13.18/4.76 YES 13.18/4.77 proof of /export/starexec/sandbox2/benchmark/theBenchmark.c 13.18/4.77 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 13.18/4.77 13.18/4.77 13.18/4.77 Termination of the given C Problem could be proven: 13.18/4.77 13.18/4.77 (0) C Problem 13.18/4.77 (1) CToLLVMProof [EQUIVALENT, 175 ms] 13.18/4.77 (2) LLVM problem 13.18/4.77 (3) LLVMToTerminationGraphProof [EQUIVALENT, 1089 ms] 13.18/4.77 (4) LLVM Symbolic Execution Graph 13.18/4.77 (5) SymbolicExecutionGraphToLassoProof [EQUIVALENT, 0 ms] 13.18/4.77 (6) LLVM Symbolic Execution Lasso 13.18/4.77 (7) Lasso2IRS [EQUIVALENT, 65 ms] 13.18/4.77 (8) IntTRS 13.18/4.77 (9) IRS2T2 [EQUIVALENT, 0 ms] 13.18/4.77 (10) T2IntSys 13.18/4.77 (11) T2 [EQUIVALENT, 1532 ms] 13.18/4.77 (12) YES 13.18/4.77 13.18/4.77 13.18/4.77 ---------------------------------------- 13.18/4.77 13.18/4.77 (0) 13.18/4.77 Obligation: 13.18/4.77 c file /export/starexec/sandbox2/benchmark/theBenchmark.c 13.18/4.77 ---------------------------------------- 13.18/4.77 13.18/4.77 (1) CToLLVMProof (EQUIVALENT) 13.18/4.77 Compiled c-file /export/starexec/sandbox2/benchmark/theBenchmark.c to LLVM. 13.18/4.77 ---------------------------------------- 13.18/4.77 13.18/4.77 (2) 13.18/4.77 Obligation: 13.18/4.77 LLVM Problem 13.18/4.77 13.18/4.77 Aliases: 13.18/4.77 13.18/4.77 Data layout: 13.18/4.77 13.18/4.77 "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" 13.18/4.77 13.18/4.77 Machine: 13.18/4.77 13.18/4.77 "x86_64-pc-linux-gnu" 13.18/4.77 13.18/4.77 Type definitions: 13.18/4.77 13.18/4.77 Global variables: 13.18/4.77 13.18/4.77 Function declarations and definitions: 13.18/4.77 13.18/4.77 *BasicFunctionTypename: "__VERIFIER_nondet_int" returnParam: i32 parameters: () variableLength: true visibilityType: DEFAULT callingConvention: ccc 13.18/4.77 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 13.18/4.77 0: 13.18/4.77 %1 = alloca i32, align 4 13.18/4.77 %x = alloca i32, align 4 13.18/4.77 %y = alloca i32, align 4 13.18/4.77 store 0, %1 13.18/4.77 %2 = call i32 (...)* @__VERIFIER_nondet_int() 13.18/4.77 store %2, %x 13.18/4.77 %3 = call i32 (...)* @__VERIFIER_nondet_int() 13.18/4.77 store %3, %y 13.18/4.77 br %4 13.18/4.77 4: 13.18/4.77 %5 = load %x 13.18/4.77 %6 = load %y 13.18/4.77 %7 = sub %5 %6 13.18/4.77 %8 = icmp sgt %7 0 13.18/4.77 br %8, %9, %15 13.18/4.77 9: 13.18/4.77 %10 = load %y 13.18/4.77 %11 = load %x 13.18/4.77 %12 = sub %10 %11 13.18/4.77 store %12, %x 13.18/4.77 %13 = load %y 13.18/4.77 %14 = add %13 1 13.18/4.77 store %14, %y 13.18/4.77 br %4 13.18/4.77 15: 13.18/4.77 ret 0 13.18/4.77 13.18/4.77 13.18/4.77 Analyze Termination of all function calls matching the pattern: 13.18/4.77 main() 13.18/4.77 ---------------------------------------- 13.18/4.77 13.18/4.77 (3) LLVMToTerminationGraphProof (EQUIVALENT) 13.18/4.77 Constructed symbolic execution graph for LLVM program and proved memory safety. 