17.11/5.81 YES 17.11/5.82 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 17.11/5.82 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 17.11/5.82 17.11/5.82 17.11/5.82 Termination of the given C Problem could be proven: 17.11/5.82 17.11/5.82 (0) C Problem 17.11/5.82 (1) CToLLVMProof [EQUIVALENT, 173 ms] 17.11/5.82 (2) LLVM problem 17.11/5.82 (3) LLVMToTerminationGraphProof [EQUIVALENT, 2793 ms] 17.11/5.82 (4) LLVM Symbolic Execution Graph 17.11/5.82 (5) SymbolicExecutionGraphToSCCProof [SOUND, 1 ms] 17.11/5.82 (6) LLVM Symbolic Execution SCC 17.11/5.82 (7) SCC2IRS [SOUND, 105 ms] 17.11/5.82 (8) IntTRS 17.11/5.82 (9) IntTRSCompressionProof [EQUIVALENT, 1 ms] 17.11/5.82 (10) IntTRS 17.11/5.82 (11) PolynomialOrderProcessor [EQUIVALENT, 0 ms] 17.11/5.82 (12) YES 17.11/5.82 17.11/5.82 17.11/5.82 ---------------------------------------- 17.11/5.82 17.11/5.82 (0) 17.11/5.82 Obligation: 17.11/5.82 c file /export/starexec/sandbox/benchmark/theBenchmark.c 17.11/5.82 ---------------------------------------- 17.11/5.82 17.11/5.82 (1) CToLLVMProof (EQUIVALENT) 17.11/5.82 Compiled c-file /export/starexec/sandbox/benchmark/theBenchmark.c to LLVM. 17.11/5.82 ---------------------------------------- 17.11/5.82 17.11/5.82 (2) 17.11/5.82 Obligation: 17.11/5.82 LLVM Problem 17.11/5.82 17.11/5.82 Aliases: 17.11/5.82 17.11/5.82 Data layout: 17.11/5.82 17.11/5.82 "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" 17.11/5.82 17.11/5.82 Machine: 17.11/5.82 17.11/5.82 "x86_64-pc-linux-gnu" 17.11/5.82 17.11/5.82 Type definitions: 17.11/5.82 17.11/5.82 Global variables: 17.11/5.82 17.11/5.82 Function declarations and definitions: 17.11/5.82 17.11/5.82 *BasicFunctionTypename: "__VERIFIER_nondet_int" returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 17.11/5.82 *BasicFunctionTypename: "__VERIFIER_error" returnParam: BasicVoidType parameters: () variableLength: true visibilityType: DEFAULT callingConvention: ccc 17.11/5.82 *BasicFunctionTypename: "addition" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: (m i32, n i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc 17.11/5.82 0: 17.11/5.82 %1 = alloca i32, align 4 17.11/5.82 %2 = alloca i32, align 4 17.11/5.82 %3 = alloca i32, align 4 17.11/5.82 store %m, %2 17.11/5.82 store %n, %3 17.11/5.82 %4 = load %3 17.11/5.82 %5 = icmp eq %4 0 17.11/5.82 br %5, %6, %8 17.11/5.82 6: 17.11/5.82 %7 = load %2 17.11/5.82 store %7, %1 17.11/5.82 br %26 17.11/5.82 8: 17.11/5.82 %9 = load %3 17.11/5.82 %10 = icmp sgt %9 0 17.11/5.82 br %10, %11, %17 17.11/5.82 11: 17.11/5.82 %12 = load %2 17.11/5.82 %13 = add %12 1 17.11/5.82 %14 = load %3 17.11/5.82 %15 = sub %14 1 17.11/5.82 %16 = call i32 @addition(i32 %13, i32 %15) 17.11/5.82 store %16, %1 17.11/5.82 br %26 17.11/5.82 17: 17.11/5.82 %18 = load %3 17.11/5.82 %19 = icmp slt %18 0 17.11/5.82 br %19, %20, %26 17.11/5.82 20: 17.11/5.82 %21 = load %2 17.11/5.82 %22 = sub %21 1 17.11/5.82 %23 = load %3 17.11/5.82 %24 = add %23 1 17.11/5.82 %25 = call i32 @addition(i32 %22, i32 %24) 17.11/5.82 store %25, %1 17.11/5.82 br %26 17.11/5.82 26: 17.11/5.82 %27 = load %1 17.11/5.82 ret %27 17.11/5.82 17.11/5.82 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 17.11/5.82 0: 17.11/5.82 %1 = alloca i32, align 4 17.11/5.82 %m = alloca i32, align 4 17.11/5.82 %n = alloca i32, align 4 17.11/5.82 %result = alloca i32, align 4 17.11/5.82 store 0, %1 17.11/5.82 %2 = call i32 @__VERIFIER_nondet_int() 17.11/5.82 store %2, %m 17.11/5.82 %3 = load %m 17.11/5.82 %4 = icmp slt %3 0 17.11/5.82 br %4, %8, %5 17.11/5.82 5: 17.11/5.82 %6 = load %m 17.11/5.82 %7 = icmp sgt %6 2147483647 17.11/5.82 br %7, %8, %9 17.11/5.82 8: 17.11/5.82 store 0, %1 17.11/5.82 br %29 17.11/5.82 9: 17.11/5.82 %10 = call i32 @__VERIFIER_nondet_int() 17.11/5.82 store %10, %n 17.11/5.82 %11 = load %n 17.11/5.82 %12 = icmp slt %11 0 17.11/5.82 br %12, %16, %13 17.11/5.82 13: 17.11/5.82 %14 = load %n 17.11/5.82 %15 = icmp sgt %14 2147483647 17.11/5.82 br %15, %16, %17 17.11/5.82 16: 17.11/5.82 store 0, %1 17.11/5.82 br %29 17.11/5.82 17: 17.11/5.82 %18 = load %m 17.11/5.82 %19 = load %n 17.11/5.82 %20 = call i32 @addition(i32 %18, i32 %19) 17.11/5.82 store %20, %result 17.11/5.82 %21 = load %result 17.11/5.82 %22 = load %m 17.11/5.82 %23 = load %n 17.11/5.82 %24 = add %22 %23 17.11/5.82 %25 = icmp eq %21 %24 17.11/5.82 br %25, %26, %27 17.11/5.82 26: 17.11/5.82 store 0, %1 17.11/5.82 br %29 17.11/5.82 27: 17.11/5.82 br %28 17.11/5.82 28: 17.11/5.82 Unnamed Call-Instruction = call BasicVoidType (...)* @__VERIFIER_error() noreturn 17.11/5.82 unreachable 17.11/5.82 29: 17.11/5.82 %30 = load %1 17.11/5.82 ret %30 17.11/5.82 17.11/5.82 17.11/5.82 Analyze Termination of all function calls matching the pattern: 17.11/5.82 main() 17.11/5.82 ---------------------------------------- 17.11/5.82 17.11/5.82 (3) LLVMToTerminationGraphProof (EQUIVALENT) 17.11/5.82 Constructed symbolic execution graph for LLVM program and proved memory safety. 