6.82/2.79 YES 7.38/2.85 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 7.38/2.85 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 7.38/2.85 7.38/2.85 7.38/2.85 Termination of the given C Problem could be proven: 7.38/2.85 7.38/2.85 (0) C Problem 7.38/2.85 (1) CToLLVMProof [EQUIVALENT, 172 ms] 7.38/2.85 (2) LLVM problem 7.38/2.85 (3) LLVMToTerminationGraphProof [EQUIVALENT, 287 ms] 7.38/2.85 (4) LLVM Symbolic Execution Graph 7.38/2.85 (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] 7.38/2.85 (6) LLVM Symbolic Execution SCC 7.38/2.85 (7) SCC2IRS [SOUND, 69 ms] 7.38/2.85 (8) IntTRS 7.38/2.85 (9) IntTRSCompressionProof [EQUIVALENT, 0 ms] 7.38/2.85 (10) IntTRS 7.38/2.85 (11) RankingReductionPairProof [EQUIVALENT, 27 ms] 7.38/2.85 (12) YES 7.38/2.85 7.38/2.85 7.38/2.85 ---------------------------------------- 7.38/2.85 7.38/2.85 (0) 7.38/2.85 Obligation: 7.38/2.85 c file /export/starexec/sandbox/benchmark/theBenchmark.c 7.38/2.85 ---------------------------------------- 7.38/2.85 7.38/2.85 (1) CToLLVMProof (EQUIVALENT) 7.38/2.85 Compiled c-file /export/starexec/sandbox/benchmark/theBenchmark.c to LLVM. 7.38/2.85 ---------------------------------------- 7.38/2.85 7.38/2.85 (2) 7.38/2.85 Obligation: 7.38/2.85 LLVM Problem 7.38/2.85 7.38/2.85 Aliases: 7.38/2.85 7.38/2.85 Data layout: 7.38/2.85 7.38/2.85 "e-p:64:64:64-i1:8:8-i8:8:8-i16:16:16-i32:32:32-i64:64:64-f32:32:32-f64:64:64-v64:64:64-v128:128:128-a0:0:64-s0:64:64-f80:128:128-n8:16:32:64-S128" 7.38/2.85 7.38/2.85 Machine: 7.38/2.85 7.38/2.85 "x86_64-pc-linux-gnu" 7.38/2.85 7.38/2.85 Type definitions: 7.38/2.85 7.38/2.85 Global variables: 7.38/2.85 7.38/2.85 Function declarations and definitions: 7.38/2.85 7.38/2.85 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 7.38/2.85 0: 7.38/2.85 %1 = alloca i32, align 4 7.38/2.85 %a = alloca [1048 x i32], align 16 7.38/2.85 store 0, %1 7.38/2.85 br %2 7.38/2.85 2: 7.38/2.85 %3 = getelementptr %a, 0, 3 7.38/2.85 %4 = load %3 7.38/2.85 %5 = icmp sge %4 0 7.38/2.85 br %5, %6, %11 7.38/2.85 6: 7.38/2.85 %7 = getelementptr %a, 0, 3 7.38/2.85 %8 = load %7 7.38/2.85 %9 = sub %8 1 7.38/2.85 %10 = getelementptr %a, 0, 3 7.38/2.85 store %9, %10 7.38/2.85 br %2 7.38/2.85 11: 7.38/2.85 ret 0 7.38/2.85 7.38/2.85 7.38/2.85 Analyze Termination of all function calls matching the pattern: 7.38/2.85 main() 7.38/2.85 ---------------------------------------- 7.38/2.85 7.38/2.85 (3) LLVMToTerminationGraphProof (EQUIVALENT) 7.38/2.85 Constructed symbolic execution graph for LLVM program and proved memory safety. 