8.29/3.17 YES 8.55/3.20 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 8.55/3.20 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 8.55/3.20 8.55/3.20 8.55/3.20 Termination of the given C Problem could be proven: 8.55/3.20 8.55/3.20 (0) C Problem 8.55/3.20 (1) CToLLVMProof [EQUIVALENT, 172 ms] 8.55/3.20 (2) LLVM problem 8.55/3.20 (3) LLVMToTerminationGraphProof [EQUIVALENT, 880 ms] 8.55/3.20 (4) LLVM Symbolic Execution Graph 8.55/3.20 (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] 8.55/3.20 (6) LLVM Symbolic Execution SCC 8.55/3.20 (7) SCC2IRS [SOUND, 44 ms] 8.55/3.20 (8) IntTRS 8.55/3.20 (9) TerminationGraphProcessor [EQUIVALENT, 28 ms] 8.55/3.20 (10) IntTRS 8.55/3.20 (11) IntTRSCompressionProof [EQUIVALENT, 0 ms] 8.55/3.20 (12) IntTRS 8.55/3.20 (13) PolynomialOrderProcessor [EQUIVALENT, 11 ms] 8.55/3.20 (14) YES 8.55/3.20 8.55/3.20 8.55/3.20 ---------------------------------------- 8.55/3.20 8.55/3.20 (0) 8.55/3.20 Obligation: 8.55/3.20 c file /export/starexec/sandbox/benchmark/theBenchmark.c 8.55/3.20 ---------------------------------------- 8.55/3.20 8.55/3.20 (1) CToLLVMProof (EQUIVALENT) 8.55/3.20 Compiled c-file /export/starexec/sandbox/benchmark/theBenchmark.c to LLVM. 8.55/3.20 ---------------------------------------- 8.55/3.20 8.55/3.20 (2) 8.55/3.20 Obligation: 8.55/3.20 LLVM Problem 8.55/3.20 8.55/3.20 Aliases: 8.55/3.20 8.55/3.20 Data layout: 8.55/3.20 8.55/3.20 "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" 8.55/3.20 8.55/3.20 Machine: 8.55/3.20 8.55/3.20 "x86_64-pc-linux-gnu" 8.55/3.20 8.55/3.20 Type definitions: 8.55/3.20 8.55/3.20 Global variables: 8.55/3.20 8.55/3.20 Function declarations and definitions: 8.55/3.20 8.55/3.20 *BasicFunctionTypename: "__VERIFIER_nondet_int" returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 8.55/3.20 *BasicFunctionTypename: "mlog" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: (x i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc 8.55/3.20 0: 8.55/3.20 %1 = alloca i32, align 4 8.55/3.20 %res = alloca i32, align 4 8.55/3.20 store %x, %1 8.55/3.20 store 0, %res 8.55/3.20 br %2 8.55/3.20 2: 8.55/3.20 %3 = load %1 8.55/3.20 %4 = icmp sgt %3 1 8.55/3.20 br %4, %5, %10 8.55/3.20 5: 8.55/3.20 %6 = load %1 8.55/3.20 %7 = sdiv %6 2 8.55/3.20 store %7, %1 8.55/3.20 %8 = load %res 8.55/3.20 %9 = add %8 1 8.55/3.20 store %9, %res 8.55/3.20 br %2 8.55/3.20 10: 8.55/3.20 %11 = load %res 8.55/3.20 ret %11 8.55/3.20 8.55/3.20 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 8.55/3.20 0: 8.55/3.20 %1 = alloca i32, align 4 8.55/3.20 store 0, %1 8.55/3.20 %2 = call i32 @__VERIFIER_nondet_int() 8.55/3.20 %3 = call i32 @mlog(i32 %2) 8.55/3.20 ret %3 8.55/3.20 8.55/3.20 8.55/3.20 Analyze Termination of all function calls matching the pattern: 8.55/3.20 main() 8.55/3.20 ---------------------------------------- 8.55/3.20 8.55/3.20 (3) LLVMToTerminationGraphProof (EQUIVALENT) 8.55/3.20 Constructed symbolic execution graph for LLVM program and proved memory safety. 