7.66/2.95 YES 7.71/2.98 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 7.71/2.98 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 7.71/2.98 7.71/2.98 7.71/2.98 Termination of the given C Problem could be proven: 7.71/2.98 7.71/2.98 (0) C Problem 7.71/2.98 (1) CToLLVMProof [EQUIVALENT, 176 ms] 7.71/2.98 (2) LLVM problem 7.71/2.98 (3) LLVMToTerminationGraphProof [EQUIVALENT, 491 ms] 7.71/2.98 (4) LLVM Symbolic Execution Graph 7.71/2.98 (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] 7.71/2.98 (6) LLVM Symbolic Execution SCC 7.71/2.98 (7) SCC2IRS [SOUND, 56 ms] 7.71/2.98 (8) IntTRS 7.71/2.98 (9) IntTRSCompressionProof [EQUIVALENT, 0 ms] 7.71/2.98 (10) IntTRS 7.71/2.98 (11) RankingReductionPairProof [EQUIVALENT, 24 ms] 7.71/2.98 (12) YES 7.71/2.98 7.71/2.98 7.71/2.98 ---------------------------------------- 7.71/2.98 7.71/2.98 (0) 7.71/2.98 Obligation: 7.71/2.98 c file /export/starexec/sandbox/benchmark/theBenchmark.c 7.71/2.98 ---------------------------------------- 7.71/2.98 7.71/2.98 (1) CToLLVMProof (EQUIVALENT) 7.71/2.98 Compiled c-file /export/starexec/sandbox/benchmark/theBenchmark.c to LLVM. 7.71/2.98 ---------------------------------------- 7.71/2.98 7.71/2.98 (2) 7.71/2.98 Obligation: 7.71/2.98 LLVM Problem 7.71/2.98 7.71/2.98 Aliases: 7.71/2.98 7.71/2.98 Data layout: 7.71/2.98 7.71/2.98 "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" 7.71/2.98 7.71/2.98 Machine: 7.71/2.98 7.71/2.98 "x86_64-pc-linux-gnu" 7.71/2.98 7.71/2.98 Type definitions: 7.71/2.98 7.71/2.98 Global variables: 7.71/2.98 7.71/2.98 Function declarations and definitions: 7.71/2.98 7.71/2.98 *BasicFunctionTypename: "__VERIFIER_nondet_int" returnParam: i32 parameters: () variableLength: true visibilityType: DEFAULT callingConvention: ccc 7.71/2.98 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 7.71/2.98 0: 7.71/2.98 %1 = alloca i32, align 4 7.71/2.98 %x = alloca i32, align 4 7.71/2.98 %old_x = alloca i32, align 4 7.71/2.98 store 0, %1 7.71/2.98 %2 = call i32 (...)* @__VERIFIER_nondet_int() 7.71/2.98 store %2, %x 7.71/2.98 br %3 7.71/2.98 3: 7.71/2.98 %4 = load %x 7.71/2.98 %5 = icmp sgt %4 1 7.71/2.98 br %5, %6, %15 7.71/2.98 6: 7.71/2.98 %7 = load %x 7.71/2.98 store %7, %old_x 7.71/2.98 %8 = call i32 (...)* @__VERIFIER_nondet_int() 7.71/2.98 store %8, %x 7.71/2.98 %9 = load %x 7.71/2.98 %10 = mul 2 %9 7.71/2.98 %11 = load %old_x 7.71/2.98 %12 = icmp sgt %10 %11 7.71/2.98 br %12, %13, %14 7.71/2.98 13: 7.71/2.98 br %15 7.71/2.98 14: 7.71/2.98 br %3 7.71/2.98 15: 7.71/2.98 ret 0 7.71/2.98 7.71/2.98 7.71/2.98 Analyze Termination of all function calls matching the pattern: 7.71/2.98 main() 7.71/2.98 ---------------------------------------- 7.71/2.98 7.71/2.98 (3) LLVMToTerminationGraphProof (EQUIVALENT) 7.71/2.98 Constructed symbolic execution graph for LLVM program and proved memory safety. 