17.06/5.68 YES 17.06/5.68 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 17.06/5.68 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 17.06/5.68 17.06/5.68 17.06/5.68 Termination of the given C Problem could be proven: 17.06/5.68 17.06/5.68 (0) C Problem 17.06/5.68 (1) CToLLVMProof [EQUIVALENT, 172 ms] 17.06/5.68 (2) LLVM problem 17.06/5.68 (3) LLVMToTerminationGraphProof [EQUIVALENT, 2598 ms] 17.06/5.68 (4) LLVM Symbolic Execution Graph 17.06/5.68 (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] 17.06/5.68 (6) LLVM Symbolic Execution SCC 17.06/5.68 (7) SCC2IRS [SOUND, 110 ms] 17.06/5.68 (8) IntTRS 17.06/5.68 (9) IntTRSCompressionProof [EQUIVALENT, 0 ms] 17.06/5.68 (10) IntTRS 17.06/5.68 (11) RankingReductionPairProof [EQUIVALENT, 151 ms] 17.06/5.68 (12) YES 17.06/5.68 17.06/5.68 17.06/5.68 ---------------------------------------- 17.06/5.68 17.06/5.68 (0) 17.06/5.68 Obligation: 17.06/5.68 c file /export/starexec/sandbox/benchmark/theBenchmark.c 17.06/5.68 ---------------------------------------- 17.06/5.68 17.06/5.68 (1) CToLLVMProof (EQUIVALENT) 17.06/5.68 Compiled c-file /export/starexec/sandbox/benchmark/theBenchmark.c to LLVM. 17.06/5.68 ---------------------------------------- 17.06/5.68 17.06/5.68 (2) 17.06/5.68 Obligation: 17.06/5.68 LLVM Problem 17.06/5.68 17.06/5.68 Aliases: 17.06/5.68 17.06/5.68 Data layout: 17.06/5.68 17.06/5.68 "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" 17.06/5.68 17.06/5.68 Machine: 17.06/5.68 17.06/5.68 "x86_64-pc-linux-gnu" 17.06/5.68 17.06/5.68 Type definitions: 17.06/5.68 17.06/5.68 Global variables: 17.06/5.68 17.06/5.68 Function declarations and definitions: 17.06/5.68 17.06/5.68 *BasicFunctionTypename: "__VERIFIER_nondet_int" returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 17.06/5.68 *BasicFunctionTypename: "test_fun" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: (x i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc 17.06/5.68 0: 17.06/5.68 %1 = alloca i32, align 4 17.06/5.68 %x_ref = alloca *i32, align 8 17.06/5.68 %c = alloca *i32, align 8 17.06/5.68 store %x, %1 17.06/5.68 %2 = alloca i8, numElementsLit: 4 17.06/5.68 %3 = bitcast *i8 %2 to *i32 17.06/5.68 store %3, %x_ref 17.06/5.68 %4 = alloca i8, numElementsLit: 4 17.06/5.68 %5 = bitcast *i8 %4 to *i32 17.06/5.68 store %5, %c 17.06/5.68 %6 = load %1 17.06/5.68 %7 = load %x_ref 17.06/5.68 store %6, %7 17.06/5.68 %8 = load %c 17.06/5.68 store 0, %8 17.06/5.68 br %9 17.06/5.68 9: 17.06/5.68 %10 = load %x_ref 17.06/5.68 %11 = load %10 17.06/5.68 %12 = icmp sgt %11 1 17.06/5.68 br %12, %13, %17 17.06/5.68 13: 17.06/5.68 %14 = load %x_ref 17.06/5.68 %15 = load %14 17.06/5.68 %16 = icmp slt %15 100 17.06/5.68 br %17 17.06/5.68 17: 17.06/5.68 %18 = phi [0, %9], [%16, %13] 17.06/5.68 br %18, %19, %30 17.06/5.68 19: 17.06/5.68 %20 = load %x_ref 17.06/5.68 %21 = load %20 17.06/5.68 %22 = load %x_ref 17.06/5.68 %23 = load %22 17.06/5.68 %24 = mul %21 %23 17.06/5.68 %25 = load %x_ref 17.06/5.68 store %24, %25 17.06/5.68 %26 = load %c 17.06/5.68 %27 = load %26 17.06/5.68 %28 = add %27 1 17.06/5.68 %29 = load %c 17.06/5.68 store %28, %29 17.06/5.68 br %9 17.06/5.68 30: 17.06/5.68 %31 = load %c 17.06/5.68 %32 = load %31 17.06/5.68 ret %32 17.06/5.68 17.06/5.68 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 17.06/5.68 0: 17.06/5.68 %1 = alloca i32, align 4 17.06/5.68 store 0, %1 17.06/5.68 %2 = call i32 @__VERIFIER_nondet_int() 17.06/5.68 %3 = call i32 @test_fun(i32 %2) 17.06/5.68 ret %3 17.06/5.68 17.06/5.68 17.06/5.68 Analyze Termination of all function calls matching the pattern: 17.06/5.68 main() 17.06/5.68 ---------------------------------------- 17.06/5.68 17.06/5.68 (3) LLVMToTerminationGraphProof (EQUIVALENT) 17.06/5.68 Constructed symbolic execution graph for LLVM program and proved memory safety. 