7.76/2.90 YES 7.76/2.92 proof of /export/starexec/sandbox2/benchmark/theBenchmark.c 7.76/2.92 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 7.76/2.92 7.76/2.92 7.76/2.92 Termination of the given C Problem could be proven: 7.76/2.92 7.76/2.92 (0) C Problem 7.76/2.92 (1) CToLLVMProof [EQUIVALENT, 175 ms] 7.76/2.92 (2) LLVM problem 7.76/2.92 (3) LLVMToTerminationGraphProof [EQUIVALENT, 595 ms] 7.76/2.92 (4) LLVM Symbolic Execution Graph 7.76/2.92 (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] 7.76/2.92 (6) LLVM Symbolic Execution SCC 7.76/2.92 (7) SCC2IRS [SOUND, 31 ms] 7.76/2.92 (8) IntTRS 7.76/2.92 (9) IntTRSCompressionProof [EQUIVALENT, 0 ms] 7.76/2.92 (10) IntTRS 7.76/2.92 (11) PolynomialOrderProcessor [EQUIVALENT, 13 ms] 7.76/2.92 (12) YES 7.76/2.92 7.76/2.92 7.76/2.92 ---------------------------------------- 7.76/2.92 7.76/2.92 (0) 7.76/2.92 Obligation: 7.76/2.92 c file /export/starexec/sandbox2/benchmark/theBenchmark.c 7.76/2.92 ---------------------------------------- 7.76/2.92 7.76/2.92 (1) CToLLVMProof (EQUIVALENT) 7.76/2.92 Compiled c-file /export/starexec/sandbox2/benchmark/theBenchmark.c to LLVM. 7.76/2.92 ---------------------------------------- 7.76/2.92 7.76/2.92 (2) 7.76/2.92 Obligation: 7.76/2.92 LLVM Problem 7.76/2.92 7.76/2.92 Aliases: 7.76/2.92 7.76/2.92 Data layout: 7.76/2.92 7.76/2.92 "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" 7.76/2.92 7.76/2.92 Machine: 7.76/2.92 7.76/2.92 "x86_64-pc-linux-gnu" 7.76/2.92 7.76/2.92 Type definitions: 7.76/2.92 7.76/2.92 Global variables: 7.76/2.92 7.76/2.92 Function declarations and definitions: 7.76/2.92 7.76/2.92 *BasicFunctionTypename: "__VERIFIER_nondet_int" returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 7.76/2.92 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 7.76/2.92 0: 7.76/2.92 %1 = alloca i32, align 4 7.76/2.92 %n = alloca i32, align 4 7.76/2.92 %i = alloca i32, align 4 7.76/2.92 store 0, %1 7.76/2.92 %2 = call i32 @__VERIFIER_nondet_int() 7.76/2.92 store %2, %n 7.76/2.92 %3 = load %n 7.76/2.92 %4 = sub %3 1 7.76/2.92 store %4, %i 7.76/2.92 br %5 7.76/2.92 5: 7.76/2.92 %6 = load %i 7.76/2.92 %7 = icmp sgt %6 1 7.76/2.92 br %7, %8, %11 7.76/2.92 8: 7.76/2.92 %9 = load %i 7.76/2.92 %10 = add %9 -1 7.76/2.92 store %10, %i 7.76/2.92 br %5 7.76/2.92 11: 7.76/2.92 ret 0 7.76/2.92 7.76/2.92 7.76/2.92 Analyze Termination of all function calls matching the pattern: 7.76/2.92 main() 7.76/2.92 ---------------------------------------- 7.76/2.92 7.76/2.92 (3) LLVMToTerminationGraphProof (EQUIVALENT) 7.76/2.92 Constructed symbolic execution graph for LLVM program and proved memory safety. 7.76/2.92 ---------------------------------------- 7.76/2.92 7.76/2.92 (4) 7.76/2.92 Obligation: 7.76/2.92 SE Graph 7.76/2.92 ---------------------------------------- 7.76/2.92 7.76/2.92 (5) SymbolicExecutionGraphToSCCProof (SOUND) 7.76/2.92 Splitted symbolic execution graph to 1 SCC. 7.76/2.92 ---------------------------------------- 7.76/2.92 7.76/2.92 (6) 7.76/2.92 Obligation: 7.76/2.92 SCC 7.76/2.92 ---------------------------------------- 7.76/2.92 7.76/2.92 (7) SCC2IRS (SOUND) 7.76/2.92 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 7.76/2.92 Generated rules. Obtained 9 rulesP rules: 7.76/2.92 f_103(v29, v30, v31, v32, v33, v36, 1, v34, v37, v38, v39, 0, 3, 2, 4) -> f_104(v29, v30, v31, v32, v33, v36, 1, v34, v37, v38, v39, 0, 3, 4, 2) :|: 1 < v36 && 3 <= v34 && 4 <= v32 && 3 <= v33 7.76/2.92 f_104(v29, v30, v31, v32, v33, v36, 1, v34, v37, v38, v39, 0, 3, 4, 2) -> f_106(v29, v30, v31, v32, v33, v36, 