14.66/4.78 YES 14.66/4.78 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 14.66/4.78 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 14.66/4.78 14.66/4.78 14.66/4.78 Termination of the given C Problem could be proven: 14.66/4.78 14.66/4.78 (0) C Problem 14.66/4.78 (1) CToLLVMProof [EQUIVALENT, 171 ms] 14.66/4.78 (2) LLVM problem 14.66/4.78 (3) LLVMToTerminationGraphProof [EQUIVALENT, 881 ms] 14.66/4.78 (4) LLVM Symbolic Execution Graph 14.66/4.78 (5) SymbolicExecutionGraphToLassoProof [EQUIVALENT, 0 ms] 14.66/4.78 (6) LLVM Symbolic Execution Lasso 14.66/4.78 (7) Lasso2IRS [EQUIVALENT, 49 ms] 14.66/4.78 (8) IntTRS 14.66/4.78 (9) IRS2T2 [EQUIVALENT, 0 ms] 14.66/4.78 (10) T2IntSys 14.66/4.78 (11) T2 [EQUIVALENT, 1381 ms] 14.66/4.78 (12) YES 14.66/4.78 14.66/4.78 14.66/4.78 ---------------------------------------- 14.66/4.78 14.66/4.78 (0) 14.66/4.78 Obligation: 14.66/4.78 c file /export/starexec/sandbox/benchmark/theBenchmark.c 14.66/4.78 ---------------------------------------- 14.66/4.78 14.66/4.78 (1) CToLLVMProof (EQUIVALENT) 14.66/4.78 Compiled c-file /export/starexec/sandbox/benchmark/theBenchmark.c to LLVM. 14.66/4.78 ---------------------------------------- 14.66/4.78 14.66/4.78 (2) 14.66/4.78 Obligation: 14.66/4.78 LLVM Problem 14.66/4.78 14.66/4.78 Aliases: 14.66/4.78 14.66/4.78 Data layout: 14.66/4.78 14.66/4.78 "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" 14.66/4.78 14.66/4.78 Machine: 14.66/4.78 14.66/4.78 "x86_64-pc-linux-gnu" 14.66/4.78 14.66/4.78 Type definitions: 14.66/4.78 14.66/4.78 Global variables: 14.66/4.78 14.66/4.78 Function declarations and definitions: 14.66/4.78 14.66/4.78 *BasicFunctionTypename: "__VERIFIER_nondet_int" returnParam: i32 parameters: () variableLength: true visibilityType: DEFAULT callingConvention: ccc 14.66/4.78 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 14.66/4.78 0: 14.66/4.78 %1 = alloca i32, align 4 14.66/4.78 %x = alloca i32, align 4 14.66/4.78 %y = alloca i32, align 4 14.66/4.78 store 0, %1 14.66/4.78 %2 = call i32 (...)* @__VERIFIER_nondet_int() 14.66/4.78 store %2, %x 14.66/4.78 %3 = call i32 (...)