13.34/4.67 YES 13.34/4.68 proof of /export/starexec/sandbox2/benchmark/theBenchmark.c 13.34/4.68 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 13.34/4.68 13.34/4.68 13.34/4.68 Termination of the given C Problem could be proven: 13.34/4.68 13.34/4.68 (0) C Problem 13.34/4.68 (1) CToLLVMProof [EQUIVALENT, 177 ms] 13.34/4.68 (2) LLVM problem 13.34/4.68 (3) LLVMToTerminationGraphProof [EQUIVALENT, 2137 ms] 13.34/4.68 (4) LLVM Symbolic Execution Graph 13.34/4.68 (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] 13.34/4.68 (6) LLVM Symbolic Execution SCC 13.34/4.68 (7) SCC2IRS [SOUND, 15 ms] 13.34/4.68 (8) IntTRS 13.34/4.68 (9) IntTRSCompressionProof [EQUIVALENT, 0 ms] 13.34/4.68 (10) IntTRS 13.34/4.68 (11) PolynomialOrderProcessor [EQUIVALENT, 11 ms] 13.34/4.68 (12) YES 13.34/4.68 13.34/4.68 13.34/4.68 ---------------------------------------- 13.34/4.68 13.34/4.68 (0) 13.34/4.68 Obligation: 13.34/4.68 c file /export/starexec/sandbox2/benchmark/theBenchmark.c 13.34/4.68 ---------------------------------------- 13.34/4.68 13.34/4.68 (1) CToLLVMProof (EQUIVALENT) 13.34/4.68 Compiled c-file /export/starexec/sandbox2/benchmark/theBenchmark.c to LLVM. 13.34/4.68 ---------------------------------------- 13.34/4.68 13.34/4.68 (2) 13.34/4.68 Obligation: 13.34/4.68 LLVM Problem 13.34/4.68 13.34/4.68 Aliases: 13.34/4.68 13.34/4.68 Data layout: 13.34/4.68 13.34/4.68 "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" 13.34/4.68 13.34/4.68 Machine: 13.34/4.68 13.34/4.68 "x86_64-pc-linux-gnu" 13.34/4.68 13.34/4.68 Type definitions: 13.34/4.68 13.34/4.68 Global variables: 13.34/4.68 13.34/4.68 Function declarations and definitions: 13.34/4.68 13.34/4.68 *BasicFunctionTypename: "__VERIFIER_error" returnParam: BasicVoidType parameters: () variableLength: true visibilityType: DEFAULT callingConvention: ccc 13.34/4.68 *BasicFunctionTypename: "sum" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: (n i32, m i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc 13.34/4.68 0: 13.34/4.68 %1 = alloca i32, align 4 13.34/4.68 %2 = alloca i32, align 4 13.34/4.68 %3 = alloca i32, align 4 13.34/4.68 store %n, %2 13.34/4.68 store %m, %3 13.34/4.68 %4 = load %2 13.34/4.68 %5 = icmp sle %4 0 13.34/4.68 br %5, %6, %10 13.34/4.68 6: 13.34/4.68 %7 = load %3 13.34/4.68 %8 = load %2 13.34/4.68 %9 = add %7 %8 13.34/4.68 store %9, %1 13.34/4.68 br %16 13.34/4.68 10: 13.34/4.68 %11 = load %2 13.34/4.68 %12 = sub %11 1 13.34/4.68 %13 = load %3 13.34/4.68 %14 = add %13 1 13.34/4.68 %15 = call i32 @sum(i32 %12, i32 %14) 13.34/4.68 store %15, %1 13.34/4.68 