17.06/5.68 ---------------------------------------- 17.06/5.68 17.06/5.68 (4) 17.06/5.68 Obligation: 17.06/5.68 SE Graph 17.06/5.68 ---------------------------------------- 17.06/5.68 17.06/5.68 (5) SymbolicExecutionGraphToSCCProof (SOUND) 17.06/5.68 Splitted symbolic execution graph to 1 SCC. 17.06/5.68 ---------------------------------------- 17.06/5.68 17.06/5.68 (6) 17.06/5.68 Obligation: 17.06/5.68 SCC 17.06/5.68 ---------------------------------------- 17.06/5.68 17.06/5.68 (7) SCC2IRS (SOUND) 17.06/5.68 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 17.06/5.68 Generated rules. Obtained 25 rulesP rules: 17.06/5.68 f_438(v427, v428, v429, v430, v431, v432, v433, 1, v435, v436, v437, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) -> f_439(v427, v428, v429, v430, v431, v432, v435, 1, v433, v436, v437, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) :|: 0 = 0 17.06/5.68 f_439(v427, v428, v429, v430, v431, v432, v435, 1, v433, v436, v437, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) -> f_440(v427, v428, v429, v430, v431, v432, v435, 1, v433, v436, v437, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) :|: 1 < v435 17.06/5.68 f_440(v427, v428, v429, v430, v431, v432, v435, 1, v433, v436, v437, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) -> f_442(v427, v428, v429, v430, v431, v432, v435, 1, v433, v436, v437, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) :|: 0 = 0 17.06/5.68 f_442(v427, v428, v429, v430, v431, v432, v435, 1, v433, v436, v437, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) -> f_444(v427, v428, v429, v430, v431, v432, v435, 1, v433, v436, v437, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) :|: TRUE 17.06/5.68 f_444(v427, v428, v429, v430, v431, v432, v435, 1, v433, v436, v437, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) -> f_446(v427, v428, v429, v430, v431, v432, v435, 1, v433, v436, v437, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) :|: 0 = 0 17.06/5.68 f_446(v427, v428, v429, v430, v431, v432, v435, 1, v433, v436, v437, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) -> f_448(v427, v428, v429, v430, v431, v432, v435, 1, v433, v436, v437, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) :|: 0 = 0 17.06/5.68 f_448(v427, v428, v429, v430, v431, v432, v435, 1, v433, v436, v437, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) -> f_450(v427, v428, v429, v430, v431, v432, v435, 1, v433, v436, v437, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) :|: v435 < 100 17.06/5.68 f_450(v427, v428, v429, v430, v431, v432, v435, 1, v433, v436, v437, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) -> f_453(v427, v428, v429, v430, v431, v432, v435, 1, v433, v436, v437, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) :|: 0 = 0 17.06/5.68 f_453(v427, v428, v429, v430, v431, v432, v435, 