7.38/2.85 ---------------------------------------- 7.38/2.85 7.38/2.85 (4) 7.38/2.85 Obligation: 7.38/2.85 SE Graph 7.38/2.85 ---------------------------------------- 7.38/2.85 7.38/2.85 (5) SymbolicExecutionGraphToSCCProof (SOUND) 7.38/2.85 Splitted symbolic execution graph to 1 SCC. 7.38/2.85 ---------------------------------------- 7.38/2.85 7.38/2.85 (6) 7.38/2.85 Obligation: 7.38/2.85 SCC 7.38/2.85 ---------------------------------------- 7.38/2.85 7.38/2.85 (7) SCC2IRS (SOUND) 7.38/2.85 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 7.38/2.85 Generated rules. Obtained 12 rulesP rules: 7.38/2.85 f_66(v1, v3, v5, v6, 1, v8, v2, v4, 0, 3, 4191, 12, 4, 4192, 13) -> f_67(v1, v3, v5, v8, 1, v6, v2, v4, 0, 3, 4191, 12, 4, 4192, 13) :|: 0 = 0 7.38/2.85 f_67(v1, v3, v5, v8, 1, v6, v2, v4, 0, 3, 4191, 12, 4, 4192, 13) -> f_68(v1, v3, v5, v8, 1, v6, v2, v4, 0, 3, 4191, 12, 4, 4192, 13) :|: 0 <= v8 && 1 <= v6 7.38/2.85 f_68(v1, v3, v5, v8, 1, v6, v2, v4, 0, 3, 4191, 12, 4, 4192, 13) -> f_70(v1, v3, v5, v8, 1, v6, v2, v4, 0, 3, 4191, 12, 4, 4192, 13) :|: 0 = 0 7.38/2.85 f_70(v1, v3, v5, v8, 1, v6, v2, v4, 0, 3, 4191, 12, 4, 4192, 13) -> f_72(v1, v3, v5, v8, 1, v6, v2, v4, 0, 3, 4191, 12, 4, 4192, 13) :|: TRUE 7.38/2.85 f_72(v1, v3, v5, v8, 1, v6, v2, v4, 0, 3, 4191, 12, 4, 4192, 13) -> f_74(v1, v3, v5, v8, 1, v6, v2, v4, 0, 3, 4191, 12, 4, 4192, 13) :|: v5 = 12 + v3 7.38/2.85 f_74(v1, v3, v5, v8, 1, v6, v2, v4, 0, 3, 4191, 12, 4, 4192, 13) -> f_75(v1, v3, v5, v8, 1, v2, v4, 0, 3, 4191, 12, 4, 4192, 13) :|: 0 = 0 7.38/2.85 f_75(v1, v3, v5, v8, 1, v2, v4, 0, 3, 4191, 12, 4, 4192, 13) -> f_76(v1, v3, v5, v8, 1, v10, v2, v4, 0, 3, 4191, 12, 4, 4192, 13) :|: 1 + v10 = v8 && 0 <= 1 + v10 7.38/2.85 f_76(v1, v3, v5, v8, 1, v10, v2, v4, 0, 3, 4191, 12, 4, 4192, 13) -> f_77(v1, v3, v5, v8, 1, v10, v2, v4, 0, 3, 4191, 12, 4, 4192, 13) :|: v5 = 12 + v3 7.38/2.85 f_77(v1, v3, v5, v8, 1, v10, v2, v4, 0, 3, 4191, 12, 4, 4192, 13) -> f_78(v1, v3, v5, v8, 1, v10, v2, v4, 0, 3, 4191, 12, 4, 4192, 13) :|: TRUE 7.38/2.85 f_78(v1, v3, v5, v8, 1, v10, v2, v4, 0, 3, 4191, 12, 4, 4192, 13) -> f_79(v1, v3, v5, v8, 1, v10, v2, v4, 0, 3, 4191, 12, 4, 4192, 13) :|: TRUE 7.38/2.85 f_79(v1, v3, v5, v8, 1, v10, v2, v4, 0, 3, 4191, 12, 4, 4192, 13) -> f_65(v1, v3, v5, v8, 1, v10, v2, v4, 0, 3, 4191, 12, 4, 4192, 13) :|: TRUE 7.38/2.85 f_65(v1, v3, v5, v6, 