19.65/6.85 YES 19.65/6.86 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 19.65/6.86 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 19.65/6.86 19.65/6.86 19.65/6.86 Termination of the given C Problem could be proven: 19.65/6.86 19.65/6.86 (0) C Problem 19.65/6.86 (1) CToLLVMProof [EQUIVALENT, 167 ms] 19.65/6.86 (2) LLVM problem 19.65/6.86 (3) LLVMToTerminationGraphProof [EQUIVALENT, 3497 ms] 19.65/6.86 (4) LLVM Symbolic Execution Graph 19.65/6.86 (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] 19.65/6.86 (6) LLVM Symbolic Execution SCC 19.65/6.86 (7) SCC2IRS [SOUND, 119 ms] 19.65/6.86 (8) IntTRS 19.65/6.86 (9) IntTRSCompressionProof [EQUIVALENT, 0 ms] 19.65/6.86 (10) IntTRS 19.65/6.86 (11) PolynomialOrderProcessor [EQUIVALENT, 13 ms] 19.65/6.86 (12) YES 19.65/6.86 19.65/6.86 19.65/6.86 ---------------------------------------- 19.65/6.86 19.65/6.86 (0) 19.65/6.86 Obligation: 19.65/6.86 c file /export/starexec/sandbox/benchmark/theBenchmark.c 19.65/6.86 ---------------------------------------- 19.65/6.86 19.65/6.86 (1) CToLLVMProof (EQUIVALENT) 19.65/6.86 Compiled c-file /export/starexec/sandbox/benchmark/theBenchmark.c to LLVM. 19.65/6.86 ---------------------------------------- 19.65/6.86 19.65/6.86 (2) 19.65/6.86 Obligation: 19.65/6.86 LLVM Problem 19.65/6.86 19.65/6.86 Aliases: 19.65/6.86 19.65/6.86 Data layout: 19.65/6.86 19.65/6.86 "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" 19.65/6.86 19.65/6.86 Machine: 19.65/6.86 19.65/6.86 "x86_64-pc-linux-gnu" 19.65/6.86 19.65/6.86 Type definitions: 19.65/6.86 19.65/6.86 Global variables: 19.65/6.86 19.65/6.86 Function declarations and definitions: 19.65/6.86 19.65/6.86 *BasicFunctionTypename: "__VERIFIER_nondet_int" returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 19.65/6.86 *BasicFunctionTypename: "cbzero" linkageType: EXTERNALLY_VISIBLE returnParam: BasicVoidType parameters: (b *i8, length i64) variableLength: false visibilityType: DEFAULT callingConvention: ccc 19.65/6.86 0: 19.65/6.86 %1 = alloca *i8, align 8 19.65/6.86 %2 = alloca i64, align 8 19.65/6.86 %p = alloca *i8, align 8 19.65/6.86 store %b, %1 19.65/6.86 store %length, %2 19.65/6.86 %3 = load %1 19.65/6.86 store %3, %p 19.65/6.86 br %4 19.65/6.86 4: 19.65/6.86 %5 = load %2 19.65/6.86 %6 = add %5 -1 19.65/6.86 store %6, %2 19.65/6.86 %7 = icmp ne %5 0 19.65/6.86 br %7, %8, %11 19.65/6.86 8: 19.65/6.86 %9 = load %p 19.65/6.86 %10 = getelementptr %9, 1 19.65/6.86 store %10, %p 19.65/6.86 store 0, %9 19.65/6.86 br %4 19.65/6.86 11: 19.65/6.86 ret void 19.65/6.86 19.65/6.86 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 19.65/6.86 0: 19.65/6.86 %1 = alloca i32, align 4 19.65/6.86 %length = alloca i32, align 4 19.65/6.86 %n = alloca i32, align 4 19.65/6.86 %nondetArea = alloca *i8, align 8 19.65/6.86 store 0, %1 19.65/6.86 %2 = call i32 @__VERIFIER_nondet_int() 19.65/6.86 store %2, %length 19.65/6.86 %3 = call i32 @__VERIFIER_nondet_int() 19.65/6.86 store %3, %n 19.65/6.86 %4 = load %length 