17.11/5.82 ---------------------------------------- 17.11/5.82 17.11/5.82 (4) 17.11/5.82 Obligation: 17.11/5.82 SE Graph 17.11/5.82 ---------------------------------------- 17.11/5.82 17.11/5.82 (5) SymbolicExecutionGraphToSCCProof (SOUND) 17.11/5.82 Splitted symbolic execution graph to 1 SCC. 17.11/5.82 ---------------------------------------- 17.11/5.82 17.11/5.82 (6) 17.11/5.82 Obligation: 17.11/5.82 SCC 17.11/5.82 ---------------------------------------- 17.11/5.82 17.11/5.82 (7) SCC2IRS (SOUND) 17.11/5.82 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 17.11/5.82 Generated rules. Obtained 19 rulesP rules: 17.11/5.82 f_347(v100, v101, v113, v102, v103, v104, v105, v106, v107, v108, v109, v114, 0, v111, v112, 3, 1, 4) -> f_349(v100, v101, v113, v115, v102, v103, v104, v105, v106, v107, v108, v109, v114, v116, 0, v111, v112, 3, 1, 4) :|: 1 <= v115 && v116 = 3 + v115 && 4 <= v116 17.11/5.82 f_349(v100, v101, v113, v115, v102, v103, v104, v105, v106, v107, v108, v109, v114, v116, 0, v111, v112, 3, 1, 4) -> f_350(v100, v101, v113, v115, v117, v102, v103, v104, v105, v106, v107, v108, v109, v114, v116, v118, 0, v111, v112, 3, 1, 4) :|: 1 <= v117 && v118 = 3 + v117 && 4 <= v118 17.11/5.82 f_350(v100, v101, v113, v115, v117, v102, v103, v104, v105, v106, v107, v108, v109, v114, v116, v118, 0, v111, v112, 3, 1, 4) -> f_351(v100, v101, v113, v115, v117, v102, v103, v104, v105, v106, v107, v108, v109, v114, v116, v118, 0, v111, v112, 3, 1, 4) :|: TRUE 17.11/5.82 f_351(v100, v101, v113, v115, v117, v102, v103, v104, v105, v106, v107, v108, v109, v114, v116, v118, 0, v111, v112, 3, 1, 4) -> f_352(v100, v101, v113, v115, v117, v102, v103, v104, v105, v106, v107, v108, v109, v114, v116, v118, 0, v111, v112, 3, 1, 4) :|: TRUE 17.11/5.82 f_352(v100, v101, v113, v115, v117, v102, v103, v104, v105, v106, v107, v108, v109, v114, v116, v118, 0, v111, v112, 3, 1, 4) -> f_353(v100, v101, v113, v115, v117, v102, v103, v104, v105, v106, v107, v108, v109, v114, v116, v118, 0, v111, v112, 3, 1, 4) :|: 0 = 0 17.11/5.82 f_353(v100, v101, v113, v115, v117, v102, v103, v104, v105, v106, v107, v108, v109, v114, v116, v118, 0, v111, v112, 3, 1, 4) -> f_355(v100, v101, v113, v115, v117, v102, v103, v104, v105, v106, v107, v108, v109, v114, v116, v118, 0, v111, v112, 3, 1, 4) :|: v101 != 0 && 1 <= v112 17.11/5.82 f_355(v100, v101, v113, v115, v117, v102, v103, v104, v105, v106, v107, v108, v109, v114, v116, v118, 0, v111, v112, 3, 1, 4) -> f_357(v100, v101, v113, v115, v117, 0, v102, v103, v104, v105, v106, v107, v108, v109, v114, v116, v118, v111, v112, 3, 1, 4) :|: 0 = 0 17.11/5.82 f_357(v100, v101, v113, v115, v117, 0, v102, v103, v104, v105, v106, v107, v108, v109, v114, v116, v118, v111, v112, 3, 1, 4) -> f_359(v100, v101, v113, v115, v117, 0, v102, v103, v104, v105, v106, v107, v108, v109, v114, v116, v118, v111, v112, 3, 1, 4) :|: TRUE 17.11/5.82 f_359(v100, v101, v113, v115, v117, 0, v102, v103, v104, v105, v106, v107, v108, v109, v114, v116, v118, v111, v112, 3, 1, 4) -> f_361(v100, v101, v113, v115, v117, 