br %16 13.34/4.68 16: 13.34/4.68 %17 = load %1 13.34/4.68 ret %17 13.34/4.68 13.34/4.68 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 13.34/4.68 0: 13.34/4.68 %1 = alloca i32, align 4 13.34/4.68 %a = alloca i32, align 4 13.34/4.68 %b = alloca i32, align 4 13.34/4.68 %result = alloca i32, align 4 13.34/4.68 store 0, %1 13.34/4.68 store 2, %a 13.34/4.68 store 3, %b 13.34/4.68 %2 = load %a 13.34/4.68 %3 = load %b 13.34/4.68 %4 = call i32 @sum(i32 %2, i32 %3) 13.34/4.68 store %4, %result 13.34/4.68 %5 = load %result 13.34/4.68 %6 = load %a 13.34/4.68 %7 = load %b 13.34/4.68 %8 = add %6 %7 13.34/4.68 %9 = icmp eq %5 %8 13.34/4.68 br %9, %10, %12 13.34/4.68 10: 13.34/4.68 br %11 13.34/4.68 11: 13.34/4.68 Unnamed Call-Instruction = call BasicVoidType (...)* @__VERIFIER_error() 13.34/4.68 br %12 13.34/4.68 12: 13.34/4.68 %13 = load %1 13.34/4.68 ret %13 13.34/4.68 13.34/4.68 13.34/4.68 Analyze Termination of all function calls matching the pattern: 13.34/4.68 main() 13.34/4.68 ---------------------------------------- 13.34/4.68 13.34/4.68 (3) LLVMToTerminationGraphProof (EQUIVALENT) 13.34/4.68 Constructed symbolic execution graph for LLVM program and proved memory safety. 13.34/4.68 ---------------------------------------- 13.34/4.68 13.34/4.68 (4) 13.34/4.68 Obligation: 13.34/4.68 SE Graph 13.34/4.68 ---------------------------------------- 13.34/4.68 13.34/4.68 (5) SymbolicExecutionGraphToSCCProof (SOUND) 13.34/4.68 Splitted symbolic execution graph to 1 SCC. 13.34/4.68 ---------------------------------------- 13.34/4.68 13.34/4.68 (6) 13.34/4.68 Obligation: 13.34/4.68 SCC 13.34/4.68 ---------------------------------------- 13.34/4.68 13.34/4.68 (7) SCC2IRS (SOUND) 13.34/4.68 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 13.34/4.68 Generated rules. Obtained 16 rulesP rules: 13.34/4.68 f_204(v77, v78, v90, v79, v80, v81, v82, v83, v84, v85, v86, v91, 0, 2, 3, 1, 4) -> f_205(v77, v78, v90, v92, v79, v80, v81, v82, v83, v84, v85, v86, v91, v93, 0, 2, 3, 1, 4) :|: 1 <= v92 && v93 = 3 + v92 && 4 <= v93 13.34/4.68 f_205(v77, v78, v90, v92, v79, v80, v81, v82, v83, v84, v85, v86, v91, v93, 0, 2, 3, 1, 4) -> f_206(v77, v78, v90, v92, v94, v79, v80, v81, v82, v83, v84, v85, v86, v91, v93, v95, 0, 2, 3, 1, 4) :|: 1 <= v94 && v95 = 3 + v94 && 4 <= v95 13.34/4.68 f_206(v77, v78, v90, v92, v94, v79, v80, v81, v82, v83, v84, v85, v86, v91, v93, v95, 0, 2, 3, 1, 4) -> f_207(v77, v78, v90, v92, v94, v79, v80, v81, v82, v83, v84, v85, v86, v91, v93, v95, 0, 2, 3, 1, 4) :|: TRUE 13.34/4.68 