19.65/6.86 %5 = icmp slt %4 1 19.65/6.86 br %5, %6, %7 19.65/6.86 6: 19.65/6.86 store 1, %length 19.65/6.86 br %7 19.65/6.86 7: 19.65/6.86 %8 = load %n 19.65/6.86 %9 = icmp slt %8 1 19.65/6.86 br %9, %10, %11 19.65/6.86 10: 19.65/6.86 store 1, %n 19.65/6.86 br %11 19.65/6.86 11: 19.65/6.86 %12 = load %n 19.65/6.86 %13 = load %length 19.65/6.86 %14 = icmp sgt %12 %13 19.65/6.86 br %14, %15, %16 19.65/6.86 15: 19.65/6.86 store 0, %1 19.65/6.86 br %24 19.65/6.86 16: 19.65/6.86 %17 = load %length 19.65/6.86 %18 = sext i32 %17 to i64 19.65/6.86 %19 = mul %18 1 19.65/6.86 %20 = alloca i8, numElementsLit: %19 19.65/6.86 store %20, %nondetArea 19.65/6.86 %21 = load %nondetArea 19.65/6.86 %22 = load %n 19.65/6.86 %23 = sext i32 %22 to i64 19.65/6.86 Unnamed Call-Instruction = call BasicVoidType @cbzero(*i8 %21, i64 %23) 19.65/6.86 store 0, %1 19.65/6.86 br %24 19.65/6.86 24: 19.65/6.86 %25 = load %1 19.65/6.86 ret %25 19.65/6.86 19.65/6.86 19.65/6.86 Analyze Termination of all function calls matching the pattern: 19.65/6.86 main() 19.65/6.86 ---------------------------------------- 19.65/6.86 19.65/6.86 (3) LLVMToTerminationGraphProof (EQUIVALENT) 19.65/6.86 Constructed symbolic execution graph for LLVM program and proved memory safety. 19.65/6.86 ---------------------------------------- 19.65/6.86 19.65/6.86 (4) 19.65/6.86 Obligation: 19.65/6.86 SE Graph 19.65/6.86 ---------------------------------------- 19.65/6.86 19.65/6.86 (5) SymbolicExecutionGraphToSCCProof (SOUND) 19.65/6.86 Splitted symbolic execution graph to 1 SCC. 19.65/6.86 ---------------------------------------- 19.65/6.86 19.65/6.86 (6) 19.65/6.86 Obligation: 19.65/6.86 SCC 19.65/6.86 ---------------------------------------- 19.65/6.86 19.65/6.86 (7) SCC2IRS (SOUND) 19.65/6.86 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 19.65/6.86 Generated rules. Obtained 12 rulesP rules: 19.65/6.86 f_406(v408, v409, v410, v411, v412, v413, v414, 1, v417, v418, v426, v419, v427, v420, v428, v421, v429, v430, v431, v432, v433, 0, v416, v425, v422, v423, 3, 7, 2, 4, 8) -> f_407(v408, v409, v410, v411, v412, v413, v414, 1, v417, v434, v418, v426, v419, v427, v420, v428, v421, v429, v430, v431, v432, v433, 0, v416, v425, v422, v423, 3, 7, 2, 4, 8) :|: v434 = 1 + v417 && 3 <= v434 19.65/6.86 f_407(v408, v409, v410, v411, v412, v413, v414, 1, v417, v434, v418, v426, v419, v427, v420, v428, v421, v429, v430, v431, v432, v433, 0, v416, v425, v422, v423, 3, 7, 2, 4, 8) -> f_408(v408, v409, v410, v411, v412, v413, v414, 1, v417, v434, v418, v426, v419, v427, v420, v428, v421, v429, v430, v431, v432, v433, 0, v416, v425, v422, v423, 3, 7, 2, 4, 8) :|: TRUE 19.65/6.87 f_408(v408, v409, v410, v411, v412, v413, v414, 1, v417, v434, v418, v426, v419, v427, v420, v428, v421, v429, v430, v431, v432, v433, 0, v416, v425, v422, v423, 3, 7, 2, 4, 8) -> f_409(v408, v409, v410, v411, v412, v413, v414, 1, v417, v434, v418, v426, v419, v427, v420, v428, v421, v429, v430, v431, v432, v433, 0, v416, v425, v422, v423, 