6.68/2.83 YES 6.68/2.84 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 6.68/2.84 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 6.68/2.84 6.68/2.84 6.68/2.84 Termination of the given C Problem could be proven: 6.68/2.84 6.68/2.84 (0) C Problem 6.68/2.84 (1) CToLLVMProof [EQUIVALENT, 174 ms] 6.68/2.84 (2) LLVM problem 6.68/2.84 (3) LLVMToTerminationGraphProof [EQUIVALENT, 486 ms] 6.68/2.84 (4) LLVM Symbolic Execution Graph 6.68/2.84 (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] 6.68/2.84 (6) LLVM Symbolic Execution SCC 6.68/2.84 (7) SCC2IRS [SOUND, 74 ms] 6.68/2.84 (8) IntTRS 6.68/2.84 (9) IntTRSCompressionProof [EQUIVALENT, 0 ms] 6.68/2.84 (10) IntTRS 6.68/2.84 (11) RankingReductionPairProof [EQUIVALENT, 21 ms] 6.68/2.84 (12) YES 6.68/2.84 6.68/2.84 6.68/2.84 ---------------------------------------- 6.68/2.84 6.68/2.84 (0) 6.68/2.84 Obligation: 6.68/2.84 c file /export/starexec/sandbox/benchmark/theBenchmark.c 6.68/2.84 ---------------------------------------- 6.68/2.84 6.68/2.84 (1) CToLLVMProof (EQUIVALENT) 6.68/2.84 Compiled c-file /export/starexec/sandbox/benchmark/theBenchmark.c to LLVM. 6.68/2.84 ---------------------------------------- 6.68/2.84 6.68/2.84 (2) 6.68/2.84 Obligation: 6.68/2.84 LLVM Problem 6.68/2.84 6.68/2.84 Aliases: 6.68/2.84 6.68/2.84 Data layout: 6.68/2.84 6.68/2.84 "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" 6.68/2.84 6.68/2.84 Machine: 6.68/2.84 6.68/2.84 "x86_64-pc-linux-gnu" 6.68/2.84 6.68/2.84 Type definitions: 6.68/2.84 6.68/2.84 Global variables: 6.68/2.84 6.68/2.84 Function declarations and definitions: 6.68/2.84 6.68/2.84 *BasicFunctionTypename: "__VERIFIER_nondet_int" returnParam: i32 parameters: () variableLength: true visibilityType: DEFAULT callingConvention: ccc 6.68/2.84 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 6.68/2.84 0: 6.68/2.84 %1 = alloca i32, align 4 6.68/2.84 %x = alloca i32, align 4 6.68/2.84 %old_x = alloca i32, align 4 6.68/2.84 store 0, %1 6.68/2.84 %2 = call i32 (...)* @__VERIFIER_nondet_int() 6.68/2.84 store %2, %x 6.68/2.84 br %3 6.68/2.84 3: 6.68/2.84 %4 = load %x 6.68/2.84 %5 = icmp sgt %4 0 6.68/2.84 br %5, %6, %15 6.68/2.84 6: 6.68/2.84 %7 = load %x 6.68/2.84 store %7, %old_x 6.68/2.84 %8 = call i32 (...)* @__VERIFIER_nondet_int() 6.68/2.84 store %8, %x 6.68/2.84 %9 = load %x 6.68/2.84 %10 = mul 2 %9 6.68/2.84 %11 = load %old_x 6.68/2.84 %12 = icmp sgt %10 %11 6.68/2.84 br %12, %13, %14 6.68/2.84 13: 6.68/2.84 br %15 6.68/2.84 14: 6.68/2.84 br %3 6.68/2.84 15: 6.68/2.84 ret 0 6.68/2.84 6.68/2.84 6.68/2.84 Analyze Termination of all function calls matching the pattern: 6.68/2.84 main() 6.68/2.84 ---------------------------------------- 6.68/2.84 6.68/2.84 (3) LLVMToTerminationGraphProof (EQUIVALENT) 6.68/2.84 Constructed symbolic execution graph for LLVM program and proved memory safety. 