8.55/3.20 ---------------------------------------- 8.55/3.20 8.55/3.20 (4) 8.55/3.20 Obligation: 8.55/3.20 SE Graph 8.55/3.20 ---------------------------------------- 8.55/3.20 8.55/3.20 (5) SymbolicExecutionGraphToSCCProof (SOUND) 8.55/3.20 Splitted symbolic execution graph to 1 SCC. 8.55/3.20 ---------------------------------------- 8.55/3.20 8.55/3.20 (6) 8.55/3.20 Obligation: 8.55/3.20 SCC 8.55/3.20 ---------------------------------------- 8.55/3.20 8.55/3.20 (7) SCC2IRS (SOUND) 8.55/3.20 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 8.55/3.20 Generated rules. Obtained 12 rulesP rules: 8.55/3.20 f_181(v81, v82, v83, v86, 1, v84, v87, v88, v89, v90, v91, v92, 0, 3, 2, 4) -> f_182(v81, v82, v83, v86, 1, v84, v87, v88, v89, v90, v91, v92, 0, 3, 2, 4) :|: 1 < v86 8.55/3.20 f_182(v81, v82, v83, v86, 1, v84, v87, v88, v89, v90, v91, v92, 0, 3, 2, 4) -> f_184(v81, v82, v83, v86, 1, v84, v87, v88, v89, v90, v91, v92, 0, 3, 2, 4) :|: 0 = 0 8.55/3.20 f_184(v81, v82, v83, v86, 1, v84, v87, v88, v89, v90, v91, v92, 0, 3, 2, 4) -> f_186(v81, v82, v83, v86, 1, v84, v87, v88, v89, v90, v91, v92, 0, 3, 2, 4) :|: TRUE 8.55/3.20 f_186(v81, v82, v83, v86, 1, v84, v87, v88, v89, v90, v91, v92, 0, 3, 2, 4) -> f_188(v81, v82, v83, v86, 1, v87, v88, v89, v90, v91, v92, 0, 3, 2, 4) :|: 0 = 0 8.55/3.20 f_188(v81, v82, v83, v86, 1, v87, v88, v89, v90, v91, v92, 0, 3, 2, 4) -> f_190(v81, v82, v83, v86, 1, v94, v87, v88, v89, v90, v91, v92, 0, 3, 2, 4) :|: v94 = v86 / 2 8.55/3.20 f_190(v81, v82, v83, v86, 1, v94, v87, v88, v89, v90, v91, v92, 0, 3, 2, 4) -> f_192(v81, v82, v83, v86, 1, v94, v87, v88, v89, v90, v91, v92, 0, 3, 2, 4) :|: TRUE 8.55/3.20 f_192(v81, v82, v83, v86, 1, v94, v87, v88, v89, v90, v91, v92, 0, 3, 2, 4) -> f_193(v81, v82, v83, v86, 1, v94, v88, v89, v90, v91, v92, 0, 3, 2, 4) :|: 0 = 0 8.55/3.20 f_193(v81, v82, v83, v86, 1, v94, v88, v89, v90, v91, v92, 0, 3, 2, 4) -> f_194(v81, v82, v83, v86, 1, v94, v88, v96, v89, v90, v91, v92, 0, 3, 2, 4) :|: v96 = 1 + v88 && 2 <= v96 8.55/3.20 f_194(v81, v82, v83, v86, 1, v94, v88, v96, v89, v90, v91, v92, 0, 3, 2, 4) -> f_195(v81, v82, v83, v86, 1, v94, v88, v96, v89, v90, v91, v92, 0, 3, 2, 4) :|: TRUE 8.55/3.20 f_195(v81, v82, v83, v86, 1, v94, v88, v96, v89, v90, v91, v92, 0, 3, 2, 4) -> f_196(v81, v82, v83, v86, 1, v94, v88, v96, v89, v90, v91, v92, 0, 3, 2, 4) :|: TRUE 8.55/3.20 f_196(v81, v82, v83, v86, 1, v94, v88, v96, v89, v90, v91, v92, 0, 3, 2, 4) -> f_180(v81, v82, v83, v86, 1, v94, v88, v96, v89, v90, v91, v92, 0, 3, 2, 4) :|: TRUE 8.55/3.20 f_180(v81, v82, v83, v84, 1, v86, v87, v88, v89, v90, v91, v92, 0, 3, 2, 4) -> f_181(v81, v82, v83, v86, 1, v84, v87, v88, v89, v90, v91, v92, 0, 3, 2, 4) :|: 0 = 0 8.55/3.20 Combined rules. Obtained 1 rulesP rules: 8.55/3.20 