3, 7, 2, 4, 8) :|: TRUE 19.65/6.87 f_409(v408, v409, v410, v411, v412, v413, v414, 1, v417, v434, v418, v426, v419, v427, v420, v428, v421, v429, v430, v431, v432, v433, 0, v416, v425, v422, v423, 3, 7, 2, 4, 8) -> f_410(v408, v409, v410, v411, v412, v413, v414, 1, v417, v434, v418, v426, v419, v427, v420, v428, v421, v429, v430, v431, v432, v433, 0, v416, v425, v422, v423, 3, 7, 2, 4, 8) :|: TRUE 19.65/6.87 f_410(v408, v409, v410, v411, v412, v413, v414, 1, v417, v434, v418, v426, v419, v427, v420, v428, v421, v429, v430, v431, v432, v433, 0, v416, v425, v422, v423, 3, 7, 2, 4, 8) -> f_411(v408, v409, v410, v411, v412, v414, 1, v417, v434, v418, v426, v419, v427, v420, v428, v421, v429, v430, v431, v432, v433, 0, v416, v425, v422, v423, 3, 7, 2, 4, 8) :|: 0 = 0 19.65/6.87 f_411(v408, v409, v410, v411, v412, v414, 1, v417, v434, v418, v426, v419, v427, v420, v428, v421, v429, v430, v431, v432, v433, 0, v416, v425, v422, v423, 3, 7, 2, 4, 8) -> f_412(v408, v409, v410, v411, v412, v414, v446, 1, v417, v434, v418, v426, v419, v427, v420, v428, v421, v429, v430, v431, v432, v433, 0, v416, v425, v422, v423, 3, 7, 2, 4, 8) :|: 1 + v446 = v414 && 0 <= 1 + v446 19.65/6.87 f_412(v408, v409, v410, v411, v412, v414, v446, 1, v417, v434, v418, v426, v419, v427, v420, v428, v421, v429, v430, v431, v432, v433, 0, v416, v425, v422, v423, 3, 7, 2, 4, 8) -> f_413(v408, v409, v410, v411, v412, v414, v446, 1, v417, v434, v418, v426, v419, v427, v420, v428, v421, v429, v430, v431, v432, v433, 0, v416, v425, v422, v423, 3, 7, 2, 4, 8) :|: TRUE 19.65/6.87 f_413(v408, v409, v410, v411, v412, v414, v446, 1, v417, v434, v418, v426, v419, v427, v420, v428, v421, v429, v430, v431, v432, v433, 0, v416, v425, v422, v423, 3, 7, 2, 4, 8) -> f_414(v408, v409, v410, v411, v412, v414, v446, 1, v417, v434, v418, v426, v419, v427, v420, v428, v421, v429, v430, v431, v432, v433, 0, v416, v425, v422, v423, 3, 7, 2, 4, 8) :|: v414 != 0 && 0 <= v446 && 3 <= v430 19.65/6.87 f_414(v408, v409, v410, v411, v412, v414, v446, 1, v417, v434, v418, v426, v419, v427, v420, v428, v421, v429, v430, v431, v432, v433, 0, v416, v425, v422, v423, 3, 7, 2, 4, 8) -> f_416(v408, v409, v410, v411, v412, v414, v446, 1, v417, v434, v418, v426, v419, v427, v420, v428, v421, v429, v430, v431, v432, v433, 0, v416, v425, v422, v423, 3, 7, 2, 4, 8) :|: 0 = 0 19.65/6.87 f_416(v408, v409, v410, v411, v412, v414, v446, 1, v417, v434, v418, v426, v419, v427, v420, v428, v421, v429, v430, v431, v432, v433, 0, v416, v425, v422, v423, 3, 7, 2, 4, 8) -> f_418(v408, v409, v410, v411, v412, v414, v446, 1, v417, v434, v418, v426, v419, v427, v420, v428, v421, v429, v430, v431, v432, v433, 0, v416, v425, v422, v423, 3, 7, 2, 4, 8) :|: TRUE 19.65/6.87 f_418(v408, v409, v410, v411, v412, v414, v446, 1, v417, v434, v418, v426, v419, v427, v420, v428, v421, v429, v430, v431, v432, v433, 0, v416, v425, v422, v423, 3, 7, 2, 4, 8) -> f_405(v408, v409, v410, v411, v412, v414, v446, 