1, v8, v2, v4, 0, 3, 4191, 12, 4, 4192, 13) -> f_66(v1, v3, v5, v6, 1, v8, v2, v4, 0, 3, 4191, 12, 4, 4192, 13) :|: v5 = 12 + v3 7.38/2.85 Combined rules. Obtained 1 rulesP rules: 7.38/2.85 f_66(v1:0, v3:0, 12 + v3:0, v6:0, 1, 1 + v10:0, v2:0, v4:0, 0, 3, 4191, 12, 4, 4192, 13) -> f_66(v1:0, v3:0, 12 + v3:0, 1 + v10:0, 1, v10:0, v2:0, v4:0, 0, 3, 4191, 12, 4, 4192, 13) :|: v6:0 > 0 && v10:0 > -2 7.38/2.85 Filtered unneeded arguments: 7.38/2.85 f_66(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) -> f_66(x2, x3, x4, x6) 7.38/2.85 Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: 7.38/2.85 f_66(v3:0, sum~cons_12~v3:0, v6:0, sum~cons_1~v10:0) -> f_66(v3:0, 12 + v3:0, 1 + v10:0, v10:0) :|: v6:0 > 0 && v10:0 > -2 && sum~cons_12~v3:0 = 12 + v3:0 && sum~cons_1~v10:0 = 1 + v10:0 7.38/2.85 7.38/2.85 ---------------------------------------- 7.38/2.85 7.38/2.85 (8) 7.38/2.85 Obligation: 7.38/2.85 Rules: 7.38/2.85 f_66(v3:0, sum~cons_12~v3:0, v6:0, sum~cons_1~v10:0) -> f_66(v3:0, 12 + v3:0, 1 + v10:0, v10:0) :|: v6:0 > 0 && v10:0 > -2 && sum~cons_12~v3:0 = 12 + v3:0 && sum~cons_1~v10:0 = 1 + v10:0 7.38/2.85 7.38/2.85 ---------------------------------------- 7.38/2.85 7.38/2.85 (9) IntTRSCompressionProof (EQUIVALENT) 7.38/2.85 Compressed rules. 7.38/2.85 ---------------------------------------- 7.38/2.85 7.38/2.85 (10) 7.38/2.85 Obligation: 7.38/2.85 Rules: 7.38/2.85 f_66(v3:0:0, sum~cons_12~v3:0:0, v6:0:0, sum~cons_1~v10:0:0) -> f_66(v3:0:0, 12 + v3:0:0, 1 + v10:0:0, v10:0:0) :|: v6:0:0 > 0 && v10:0:0 > -2 && sum~cons_12~v3:0:0 = 12 + v3:0:0 && sum~cons_1~v10:0:0 = 1 + v10:0:0 7.38/2.85 7.38/2.85 ---------------------------------------- 7.38/2.85 7.38/2.85 (11) RankingReductionPairProof (EQUIVALENT) 7.38/2.85 Interpretation: 7.38/2.85 [ f_66 ] = f_66_4 7.38/2.85 7.38/2.85 The following rules are decreasing: 7.38/2.85 f_66(v3:0:0, sum~cons_12~v3:0:0, v6:0:0, sum~cons_1~v10:0:0) -> f_66(v3:0:0, 12 + v3:0:0, 1 + v10:0:0, v10:0:0) :|: v6:0:0 > 0 && v10:0:0 > -2 && sum~cons_12~v3:0:0 = 12 + v3:0:0 && sum~cons_1~v10:0:0 = 1 + v10:0:0 7.38/2.85 7.38/2.85 The following rules are bounded: 7.38/2.85 f_66(v3:0:0, sum~cons_12~v3:0:0, v6:0:0, sum~cons_1~v10:0:0) -> f_66(v3:0:0, 12 + v3:0:0, 1 + v10:0:0, v10:0:0) :|: v6:0:0 > 0 && v10:0:0 > -2 && sum~cons_12~v3:0:0 = 12 + v3:0:0 && sum~cons_1~v10:0:0 = 1 + v10:0:0 7.38/2.85 7.38/2.85 7.38/2.85 ---------------------------------------- 7.38/2.85 7.38/2.85 (12) 7.38/2.85 YES 7.38/2.88 EOF