0, v102, v103, v104, v105, v106, v107, v108, v109, v114, v116, v118, v111, v112, 3, 1, 4) :|: 0 = 0 17.11/5.82 f_361(v100, v101, v113, v115, v117, 0, v102, v103, v104, v105, v106, v107, v108, v109, v114, v116, v118, v111, v112, 3, 1, 4) -> f_363(v100, v101, v113, v115, v117, 0, 1, v102, v103, v104, v105, v106, v107, v108, v109, v114, v116, v118, v111, v112, 3, 4) :|: 0 = 0 17.11/5.82 f_363(v100, v101, v113, v115, v117, 0, 1, v102, v103, v104, v105, v106, v107, v108, v109, v114, v116, v118, v111, v112, 3, 4) -> f_365(v100, v101, v113, v115, v117, 0, 1, v102, v103, v104, v105, v106, v107, v108, v109, v114, v116, v118, v111, v112, 3, 4) :|: TRUE 17.11/5.82 f_365(v100, v101, v113, v115, v117, 0, 1, v102, v103, v104, v105, v106, v107, v108, v109, v114, v116, v118, v111, v112, 3, 4) -> f_367(v100, v101, v113, v115, v117, 0, 1, v102, v103, v104, v105, v106, v107, v108, v109, v114, v116, v118, v111, v112, 3, 4) :|: 0 = 0 17.11/5.82 f_367(v100, v101, v113, v115, v117, 0, 1, v102, v103, v104, v105, v106, v107, v108, v109, v114, v116, v118, v111, v112, 3, 4) -> f_369(v100, v101, v113, v115, v117, 0, 1, v139, v102, v103, v104, v105, v106, v107, v108, v109, v114, v116, v118, v111, v112, 3, 4) :|: v139 = 1 + v100 && 1 <= v139 17.11/5.82 f_369(v100, v101, v113, v115, v117, 0, 1, v139, v102, v103, v104, v105, v106, v107, v108, v109, v114, v116, v118, v111, v112, 3, 4) -> f_371(v100, v101, v113, v115, v117, 0, 1, v139, v102, v103, v104, v105, v106, v107, v108, v109, v114, v116, v118, v111, v112, 3, 4) :|: 0 = 0 17.11/5.82 f_371(v100, v101, v113, v115, v117, 0, 1, v139, v102, v103, v104, v105, v106, v107, v108, v109, v114, v116, v118, v111, v112, 3, 4) -> f_373(v100, v101, v113, v115, v117, 0, 1, v139, v141, v102, v103, v104, v105, v106, v107, v108, v109, v114, v116, v118, v111, v112, 3, 4) :|: 1 + v141 = v101 && 0 <= v141 17.11/5.82 f_373(v100, v101, v113, v115, v117, 0, 1, v139, v141, v102, v103, v104, v105, v106, v107, v108, v109, v114, v116, v118, v111, v112, 3, 4) -> f_375(v139, v141, v102, v103, v104, v105, v106, v107, v108, v109, v113, v114, v115, v116, v117, v118, 0, v111, v112, v100, v101, 1, 3, 4) :|: 0 = 0 17.11/5.82 f_375(v139, v141, v102, v103, v104, v105, v106, v107, v108, v109, v113, v114, v115, v116, v117, v118, 0, v111, v112, v100, v101, 1, 3, 4) -> f_377(v139, v141, v102, v103, v104, v105, v106, v107, v108, v109, v113, v114, v115, v116, v117, v118, 0, v111, v112, v100, v101, 3, 1, 4) :|: TRUE 17.11/5.82 f_377(v139, v141, v102, v103, v104, v105, v106, v107, v108, v109, v113, v114, v115, v116, v117, v118, 0, v111, v112, v100, v101, 3, 1, 4) -> f_345(v139, v141, v102, v103, v104, v105, v106, v107, v108, v109, 