13.18/4.77 ---------------------------------------- 13.18/4.77 13.18/4.77 (4) 13.18/4.77 Obligation: 13.18/4.77 SE Graph 13.18/4.77 ---------------------------------------- 13.18/4.77 13.18/4.77 (5) SymbolicExecutionGraphToLassoProof (EQUIVALENT) 13.18/4.77 Converted SEGraph to 1 independent lasso. 13.18/4.77 ---------------------------------------- 13.18/4.77 13.18/4.77 (6) 13.18/4.77 Obligation: 13.18/4.77 Lasso 13.18/4.77 ---------------------------------------- 13.18/4.77 13.18/4.77 (7) Lasso2IRS (EQUIVALENT) 13.18/4.77 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 13.18/4.77 Generated rules. Obtained 40 rulesP rules: 13.18/4.77 f_135(v41, v42, v43, v44, v45, v50, v47, v48, 1, v46, v51, v52, v53, v54, 0, 3, 4) -> f_136(v41, v42, v43, v44, v45, v50, v51, v48, 1, v47, v46, v52, v53, v54, 0, 3, 4) :|: 0 = 0 13.18/4.77 f_136(v41, v42, v43, v44, v45, v50, v51, v48, 1, v47, v46, v52, v53, v54, 0, 3, 4) -> f_137(v41, v42, v43, v44, v45, v50, v51, v56, 1, v47, v46, v52, v53, v54, 0, 3, 4) :|: v56 + v51 = v50 13.18/4.77 f_137(v41, v42, v43, v44, v45, v50, v51, v56, 1, v47, v46, v52, v53, v54, 0, 3, 4) -> f_138(v41, v42, v43, v44, v45, v50, v51, v56, 1, v47, v46, v52, v53, v54, 0, 3, 4) :|: 0 < v56 13.18/4.77 f_138(v41, v42, v43, v44, v45, v50, v51, v56, 1, v47, v46, v52, v53, v54, 0, 3, 4) -> f_140(v41, v42, v43, v44, v45, v50, v51, v56, 1, v47, v46, v52, v53, v54, 0, 3, 4) :|: 0 = 0 13.18/4.77 f_140(v41, v42, v43, v44, v45, v50, v51, v56, 1, v47, v46, v52, v53, v54, 0, 3, 4) -> f_142(v41, v42, v43, v44, v45, v50, v51, v56, 1, v47, v46, v52, v53, v54, 0, 3, 4) :|: TRUE 13.18/4.77 f_142(v41, v42, v43, v44, v45, v50, v51, v56, 1, v47, v46, v52, v53, v54, 0, 3, 4) -> f_144(v41, v42, v43, v44, v45, v50, v51, v56, 1, v46, v47, v52, v53, v54, 0, 3, 4) :|: 0 = 0 13.18/4.77 f_144(v41, v42, v43, v44, v45, v50, v51, v56, 1, v46, v47, v52, v53, v54, 0, 3, 4) -> f_145(v41, v42, v43, v44, v45, v50, v51, v56, 1, v47, v52, v53, v54, 0, 3, 4) :|: 0 = 0 13.18/4.77 f_145(v41, v42, v43, v44, v45, v50, v51, v56, 1, v47, v52, v53, v54, 0, 3, 4) -> f_146(v41, v42, v43, v44, v45, v50, v51, v56, 1, v57, v47, v52, v53, v54, 0, 3, 4) :|: v57 + v50 = v51 13.18/4.77 f_146(v41, v42, v43, v44, v45, v50, v51, v56, 1, v57, v47, v52, v53, v54, 0, 3, 4) -> f_147(v41, v42, v43, v44, v45, v50, v51, v56, 1, v57, v47, v52, v53, v54, 