/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given C Problem could be proven: (0) C Problem (1) CToLLVMProof [EQUIVALENT, 78 ms] (2) LLVM problem (3) LLVMToTerminationGraphProof [EQUIVALENT, 495 ms] (4) LLVM Symbolic Execution Graph (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] (6) LLVM Symbolic Execution SCC (7) SCC2IRS [SOUND, 64 ms] (8) IntTRS (9) IntTRSCompressionProof [EQUIVALENT, 0 ms] (10) IntTRS (11) RankingReductionPairProof [EQUIVALENT, 26 ms] (12) 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: true visibilityType: DEFAULT callingConvention: ccc *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 0: %1 = alloca i32, align 4 %x = alloca i32, align 4 %old_x = alloca i32, align 4 store 0, %1 %2 = call i32 (...)* @__VERIFIER_nondet_int() store %2, %x br %3 3: %4 = load %x %5 = icmp sgt %4 0 br %5, %6, %15 6: %7 = load %x store %7, %old_x %8 = call i32 (...)* @__VERIFIER_nondet_int() store %8, %x %9 = load %x %10 = mul 2 %9 %11 = load %old_x %12 = icmp sgt %10 %11 br %12, %13, %14 13: br %15 14: br %3 15: ret 0 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 16 rulesP rules: 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 Combined rules. Obtained 1 rulesP rules: 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 Filtered unneeded arguments: f_122(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) -> f_122(x5, x7, x8) Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: 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 ---------------------------------------- (8) Obligation: Rules: 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 ---------------------------------------- (9) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (10) Obligation: Rules: 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 ---------------------------------------- (11) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f_122 ] = 1/2*f_122_3 + f_122_1 The following rules are decreasing: 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 The following rules are bounded: 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 ---------------------------------------- (12) YES