7.71/2.98 ---------------------------------------- 7.71/2.98 7.71/2.98 (4) 7.71/2.98 Obligation: 7.71/2.98 SE Graph 7.71/2.98 ---------------------------------------- 7.71/2.98 7.71/2.98 (5) SymbolicExecutionGraphToSCCProof (SOUND) 7.71/2.98 Splitted symbolic execution graph to 1 SCC. 7.71/2.98 ---------------------------------------- 7.71/2.98 7.71/2.98 (6) 7.71/2.98 Obligation: 7.71/2.98 SCC 7.71/2.98 ---------------------------------------- 7.71/2.98 7.71/2.98 (7) SCC2IRS (SOUND) 7.71/2.98 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 7.71/2.98 Generated rules. Obtained 16 rulesP rules: 7.71/2.98 f_122(v30, v31, v32, v33, v36, 1, v34, v37, 0, v39, v40, v41, 3, 2, 4) -> f_123(v30, v31, v32, v33, v36, 1, v34, v37, 0, v39, v40, v41, 3, 2, 4) :|: 1 < v36 && 4 <= v37 && 4 <= v34 7.71/2.98 f_123(v30, v31, v32, v33, v36, 1, v34, v37, 0, v39, v40, v41, 3, 2, 4) -> f_125(v30, v31, v32, v33, v36, 1, v34, v37, 0, v39, v40, v41, 3, 2, 4) :|: 0 = 0 7.71/2.98 f_125(v30, v31, v32, v33, v36, 1, v34, v37, 0, v39, v40, v41, 3, 2, 4) -> f_127(v30, v31, v32, v33, v36, 1, v34, v37, 0, v39, v40, v41, 3, 2, 4) :|: TRUE 7.71/2.98 f_127(v30, v31, v32, v33, v36, 1, v34, v37, 0, v39, v40, v41, 3, 2, 4) -> f_129(v30, v31, v32, v33, v36, 1, v37, v34, 0, v39, v40, v41, 3, 2, 4) :|: 0 = 0 7.71/2.98 f_129(v30, v31, v32, v33, v36, 1, v37, v34, 0, v39, v40, v41, 3, 2, 4) -> f_130(v30, v31, v32, v33, v36, 1, v37, v34, 0, v39, v40, v41, 3, 2, 4) :|: TRUE 7.71/2.98 f_130(v30, v31, v32, v33, v36, 1, v37, v34, 0, v39, v40, v41, 3, 2, 4) -> f_131(v30, v31, v32, v33, v36, 1, v47, v37, v34, 0, v39, v40, v41, 3, 2, 4) :|: TRUE 7.71/2.98 f_131(v30, v31, v32, v33, v36, 1, v47, v37, v34, 0, v39, v40, v41, 3, 2, 4) -> f_132(v30, v31, v32, v33, v36, 1, v47, v37, v34, 0, v39, v40, v41, 3, 2, 4) :|: TRUE 7.71/2.98 f_132(v30, v31, v32, v33, v36, 1, v47, v37, v34, 0, v39, v40, v41, 3, 2, 4) -> f_133(v30, v31, v32, v33, v36, 1, v47, v37, v34, 0, v39, v40, v41, 3, 2, 4) :|: 0 = 0 7.71/2.98 f_133(v30, v31, v32, v33, v36, 1, v47, v37, v34, 0, v39, v40, v41, 3, 2, 4) -> f_134(v30, v31, v32, v33, v36, 1, v47, v49, v34, 0, v39, v40, v41, 3, 2, 4) :|: v49 = 2 * v47 7.71/2.98 f_134(v30, v31, v32, v33, v36, 1, v47, v49, v34, 0, v39, v40, v41, 3, 2, 4) -> f_135(v30, v31, v32, v33, v36, 1, v47, v49, 0, v39, v40, v41, 3, 2, 4) :|: 0 = 0 7.71/2.98 f_135(v30, v31, v32, v33, v36, 1, v47, v49, 0, v39, v40, v41, 3, 2, 4) -> f_137(v30, v31, v32, v33, v36, 1, v47, v49, 0, v39, v40, v41, 3, 2, 4) :|: v49 <= v36 7.71/2.98 f_137(v30, v31, v32, v33, v36, 1, v47, v49, 0, v39, v40, v41, 3, 2, 4) -> f_139(v30, v31, v32, v33, v36, 1, v47, v49, 0, v39, v40, v41, 