0, 3, 4) :|: TRUE 13.18/4.77 f_147(v41, v42, v43, v44, v45, v50, v51, v56, 1, v57, v47, v52, v53, v54, 0, 3, 4) -> f_148(v41, v42, v43, v44, v45, v50, v51, v56, 1, v57, v52, v53, v54, 0, 3, 4) :|: 0 = 0 13.18/4.77 f_148(v41, v42, v43, v44, v45, v50, v51, v56, 1, v57, v52, v53, v54, 0, 3, 4) -> f_149(v41, v42, v43, v44, v45, v50, v51, v56, 1, v57, v59, v52, v53, v54, 0, 3, 4) :|: v59 = 1 + v51 13.18/4.77 f_149(v41, v42, v43, v44, v45, v50, v51, v56, 1, v57, v59, v52, v53, v54, 0, 3, 4) -> f_150(v41, v42, v43, v44, v45, v50, v51, v56, 1, v57, v59, v52, v53, v54, 0, 3, 4) :|: TRUE 13.18/4.77 f_150(v41, v42, v43, v44, v45, v50, v51, v56, 1, v57, v59, v52, v53, v54, 0, 3, 4) -> f_151(v41, v42, v43, v44, v45, v50, v51, v56, 1, v57, v59, v52, v53, v54, 0, 3, 4) :|: TRUE 13.18/4.77 f_151(v41, v42, v43, v44, v45, v50, v51, v56, 1, v57, v59, v52, v53, v54, 0, 3, 4) -> f_134(v41, v42, v43, v44, v45, v50, v51, v56, 1, v57, v59, v52, v53, v54, 0, 3, 4) :|: TRUE 13.18/4.77 f_134(v41, v42, v43, v44, v45, v46, v47, v48, 1, v50, v51, v52, v53, v54, 0, 3, 4) -> f_135(v41, v42, v43, v44, v45, v50, v47, v48, 1, v46, v51, v52, v53, v54, 0, 3, 4) :|: 0 = 0 13.18/4.77 f_72 -> f_73(v1, v2, 3, 1, 4) :|: 1 <= v1 && v2 = 3 + v1 && 4 <= v2 13.18/4.77 f_73(v1, v2, 3, 1, 4) -> f_74(v1, v3, v2, v4, 3, 1, 4) :|: 1 <= v3 && v4 = 3 + v3 && 4 <= v4 13.18/4.77 f_74(v1, v3, v2, v4, 3, 1, 4) -> f_75(v1, v3, v5, v2, v4, v6, 3, 1, 4) :|: 1 <= v5 && v6 = 3 + v5 && 4 <= v6 13.18/4.77 f_75(v1, v3, v5, v2, v4, v6, 3, 1, 4) -> f_76(v1, v3, v5, v2, v4, v6, 0, 3, 1, 4) :|: TRUE 13.18/4.77 f_76(v1, v3, v5, v2, v4, v6, 0, 3, 1, 4) -> f_77(v1, v3, v5, v7, v2, v4, v6, 0, 3, 1, 4) :|: TRUE 13.18/4.77 f_77(v1, v3, v5, v7, v2, v4, v6, 0, 3, 1, 4) -> f_78(v1, v3, v5, v7, v2, v4, v6, 0, 3, 1, 4) :|: TRUE 13.18/4.77 f_78(v1, v3, v5, v7, v2, v4, v6, 0, 3, 1, 4) -> f_79(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) :|: TRUE 13.18/4.77 f_79(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) -> f_80(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) :|: TRUE 13.18/4.77 f_80(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) -> f_81(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) :|: TRUE 13.18/4.77 f_81(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) -> f_82(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) :|: 0 = 0 13.18/4.77 f_82(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) -> f_83(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) :|: 0 = 0 13.18/4.77 f_83(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) -> f_84(v1, v3, v5, v7, v9, v11, v2, v4, v6, 0, 3, 1, 4) :|: v11 + v9 = v7 13.18/4.77 f_84(v1, v3, v5, v7, v9, v11, v2, v4, v6, 0, 3, 1, 4) -> f_85(v1, v3, v5, v7, v9, v11, v2, v4, v6, 0, 3, 1, 4) :|: 0 < v11 13.18/4.77 f_85(v1, v3, v5, v7, v9, v11, v2, v4, v6, 0, 3, 1, 4) -> f_87(v1, v3, v5, v7, v9, v11, 1, v2, v4, v6, 0, 3, 4) :|: 0 = 0 13.18/4.77 f_87(v1, v3, v5, v7, v9, v11, 1, v2, v4, v6, 0, 3, 4) -> f_89(v1, v3, v5, v7, v9, v11, 1, v2, v4, v6, 0, 3, 4) :|: TRUE 13.18/4.77 f_89(v1, v3, v5, v7, v9, v11, 1, v2, v4, v6, 0, 3, 4) -> f_91(v1, v3, v5, v7, v9, v11, 1, v2, v4, v6, 0, 3, 4) :|: 0 = 0 13.18/4.77 f_91(v1, v3, v5, v7, v9, v11, 1, v2, v4, v6, 0, 3, 4) -> f_92(v1, v3, v5, v7, v9, v11, 1, v2, v4, v6, 0, 3, 4) :|: 0 = 0 13.18/4.77 f_92(v1, v3, v5, v7, v9, v11, 1, v2, v4, v6, 0, 3, 4) -> f_93(v1, v3, v5, v7, v9, v11, 1, v12, v2, v4, v6, 0, 3, 4) :|: v12 + v7 = v9 13.18/4.77 f_93(v1, v3, v5, v7, v9, v11, 1, v12, v2, v4, v6, 0, 3, 4) -> f_94(v1, v3, v5, v7, v9, v11, 1, v12, v2, v4, v6, 0, 3, 4) :|: TRUE 13.18/4.77 f_94(v1, v3, v5, v7, v9, v11, 1, v12, v2, v4, v6, 0, 3, 4) -> f_95(v1, v3, v5, v7, v9, v11, 1, v12, v2, v4, v6, 0, 3, 4) :|: 0 = 0 13.18/4.77 f_95(v1, v3, v5, v7, v9, v11, 1, v12, v2, v4, v6, 0, 3, 4) -> f_96(v1, v3, v5, v7, v9, v11, 1, v12, v14, v2, v4, v6, 0, 3, 4) :|: v14 = 1 + v9 13.18/4.77 f_96(v1, v3, v5, v7, v9, v11, 1, v12, v14, v2, v4, v6, 0, 3, 4) -> f_97(v1, v3, v5, v7, v9, v11, 1, v12, v14, v2, v4, v6, 0, 3, 4) :|: TRUE 13.18/4.77 f_97(v1, v3, v5, v7, v9, v11, 1, v12, v14, v2, v4, v6, 0, 3, 4) -> f_98(v1, v3, v5, v7, v9, v11, 1, v12, v14, v2, v4, v6, 0, 3, 4) :|: TRUE 13.18/4.77 f_98(v1, v3, v5, v7, v9, v11, 1, v12, v14, v2, v4, v6, 0, 3, 4) -> f_116(v1, v3, v5, v7, v9, v7, v9, v11, 1, v12, v14, v2, v4, v6, 0, 3, 4) :|: TRUE 13.18/4.77 f_116(v21, v22, v23, v24, v25, v26, v27, v28, 1, v30, v31, v32, v33, v34, 0, 3, 4) -> f_134(v21, v22, v23, v24, v25, v26, v27, v28, 1, v30, v31, v32, v33, v34, 0, 3, 4) :|: TRUE 13.18/4.77 Combined rules. Obtained 2 rulesP rules: 13.18/4.77 f_135(v41:0, v42:0, v43:0, v44:0, v45:0, v50:0, v47:0, v48:0, 1, v46:0, v57:0 + v50:0, v52:0, v53:0, v54:0, 0, 3, 4) -> f_135(v41:0, v42:0, v43:0, v44:0, v45:0, v57:0, v57:0 + v50:0, v56:0, 1, v50:0, 1 + (v57:0 + v50:0), v52:0, v53:0, v54:0, 0, 3, 4) :|: v56:0 > 0 && v56:0 + (v57:0 + v50:0) = v50:0 13.18/4.77 f_72 -> f_135(v1:0, v3:0, v5:0, v7:0, v12:0 + v7:0, v12:0, v12:0 + v7:0, v11:0, 1, v7:0, 1 + (v12:0 + v7:0), 3 + v1:0, 3 + v3:0, 3 + v5:0, 0, 3, 4) :|: v3:0 > 0 && v1:0 > 0 && v5:0 > 0 && v11:0 > 0 && v7:0 = v11:0 + (v12:0 + v7:0) 13.18/4.77 Filtered unneeded arguments: 13.18/4.77 f_135(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17) -> f_135(x6, x7, x8, x10, x11) 