreasing: f829_0_main_LE(x1:0) -> f829_0_main_LE(c) :|: c = x1:0 - 1 && x1:0 > 0 The following rules are bounded: f829_0_main_LE(x1:0) -> f829_0_main_LE(c) :|: c = x1:0 - 1 && x1:0 > 0 ---------------------------------------- (30) YES