f_207(v77, v78, v90, v92, v94, v79, v80, v81, v82, v83, v84, v85, v86, v91, v93, v95, 0, 2, 3, 1, 4) -> f_208(v77, v78, v90, v92, v94, v79, v80, v81, v82, v83, v84, v85, v86, v91, v93, v95, 0, 2, 3, 1, 4) :|: TRUE 13.34/4.68 f_208(v77, v78, v90, v92, v94, v79, v80, v81, v82, v83, v84, v85, v86, v91, v93, v95, 0, 2, 3, 1, 4) -> f_209(v77, v78, v90, v92, v94, v79, v80, v81, v82, v83, v84, v85, v86, v91, v93, v95, 0, 2, 3, 1, 4) :|: 0 = 0 13.34/4.68 f_209(v77, v78, v90, v92, v94, v79, v80, v81, v82, v83, v84, v85, v86, v91, v93, v95, 0, 2, 3, 1, 4) -> f_211(v77, v78, v90, v92, v94, v79, v80, v81, v82, v83, v84, v85, v86, v91, v93, v95, 0, 2, 3, 1, 4) :|: 0 < v77 13.34/4.68 f_211(v77, v78, v90, v92, v94, v79, v80, v81, v82, v83, v84, v85, v86, v91, v93, v95, 0, 2, 3, 1, 4) -> f_213(v77, v78, v90, v92, v94, 0, v79, v80, v81, v82, v83, v84, v85, v86, v91, v93, v95, 2, 3, 1, 4) :|: 0 = 0 13.34/4.68 f_213(v77, v78, v90, v92, v94, 0, v79, v80, v81, v82, v83, v84, v85, v86, v91, v93, v95, 2, 3, 1, 4) -> f_215(v77, v78, v90, v92, v94, 0, v79, v80, v81, v82, v83, v84, v85, v86, v91, v93, v95, 2, 3, 1, 4) :|: TRUE 13.34/4.68 f_215(v77, v78, v90, v92, v94, 0, v79, v80, v81, v82, v83, v84, v85, v86, v91, v93, v95, 2, 3, 1, 4) -> f_217(v77, v78, v90, v92, v94, 0, v79, v80, v81, v82, v83, v84, v85, v86, v91, v93, v95, 2, 3, 1, 4) :|: 0 = 0 13.34/4.68 f_217(v77, v78, v90, v92, v94, 0, v79, v80, v81, v82, v83, v84, v85, v86, v91, v93, v95, 2, 3, 1, 4) -> f_219(v77, v78, v90, v92, v94, 0, v98, v79, v80, v81, v82, v83, v84, v85, v86, v91, v93, v95, 2, 3, 1, 4) :|: 1 + v98 = v77 && 0 <= v98 && v98 <= 1 13.34/4.68 f_219(v77, v78, v90, v92, v94, 0, v98, v79, v80, v81, v82, v83, v84, v85, v86, v91, v93, v95, 2, 3, 1, 4) -> f_221(v77, v78, v90, v92, v94, 0, v98, v79, v80, v81, v82, v83, v84, v85, v86, v91, v93, v95, 2, 3, 1, 4) :|: 0 = 0 13.34/4.68 f_221(v77, v78, v90, v92, v94, 0, v98, v79, v80, v81, v82, v83, v84, v85, v86, v91, v93, v95, 2, 3, 1, 4) -> f_223(v77, v78, v90, v92, v94, 0, v98, v100, v79, v80, v81, v82, v83, v84, v85, v86, v91, v93, v95, 2, 3, 1, 4) :|: v100 = 1 + v78 && 4 <= v100 13.34/4.68 f_223(v77, v78, v90, v92, v94, 0, v98, v100, v79, v80, v81, v82, v83, v84, v85, v86, v91, v93, v95, 2, 3, 1, 4) -> f_225(v98, v100, v79, v80, v81, v82, v83, v84, v85, v86, v90, v91, v92, v93, v94, v95, 0, 2, 3, v77, v78, 1, 4) :|: 0 = 0 13.34/4.68 f_225(v98, v100, v79, v80, v81, v82, v83, v84, v85, v86, v90, v91, v92, v93, v94, v95, 0, 2, 3, v77, v78, 1, 4) -> f_227(v98, v100, v79, v80, v81, v82, v83, v84, v85, v86, v90, v91, v92, v93, v94, v95, 0, 2, 3, v77, v78, 1, 4) :|: TRUE 13.34/4.68 