7.13/2.85 YES 7.13/2.85 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 7.13/2.85 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 7.13/2.85 7.13/2.85 7.13/2.85 Termination of the given C Problem could be proven: 7.13/2.85 7.13/2.85 (0) C Problem 7.13/2.85 (1) CToLLVMProof [EQUIVALENT, 172 ms] 7.13/2.85 (2) LLVM problem 7.13/2.85 (3) LLVMToTerminationGraphProof [EQUIVALENT, 289 ms] 7.13/2.85 (4) LLVM Symbolic Execution Graph 7.13/2.85 (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] 7.13/2.85 (6) LLVM Symbolic Execution SCC 7.13/2.85 (7) SCC2IRS [SOUND, 54 ms] 7.13/2.85 (8) IntTRS 7.13/2.85 (9) IntTRSCompressionProof [EQUIVALENT, 0 ms] 7.13/2.85 (10) IntTRS 7.13/2.85 (11) PolynomialOrderProcessor [EQUIVALENT, 4 ms] 7.13/2.85 (12) YES 7.13/2.85 7.13/2.85 7.13/2.85 ---------------------------------------- 7.13/2.85 7.13/2.85 (0) 7.13/2.85 Obligation: 7.13/2.85 c file /export/starexec/sandbox/benchmark/theBenchmark.c 7.13/2.85 ---------------------------------------- 7.13/2.85 7.13/2.85 (1) CToLLVMProof (EQUIVALENT) 7.13/2.85 Compiled c-file /export/starexec/sandbox/benchmark/theBenchmark.c to LLVM. 7.13/2.85 ---------------------------------------- 7.13/2.85 7.13/2.85 (2) 7.13/2.85 Obligation: 7.13/2.85 LLVM Problem 7.13/2.85 7.13/2.85 Aliases: 7.13/2.85 7.13/2.85 Data layout: 7.13/2.85 7.13/2.85 "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" 7.13/2.85 7.13/2.85 Machine: 7.13/2.85 7.13/2.85 "x86_64-pc-linux-gnu" 7.13/2.85 7.13/2.85 Type definitions: 7.13/2.85 7.13/2.85 Global variables: 7.13/2.85 7.13/2.85 Function declarations and definitions: 7.13/2.85 7.13/2.85 *BasicFunctionTypename: "malloc" returnParam: *i8 parameters: (i64) variableLength: false visibilityType: DEFAULT callingConvention: ccc 7.13/2.85 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 7.13/2.85 0: 7.13/2.85 %1 = alloca i32, align 4 7.13/2.85 %p = alloca *i32, align 8 7.13/2.85 store 0, %1 7.13/2.85 %2 = call *i8 @malloc(i64 4) 7.13/2.85 %3 = bitcast *i8 %2 to *i32 7.13/2.85 store %3, %p 7.13/2.85 br %4 7.13/2.85 4: 7.13/2.85 %5 = load %p 7.13/2.85 %6 = load %5 7.13/2.85 %7 = icmp sge %6 0 7.13/2.85 br %7, %8, %12 7.13/2.85 8: 7.13/2.85 %9 = load %p 7.13/2.85 %10 = load %9 7.13/2.85 %11 = add %10 -1 7.13/2.85 store %11, %9 7.13/2.85 br %4 7.13/2.85 12: 7.13/2.85 ret 0 7.13/2.85 7.13/2.85 7.13/2.85 Analyze Termination of all function calls matching the pattern: 7.13/2.85 main() 7.13/2.85 ---------------------------------------- 7.13/2.85 7.13/2.85 (3) LLVMToTerminationGraphProof (EQUIVALENT) 7.13/2.85 Constructed symbolic execution graph for LLVM program and proved memory safety. 7.13/2.85 ---------------------------------------- 7.13/2.85 7.13/2.85 (4) 7.13/2.85 Obligation: 7.13/2.85 SE Graph 7.13/2.85 ---------------------------------------- 7.13/2.85 7.13/2.85 (5) SymbolicExecutionGraphToSCCProof (SOUND) 7.13/2.85 Splitted symbolic execution graph to 1 SCC. 7.13/2.85 ---------------------------------------- 7.13/2.85 7.13/2.85 (6) 7.13/2.85 Obligation: 7.13/2.85 SCC 7.13/2.85 ---------------------------------------- 7.13/2.85 7.13/2.85 (7) SCC2IRS (SOUND) 7.13/2.85 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 7.13/2.85 Generated rules. Obtained 11 rulesP rules: 7.13/2.85 f_75(v1, v3, v5, v8, 1, v10, v2, v4, v6, 0, 3, 7, 4, 8) -> f_76(v1, v3, v5, v10, 