1, v417, v434, v418, v426, v419, v427, v420, v428, v421, v429, v430, v431, v432, v433, 0, v425, v422, v423, 3, 7, 2, 4, 8) :|: TRUE 19.65/6.87 f_405(v408, v409, v410, v411, v412, v413, v414, 1, v416, v417, v418, v426, v419, v427, v420, v428, v421, v429, v430, v431, v432, v433, 0, v425, v422, v423, 3, 7, 2, 4, 8) -> f_406(v408, v409, v410, v411, v412, v413, v414, 1, v417, v418, v426, v419, v427, v420, v428, v421, v429, v430, v431, v432, v433, 0, v416, v425, v422, v423, 3, 7, 2, 4, 8) :|: 0 = 0 19.65/6.87 Combined rules. Obtained 1 rulesP rules: 19.65/6.87 f_406(v408:0, v409:0, v410:0, v411:0, v412:0, v413:0, 1 + v446:0, 1, v417:0, v418:0, v426:0, v419:0, v427:0, v420:0, v428:0, v421:0, v429:0, v430:0, v431:0, v432:0, v433:0, 0, v416:0, v425:0, v422:0, v423:0, 3, 7, 2, 4, 8) -> f_406(v408:0, v409:0, v410:0, v411:0, v412:0, 1 + v446:0, v446:0, 1, 1 + v417:0, v418:0, v426:0, v419:0, v427:0, v420:0, v428:0, v421:0, v429:0, v430:0, v431:0, v432:0, v433:0, 0, v417:0, v425:0, v422:0, v423:0, 3, 7, 2, 4, 8) :|: v446:0 > -1 && v417:0 > 1 && v430:0 > 2 19.65/6.87 Filtered unneeded arguments: 19.65/6.87 f_406(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, x26, x27, x28, x29, x30, x31) -> f_406(x7, x9, x18) 19.65/6.87 Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: 19.65/6.87 f_406(sum~cons_1~v446:0, v417:0, v430:0) -> f_406(v446:0, 1 + v417:0, v430:0) :|: v417:0 > 1 && v430:0 > 2 && v446:0 > -1 && sum~cons_1~v446:0 = 1 + v446:0 19.65/6.87 19.65/6.87 ---------------------------------------- 19.65/6.87 19.65/6.87 (8) 19.65/6.87 Obligation: 19.65/6.87 Rules: 19.65/6.87 f_406(sum~cons_1~v446:0, v417:0, v430:0) -> f_406(v446:0, 1 + v417:0, v430:0) :|: v417:0 > 1 && v430:0 > 2 && v446:0 > -1 && sum~cons_1~v446:0 = 1 + v446:0 19.65/6.87 19.65/6.87 ---------------------------------------- 19.65/6.87 19.65/6.87 (9) IntTRSCompressionProof (EQUIVALENT) 19.65/6.87 Compressed rules. 19.65/6.87 ---------------------------------------- 19.65/6.87 19.65/6.87 (10) 19.65/6.87 Obligation: 19.65/6.87 Rules: 19.65/6.87 f_406(sum~cons_1~v446:0:0, v417:0:0, v430:0:0) -> f_406(v446:0:0, 1 + v417:0:0, v430:0:0) :|: v417:0:0 > 1 && v430:0:0 > 2 && v446:0:0 > -1 && sum~cons_1~v446:0:0 = 1 + v446:0:0 19.65/6.87 19.65/6.87 ---------------------------------------- 19.65/6.87 19.65/6.87 (11) PolynomialOrderProcessor (EQUIVALENT) 19.65/6.87 Found the following polynomial interpretation: 19.65/6.87 [f_406(x, x1, x2)] = x 19.65/6.87 19.65/6.87 The following rules are decreasing: 19.65/6.87 f_406(sum~cons_1~v446:0:0, v417:0:0, v430:0:0) -> f_406(v446:0:0, 1 + v417:0:0, v430:0:0) :|: v417:0:0 > 1 && v430:0:0 > 2 && v446:0:0 > -1 && sum~cons_1~v446:0:0 = 1 + v446:0:0 19.65/6.87 The following rules are bounded: 19.65/6.87 f_406(sum~cons_1~v446:0:0, v417:0:0, v430:0:0) -> f_406(v446:0:0, 1 + v417:0:0, v430:0:0) :|: v417:0:0 > 1 && v430:0:0 > 2 && v446:0:0 > -1 && sum~cons_1~v446:0:0 = 1 + v446:0:0 19.65/6.87 19.65/6.87 ---------------------------------------- 19.65/6.87 19.65/6.87 (12) 19.65/6.87 YES 20.71/7.43 EOF