* @__VERIFIER_nondet_int() 14.66/4.78 store %3, %y 14.66/4.78 br %4 14.66/4.78 4: 14.66/4.78 %5 = load %x 14.66/4.78 %6 = icmp sgt %5 0 14.66/4.78 br %6, %7, %14 14.66/4.78 7: 14.66/4.78 %8 = load %x 14.66/4.78 %9 = load %y 14.66/4.78 %10 = mul 2 %9 14.66/4.78 %11 = sub %8 %10 14.66/4.78 store %11, %x 14.66/4.78 %12 = load %y 14.66/4.78 %13 = add %12 1 14.66/4.78 store %13, %y 14.66/4.78 br %4 14.66/4.78 14: 14.66/4.78 ret 0 14.66/4.78 14.66/4.78 14.66/4.78 Analyze Termination of all function calls matching the pattern: 14.66/4.78 main() 14.66/4.78 ---------------------------------------- 14.66/4.78 14.66/4.78 (3) LLVMToTerminationGraphProof (EQUIVALENT) 14.66/4.78 Constructed symbolic execution graph for LLVM program and proved memory safety. 14.66/4.78 ---------------------------------------- 14.66/4.78 14.66/4.78 (4) 14.66/4.78 Obligation: 14.66/4.78 SE Graph 14.66/4.78 ---------------------------------------- 14.66/4.78 14.66/4.78 (5) SymbolicExecutionGraphToLassoProof (EQUIVALENT) 14.66/4.78 Converted SEGraph to 1 independent lasso. 14.66/4.78 ---------------------------------------- 14.66/4.78 14.66/4.78 (6) 14.66/4.78 Obligation: 14.66/4.78 Lasso 14.66/4.78 ---------------------------------------- 14.66/4.78 14.66/4.78 (7) Lasso2IRS (EQUIVALENT) 14.66/4.78 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 14.66/4.78 Generated rules. Obtained 38 rulesP rules: 14.66/4.78 f_129(v41, v42, v43, v44, v45, v50, 1, v46, v48, v49, v51, v52, v53, v54, 0, 3, 2, 4) -> f_130(v41, v42, v43, v44, v45, v50, 1, v46, v48, v49, v51, v52, v53, v54, 0, 3, 2, 4) :|: 0 < v50 14.66/4.78 f_130(v41, v42, v43, v44, v45, v50, 1, v46, v48, v49, v51, v52, v53, v54, 0, 3, 2, 4) -> f_132(v41, v42, v43, v44, v45, v50, 1, v46, v48, v49, v51, v52, v53, v54, 0, 3, 2, 4) :|: 0 = 0 14.66/4.78 f_132(v41, v42, v43, v44, v45, v50, 1, v46, v48, v49, v51, v52, v53, v54, 0, 3, 2, 4) -> f_134(v41, v42, v43, v44, v45, v50, 1, v46, v48, v49, v51, v52, v53, v54, 0, 3, 2, 4) :|: TRUE 14.66/4.78 f_134(v41, v42, v43, v44, v45, v50, 1, v46, v48, v49, v51, v52, v53, v54, 0, 3, 2, 4) -> f_136(v41, v42, v43, v44, v45, v50, 1, v48, v49, v51, v52, v53, v54, 0, 3, 2, 4) :|: 0 = 0 14.66/4.78 f_136(v41, v42, v43, v44, v45, v50, 1, v48, v49, v51, v52, v53, v54, 0, 3, 2, 4) -> f_137(v41, v42, v43, v44, v45, v50, 1, v51, v49, v48, v52, v53, v54, 0, 3, 2, 4) :|: 0 = 0 14.66/4.78 f_137(v41, v42, v43, v44, v45, v50, 1, v51, v49, v48, v52, v53, v54, 0, 3, 2, 4) -> f_138(v41, v42, v43, v44, v45, v50, 1, v51, v56, v48, v52, v53, v54, 0, 3, 2, 4) :|: v56 = 2 * v51 14.66/4.78 f_138(v41, v42, v43, v44, v45, v50, 1, v51, v56, v48, v52, v53, v54, 0, 3, 2, 4) -> f_139(v41, v42, v43, v44, v45, v50, 