/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 97 ms] (2) JBC problem (3) JBCToGraph [EQUIVALENT, 584 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 0 ms] (6) AND (7) JBCTerminationSCC (8) SCCToIRSProof [SOUND, 25 ms] (9) IRSwT (10) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (11) IRSwT (12) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms] (13) IRSwT (14) IntTRSCompressionProof [EQUIVALENT, 0 ms] (15) IRSwT (16) IRSwTChainingProof [EQUIVALENT, 0 ms] (17) IRSwT (18) IRSwTTerminationDigraphProof [EQUIVALENT, 4 ms] (19) IRSwT (20) IntTRSCompressionProof [EQUIVALENT, 0 ms] (21) IRSwT (22) IRSwTChainingProof [EQUIVALENT, 0 ms] (23) IRSwT (24) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms] (25) IRSwT (26) IntTRSCompressionProof [EQUIVALENT, 0 ms] (27) IRSwT (28) TempFilterProof [SOUND, 17 ms] (29) IntTRS (30) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (31) YES (32) JBCTerminationSCC (33) SCCToIRSProof [SOUND, 73 ms] (34) IRSwT (35) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (36) IRSwT (37) IRSwTTerminationDigraphProof [EQUIVALENT, 14 ms] (38) IRSwT (39) IntTRSCompressionProof [EQUIVALENT, 0 ms] (40) IRSwT (41) IRSwTChainingProof [EQUIVALENT, 0 ms] (42) IRSwT (43) IRSwTTerminationDigraphProof [EQUIVALENT, 3 ms] (44) IRSwT (45) IntTRSCompressionProof [EQUIVALENT, 0 ms] (46) IRSwT (47) IRSwTChainingProof [EQUIVALENT, 0 ms] (48) IRSwT (49) IRSwTTerminationDigraphProof [EQUIVALENT, 5 ms] (50) IRSwT (51) IntTRSCompressionProof [EQUIVALENT, 0 ms] (52) IRSwT (53) TempFilterProof [SOUND, 38 ms] (54) IntTRS (55) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (56) YES ---------------------------------------- (0) Obligation: need to prove termination of the following program: public class Et3 { public static void main(String[] args) { Random.args = args; int a = Random.random(); int b = Random.random(); while (a > 0) { a = a + b; b = b - 1; } } } // bin(entry(C,D),[C>=1,A=C+D,B=D-1],entry(A,B)) public class Random { static String[] args; static int index = 0; public static int random() { if (index >= args.length) return 0; String string = args[index]; index++; return string.length(); } } ---------------------------------------- (1) BareJBCToJBCProof (EQUIVALENT) initialized classpath ---------------------------------------- (2) Obligation: need to prove termination of the following program: public class Et3 { public static void main(String[] args) { Random.args = args; int a = Random.random(); int b = Random.random(); while (a > 0) { a = a + b; b = b - 1; } } } // bin(entry(C,D),[C>=1,A=C+D,B=D-1],entry(A,B)) public class Random { static String[] args; static int index = 0; public static int random() { if (index >= args.length) return 0; String string = args[index]; index++; return string.length(); } } ---------------------------------------- (3) JBCToGraph (EQUIVALENT) Constructed TerminationGraph. ---------------------------------------- (4) Obligation: Termination Graph based on JBC Program: Et3.main([Ljava/lang/String;)V: Graph of 234 nodes with 2 SCCs. ---------------------------------------- (5) TerminationGraphToSCCProof (SOUND) Splitted TerminationGraph to 2 SCCss. ---------------------------------------- (6) Complex Obligation (AND) ---------------------------------------- (7) Obligation: SCC of termination graph based on JBC Program. SCC contains nodes from the following methods: Et3.