/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 96 ms] (2) JBC problem (3) JBCToGraph [EQUIVALENT, 616 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 5 ms] (6) AND (7) JBCTerminationSCC (8) SCCToIRSProof [SOUND, 0 ms] (9) IRSwT (10) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (11) IRSwT (12) IRSwTTerminationDigraphProof [EQUIVALENT, 24 ms] (13) IRSwT (14) IntTRSCompressionProof [EQUIVALENT, 0 ms] (15) IRSwT (16) IRSwTChainingProof [EQUIVALENT, 0 ms] (17) IRSwT (18) IRSwTTerminationDigraphProof [EQUIVALENT, 0 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, 82 ms] (29) IntTRS (30) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (31) YES (32) JBCTerminationSCC (33) SCCToIRSProof [SOUND, 0 ms] (34) IRSwT (35) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (36) IRSwT (37) IRSwTTerminationDigraphProof [EQUIVALENT, 15 ms] (38) IRSwT (39) IntTRSCompressionProof [EQUIVALENT, 0 ms] (40) IRSwT (41) IRSwTChainingProof [EQUIVALENT, 0 ms] (42) IRSwT (43) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms] (44) IRSwT (45) IntTRSCompressionProof [EQUIVALENT, 0 ms] (46) IRSwT (47) IRSwTChainingProof [EQUIVALENT, 0 ms] (48) IRSwT (49) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms] (50) IRSwT (51) IntTRSCompressionProof [EQUIVALENT, 0 ms] (52) IRSwT (53) TempFilterProof [SOUND, 16 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: f3937_0_main_LE(EOS(STATIC_3937), i1129, i953, i1129) -> f4034_0_main_LE(EOS(STATIC_4034), i1129, i953, i1129) :|: TRUE f4034_0_main_LE(EOS(STATIC_4034), i1129, i953, i1129) -> f4037_0_main_Load(EOS(STATIC_4037), i1129, i953) :|: i1129 > 0 f4037_0_main_Load(EOS(STATIC_4037), i1129, i953) -> f4040_0_main_Load(EOS(STATIC_4040), i953, i1129) :|: TRUE f4040_0_main_Load(EOS(STATIC_4040), i953, i1129) -> f4042_0_main_IntArithmetic(EOS(STATIC_4042), i953, i1129, i953) :|: TRUE f4042_0_main_IntArithmetic(EOS(STATIC_4042), i953, i1129, i953) -> f4044_0_main_Store(EOS(STATIC_4044), i953, i1129 + i953) :|: i1129 > 0 f4044_0_main_Store(EOS(STATIC_4044), i953, i1131) -> f4125_0_main_Load(EOS(STATIC_4125), i1131, i953) :|: TRUE f4125_0_main_Load(EOS(STATIC_4125), i1131, i953) -> f4127_0_main_ConstantStackPush(EOS(STATIC_4127), i1131, i953) :|: TRUE f4127_0_main_ConstantStackPush(EOS(STATIC_4127), i1131, i953) -> f4128_0_main_IntArithmetic(EOS(STATIC_4128), i1131, i953, 1) :|: TRUE f4128_0_main_IntArithmetic(EOS(STATIC_4128), i1131, i953, matching1) -> f4129_0_main_Store(EOS(STATIC_4129), i1131, i953 - 1) :|: TRUE && matching1 = 1 f4129_0_main_Store(EOS(STATIC_4129), i1131, i1153) -> f4130_0_main_JMP(EOS(STATIC_4130), i1131, i1153) :|: TRUE f4130_0_main_JMP(EOS(STATIC_4130), i1131, i1153) -> f4217_0_main_Load(EOS(STATIC_4217), i1131, i1153) :|: TRUE f4217_0_main_Load(EOS(STATIC_4217), i1131, i1153) -> f3580_0_main_Load(EOS(STATIC_3580), i1131, i1153) :|: TRUE f3580_0_main_Load(EOS(STATIC_3580), i952, i953) -> f3937_0_main_LE(EOS(STATIC_3937), i952, i953, i952) :|: TRUE Combined rules. Obtained 1 IRulesP rules: f3937_0_main_LE(EOS(STATIC_3937), i1129:0, i953:0, i1129:0) -> f3937_0_main_LE(EOS(STATIC_3937), i1129:0 + i953:0, i953:0 - 1, i1129:0 + i953:0) :|: i1129:0 > 0 Filtered constant ground arguments: f3937_0_main_LE(x1, x2, x3, x4) -> f3937_0_main_LE(x2, x3, x4) EOS(x1) -> EOS Filtered duplicate arguments: f3937_0_main_LE(x1, x2, x3) -> f3937_0_main_LE(x2, x3) Finished conversion. Obtained 1 rules.P rules: f3937_0_main_LE(i953:0, i1129:0) -> f3937_0_main_LE(i953:0 - 1, i1129:0 + i953:0) :|: i1129:0 > 0 ---------------------------------------- (9) Obligation: Rules: f3937_0_main_LE(i953:0, i1129:0) -> f3937_0_main_LE(i953:0 - 1, i1129:0 + i953:0) :|: i1129:0 > 0 ---------------------------------------- (10) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (11) Obligation: Rules: f3937_0_main_LE(i953:0, i1129:0) -> f3937_0_main_LE(arith, arith1) :|: i1129:0 > 0 && arith = i953:0 - 1 && arith1 = i1129:0 + i953:0 ---------------------------------------- (12) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f3937_0_main_LE(i953:0, i1129:0) -> f3937_0_main_LE(arith, arith1) :|: i1129:0 > 0 && arith = i953:0 - 1 && arith1 = i1129:0 + i953:0 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (13) Obligation: Termination digraph: Nodes: (1) f3937_0_main_LE(i953:0, i1129:0) -> f3937_0_main_LE(arith, arith1) :|: i1129:0 > 0 && arith = i953:0 - 1 && arith1 = i1129:0 + i953:0 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (14) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (15) Obligation: Rules: f3937_0_main_LE(i953:0:0, i1129:0:0) -> f3937_0_main_LE(i953:0:0 - 1, i1129:0:0 + i953:0:0) :|: i1129:0:0 > 0 ---------------------------------------- (16) IRSwTChainingProof (EQUIVALENT) Chaining! ---------------------------------------- (17) Obligation: Rules: f3937_0_main_LE(x, x1) -> f3937_0_main_LE(x + -2, x1 + 2 * x + -1) :|: TRUE && x1 >= 1 && x1 + x >= 1 ---------------------------------------- (18) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f3937_0_main_LE(x, x1) -> f3937_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) f3937_0_main_LE(x, x1) -> f3937_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: f3937_0_main_LE(x:0, x1:0) -> f3937_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: f3937_0_main_LE(x, x1) -> f3937_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) f3937_0_main_LE(x, x1) -> f3937_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) f3937_0_main_LE(x, x1) -> f3937_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: f3937_0_main_LE(x:0, x1:0) -> f3937_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: f3937_0_main_LE(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (29) Obligation: Rules: f3937_0_main_LE(x:0, x1:0) -> f3937_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: [f3937_0_main_LE(x, x1)] = -2 + 2*x + x^2 + 2*x1 The following rules are decreasing: f3937_0_main_LE(x:0, x1:0) -> f3937_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: f3937_0_main_LE(x:0, x1:0) -> f3937_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: f3051_0_main_LE(EOS(STATIC_3051), i858, i770, i858) -> f3060_0_main_LE(EOS(STATIC_3060), i858, i770, i858) :|: TRUE f3060_0_main_LE(EOS(STATIC_3060), i858, i770, i858) -> f3272_0_main_Load(EOS(STATIC_3272), i858, i770) :|: i858 > 0 f3272_0_main_Load(EOS(STATIC_3272), i858, i770) -> f3275_0_main_Load(EOS(STATIC_3275), i770, i858) :|: TRUE f3275_0_main_Load(EOS(STATIC_3275), i770, i858) -> f3581_0_main_IntArithmetic(EOS(STATIC_3581), i770, i858, i770) :|: TRUE f3581_0_main_IntArithmetic(EOS(STATIC_3581), i770, i858, i770) -> f4032_0_main_Store(EOS(STATIC_4032), i770, i858 + i770) :|: i858 > 0 f4032_0_main_Store(EOS(STATIC_4032), i770, i1127) -> f4035_0_main_Load(EOS(STATIC_4035), i1127, i770) :|: TRUE f4035_0_main_Load(EOS(STATIC_4035), i1127, i770) -> f4038_0_main_ConstantStackPush(EOS(STATIC_4038), i1127, i770) :|: TRUE f4038_0_main_ConstantStackPush(EOS(STATIC_4038), i1127, i770) -> f4041_0_main_IntArithmetic(EOS(STATIC_4041), i1127, i770, 1) :|: TRUE f4041_0_main_IntArithmetic(EOS(STATIC_4041), i1127, i770, matching1) -> f4043_0_main_Store(EOS(STATIC_4043), i1127, i770 - 1) :|: TRUE && matching1 = 1 f4043_0_main_Store(EOS(STATIC_4043), i1127, i1130) -> f4124_0_main_JMP(EOS(STATIC_4124), i1127, i1130) :|: TRUE f4124_0_main_JMP(EOS(STATIC_4124), i1127, i1130) -> f4126_0_main_Load(EOS(STATIC_4126), i1127, i1130) :|: TRUE f4126_0_main_Load(EOS(STATIC_4126), i1127, i1130) -> f3030_0_main_Load(EOS(STATIC_3030), i1127, i1130) :|: TRUE f3030_0_main_Load(EOS(STATIC_3030), i769, i770) -> f3051_0_main_LE(EOS(STATIC_3051), i769, i770, i769) :|: TRUE Combined rules. Obtained 1 IRulesP rules: f3051_0_main_LE(EOS(STATIC_3051), i858:0, i770:0, i858:0) -> f3051_0_main_LE(EOS(STATIC_3051), i858:0 + i770:0, i770:0 - 1, i858:0 + i770:0) :|: i858:0 > 0 Filtered constant ground arguments: f3051_0_main_LE(x1, x2, x3, x4) -> f3051_0_main_LE(x2, x3, x4) EOS(x1) -> EOS Filtered duplicate arguments: f3051_0_main_LE(x1, x2, x3) -> f3051_0_main_LE(x2, x3) Finished conversion. Obtained 1 rules.P rules: f3051_0_main_LE(i770:0, i858:0) -> f3051_0_main_LE(i770:0 - 1, i858:0 + i770:0) :|: i858:0 > 0 ---------------------------------------- (34) Obligation: Rules: f3051_0_main_LE(i770:0, i858:0) -> f3051_0_main_LE(i770:0 - 1, i858:0 + i770:0) :|: i858:0 > 0 ---------------------------------------- (35) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (36) Obligation: Rules: f3051_0_main_LE(i770:0, i858:0) -> f3051_0_main_LE(arith, arith1) :|: i858:0 > 0 && arith = i770:0 - 1 && arith1 = i858:0 + i770:0 ---------------------------------------- (37) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f3051_0_main_LE(i770:0, i858:0) -> f3051_0_main_LE(arith, arith1) :|: i858:0 > 0 && arith = i770:0 - 1 && arith1 = i858:0 + i770:0 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (38) Obligation: Termination digraph: Nodes: (1) f3051_0_main_LE(i770:0, i858:0) -> f3051_0_main_LE(arith, arith1) :|: i858:0 > 0 && arith = i770:0 - 1 && arith1 = i858:0 + i770:0 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (39) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (40) Obligation: Rules: f3051_0_main_LE(i770:0:0, i858:0:0) -> f3051_0_main_LE(i770:0:0 - 1, i858:0:0 + i770:0:0) :|: i858:0:0 > 0 ---------------------------------------- (41) IRSwTChainingProof (EQUIVALENT) Chaining! ---------------------------------------- (42) Obligation: Rules: f3051_0_main_LE(x, x1) -> f3051_0_main_LE(x + -2, x1 + 2 * x + -1) :|: TRUE && x1 >= 1 && x1 + x >= 1 ---------------------------------------- (43) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f3051_0_main_LE(x, x1) -> f3051_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) f3051_0_main_LE(x, x1) -> f3051_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: f3051_0_main_LE(x:0, x1:0) -> f3051_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: f3051_0_main_LE(x, x1) -> f3051_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) f3051_0_main_LE(x, x1) -> f3051_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) f3051_0_main_LE(x, x1) -> f3051_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: f3051_0_main_LE(x:0, x1:0) -> f3051_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: f3051_0_main_LE(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (54) Obligation: Rules: f3051_0_main_LE(x:0, x1:0) -> f3051_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: [f3051_0_main_LE(x, x1)] = -2 + 2*x + x^2 + 2*x1 The following rules are decreasing: f3051_0_main_LE(x:0, x1:0) -> f3051_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: f3051_0_main_LE(x:0, x1:0) -> f3051_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