f_181(v81:0, v82:0, v83:0, v86:0, 1, v84:0, v87:0, v88:0, v89:0, v90:0, v91:0, v92:0, 0, 3, 2, 4) -> f_181(v81:0, v82:0, v83:0, v94:0, 1, v86:0, v88:0, 1 + v88:0, v89:0, v90:0, v91:0, v92:0, 0, 3, 2, 4) :|: v86:0 > 1 && v88:0 > 0 && v94:0 = v86:0 / 2 8.55/3.20 Filtered unneeded arguments: 8.55/3.20 f_181(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16) -> f_181(x4, x8) 8.55/3.20 Removed division, modulo operations, cleaned up constraints. Obtained 3 rules.P rules: 8.55/3.20 f_181(v86:0, v88:0) -> f_181'(v86:0, v88:0) :|: v86:0 > 1 && v88:0 > 0 8.55/3.20 f_181'(v86:0, v88:0) -> f_181(div, 1 + v88:0) :|: v88:0 > 0 && v86:0 > 1 && v86:0 < 0 && v86:0 - 2 * div <= 0 && v86:0 - 2 * div > -2 8.55/3.20 f_181'(v86:0, v88:0) -> f_181(div, 1 + v88:0) :|: v86:0 > 1 && v88:0 > 0 && v86:0 - 2 * div < 2 && v86:0 - 2 * div >= 0 8.55/3.20 8.55/3.20 ---------------------------------------- 8.55/3.20 8.55/3.20 (8) 8.55/3.20 Obligation: 8.55/3.20 Rules: 8.55/3.20 f_181(v86:0, v88:0) -> f_181'(v86:0, v88:0) :|: v86:0 > 1 && v88:0 > 0 8.55/3.20 f_181'(x, x1) -> f_181(x2, 1 + x1) :|: x1 > 0 && x > 1 && x < 0 && x - 2 * x2 <= 0 && x - 2 * x2 > -2 8.55/3.20 f_181'(x3, x4) -> f_181(x5, 1 + x4) :|: x3 > 1 && x4 > 0 && x3 - 2 * x5 < 2 && x3 - 2 * x5 >= 0 8.55/3.20 8.55/3.20 ---------------------------------------- 8.55/3.20 8.55/3.20 (9) TerminationGraphProcessor (EQUIVALENT) 8.55/3.20 Constructed the termination graph and obtained one non-trivial SCC. 8.55/3.20 8.55/3.20 ---------------------------------------- 8.55/3.20 8.55/3.20 (10) 8.55/3.20 Obligation: 8.55/3.20 Rules: 8.55/3.20 f_181(v86:0, v88:0) -> f_181'(v86:0, v88:0) :|: v86:0 > 1 && v88:0 > 0 8.55/3.20 f_181'(x3, x4) -> f_181(x5, 1 + x4) :|: x3 > 1 && x4 > 0 && x3 - 2 * x5 < 2 && x3 - 2 * x5 >= 0 8.55/3.20 8.55/3.20 ---------------------------------------- 8.55/3.20 8.55/3.20 (11) IntTRSCompressionProof (EQUIVALENT) 8.55/3.20 Compressed rules. 8.55/3.20 ---------------------------------------- 8.55/3.20 8.55/3.20 (12) 8.55/3.20 Obligation: 8.55/3.20 Rules: 8.55/3.20 f_181(v86:0:0, v88:0:0) -> f_181(x5:0, 1 + v88:0:0) :|: v86:0:0 - 2 * x5:0 >= 0 && v86:0:0 - 2 * x5:0 < 2 && v88:0:0 > 0 && v86:0:0 > 1 8.55/3.20 8.55/3.20 ---------------------------------------- 8.55/3.20 8.55/3.20 (13) PolynomialOrderProcessor (EQUIVALENT) 8.55/3.20 Found the following polynomial interpretation: 8.55/3.20 [f_181(x, x1)] = -2 + x 8.55/3.20 8.55/3.20 The following rules are decreasing: 8.55/3.20 f_181(v86:0:0, v88:0:0) -> f_181(x5:0, 1 + v88:0:0) :|: v86:0:0 - 2 * x5:0 >= 0 && v86:0:0 - 2 * x5:0 < 2 && v88:0:0 > 0 && v86:0:0 > 1 8.55/3.20 The following rules are bounded: 8.55/3.20 f_181(v86:0:0, v88:0:0) -> f_181(x5:0, 1 + v88:0:0) :|: v86:0:0 - 2 * x5:0 >= 0 && v86:0:0 - 2 * x5:0 < 2 && v88:0:0 > 0 && v86:0:0 > 1 8.55/3.20 8.55/3.20 ---------------------------------------- 8.55/3.20 8.55/3.20 (14) 8.55/3.20 YES 8.55/3.24 EOF