/export/starexec/sandbox/solver/bin/starexec_run_c /export/starexec/sandbox/benchmark/theBenchmark.c /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.c # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given C Problem could be proven: (0) C Problem (1) CToLLVMProof [EQUIVALENT, 180 ms] (2) LLVM problem (3) LLVMToTerminationGraphProof [EQUIVALENT, 803 ms] (4) LLVM Symbolic Execution Graph (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] (6) LLVM Symbolic Execution SCC (7) SCC2IRS [SOUND, 43 ms] (8) IntTRS (9) TerminationGraphProcessor [EQUIVALENT, 33 ms] (10) IntTRS (11) IntTRSCompressionProof [EQUIVALENT, 0 ms] (12) IntTRS (13) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (14) YES ---------------------------------------- (0) Obligation: c file /export/starexec/sandbox/benchmark/theBenchmark.c ---------------------------------------- (1) CToLLVMProof (EQUIVALENT) Compiled c-file /export/starexec/sandbox/benchmark/theBenchmark.c to LLVM. ---------------------------------------- (2) Obligation: LLVM Problem Aliases: Data layout: "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" Machine: "x86_64-pc-linux-gnu" Type definitions: Global variables: Function declarations and definitions: *BasicFunctionTypename: "__VERIFIER_nondet_int" returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc *BasicFunctionTypename: "mlog" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: (x i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc 0: %1 = alloca i32, align 4 %res = alloca i32, align 4 store %x, %1 store 0, %res br %2 2: %3 = load %1 %4 = icmp sgt %3 1 br %4, %5, %10 5: %6 = load %1 %7 = sdiv %6 2 store %7, %1 %8 = load %res %9 = add %8 1 store %9, %res br %2 10: %11 = load %res ret %11 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 0: %1 = alloca i32, align 4 store 0, %1 %2 = call i32 @__VERIFIER_nondet_int() %3 = call i32 @mlog(i32 %2) ret %3 Analyze Termination of all function calls matching the pattern: main() ---------------------------------------- (3) LLVMToTerminationGraphProof (EQUIVALENT) Constructed symbolic execution graph for LLVM program and proved memory safety. ---------------------------------------- (4) Obligation: SE Graph ---------------------------------------- (5) SymbolicExecutionGraphToSCCProof (SOUND) Splitted symbolic execution graph to 1 SCC. ---------------------------------------- (6) Obligation: SCC ---------------------------------------- (7) SCC2IRS (SOUND) Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: Generated rules. Obtained 12 rulesP rules: 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 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 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 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 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 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 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 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 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 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 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 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 Combined rules. Obtained 1 rulesP rules: 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 Filtered unneeded arguments: f_181(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16) -> f_181(x4, x8) Removed division, modulo operations, cleaned up constraints. Obtained 3 rules.P rules: f_181(v86:0, v88:0) -> f_181'(v86:0, v88:0) :|: v86:0 > 1 && v88:0 > 0 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 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) Obligation: Rules: f_181(v86:0, v88:0) -> f_181'(v86:0, v88:0) :|: v86:0 > 1 && v88:0 > 0 f_181'(x, x1) -> f_181(x2, 1 + x1) :|: x1 > 0 && x > 1 && x < 0 && x - 2 * x2 <= 0 && x - 2 * x2 > -2 f_181'(x3, x4) -> f_181(x5, 1 + x4) :|: x3 > 1 && x4 > 0 && x3 - 2 * x5 < 2 && x3 - 2 * x5 >= 0 ---------------------------------------- (9) TerminationGraphProcessor (EQUIVALENT) Constructed the termination graph and obtained one non-trivial SCC. ---------------------------------------- (10) Obligation: Rules: f_181(v86:0, v88:0) -> f_181'(v86:0, v88:0) :|: v86:0 > 1 && v88:0 > 0 f_181'(x3, x4) -> f_181(x5, 1 + x4) :|: x3 > 1 && x4 > 0 && x3 - 2 * x5 < 2 && x3 - 2 * x5 >= 0 ---------------------------------------- (11) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (12) Obligation: Rules: 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 ---------------------------------------- (13) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f_181(x, x1)] = -2 + x The following rules are decreasing: 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 The following rules are bounded: 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 ---------------------------------------- (14) YES