1, v433, v436, v437, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) -> f_456(v427, v428, v429, v430, v431, v432, v435, 1, v433, v436, v437, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) :|: 0 = 0 17.06/5.68 f_456(v427, v428, v429, v430, v431, v432, v435, 1, v433, v436, v437, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) -> f_458(v427, v428, v429, v430, v431, v432, v435, 1, v433, v436, v437, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) :|: TRUE 17.06/5.68 f_458(v427, v428, v429, v430, v431, v432, v435, 1, v433, v436, v437, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) -> f_460(v427, v428, v429, v430, v431, v432, v435, 1, v433, v436, v437, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) :|: 0 = 0 17.06/5.68 f_460(v427, v428, v429, v430, v431, v432, v435, 1, v433, v436, v437, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) -> f_462(v427, v428, v429, v430, v431, v432, v435, 1, v433, v436, v437, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) :|: 0 = 0 17.06/5.68 f_462(v427, v428, v429, v430, v431, v432, v435, 1, v433, v436, v437, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) -> f_464(v427, v428, v429, v430, v431, v432, v435, 1, v433, v436, v437, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) :|: 0 = 0 17.06/5.68 f_464(v427, v428, v429, v430, v431, v432, v435, 1, v433, v436, v437, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) -> f_466(v427, v428, v429, v430, v431, v432, v435, 1, v436, v437, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) :|: 0 = 0 17.06/5.68 f_466(v427, v428, v429, v430, v431, v432, v435, 1, v436, v437, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) -> f_467(v427, v428, v429, v430, v431, v432, v435, 1, v489, v436, v437, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) :|: v489 = v435 * v435 17.06/5.68 f_467(v427, v428, v429, v430, v431, v432, v435, 1, v489, v436, v437, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) -> f_468(v427, v428, v429, v430, v431, v432, v435, 1, v489, v436, v437, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) :|: 0 = 0 17.06/5.68 f_468(v427, v428, v429, v430, v431, v432, v435, 1, v489, v436, v437, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) -> f_469(v427, v428, v429, v430, v431, v432, v435, 1, v489, v436, v437, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) :|: TRUE 17.06/5.68 f_469(v427, v428, v429, v430, v431, v432, v435, 1, v489, v436, v437, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) -> f_470(v427, v428, v429, v430, v431, v432, v435, 1, v489, v436, v437, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) :|: 0 = 0 17.06/5.68 f_470(v427, v428, v429, v430, v431, v432, v435, 1, v489, v436, v437, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) -> f_471(v427, v428, v429, v430, v431, v432, v435, 1, v489, v437, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) :|: 0 = 0 17.06/5.68 f_471(v427, v428, v429, v430, v431, v432, v435, 1, v489, v437, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) -> f_472(v427, v428, v429, v430, v431, v432, v435, 1, v489, v437, v491, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) :|: v491 = 1 + v437 && 2 <= v491 17.06/5.68 f_472(v427, v428, v429, v430, v431, v432, v435, 1, v489, v437, v491, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) -> f_473(v427, v428, v429, v430, v431, v432, v435, 