f_227(v98, v100, v79, v80, v81, v82, v83, v84, v85, v86, v90, v91, v92, v93, v94, v95, 0, 2, 3, v77, v78, 1, 4) -> f_203(v98, v100, v79, v80, v81, v82, v83, v84, v85, v86, 0, 2, 3, 1, 4) :|: TRUE 13.34/4.68 f_203(v77, v78, v79, v80, v81, v82, v83, v84, v85, v86, 0, 2, 3, 1, 4) -> f_204(v77, v78, v90, v79, v80, v81, v82, v83, v84, v85, v86, v91, 0, 2, 3, 1, 4) :|: 1 <= v90 && v91 = 3 + v90 && 4 <= v91 13.34/4.68 Combined rules. Obtained 1 rulesP rules: 13.34/4.68 f_204(1 + v98:0, v78:0, v90:0, v79:0, v80:0, v81:0, v82:0, v83:0, v84:0, v85:0, v86:0, v91:0, 0, 2, 3, 1, 4) -> f_204(v98:0, 1 + v78:0, v90:1, v79:0, v80:0, v81:0, v82:0, v83:0, v84:0, v85:0, v86:0, 3 + v90:1, 0, 2, 3, 1, 4) :|: v94:0 > 0 && v92:0 > 0 && v98:0 > -1 && v98:0 < 2 && v78:0 > 2 && v90:1 > 0 13.34/4.68 Filtered unneeded arguments: 13.34/4.68 f_204(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17) -> f_204(x1, x2) 13.34/4.68 Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: 13.34/4.68 f_204(sum~cons_1~v98:0, v78:0) -> f_204(v98:0, 1 + v78:0) :|: v98:0 < 2 && v78:0 > 2 && v98:0 > -1 && sum~cons_1~v98:0 = 1 + v98:0 13.34/4.68 13.34/4.68 ---------------------------------------- 13.34/4.68 13.34/4.68 (8) 13.34/4.68 Obligation: 13.34/4.68 Rules: 13.34/4.68 f_204(sum~cons_1~v98:0, v78:0) -> f_204(v98:0, 1 + v78:0) :|: v98:0 < 2 && v78:0 > 2 && v98:0 > -1 && sum~cons_1~v98:0 = 1 + v98:0 13.34/4.68 13.34/4.68 ---------------------------------------- 13.34/4.68 13.34/4.68 (9) IntTRSCompressionProof (EQUIVALENT) 13.34/4.68 Compressed rules. 13.34/4.68 ---------------------------------------- 13.34/4.68 13.34/4.68 (10) 13.34/4.68 Obligation: 13.34/4.68 Rules: 13.34/4.68 f_204(sum~cons_1~v98:0:0, v78:0:0) -> f_204(v98:0:0, 1 + v78:0:0) :|: v98:0:0 < 2 && v78:0:0 > 2 && v98:0:0 > -1 && sum~cons_1~v98:0:0 = 1 + v98:0:0 13.34/4.68 13.34/4.68 ---------------------------------------- 13.34/4.68 13.34/4.68 (11) PolynomialOrderProcessor (EQUIVALENT) 13.34/4.68 Found the following polynomial interpretation: 13.34/4.68 [f_204(x, x1)] = x 13.34/4.68 13.34/4.68 The following rules are decreasing: 13.34/4.68 f_204(sum~cons_1~v98:0:0, v78:0:0) -> f_204(v98:0:0, 1 + v78:0:0) :|: v98:0:0 < 2 && v78:0:0 > 2 && v98:0:0 > -1 && sum~cons_1~v98:0:0 = 1 + v98:0:0 13.34/4.68 The following rules are bounded: 13.34/4.68 f_204(sum~cons_1~v98:0:0, v78:0:0) -> f_204(v98:0:0, 1 + v78:0:0) :|: v98:0:0 < 2 && v78:0:0 > 2 && v98:0:0 > -1 && sum~cons_1~v98:0:0 = 1 + v98:0:0 13.34/4.68 13.34/4.68 ---------------------------------------- 13.34/4.68 13.34/4.68 (12) 13.34/4.68 YES 13.70/4.71 EOF