3, 2, 4) :|: 0 = 0 7.71/2.98 f_139(v30, v31, v32, v33, v36, 1, v47, v49, 0, v39, v40, v41, 3, 2, 4) -> f_141(v30, v31, v32, v33, v36, 1, v47, v49, 0, v39, v40, v41, 3, 2, 4) :|: TRUE 7.71/2.98 f_141(v30, v31, v32, v33, v36, 1, v47, v49, 0, v39, v40, v41, 3, 2, 4) -> f_143(v30, v31, v32, v33, v36, 1, v47, v49, 0, v39, v40, v41, 3, 2, 4) :|: TRUE 7.71/2.98 f_143(v30, v31, v32, v33, v36, 1, v47, v49, 0, v39, v40, v41, 3, 2, 4) -> f_121(v30, v31, v32, v33, v36, 1, v47, v49, 0, v39, v40, v41, 3, 2, 4) :|: TRUE 7.71/2.98 f_121(v30, v31, v32, v33, v34, 1, v36, v37, 0, v39, v40, v41, 3, 2, 4) -> f_122(v30, v31, v32, v33, v36, 1, v34, v37, 0, v39, v40, v41, 3, 2, 4) :|: 0 = 0 7.71/2.98 Combined rules. Obtained 1 rulesP rules: 7.71/2.98 f_122(v30:0, v31:0, v32:0, v33:0, v36:0, 1, v34:0, v37:0, 0, v39:0, v40:0, v41:0, 3, 2, 4) -> f_122(v30:0, v31:0, v32:0, v33:0, v47:0, 1, v36:0, 2 * v47:0, 0, v39:0, v40:0, v41:0, 3, 2, 4) :|: v37:0 > 3 && v36:0 > 1 && v36:0 >= 2 * v47:0 && v34:0 > 3 7.71/2.98 Filtered unneeded arguments: 7.71/2.98 f_122(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) -> f_122(x5, x7, x8) 7.71/2.98 Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: 7.71/2.98 f_122(v36:0, v34:0, v37:0) -> f_122(v47:0, v36:0, 2 * v47:0) :|: v36:0 > 1 && v37:0 > 3 && v34:0 > 3 && v36:0 >= 2 * v47:0 7.71/2.98 7.71/2.98 ---------------------------------------- 7.71/2.98 7.71/2.98 (8) 7.71/2.98 Obligation: 7.71/2.98 Rules: 7.71/2.98 f_122(v36:0, v34:0, v37:0) -> f_122(v47:0, v36:0, 2 * v47:0) :|: v36:0 > 1 && v37:0 > 3 && v34:0 > 3 && v36:0 >= 2 * v47:0 7.71/2.98 7.71/2.98 ---------------------------------------- 7.71/2.98 7.71/2.98 (9) IntTRSCompressionProof (EQUIVALENT) 7.71/2.98 Compressed rules. 7.71/2.98 ---------------------------------------- 7.71/2.98 7.71/2.98 (10) 7.71/2.98 Obligation: 7.71/2.98 Rules: 7.71/2.98 f_122(v36:0:0, v34:0:0, v37:0:0) -> f_122(v47:0:0, v36:0:0, 2 * v47:0:0) :|: v34:0:0 > 3 && v36:0:0 >= 2 * v47:0:0 && v37:0:0 > 3 && v36:0:0 > 1 7.71/2.98 7.71/2.98 ---------------------------------------- 7.71/2.98 7.71/2.98 (11) RankingReductionPairProof (EQUIVALENT) 7.71/2.98 Interpretation: 7.71/2.98 [ f_122 ] = 1/4*f_122_3 + 1/2*f_122_1 7.71/2.98 7.71/2.98 The following rules are decreasing: 7.71/2.98 f_122(v36:0:0, v34:0:0, v37:0:0) -> f_122(v47:0:0, v36:0:0, 2 * v47:0:0) :|: v34:0:0 > 3 && v36:0:0 >= 2 * v47:0:0 && v37:0:0 > 3 && v36:0:0 > 1 7.71/2.98 7.71/2.98 The following rules are bounded: 7.71/2.98 f_122(v36:0:0, v34:0:0, v37:0:0) -> f_122(v47:0:0, v36:0:0, 2 * v47:0:0) :|: v34:0:0 > 3 && v36:0:0 >= 2 * v47:0:0 && v37:0:0 > 3 && v36:0:0 > 1 7.71/2.98 7.71/2.98 7.71/2.98 ---------------------------------------- 7.71/2.98 7.71/2.98 (12) 7.71/2.98 YES 7.97/3.04 EOF