1, v489, v437, v491, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) :|: 0 = 0 17.06/5.68 f_473(v427, v428, v429, v430, v431, v432, v435, 1, v489, v437, v491, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) -> f_474(v427, v428, v429, v430, v431, v432, v435, 1, v489, v437, v491, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) :|: TRUE 17.06/5.68 f_474(v427, v428, v429, v430, v431, v432, v435, 1, v489, v437, v491, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) -> f_475(v427, v428, v429, v430, v431, v432, v435, 1, v489, v437, v491, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) :|: TRUE 17.06/5.68 f_475(v427, v428, v429, v430, v431, v432, v435, 1, v489, v437, v491, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) -> f_437(v427, v428, v429, v430, v431, v432, v435, 1, v489, v437, v491, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) :|: TRUE 17.06/5.68 f_437(v427, v428, v429, v430, v431, v432, v433, 1, v435, v436, v437, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) -> f_438(v427, v428, v429, v430, v431, v432, v433, 1, v435, v436, v437, v438, v439, v440, v441, v442, v443, v444, 0, 3, 7, 2, 99, 4, 8) :|: 0 = 0 17.06/5.68 Combined rules. Obtained 1 rulesP rules: 17.06/5.68 f_438(v427:0, v428:0, v429:0, v430:0, v431:0, v432:0, v433:0, 1, v435:0, v436:0, v437:0, v438:0, v439:0, v440:0, v441:0, v442:0, v443:0, v444:0, 0, 3, 7, 2, 99, 4, 8) -> f_438(v427:0, v428:0, v429:0, v430:0, v431:0, v432:0, v435:0, 1, v435:0 * v435:0, v437:0, 1 + v437:0, v438:0, v439:0, v440:0, v441:0, v442:0, v443:0, v444:0, 0, 3, 7, 2, 99, 4, 8) :|: v435:0 > 1 && v437:0 > 0 && v435:0 < 100 17.06/5.68 Filtered unneeded arguments: 17.06/5.68 f_438(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25) -> f_438(x9, x11) 17.06/5.68 Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: 17.06/5.68 f_438(v435:0, v437:0) -> f_438(v435:0 * v435:0, 1 + v437:0) :|: v437:0 > 0 && v435:0 < 100 && v435:0 > 1 17.06/5.68 17.06/5.68 ---------------------------------------- 17.06/5.68 17.06/5.68 (8) 17.06/5.68 Obligation: 17.06/5.68 Rules: 17.06/5.68 f_438(v435:0, v437:0) -> f_438(v435:0 * v435:0, 1 + v437:0) :|: v437:0 > 0 && v435:0 < 100 && v435:0 > 1 17.06/5.68 17.06/5.68 ---------------------------------------- 17.06/5.68 17.06/5.68 (9) IntTRSCompressionProof (EQUIVALENT) 17.06/5.68 Compressed rules. 17.06/5.68 ---------------------------------------- 17.06/5.68 17.06/5.68 (10) 17.06/5.68 Obligation: 17.06/5.68 Rules: 17.06/5.68 f_438(v435:0:0, v437:0:0) -> f_438(v435:0:0 * v435:0:0, 1 + v437:0:0) :|: v437:0:0 > 0 && v435:0:0 < 100 && v435:0:0 > 1 17.06/5.68 17.06/5.68 ---------------------------------------- 17.06/5.68 17.06/5.68 (11) RankingReductionPairProof (EQUIVALENT) 17.06/5.68 Interpretation: 17.06/5.68 [ f_438 ] = -1/2*f_438_1 17.06/5.68 17.06/5.68 The following rules are decreasing: 17.06/5.68 f_438(v435:0:0, v437:0:0) -> f_438(v435:0:0 * v435:0:0, 1 + v437:0:0) :|: v437:0:0 > 0 && v435:0:0 < 100 && v435:0:0 > 1 17.06/5.68 17.06/5.68 The following rules are bounded: 17.06/5.68 f_438(v435:0:0, v437:0:0) -> f_438(v435:0:0 * v435:0:0, 1 + v437:0:0) :|: v437:0:0 > 0 && v435:0:0 < 100 && v435:0:0 > 1 17.06/5.68 17.06/5.68 17.06/5.68 ---------------------------------------- 17.06/5.68 17.06/5.68 (12) 17.06/5.68 YES 17.28/5.79 EOF