1, v34, v37, v38, v39, 0, 3, 4, 2) :|: 0 = 0 7.76/2.92 f_106(v29, v30, v31, v32, v33, v36, 1, v34, v37, v38, v39, 0, 3, 4, 2) -> f_108(v29, v30, v31, v32, v33, v36, 1, v34, v37, v38, v39, 0, 3, 4, 2) :|: TRUE 7.76/2.92 f_108(v29, v30, v31, v32, v33, v36, 1, v34, v37, v38, v39, 0, 3, 4, 2) -> f_110(v29, v30, v31, v32, v33, v36, 1, v37, v38, v39, 0, 3, 4, 2) :|: 0 = 0 7.76/2.92 f_110(v29, v30, v31, v32, v33, v36, 1, v37, v38, v39, 0, 3, 4, 2) -> f_111(v29, v30, v31, v32, v33, v36, 1, v41, v37, v38, v39, 0, 3, 4, 2) :|: 1 + v41 = v36 && 1 <= v41 7.76/2.92 f_111(v29, v30, v31, v32, v33, v36, 1, v41, v37, v38, v39, 0, 3, 4, 2) -> f_112(v29, v30, v31, v32, v33, v36, 1, v41, v37, v38, v39, 0, 3, 4, 2) :|: TRUE 7.76/2.92 f_112(v29, v30, v31, v32, v33, v36, 1, v41, v37, v38, v39, 0, 3, 4, 2) -> f_113(v29, v30, v31, v32, v33, v36, 1, v41, v37, v38, v39, 0, 3, 4, 2) :|: TRUE 7.76/2.92 f_113(v29, v30, v31, v32, v33, v36, 1, v41, v37, v38, v39, 0, 3, 4, 2) -> f_102(v29, v30, v31, v32, v33, v36, 1, v41, v37, v38, v39, 0, 3, 2, 4) :|: TRUE 7.76/2.92 f_102(v29, v30, v31, v32, v33, v34, 1, v36, v37, v38, v39, 0, 3, 2, 4) -> f_103(v29, v30, v31, v32, v33, v36, 1, v34, v37, v38, v39, 0, 3, 2, 4) :|: 0 = 0 7.76/2.92 Combined rules. Obtained 1 rulesP rules: 7.76/2.92 f_103(v29:0, v30:0, v31:0, v32:0, v33:0, 1 + v41:0, 1, v34:0, v37:0, v38:0, v39:0, 0, 3, 2, 4) -> f_103(v29:0, v30:0, v31:0, v32:0, v33:0, v41:0, 1, 1 + v41:0, v37:0, v38:0, v39:0, 0, 3, 2, 4) :|: v34:0 > 2 && v41:0 > 0 && v32:0 > 3 && v33:0 > 2 7.76/2.92 Filtered unneeded arguments: 7.76/2.92 f_103(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) -> f_103(x4, x5, x6, x8) 7.76/2.92 Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: 7.76/2.92 f_103(v32:0, v33:0, sum~cons_1~v41:0, v34:0) -> f_103(v32:0, v33:0, v41:0, 1 + v41:0) :|: v41:0 > 0 && v34:0 > 2 && v33:0 > 2 && v32:0 > 3 && sum~cons_1~v41:0 = 1 + v41:0 7.76/2.92 7.76/2.92 ---------------------------------------- 7.76/2.92 7.76/2.92 (8) 7.76/2.92 Obligation: 7.76/2.92 Rules: 7.76/2.92 f_103(v32:0, v33:0, sum~cons_1~v41:0, v34:0) -> f_103(v32:0, v33:0, v41:0, 1 + v41:0) :|: v41:0 > 0 && v34:0 > 2 && v33:0 > 2 && v32:0 > 3 && sum~cons_1~v41:0 = 1 + v41:0 7.76/2.92 7.76/2.92 ---------------------------------------- 7.76/2.92 7.76/2.92 (9) IntTRSCompressionProof (EQUIVALENT) 7.76/2.92 Compressed rules. 7.76/2.92 ---------------------------------------- 7.76/2.92 7.76/2.92 (10) 7.76/2.92 Obligation: 7.76/2.92 Rules: 7.76/2.92 f_103(v32:0:0, v33:0:0, sum~cons_1~v41:0:0, v34:0:0) -> f_103(v32:0:0, v33:0:0, v41:0:0, 1 + v41:0:0) :|: v33:0:0 > 2 && v32:0:0 > 3 && v34:0:0 > 2 && v41:0:0 > 0 && sum~cons_1~v41:0:0 = 1 + v41:0:0 7.76/2.92 7.76/2.92 ---------------------------------------- 7.76/2.92 7.76/2.92 (11) PolynomialOrderProcessor (EQUIVALENT) 7.76/2.92 Found the following polynomial interpretation: 7.76/2.92 [f_103(x, x1, x2, x3)] = x2 7.76/2.92 7.76/2.92 The following rules are decreasing: 7.76/2.92 f_103(v32:0:0, v33:0:0, sum~cons_1~v41:0:0, v34:0:0) -> f_103(v32:0:0, v33:0:0, v41:0:0, 1 + v41:0:0) :|: v33:0:0 > 2 && v32:0:0 > 3 && v34:0:0 > 2 && v41:0:0 > 0 && sum~cons_1~v41:0:0 = 1 + v41:0:0 7.76/2.92 The following rules are bounded: 7.76/2.92 f_103(v32:0:0, v33:0:0, sum~cons_1~v41:0:0, v34:0:0) -> f_103(v32:0:0, v33:0:0, v41:0:0, 1 + v41:0:0) :|: v33:0:0 > 2 && v32:0:0 > 3 && v34:0:0 > 2 && v41:0:0 > 0 && sum~cons_1~v41:0:0 = 1 + v41:0:0 7.76/2.92 7.76/2.92 ---------------------------------------- 7.76/2.92 7.76/2.92 (12) 7.76/2.92 YES 7.76/2.96 EOF