1, v51, v56, v57, v48, v52, v53, v54, 0, 3, 2, 4) :|: v57 + v56 = v50 14.66/4.78 f_139(v41, v42, v43, v44, v45, v50, 1, v51, v56, v57, v48, v52, v53, v54, 0, 3, 2, 4) -> f_140(v41, v42, v43, v44, v45, v50, 1, v51, v56, v57, v48, v52, v53, v54, 0, 3, 2, 4) :|: TRUE 14.66/4.78 f_140(v41, v42, v43, v44, v45, v50, 1, v51, v56, v57, v48, v52, v53, v54, 0, 3, 2, 4) -> f_141(v41, v42, v43, v44, v45, v50, 1, v51, v56, v57, v52, v53, v54, 0, 3, 2, 4) :|: 0 = 0 14.66/4.78 f_141(v41, v42, v43, v44, v45, v50, 1, v51, v56, v57, v52, v53, v54, 0, 3, 2, 4) -> f_142(v41, v42, v43, v44, v45, v50, 1, v51, v56, v57, v59, v52, v53, v54, 0, 3, 2, 4) :|: v59 = 1 + v51 14.66/4.78 f_142(v41, v42, v43, v44, v45, v50, 1, v51, v56, v57, v59, v52, v53, v54, 0, 3, 2, 4) -> f_143(v41, v42, v43, v44, v45, v50, 1, v51, v56, v57, v59, v52, v53, v54, 0, 3, 2, 4) :|: TRUE 14.66/4.78 f_143(v41, v42, v43, v44, v45, v50, 1, v51, v56, v57, v59, v52, v53, v54, 0, 3, 2, 4) -> f_144(v41, v42, v43, v44, v45, v50, 1, v51, v56, v57, v59, v52, v53, v54, 0, 3, 2, 4) :|: TRUE 14.66/4.78 f_144(v41, v42, v43, v44, v45, v50, 1, v51, v56, v57, v59, v52, v53, v54, 0, 3, 2, 4) -> f_128(v41, v42, v43, v44, v45, v50, 1, v51, v56, v57, v59, v52, v53, v54, 0, 3, 2, 4) :|: TRUE 14.66/4.78 f_128(v41, v42, v43, v44, v45, v46, 1, v48, v49, v50, v51, v52, v53, v54, 0, 3, 2, 4) -> f_129(v41, v42, v43, v44, v45, v50, 1, v46, v48, v49, v51, v52, v53, v54, 0, 3, 2, 4) :|: 0 = 0 14.66/4.78 f_69 -> f_70(v1, v2, 3, 1, 4) :|: 1 <= v1 && v2 = 3 + v1 && 4 <= v2 14.66/4.78 f_70(v1, v2, 3, 1, 4) -> f_71(v1, v3, v2, v4, 3, 1, 4) :|: 1 <= v3 && v4 = 3 + v3 && 4 <= v4 14.66/4.78 f_71(v1, v3, v2, v4, 3, 1, 4) -> f_72(v1, v3, v5, v2, v4, v6, 3, 1, 4) :|: 1 <= v5 && v6 = 3 + v5 && 4 <= v6 14.66/4.78 f_72(v1, v3, v5, v2, v4, v6, 3, 1, 4) -> f_73(v1, v3, v5, v2, v4, v6, 0, 3, 1, 4) :|: TRUE 14.66/4.78 f_73(v1, v3, v5, v2, v4, v6, 0, 3, 1, 4) -> f_74(v1, v3, v5, v7, v2, v4, v6, 0, 3, 1, 4) :|: TRUE 14.66/4.78 f_74(v1, v3, v5, v7, v2, v4, v6, 0, 3, 1, 4) -> f_75(v1, v3, v5, v7, v2, v4, v6, 0, 3, 1, 4) :|: TRUE 14.66/4.78 f_75(v1, v3, v5, v7, v2, v4, v6, 0, 3, 1, 4) -> f_76(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) :|: TRUE 14.66/4.78 f_76(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) -> f_77(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) :|: TRUE 14.66/4.78 