6.79/2.87 YES 6.79/2.92 proof of /export/starexec/sandbox2/benchmark/theBenchmark.c 6.79/2.92 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 6.79/2.92 6.79/2.92 6.79/2.92 Termination of the given C Problem could be proven: 6.79/2.92 6.79/2.92 (0) C Problem 6.79/2.92 (1) CToLLVMProof [EQUIVALENT, 172 ms] 6.79/2.92 (2) LLVM problem 6.79/2.92 (3) LLVMToTerminationGraphProof [EQUIVALENT, 584 ms] 6.79/2.92 (4) LLVM Symbolic Execution Graph 6.79/2.92 (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] 6.79/2.92 (6) LLVM Symbolic Execution SCC 6.79/2.92 (7) SCC2IRS [SOUND, 42 ms] 6.79/2.92 (8) IntTRS 6.79/2.92 (9) IntTRSCompressionProof [EQUIVALENT, 0 ms] 6.79/2.92 (10) IntTRS 6.79/2.92 (11) RankingReductionPairProof [EQUIVALENT, 19 ms] 6.79/2.92 (12) YES 6.79/2.92 6.79/2.92 6.79/2.92 ---------------------------------------- 6.79/2.92 6.79/2.92 (0) 6.79/2.92 Obligation: 6.79/2.92 c file /export/starexec/sandbox2/benchmark/theBenchmark.c 6.79/2.92 ---------------------------------------- 6.79/2.92 6.79/2.92 (1) CToLLVMProof (EQUIVALENT) 6.79/2.92 Compiled c-file /export/starexec/sandbox2/benchmark/theBenchmark.c to LLVM. 6.79/2.92 ---------------------------------------- 6.79/2.92 6.79/2.92 (2) 6.79/2.92 Obligation: 6.79/2.92 LLVM Problem 6.79/2.92 6.79/2.92 Aliases: 6.79/2.92 6.79/2.92 Data layout: 6.79/2.92 6.79/2.92 "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" 6.79/2.92 6.79/2.92 Machine: 6.79/2.92 6.79/2.92 "x86_64-pc-linux-gnu" 6.79/2.92 6.79/2.92 Type definitions: 6.79/2.92 6.79/2.92 Global variables: 6.79/2.92 6.79/2.92 Function declarations and definitions: 6.79/2.92 6.79/2.92 *BasicFunctionTypename: "__VERIFIER_nondet_int" returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 6.79/2.92 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 6.79/2.92 0: 6.79/2.92 %1 = alloca i32, align 4 6.79/2.92 %x = alloca i32, align 4 6.79/2.92 %y = alloca i32, align 4 6.79/2.92 store 0, %1 6.79/2.92 %2 = call i32 @__VERIFIER_nondet_int() 6.79/2.92 store %2, %x 6.79/2.92 store 2, %y 6.79/2.92 br %3 6.79/2.92 3: 6.79/2.92 %4 = load %x 6.79/2.92 %5 = icmp sge %4 0 6.79/2.92 br %5, %6, %13 6.79/2.92 6: 6.79/2.92 %7 = load %x 6.79/2.92 %8 = load %y 6.79/2.92 %9 = sub %7 %8 6.79/2.92 store %9, %x 6.79/2.92 %10 = load %y 6.79/2.92 %11 = add %10 1 6.79/2.92 %12 = sdiv %11 2 6.79/2.92 store %12, %y 6.79/2.92 br %3 6.79/2.92 13: 6.79/2.92 ret 0 6.79/2.92 6.79/2.92 6.79/2.92 Analyze Termination of all function calls matching the pattern: 6.79/2.92 main() 6.79/2.92 ---------------------------------------- 6.79/2.92 6.79/2.92 (3) LLVMToTerminationGraphProof (EQUIVALENT) 6.79/2.92 Constructed symbolic execution graph for LLVM program and proved memory safety. 