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: ---------------------------------------- (8) SCCToIRSProof (SOUND) Transformed FIGraph SCCs to intTRSs. Log: Generated rules. Obtained 13 IRulesP rules: f3633_0_main_LE(EOS(STATIC_3633), i1022, i967, i1022) -> f3641_0_main_LE(EOS(STATIC_3641), i1022, i967, i1022) :|: TRUE f3641_0_main_LE(EOS(STATIC_3641), i1022, i967, i1022) -> f3650_0_main_Load(EOS(STATIC_3650), i1022, i967) :|: i1022 > 0 f3650_0_main_Load(EOS(STATIC_3650), i1022, i967) -> f3659_0_main_Load(EOS(STATIC_3659), i967, i1022) :|: TRUE f3659_0_main_Load(EOS(STATIC_3659), i967, i1022) -> f3663_0_main_IntArithmetic(EOS(STATIC_3663), i967, i1022, i967) :|: TRUE f3663_0_main_IntArithmetic(EOS(STATIC_3663), i967, i1022, i967) -> f3673_0_main_Store(EOS(STATIC_3673), i967, i1022 + i967) :|: i1022 > 0 f3673_0_main_Store(EOS(STATIC_3673), i967, i1030) -> f3678_0_main_Load(EOS(STATIC_3678), i1030, i967) :|: TRUE f3678_0_main_Load(EOS(STATIC_3678), i1030, i967) -> f3818_0_main_ConstantStackPush(EOS(STATIC_3818), i1030, i967) :|: TRUE f3818_0_main_ConstantStackPush(EOS(STATIC_3818), i1030, i967) -> f3821_0_main_IntArithmetic(EOS(STATIC_3821), i1030, i967, 1) :|: TRUE f3821_0_main_IntArithmetic(EOS(STATIC_3821), i1030, i967, matching1) -> f3826_0_main_Store(EOS(STATIC_3826), i1030, i967 - 1) :|: TRUE && matching1 = 1 f3826_0_main_Store(EOS(STATIC_3826), i1030, i1069) -> f3830_0_main_JMP(EOS(STATIC_3830), i1030, i1069) :|: TRUE f3830_0_main_JMP(EOS(STATIC_3830), i1030, i1069) -> f3910_0_main_Load(EOS(STATIC_3910), i1030, i1069) :|: TRUE f3910_0_main_Load(EOS(STATIC_3910), i1030, i1069) -> f3525_0_main_Load(EOS(STATIC_3525), i1030, i1069) :|: TRUE f3525_0_main_Load(EOS(STATIC_3525), i966, i967) -> f3633_0_main_LE(EOS(STATIC_3633), i966, i967, i966) :|: TRUE Combined rules. Obtained 1 IRulesP rules: f3633_0_main_LE(EOS(STATIC_3633), i1022:0, i967:0, i1022:0) -> f3633_0_main_LE(EOS(STATIC_3633), i1022:0 + i967:0, i967:0 - 1, i1022:0 + i967:0) :|: i1022:0 > 0 Filtered constant ground arguments: f3633_0_main_LE(x1, x2, x3, x4) -> f3633_0_main_LE(x2, x3, x4) EOS(x1) -> EOS Filtered duplicate arguments: f3633_0_main_LE(x1, x2, x3) -> f3633_0_main_LE(x2, x3) Finished conversion. Obtained 1 rules.P rules: f3633_0_main_LE(i967:0, i1022:0) -> f3633_0_main_LE(i967:0 - 1, i1022:0 + i967:0) :|: i1022:0 > 0 ---------------------------------------- (9) Obligation: Rules: f3633_0_main_LE(i967:0, i1022:0) -> f3633_0_main_LE(i967:0 - 1, i1022:0 + i967:0) :|: i1022:0 > 0 ---------------------------------------- (10) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (11) Obligation: Rules: f3633_0_main_LE(i967:0, i1022:0) -> f3633_0_main_LE(arith, arith1) :|: i1022:0 > 0 && arith = i967:0 - 1 && arith1 = i1022:0 + i967:0 ---------------------------------------- (12) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f3633_0_main_LE(i967:0, i1022:0) -> f3633_0_main_LE(arith, arith1) :|: i1022:0 > 0 && arith = i967:0 - 1 && arith1 = i1022:0 + i967:0 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (13) Obligation: Termination digraph: Nodes: (1) f3633_0_main_LE(i967:0, i1022:0) -> f3633_0_main_LE(arith, arith1) :|: i1022:0 > 0 && arith = i967:0 - 1 && arith1 = i1022:0 + i967:0 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (14) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (15) Obligation: Rules: f3633_0_main_LE(i967:0:0, i1022:0:0) -> f3633_0_main_LE(i967:0:0 - 1, i1022:0:0 + i967:0:0) :|: i1022:0:0 > 0 ---------------------------------------- (16) IRSwTChainingProof (EQUIVALENT) Chaining! ---------------------------------------- (17) Obligation: Rules: f3633_0_main_LE(x, x1) -> f3633_0_main_LE(x + -2, x1 + 2 * x + -1) :|: TRUE && x1 >= 1 && x1 + x >= 1 ---------------------------------------- (18) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f3633_0_main_LE(x, x1) -> f3633_0_main_LE(x + -2, x1 + 2 * x + -1) :|: TRUE && x1 >= 1 && x1 + x >= 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (19) Obligation: Termination digraph: Nodes: (1) f3633_0_main_LE(x, x1) -> f3633_0_main_LE(x + -2, x1 + 2 * x + -1) :|: TRUE && x1 >= 1 && x1 + x >= 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (20) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (21) Obligation: Rules: f3633_0_main_LE(x:0, x1:0) -> f3633_0_main_LE(x:0 - 2, x1:0 + 2 * x:0 - 1) :|: x1:0 + x:0 >= 1 && x1:0 > 0 ---------------------------------------- (22) IRSwTChainingProof (EQUIVALENT) Chaining! ---------------------------------------- (23) Obligation: Rules: f3633_0_main_LE(x, x1) -> f3633_0_main_LE(x + -4, x1 + 4 * x + -6) :|: TRUE && x1 + x >= 1 && x1 >= 1 && x1 + 3 * x >= 4 && x1 + 2 * x >= 2 ---------------------------------------- (24) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f3633_0_main_LE(x, x1) -> f3633_0_main_LE(x + -4, x1 + 4 * x + -6) :|: TRUE && x1 + x >= 1 && x1 >= 1 && x1 + 3 * x >= 4 && x1 + 2 * x >= 2 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (25) Obligation: Termination digraph: Nodes: (1) f3633_0_main_LE(x, x1) -> f3633_0_main_LE(x + -4, x1 + 4 * x + -6) :|: TRUE && x1 + x >= 1 && x1 >= 1 && x1 + 3 * x >= 4 && x1 + 2 * x >= 2 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (26) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (27) Obligation: Rules: f3633_0_main_LE(x:0, x1:0) -> f3633_0_main_LE(x:0 - 4, x1:0 + 4 * x:0 - 6) :|: x1:0 + 3 * x:0 >= 4 && x1:0 + 2 * x:0 >= 2 && x1:0 + x:0 >= 1 && x1:0 > 0 ---------------------------------------- (28) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f3633_0_main_LE(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (29) Obligation: Rules: f3633_0_main_LE(x:0, x1:0) -> f3633_0_main_LE(c, c1) :|: c1 = x1:0 + 4 * x:0 - 6 && c = x:0 - 4 && (x1:0 + 3 * x:0 >= 4 && x1:0 + 2 * x:0 >= 2 && x1:0 + x:0 >= 1 && x1:0 > 0) ---------------------------------------- (30) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f3633_0_main_LE(x, x1)] = -2 + 2*x + x^2 + 2*x1 The following rules are decreasing: f3633_0_main_LE(x:0, x1:0) -> f3633_0_main_LE(c, c1) :|: c1 = x1:0 + 4 * x:0 - 6 && c = x:0 - 4 && (x1:0 + 3 * x:0 >= 4 && x1:0 + 2 * x:0 >= 2 && x1:0 + x:0 >= 1 && x1:0 > 0) The following rules are bounded: f3633_0_main_LE(x:0, x1:0) -> f3633_0_main_LE(c, c1) :|: c1 = x1:0 + 4 * x:0 - 6 && c = x:0 - 4 && (x1:0 + 3 * x:0 >= 4 && x1:0 + 2 * x:0 >= 2 && x1:0 + x:0 >= 1 && x1:0 > 0) ---------------------------------------- (31) YES ---------------------------------------- (32) Obligation: SCC of termination graph based on JBC Program. SCC contains nodes from the following methods: Et3.