1, v8, v2, v4, v6, 0, 3, 7, 4, 8) :|: 0 = 0 7.13/2.85 f_76(v1, v3, v5, v10, 1, v8, v2, v4, v6, 0, 3, 7, 4, 8) -> f_77(v1, v3, v5, v10, 1, v8, v2, v4, v6, 0, 3, 7, 4, 8) :|: 0 <= v10 && 1 <= v8 7.13/2.85 f_77(v1, v3, v5, v10, 1, v8, v2, v4, v6, 0, 3, 7, 4, 8) -> f_79(v1, v3, v5, v10, 1, v8, v2, v4, v6, 0, 3, 7, 4, 8) :|: 0 = 0 7.13/2.85 f_79(v1, v3, v5, v10, 1, v8, v2, v4, v6, 0, 3, 7, 4, 8) -> f_81(v1, v3, v5, v10, 1, v8, v2, v4, v6, 0, 3, 7, 4, 8) :|: TRUE 7.13/2.85 f_81(v1, v3, v5, v10, 1, v8, v2, v4, v6, 0, 3, 7, 4, 8) -> f_83(v1, v3, v5, v10, 1, v8, v2, v4, v6, 0, 3, 7, 4, 8) :|: 0 = 0 7.13/2.85 f_83(v1, v3, v5, v10, 1, v8, v2, v4, v6, 0, 3, 7, 4, 8) -> f_84(v1, v3, v5, v10, 1, v2, v4, v6, 0, 3, 7, 4, 8) :|: 0 = 0 7.13/2.85 f_84(v1, v3, v5, v10, 1, v2, v4, v6, 0, 3, 7, 4, 8) -> f_85(v1, v3, v5, v10, 1, v12, v2, v4, v6, 0, 3, 7, 4, 8) :|: 1 + v12 = v10 && 0 <= 1 + v12 7.13/2.85 f_85(v1, v3, v5, v10, 1, v12, v2, v4, v6, 0, 3, 7, 4, 8) -> f_86(v1, v3, v5, v10, 1, v12, v2, v4, v6, 0, 3, 7, 4, 8) :|: TRUE 7.13/2.85 f_86(v1, v3, v5, v10, 1, v12, v2, v4, v6, 0, 3, 7, 4, 8) -> f_87(v1, v3, v5, v10, 1, v12, v2, v4, v6, 0, 3, 7, 4, 8) :|: TRUE 7.13/2.85 f_87(v1, v3, v5, v10, 1, v12, v2, v4, v6, 0, 3, 7, 4, 8) -> f_74(v1, v3, v5, v10, 1, v12, v2, v4, v6, 0, 3, 7, 4, 8) :|: TRUE 7.13/2.85 f_74(v1, v3, v5, v8, 1, v10, v2, v4, v6, 0, 3, 7, 4, 8) -> f_75(v1, v3, v5, v8, 1, v10, v2, v4, v6, 0, 3, 7, 4, 8) :|: 0 = 0 7.13/2.85 Combined rules. Obtained 1 rulesP rules: 7.13/2.85 f_75(v1:0, v3:0, v5:0, v8:0, 1, 1 + v12:0, v2:0, v4:0, v6:0, 0, 3, 7, 4, 8) -> f_75(v1:0, v3:0, v5:0, 1 + v12:0, 1, v12:0, v2:0, v4:0, v6:0, 0, 3, 7, 4, 8) :|: v8:0 > 0 && v12:0 > -2 7.13/2.85 Filtered unneeded arguments: 7.13/2.85 f_75(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> f_75(x4, x6) 7.13/2.85 Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: 7.13/2.85 f_75(v8:0, sum~cons_1~v12:0) -> f_75(1 + v12:0, v12:0) :|: v8:0 > 0 && v12:0 > -2 && sum~cons_1~v12:0 = 1 + v12:0 7.13/2.85 7.13/2.85 ---------------------------------------- 7.13/2.85 7.13/2.85 (8) 7.13/2.85 Obligation: 7.13/2.85 Rules: 7.13/2.85 f_75(v8:0, sum~cons_1~v12:0) -> f_75(1 + v12:0, v12:0) :|: v8:0 > 0 && v12:0 > -2 && sum~cons_1~v12:0 = 1 + v12:0 7.13/2.85 7.13/2.85 ---------------------------------------- 7.13/2.85 7.13/2.85 (9) IntTRSCompressionProof (EQUIVALENT) 7.13/2.85 Compressed rules. 7.13/2.85 ---------------------------------------- 7.13/2.85 7.13/2.85 (10) 7.13/2.85 Obligation: 7.13/2.85 Rules: 7.13/2.85 f_75(v8:0:0, sum~cons_1~v12:0:0) -> f_75(1 + v12:0:0, v12:0:0) :|: v8:0:0 > 0 && v12:0:0 > -2 && sum~cons_1~v12:0:0 = 1 + v12:0:0 7.13/2.85 7.13/2.85 ---------------------------------------- 7.13/2.85 7.13/2.85 (11) PolynomialOrderProcessor (EQUIVALENT) 7.13/2.85 Found the following polynomial interpretation: 7.13/2.85 [f_75(x, x1)] = x1 7.13/2.85 7.13/2.85 The following rules are decreasing: 7.13/2.85 f_75(v8:0:0, sum~cons_1~v12:0:0) -> f_75(1 + v12:0:0, v12:0:0) :|: v8:0:0 > 0 && v12:0:0 > -2 && sum~cons_1~v12:0:0 = 1 + v12:0:0 7.13/2.85 The following rules are bounded: 7.13/2.85 f_75(v8:0:0, sum~cons_1~v12:0:0) -> f_75(1 + v12:0:0, v12:0:0) :|: v8:0:0 > 0 && v12:0:0 > -2 && sum~cons_1~v12:0:0 = 1 + v12:0:0 7.13/2.85 7.13/2.85 ---------------------------------------- 7.13/2.85 7.13/2.85 (12) 7.13/2.85 YES 7.71/3.22 EOF