6.79/2.92 ---------------------------------------- 6.79/2.92 6.79/2.92 (4) 6.79/2.92 Obligation: 6.79/2.92 SE Graph 6.79/2.92 ---------------------------------------- 6.79/2.92 6.79/2.92 (5) SymbolicExecutionGraphToSCCProof (SOUND) 6.79/2.92 Splitted symbolic execution graph to 1 SCC. 6.79/2.92 ---------------------------------------- 6.79/2.92 6.79/2.92 (6) 6.79/2.92 Obligation: 6.79/2.92 SCC 6.79/2.92 ---------------------------------------- 6.79/2.92 6.79/2.92 (7) SCC2IRS (SOUND) 6.79/2.92 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 6.79/2.92 Generated rules. Obtained 14 rulesP rules: 6.79/2.92 f_125(v28, v29, v30, v31, v35, 1, v32, v34, v36, v37, v38, v39, 0, 3, 2, 4) -> f_126(v28, v29, v30, v31, v35, 1, v32, v34, v36, v37, v38, v39, 0, 3, 2, 4) :|: 0 <= v35 && 1 <= v32 && 1 <= v31 6.79/2.92 f_126(v28, v29, v30, v31, v35, 1, v32, v34, v36, v37, v38, v39, 0, 3, 2, 4) -> f_128(v28, v29, v30, v31, v35, 1, v32, v34, v36, v37, v38, v39, 0, 3, 2, 4) :|: 0 = 0 6.79/2.92 f_128(v28, v29, v30, v31, v35, 1, v32, v34, v36, v37, v38, v39, 0, 3, 2, 4) -> f_130(v28, v29, v30, v31, v35, 1, v32, v34, v36, v37, v38, v39, 0, 3, 2, 4) :|: TRUE 6.79/2.92 f_130(v28, v29, v30, v31, v35, 1, v32, v34, v36, v37, v38, v39, 0, 3, 2, 4) -> f_132(v28, v29, v30, v31, v35, 1, v34, v36, v37, v38, v39, 0, 3, 2, 4) :|: 0 = 0 6.79/2.92 f_132(v28, v29, v30, v31, v35, 1, v34, v36, v37, v38, v39, 0, 3, 2, 4) -> f_133(v28, v29, v30, v31, v35, 1, v34, v36, v37, v38, v39, 0, 3, 2, 4) :|: 0 = 0 6.79/2.92 f_133(v28, v29, v30, v31, v35, 1, v34, v36, v37, v38, v39, 0, 3, 2, 4) -> f_134(v28, v29, v30, v31, v35, 1, v41, v34, v36, v37, v38, v39, 0, 3, 2, 4) :|: 1 + v41 = v35 && 0 <= 1 + v41 6.79/2.92 f_134(v28, v29, v30, v31, v35, 1, v41, v34, v36, v37, v38, v39, 0, 3, 2, 4) -> f_135(v28, v29, v30, v31, v35, 1, v41, v34, v36, v37, v38, v39, 0, 3, 2, 4) :|: TRUE 6.79/2.92 f_135(v28, v29, v30, v31, v35, 1, v41, v34, v36, v37, v38, v39, 0, 3, 2, 4) -> f_136(v28, v29, v30, v31, v35, 1, v41, v36, v37, v38, v39, 0, 3, 2, 4) :|: 0 = 0 6.79/2.92 f_136(v28, v29, v30, v31, v35, 1, v41, v36, v37, v38, v39, 0, 3, 2, 4) -> f_137(v28, v29, v30, v31, v35, 1, v41, 2, v37, v38, v39, 0, 3, 4) :|: 0 = 0 6.79/2.92 f_137(v28, v29, v30, v31, v35, 1, v41, 2, v37, v38, v39, 0, 3, 4) -> f_138(v28, v29, v30, v31, v35, 1, v41, 2, v37, v38, v39, 0, 3, 4) :|: 0 = 0 6.79/2.92 f_138(v28, v29, v30, v31, v35, 1, v41, 2, v37, v38, v39, 0, 3, 4) -> f_139(v28, v29, v30, v31, v35, 1, v41, 2, v37, v38, v39, 0, 3, 4) :|: TRUE 6.79/2.92 