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: ---------------------------------------- (33) SCCToIRSProof (SOUND) Transformed FIGraph SCCs to intTRSs. Log: Generated rules. Obtained 13 IRulesP rules: f3327_0_main_LE(EOS(STATIC_3327), i909, i845, i909) -> f3335_0_main_LE(EOS(STATIC_3335), i909, i845, i909) :|: TRUE f3335_0_main_LE(EOS(STATIC_3335), i909, i845, i909) -> f3367_0_main_Load(EOS(STATIC_3367), i909, i845) :|: i909 > 0 f3367_0_main_Load(EOS(STATIC_3367), i909, i845) -> f3401_0_main_Load(EOS(STATIC_3401), i845, i909) :|: TRUE f3401_0_main_Load(EOS(STATIC_3401), i845, i909) -> f3531_0_main_IntArithmetic(EOS(STATIC_3531), i845, i909, i845) :|: TRUE f3531_0_main_IntArithmetic(EOS(STATIC_3531), i845, i909, i845) -> f3636_0_main_Store(EOS(STATIC_3636), i845, i909 + i845) :|: i909 > 0 f3636_0_main_Store(EOS(STATIC_3636), i845, i1020) -> f3644_0_main_Load(EOS(STATIC_3644), i1020, i845) :|: TRUE f3644_0_main_Load(EOS(STATIC_3644), i1020, i845) -> f3653_0_main_ConstantStackPush(EOS(STATIC_3653), i1020, i845) :|: TRUE f3653_0_main_ConstantStackPush(EOS(STATIC_3653), i1020, i845) -> f3661_0_main_IntArithmetic(EOS(STATIC_3661), i1020, i845, 1) :|: TRUE f3661_0_main_IntArithmetic(EOS(STATIC_3661), i1020, i845, matching1) -> f3668_0_main_Store(EOS(STATIC_3668), i1020, i845 - 1) :|: TRUE && matching1 = 1 f3668_0_main_Store(EOS(STATIC_3668), i1020, i1029) -> f3675_0_main_JMP(EOS(STATIC_3675), i1020, i1029) :|: TRUE f3675_0_main_JMP(EOS(STATIC_3675), i1020, i1029) -> f3813_0_main_Load(EOS(STATIC_3813), i1020, i1029) :|: TRUE f3813_0_main_Load(EOS(STATIC_3813), i1020, i1029) -> f3319_0_main_Load(EOS(STATIC_3319), i1020, i1029) :|: TRUE f3319_0_main_Load(EOS(STATIC_3319), i844, i845) -> f3327_0_main_LE(EOS(STATIC_3327), i844, i845, i844) :|: TRUE Combined rules. Obtained 1 IRulesP rules: f3327_0_main_LE(EOS(STATIC_3327), i909:0, i845:0, i909:0) -> f3327_0_main_LE(EOS(STATIC_3327), i909:0 + i845:0, i845:0 - 1, i909:0 + i845:0) :|: i909:0 > 0 Filtered constant ground arguments: f3327_0_main_LE(x1, x2, x3, x4) -> f3327_0_main_LE(x2, x3, x4) EOS(x1) -> EOS Filtered duplicate arguments: f3327_0_main_LE(x1, x2, x3) -> f3327_0_main_LE(x2, x3) Finished conversion. Obtained 1 rules.P rules: f3327_0_main_LE(i845:0, i909:0) -> f3327_0_main_LE(i845:0 - 1, i909:0 + i845:0) :|: i909:0 > 0 ---------------------------------------- (34) Obligation: Rules: f3327_0_main_LE(i845:0, i909:0) -> f3327_0_main_LE(i845:0 - 1, i909:0 + i845:0) :|: i909:0 > 0 ---------------------------------------- (35) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (36) Obligation: Rules: f3327_0_main_LE(i845:0, i909:0) -> f3327_0_main_LE(arith, arith1) :|: i909:0 > 0 && arith = i845:0 - 1 && arith1 = i909:0 + i845:0 ---------------------------------------- (37) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f3327_0_main_LE(i845:0, i909:0) -> f3327_0_main_LE(arith, arith1) :|: i909:0 > 0 && arith = i845:0 - 1 && arith1 = i909:0 + i845:0 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (38) Obligation: Termination digraph: Nodes: (1) f3327_0_main_LE(i845:0, i909:0) -> f3327_0_main_LE(arith, arith1) :|: i909:0 > 0 && arith = i845:0 - 1 && arith1 = i909:0 + i845:0 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (39) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (40) Obligation: Rules: f3327_0_main_LE(i845:0:0, i909:0:0) -> f3327_0_main_LE(i845:0:0 - 1, i909:0:0 + i845:0:0) :|: i909:0:0 > 0 ---------------------------------------- (41) IRSwTChainingProof (EQUIVALENT) Chaining! ---------------------------------------- (42) Obligation: Rules: f3327_0_main_LE(x, x1) -> f3327_0_main_LE(x + -2, x1 + 2 * x + -1) :|: TRUE && x1 >= 1 && x1 + x >= 1 ---------------------------------------- (43) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f3327_0_main_LE(x, x1) -> f3327_0_main_LE(x + -2, x1 + 2 * x + -1) :|: TRUE && x1 >= 1 && x1 + x >= 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (44) Obligation: Termination digraph: Nodes: (1) f3327_0_main_LE(x, x1) -> f3327_0_main_LE(x + -2, x1 + 2 * x + -1) :|: TRUE && x1 >= 1 && x1 + x >= 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (45) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (46) Obligation: Rules: f3327_0_main_LE(x:0, x1:0) -> f3327_0_main_LE(x:0 - 2, x1:0 + 2 * x:0 - 1) :|: x1:0 + x:0 >= 1 && x1:0 > 0 ---------------------------------------- (47) IRSwTChainingProof (EQUIVALENT) Chaining! ---------------------------------------- (48) Obligation: Rules: f3327_0_main_LE(x, x1) -> f3327_0_main_LE(x + -4, x1 + 4 * x + -6) :|: TRUE && x1 + x >= 1 && x1 >= 1 && x1 + 3 * x >= 4 && x1 + 2 * x >= 2 ---------------------------------------- (49) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f3327_0_main_LE(x, x1) -> f3327_0_main_LE(x + -4, x1 + 4 * x + -6) :|: TRUE && x1 + x >= 1 && x1 >= 1 && x1 + 3 * x >= 4 && x1 + 2 * x >= 2 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (50) Obligation: Termination digraph: Nodes: (1) f3327_0_main_LE(x, x1) -> f3327_0_main_LE(x + -4, x1 + 4 * x + -6) :|: TRUE && x1 + x >= 1 && x1 >= 1 && x1 + 3 * x >= 4 && x1 + 2 * x >= 2 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (51) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (52) Obligation: Rules: f3327_0_main_LE(x:0, x1:0) -> f3327_0_main_LE(x:0 - 4, x1:0 + 4 * x:0 - 6) :|: x1:0 + 3 * x:0 >= 4 && x1:0 + 2 * x:0 >= 2 && x1:0 + x:0 >= 1 && x1:0 > 0 ---------------------------------------- (53) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f3327_0_main_LE(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (54) Obligation: Rules: f3327_0_main_LE(x:0, x1:0) -> f3327_0_main_LE(c, c1) :|: c1 = x1:0 + 4 * x:0 - 6 && c = x:0 - 4 && (x1:0 + 3 * x:0 >= 4 && x1:0 + 2 * x:0 >= 2 && x1:0 + x:0 >= 1 && x1:0 > 0) ---------------------------------------- (55) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f3327_0_main_LE(x, x1)] = -2 + 2*x + x^2 + 2*x1 The following rules are decreasing: f3327_0_main_LE(x:0, x1:0) -> f3327_0_main_LE(c, c1) :|: c1 = x1:0 + 4 * x:0 - 6 && c = x:0 - 4 && (x1:0 + 3 * x:0 >= 4 && x1:0 + 2 * x:0 >= 2 && x1:0 + x:0 >= 1 && x1:0 > 0) The following rules are bounded: f3327_0_main_LE(x:0, x1:0) -> f3327_0_main_LE(c, c1) :|: c1 = x1:0 + 4 * x:0 - 6 && c = x:0 - 4 && (x1:0 + 3 * x:0 >= 4 && x1:0 + 2 * x:0 >= 2 && x1:0 + x:0 >= 1 && x1:0 > 0) ---------------------------------------- (56) YES