6.68/2.84 ---------------------------------------- 6.68/2.84 6.68/2.84 (4) 6.68/2.84 Obligation: 6.68/2.84 SE Graph 6.68/2.84 ---------------------------------------- 6.68/2.84 6.68/2.84 (5) SymbolicExecutionGraphToSCCProof (SOUND) 6.68/2.84 Splitted symbolic execution graph to 1 SCC. 6.68/2.84 ---------------------------------------- 6.68/2.84 6.68/2.84 (6) 6.68/2.84 Obligation: 6.68/2.84 SCC 6.68/2.84 ---------------------------------------- 6.68/2.84 6.68/2.84 (7) SCC2IRS (SOUND) 6.68/2.84 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 6.68/2.84 Generated rules. Obtained 16 rulesP rules: 6.68/2.84 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) :|: 0 < v36 && 2 <= v37 && 2 <= v34 6.68/2.84 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 6.68/2.84 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 6.68/2.84 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 6.68/2.84 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 6.68/2.84 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 6.68/2.84 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 6.68/2.84 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 6.68/2.84 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 6.68/2.84 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 6.68/2.84 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 6.68/2.84 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 6.68/2.84 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 6.68/2.84 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 6.68/2.84 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 6.68/2.84 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 6.68/2.84 Combined rules. Obtained 1 rulesP rules: 6.68/2.84 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 > 1 && v36:0 > 0 && v36:0 >= 2 * v47:0 && v34:0 > 1 6.68/2.84 Filtered unneeded arguments: 6.68/2.84 f_122(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) -> f_122(x5, x7, x8) 6.68/2.84 Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: 6.68/2.84 f_122(v36:0, v34:0, v37:0) -> f_122(v47:0, v36:0, 2 * v47:0) :|: v36:0 > 0 && v37:0 > 1 && v34:0 > 1 && v36:0 >= 2 * v47:0 6.68/2.84 6.68/2.84 ---------------------------------------- 6.68/2.84 6.68/2.84 (8) 6.68/2.84 Obligation: 6.68/2.84 Rules: 6.68/2.84 f_122(v36:0, v34:0, v37:0) -> f_122(v47:0, v36:0, 2 * v47:0) :|: v36:0 > 0 && v37:0 > 1 && v34:0 > 1 && v36:0 >= 2 * v47:0 6.68/2.84 6.68/2.84 ---------------------------------------- 6.68/2.84 6.68/2.84 (9) IntTRSCompressionProof (EQUIVALENT) 6.68/2.84 Compressed rules. 6.68/2.84 ---------------------------------------- 6.68/2.84 6.68/2.84 (10) 6.68/2.84 Obligation: 6.68/2.84 Rules: 6.68/2.84 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 > 1 && v36:0:0 >= 2 * v47:0:0 && v37:0:0 > 1 && v36:0:0 > 0 6.68/2.84 6.68/2.84 ---------------------------------------- 6.68/2.84 6.68/2.84 (11) RankingReductionPairProof (EQUIVALENT) 6.68/2.84 Interpretation: 6.68/2.84 [ f_122 ] = 1/2*f_122_3 + f_122_1 6.68/2.84 6.68/2.84 The following rules are decreasing: 6.68/2.84 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 > 1 && v36:0:0 >= 2 * v47:0:0 && v37:0:0 > 1 && v36:0:0 > 0 6.68/2.84 6.68/2.84 The following rules are bounded: 6.68/2.84 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 > 1 && v36:0:0 >= 2 * v47:0:0 && v37:0:0 > 1 && v36:0:0 > 0 6.68/2.84 6.68/2.84 6.68/2.84 ---------------------------------------- 6.68/2.84 6.68/2.84 (12) 6.68/2.84 YES 6.68/2.87 EOF