f_139(v28, v29, v30, v31, v35, 1, v41, 2, v37, v38, v39, 0, 3, 4) -> f_140(v28, v29, v30, v31, v35, 1, v41, 2, v37, v38, v39, 0, 3, 4) :|: TRUE 6.79/2.92 f_140(v28, v29, v30, v31, v35, 1, v41, 2, v37, v38, v39, 0, 3, 4) -> f_124(v28, v29, v30, v31, v35, 1, 1, v41, 2, v37, v38, v39, 0, 3, 2, 4) :|: TRUE 6.79/2.92 f_124(v28, v29, v30, v31, v32, 1, v34, v35, v36, v37, v38, v39, 0, 3, 2, 4) -> f_125(v28, v29, v30, v31, v35, 1, v32, v34, v36, v37, v38, v39, 0, 3, 2, 4) :|: 0 = 0 6.79/2.92 Combined rules. Obtained 1 rulesP rules: 6.79/2.92 f_125(v28:0, v29:0, v30:0, v31:0, 1 + v41:0, 1, v32:0, v34:0, v36:0, v37:0, v38:0, v39:0, 0, 3, 2, 4) -> f_125(v28:0, v29:0, v30:0, v31:0, v41:0, 1, 1 + v41:0, 1, 2, v37:0, v38:0, v39:0, 0, 3, 2, 4) :|: v32:0 > 0 && v41:0 > -2 && v31:0 > 0 6.79/2.92 Filtered unneeded arguments: 6.79/2.92 f_125(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16) -> f_125(x4, x5, x7) 6.79/2.92 Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: 6.79/2.92 f_125(v31:0, sum~cons_1~v41:0, v32:0) -> f_125(v31:0, v41:0, 1 + v41:0) :|: v41:0 > -2 && v31:0 > 0 && v32:0 > 0 && sum~cons_1~v41:0 = 1 + v41:0 6.79/2.92 6.79/2.92 ---------------------------------------- 6.79/2.92 6.79/2.92 (8) 6.79/2.92 Obligation: 6.79/2.92 Rules: 6.79/2.92 f_125(v31:0, sum~cons_1~v41:0, v32:0) -> f_125(v31:0, v41:0, 1 + v41:0) :|: v41:0 > -2 && v31:0 > 0 && v32:0 > 0 && sum~cons_1~v41:0 = 1 + v41:0 6.79/2.92 6.79/2.92 ---------------------------------------- 6.79/2.92 6.79/2.92 (9) IntTRSCompressionProof (EQUIVALENT) 6.79/2.92 Compressed rules. 6.79/2.92 ---------------------------------------- 6.79/2.92 6.79/2.92 (10) 6.79/2.92 Obligation: 6.79/2.92 Rules: 6.79/2.92 f_125(v31:0:0, sum~cons_1~v41:0:0, v32:0:0) -> f_125(v31:0:0, v41:0:0, 1 + v41:0:0) :|: v41:0:0 > -2 && v31:0:0 > 0 && v32:0:0 > 0 && sum~cons_1~v41:0:0 = 1 + v41:0:0 6.79/2.92 6.79/2.92 ---------------------------------------- 6.79/2.92 6.79/2.92 (11) RankingReductionPairProof (EQUIVALENT) 6.79/2.92 Interpretation: 6.79/2.92 [ f_125 ] = f_125_2 6.79/2.92 6.79/2.92 The following rules are decreasing: 6.79/2.92 f_125(v31:0:0, sum~cons_1~v41:0:0, v32:0:0) -> f_125(v31:0:0, v41:0:0, 1 + v41:0:0) :|: v41:0:0 > -2 && v31:0:0 > 0 && v32:0:0 > 0 && sum~cons_1~v41:0:0 = 1 + v41:0:0 6.79/2.92 6.79/2.92 The following rules are bounded: 6.79/2.92 f_125(v31:0:0, sum~cons_1~v41:0:0, v32:0:0) -> f_125(v31:0:0, v41:0:0, 1 + v41:0:0) :|: v41:0:0 > -2 && v31:0:0 > 0 && v32:0:0 > 0 && sum~cons_1~v41:0:0 = 1 + v41:0:0 6.79/2.92 6.79/2.92 6.79/2.92 ---------------------------------------- 6.79/2.92 6.79/2.92 (12) 6.79/2.92 YES 7.95/3.00 EOF