f_77(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) -> f_78(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) :|: TRUE 14.66/4.78 f_78(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) -> f_79(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) :|: 0 = 0 14.66/4.78 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) :|: 0 < v7 14.66/4.78 f_80(v1, v3, v5, v7, v9, v2, v4, v6, 0, 3, 1, 4) -> f_82(v1, v3, v5, v7, v9, 1, v2, v4, v6, 0, 3, 4) :|: 0 = 0 14.66/4.78 f_82(v1, v3, v5, v7, v9, 1, v2, v4, v6, 0, 3, 4) -> f_84(v1, v3, v5, v7, v9, 1, v2, v4, v6, 0, 3, 4) :|: TRUE 14.66/4.78 f_84(v1, v3, v5, v7, v9, 1, v2, v4, v6, 0, 3, 4) -> f_86(v1, v3, v5, v7, v9, 1, v2, v4, v6, 0, 3, 4) :|: 0 = 0 14.66/4.78 f_86(v1, v3, v5, v7, v9, 1, v2, v4, v6, 0, 3, 4) -> f_87(v1, v3, v5, v7, v9, 1, v2, v4, v6, 0, 3, 4) :|: 0 = 0 14.66/4.78 f_87(v1, v3, v5, v7, v9, 1, v2, v4, v6, 0, 3, 4) -> f_88(v1, v3, v5, v7, v9, 1, v11, v2, v4, v6, 0, 3, 2, 4) :|: v11 = 2 * v9 14.66/4.78 f_88(v1, v3, v5, v7, v9, 1, v11, v2, v4, v6, 0, 3, 2, 4) -> f_89(v1, v3, v5, v7, v9, 1, v11, v12, v2, v4, v6, 0, 3, 2, 4) :|: v12 + v11 = v7 14.66/4.78 f_89(v1, v3, v5, v7, v9, 1, v11, v12, v2, v4, v6, 0, 3, 2, 4) -> f_90(v1, v3, v5, v7, v9, 1, v11, v12, v2, v4, v6, 0, 3, 2, 4) :|: TRUE 14.66/4.78 f_90(v1, v3, v5, v7, v9, 1, v11, v12, v2, v4, v6, 0, 3, 2, 4) -> f_91(v1, v3, v5, v7, v9, 1, v11, v12, v2, v4, v6, 0, 3, 2, 4) :|: 0 = 0 14.66/4.78 f_91(v1, v3, v5, v7, v9, 1, v11, v12, v2, v4, v6, 0, 3, 2, 4) -> f_92(v1, v3, v5, v7, v9, 1, v11, v12, v14, v2, v4, v6, 0, 3, 2, 4) :|: v14 = 1 + v9 14.66/4.78 f_92(v1, v3, v5, v7, v9, 1, v11, v12, v14, v2, v4, v6, 0, 3, 2, 4) -> f_93(v1, v3, v5, v7, v9, 1, v11, v12, v14, v2, v4, v6, 0, 3, 2, 4) :|: TRUE 14.66/4.78 f_93(v1, v3, v5, v7, v9, 1, v11, v12, v14, v2, v4, v6, 0, 3, 2, 4) -> f_94(v1, v3, v5, v7, v9, 1, v11, v12, v14, v2, v4, v6, 0, 3, 2, 4) :|: TRUE 14.66/4.78 f_94(v1, v3, v5, v7, v9, 1, v11, v12, v14, v2, v4, v6, 0, 3, 2, 4) -> f_111(v1, v3, v5, v7, v9, v7, 1, v9, v11, v12, v14, v2, v4, v6, 0, 3, 2, 4) :|: TRUE 14.66/4.78 f_111(v21, v22, v23, v24, v25, v26, 1, v28, v29, v30, v31, v32, v33, v34, 0, 3, 2, 4) -> f_128(v21, v22, v23, v24, v25, v26, 1, v28, v29, v30, v31, v32, v33, v34, 0, 3, 2, 4) :|: TRUE 14.66/4.78 Combined rules. Obtained 2 rulesP rules: 14.66/4.78 f_129(v41:0, v42:0, v43:0, v44:0, v45:0, v57:0 + 2 * v51:0, 1, v46:0, v48:0, v49:0, v51:0, v52:0, v53:0, v54:0, 0, 3, 2, 