13.18/4.77 Removed division, modulo operations, cleaned up constraints. Obtained 2 rules.P rules: 13.18/4.77 f_135(v50:0, v47:0, v48:0, v46:0, sum~v57:0~v50:0) -> f_135(v57:0, v57:0 + v50:0, v56:0, v50:0, 1 + (v57:0 + v50:0)) :|: v56:0 > 0 && v56:0 + (v57:0 + v50:0) = v50:0 && sum~v57:0~v50:0 = v57:0 + v50:0 13.18/4.77 f_72 -> f_135(v12:0, v12:0 + v7:0, v11:0, v7:0, 1 + (v12:0 + v7:0)) :|: v11:0 > 0 && v7:0 = v11:0 + (v12:0 + v7:0) 13.18/4.77 13.18/4.77 ---------------------------------------- 13.18/4.77 13.18/4.77 (8) 13.18/4.77 Obligation: 13.18/4.77 Rules: 13.18/4.77 f_135(v50:0, v47:0, v48:0, v46:0, sum~v57:0~v50:0) -> f_135(v57:0, v57:0 + v50:0, v56:0, v50:0, 1 + (v57:0 + v50:0)) :|: v56:0 > 0 && v56:0 + (v57:0 + v50:0) = v50:0 && sum~v57:0~v50:0 = v57:0 + v50:0 13.18/4.77 f_72 -> f_135(v12:0, v12:0 + v7:0, v11:0, v7:0, 1 + (v12:0 + v7:0)) :|: v11:0 > 0 && v7:0 = v11:0 + (v12:0 + v7:0) 13.18/4.77 Start term: f_72 13.18/4.77 13.18/4.77 ---------------------------------------- 13.18/4.77 13.18/4.77 (9) IRS2T2 (EQUIVALENT) 13.18/4.77 Transformed input IRS into an integer transition system.Used the following mapping from defined symbols to location IDs: 13.18/4.77 13.18/4.77 (f_135_5,1) 13.18/4.77 (f_72_5,2) 13.18/4.77 13.18/4.77 ---------------------------------------- 13.18/4.77 13.18/4.77 (10) 13.18/4.77 Obligation: 13.18/4.77 START: 2; 13.18/4.77 13.18/4.77 FROM: 1; 13.18/4.77 oldX0 := x0; 13.18/4.77 oldX1 := x1; 13.18/4.77 oldX2 := x2; 13.18/4.77 oldX3 := x3; 13.18/4.77 oldX4 := x4; 13.18/4.77 oldX5 := oldX4 - oldX0; 13.18/4.77 oldX6 := -(oldX5 + oldX0 - oldX0); 13.18/4.77 assume(oldX6 > 0 && oldX6 + (oldX5 + oldX0) = oldX0 && oldX4 = oldX5 + oldX0); 13.18/4.77 x0 := oldX4 - oldX0; 13.18/4.77 x1 := oldX5 + oldX0; 13.18/4.77 x2 := -(oldX5 + oldX0 - oldX0); 13.18/4.77 x3 := oldX0; 13.18/4.77 x4 := 1 + (oldX5 + oldX0); 13.18/4.77 TO: 1; 13.18/4.77 13.18/4.77 FROM: 2; 13.18/4.77 oldX0 := x0; 13.18/4.77 oldX1 := x1; 13.18/4.77 oldX2 := x2; 13.18/4.77 oldX3 := x3; 13.18/4.77 oldX4 := x4; 13.18/4.77 oldX5 := nondet(); 13.18/4.77 oldX6 := nondet(); 13.18/4.77 oldX7 := nondet(); 13.18/4.77 assume(oldX7 > 0 && oldX6 = oldX7 + (oldX5 + oldX6)); 13.18/4.77 x0 := oldX5; 13.18/4.77 x1 := oldX5 + oldX6; 13.18/4.77 x2 := oldX7; 13.18/4.77 x3 := oldX6; 13.18/4.77 x4 := 1 + (oldX5 + oldX6); 13.18/4.77 TO: 1; 13.18/4.77 13.18/4.77 13.18/4.77 ---------------------------------------- 13.18/4.77 13.18/4.77 (11) T2 (EQUIVALENT) 13.18/4.77 No proof given by T2 13.18/4.77 ---------------------------------------- 13.18/4.77 13.18/4.77 (12) 13.18/4.77 YES 13.29/7.76 EOF