0, v111, v112, 3, 1, 4) :|: TRUE 17.11/5.82 f_345(v100, v101, v102, v103, v104, v105, v106, v107, v108, v109, 0, v111, v112, 3, 1, 4) -> f_347(v100, v101, v113, v102, v103, v104, v105, v106, v107, v108, v109, v114, 0, v111, v112, 3, 1, 4) :|: 1 <= v113 && v114 = 3 + v113 && 4 <= v114 17.11/5.82 Combined rules. Obtained 1 rulesP rules: 17.11/5.82 f_347(v100:0, 1 + v141:0, v113:0, v102:0, v103:0, v104:0, v105:0, v106:0, v107:0, v108:0, v109:0, v114:0, 0, v111:0, v112:0, 3, 1, 4) -> f_347(1 + v100:0, v141:0, v113:1, v102:0, v103:0, v104:0, v105:0, v106:0, v107:0, v108:0, v109:0, 3 + v113:1, 0, v111:0, v112:0, 3, 1, 4) :|: v117:0 > 0 && v115:0 > 0 && v112:0 > 0 && v141:0 > -1 && v100:0 > -1 && v113:1 > 0 17.11/5.82 Filtered unneeded arguments: 17.11/5.82 f_347(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18) -> f_347(x1, x2, x15) 17.11/5.82 Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: 17.11/5.82 f_347(v100:0, sum~cons_1~v141:0, v112:0) -> f_347(1 + v100:0, v141:0, v112:0) :|: v141:0 > -1 && v100:0 > -1 && v112:0 > 0 && sum~cons_1~v141:0 = 1 + v141:0 17.11/5.82 17.11/5.82 ---------------------------------------- 17.11/5.82 17.11/5.82 (8) 17.11/5.82 Obligation: 17.11/5.82 Rules: 17.11/5.82 f_347(v100:0, sum~cons_1~v141:0, v112:0) -> f_347(1 + v100:0, v141:0, v112:0) :|: v141:0 > -1 && v100:0 > -1 && v112:0 > 0 && sum~cons_1~v141:0 = 1 + v141:0 17.11/5.82 17.11/5.82 ---------------------------------------- 17.11/5.82 17.11/5.82 (9) IntTRSCompressionProof (EQUIVALENT) 17.11/5.82 Compressed rules. 17.11/5.82 ---------------------------------------- 17.11/5.82 17.11/5.82 (10) 17.11/5.82 Obligation: 17.11/5.82 Rules: 17.11/5.82 f_347(v100:0:0, sum~cons_1~v141:0:0, v112:0:0) -> f_347(1 + v100:0:0, v141:0:0, v112:0:0) :|: v141:0:0 > -1 && v100:0:0 > -1 && v112:0:0 > 0 && sum~cons_1~v141:0:0 = 1 + v141:0:0 17.11/5.82 17.11/5.82 ---------------------------------------- 17.11/5.82 17.11/5.82 (11) PolynomialOrderProcessor (EQUIVALENT) 17.11/5.82 Found the following polynomial interpretation: 17.11/5.82 [f_347(x, x1, x2)] = x1 17.11/5.82 17.11/5.82 The following rules are decreasing: 17.11/5.82 f_347(v100:0:0, sum~cons_1~v141:0:0, v112:0:0) -> f_347(1 + v100:0:0, v141:0:0, v112:0:0) :|: v141:0:0 > -1 && v100:0:0 > -1 && v112:0:0 > 0 && sum~cons_1~v141:0:0 = 1 + v141:0:0 17.11/5.82 The following rules are bounded: 17.11/5.82 f_347(v100:0:0, sum~cons_1~v141:0:0, v112:0:0) -> f_347(1 + v100:0:0, v141:0:0, v112:0:0) :|: v141:0:0 > -1 && v100:0:0 > -1 && v112:0:0 > 0 && sum~cons_1~v141:0:0 = 1 + v141:0:0 17.11/5.82 17.11/5.82 ---------------------------------------- 17.11/5.82 17.11/5.82 (12) 17.11/5.82 YES 17.51/5.87 EOF