4) -> f_129(v41:0, v42:0, v43:0, v44:0, v45:0, v57:0, 1, v57:0 + 2 * v51:0, v51:0, 2 * v51:0, 1 + v51:0, v52:0, v53:0, v54:0, 0, 3, 2, 4) :|: v57:0 + 2 * v51:0 > 0 14.66/4.78 f_69 -> f_129(v1:0, v3:0, v5:0, v12:0 + 2 * v9:0, v9:0, v12:0, 1, v12:0 + 2 * v9:0, v9:0, 2 * v9:0, 1 + v9:0, 3 + v1:0, 3 + v3:0, 3 + v5:0, 0, 3, 2, 4) :|: v3:0 > 0 && v1:0 > 0 && v5:0 > 0 && v12:0 + 2 * v9:0 > 0 14.66/4.78 Filtered unneeded arguments: 14.66/4.78 f_129(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18) -> f_129(x6, x11) 14.66/4.78 Removed division, modulo operations, cleaned up constraints. Obtained 2 rules.P rules: 14.66/4.78 f_129(sum~v57:0~times~cons_2~v51:0, v51:0) -> f_129(v57:0, 1 + v51:0) :|: v57:0 + 2 * v51:0 > 0 && sum~v57:0~times~cons_2~v51:0 = v57:0 + 2 * v51:0 14.66/4.78 f_69 -> f_129(v12:0, 1 + v9:0) :|: v12:0 + 2 * v9:0 > 0 14.66/4.78 14.66/4.78 ---------------------------------------- 14.66/4.78 14.66/4.78 (8) 14.66/4.78 Obligation: 14.66/4.78 Rules: 14.66/4.78 f_129(sum~v57:0~times~cons_2~v51:0, v51:0) -> f_129(v57:0, 1 + v51:0) :|: v57:0 + 2 * v51:0 > 0 && sum~v57:0~times~cons_2~v51:0 = v57:0 + 2 * v51:0 14.66/4.78 f_69 -> f_129(v12:0, 1 + v9:0) :|: v12:0 + 2 * v9:0 > 0 14.66/4.78 Start term: f_69 14.66/4.78 14.66/4.78 ---------------------------------------- 14.66/4.78 14.66/4.78 (9) IRS2T2 (EQUIVALENT) 14.66/4.78 Transformed input IRS into an integer transition system.Used the following mapping from defined symbols to location IDs: 14.66/4.78 14.66/4.78 (f_129_2,1) 14.66/4.78 (f_69_2,2) 14.66/4.78 14.66/4.78 ---------------------------------------- 14.66/4.78 14.66/4.78 (10) 14.66/4.78 Obligation: 14.66/4.78 START: 2; 14.66/4.78 14.66/4.78 FROM: 1; 14.66/4.78 oldX0 := x0; 14.66/4.78 oldX1 := x1; 14.66/4.78 oldX2 := nondet(); 14.66/4.78 assume(oldX2 + 2 * oldX1 > 0 && oldX0 = oldX2 + 2 * oldX1); 14.66/4.78 x0 := oldX2; 14.66/4.78 x1 := 1 + oldX1; 14.66/4.78 TO: 1; 14.66/4.78 14.66/4.78 FROM: 2; 14.66/4.78 oldX0 := x0; 14.66/4.78 oldX1 := x1; 14.66/4.78 oldX2 := nondet(); 14.66/4.78 oldX3 := nondet(); 14.66/4.78 assume(oldX2 + 2 * oldX3 > 0); 14.66/4.78 x0 := oldX2; 14.66/4.78 x1 := 1 + oldX3; 14.66/4.78 TO: 1; 14.66/4.78 14.66/4.78 14.66/4.78 ---------------------------------------- 14.66/4.78 14.66/4.78 (11) T2 (EQUIVALENT) 14.66/4.78 No proof given by T2 14.66/4.78 ---------------------------------------- 14.66/4.78 14.66/4.78 (12) 14.66/4.78 YES 14.66/4.83 EOF