41.30/11.99 YES 41.50/12.02 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 41.50/12.02 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 41.50/12.02 41.50/12.02 41.50/12.02 Termination of the given C Problem could be proven: 41.50/12.02 41.50/12.02 (0) C Problem 41.50/12.02 (1) CToLLVMProof [EQUIVALENT, 174 ms] 41.50/12.02 (2) LLVM problem 41.50/12.02 (3) LLVMToTerminationGraphProof [EQUIVALENT, 2450 ms] 41.50/12.02 (4) LLVM Symbolic Execution Graph 41.50/12.02 (5) SymbolicExecutionGraphToSCCProof [SOUND, 2 ms] 41.50/12.02 (6) LLVM Symbolic Execution SCC 41.50/12.02 (7) SCC2IRS [SOUND, 70 ms] 41.50/12.02 (8) IntTRS 41.50/12.02 (9) IntTRSCompressionProof [EQUIVALENT, 0 ms] 41.50/12.02 (10) IntTRS 41.50/12.02 (11) RankingReductionPairProof [EQUIVALENT, 20 ms] 41.50/12.02 (12) YES 41.50/12.02 41.50/12.02 41.50/12.02 ---------------------------------------- 41.50/12.02 41.50/12.02 (0) 41.50/12.02 Obligation: 41.50/12.02 c file /export/starexec/sandbox/benchmark/theBenchmark.c 41.50/12.02 ---------------------------------------- 41.50/12.02 41.50/12.02 (1) CToLLVMProof (EQUIVALENT) 41.50/12.02 Compiled c-file /export/starexec/sandbox/benchmark/theBenchmark.c to LLVM. 41.50/12.02 ---------------------------------------- 41.50/12.02 41.50/12.02 (2) 41.50/12.02 Obligation: 41.50/12.02 LLVM Problem 41.50/12.02 41.50/12.02 Aliases: 41.50/12.02 41.50/12.02 Data layout: 41.50/12.02 41.50/12.02 "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" 41.50/12.02 41.50/12.02 Machine: 41.50/12.02 41.50/12.02 "x86_64-pc-linux-gnu" 41.50/12.02 41.50/12.02 Type definitions: 41.50/12.02 41.50/12.02 Global variables: 41.50/12.02 41.50/12.02 Function declarations and definitions: 41.50/12.02 41.50/12.02 *BasicFunctionTypename: "__VERIFIER_nondet_int" returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 41.50/12.02 *BasicFunctionTypename: "__VERIFIER_error" returnParam: BasicVoidType parameters: () variableLength: true visibilityType: DEFAULT callingConvention: ccc 41.50/12.02 *BasicFunctionTypename: "mult" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: (n i32, m i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc 41.50/12.02 0: 41.50/12.02 %1 = alloca i32, align 4 41.50/12.02 %2 = alloca i32, align 4 41.50/12.02 %3 = alloca i32, align 4 41.50/12.02 store %n, %2 41.50/12.02 store %m, %3 41.50/12.02 %4 = load %3 41.50/12.02 %5 = icmp slt %4 0 41.50/12.02 br %5, %6, %11 41.50/12.02 6: 41.50/12.02 %7 = load %2 41.50/12.02 %8 = load %3 41.50/12.02 %9 = sub 0 %8 41.50/12.02 %10 = call i32 @mult(i32 %7, i32 %9) 41.50/12.02 store %10, %1 41.50/12.02 br %22 41.50/12.02 11: 41.50/12.02 %12 = load %3 41.50/12.02 %13 = icmp eq %12 0 41.50/12.02 br %13, %14, %15 41.50/12.02 14: 41.50/12.02 store 0, %1 41.50/12.02 br %22 41.50/12.02 15: 41.50/12.02 %16 = load %2 41.50/12.02 %17 = load %2 41.50/12.02 %18 = load %3 41.50/12.02 %19 = sub %18 1 41.50/12.02 %20 = call i32 @mult(i32 %17, i32 %19) 41.50/12.02 %21 = add %16 %20 41.50/12.02 store %21, %1 41.50/12.02 br %22 41.50/12.02 22: 41.50/12.02 %23 = load %1 41.50/12.02 ret %23 41.50/12.02 41.50/12.02 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 41.50/12.02 0: 41.50/12.02 %1 = alloca i32, align 4 41.50/12.02 %m = alloca i32, align 4 41.50/12.02 %n = alloca i32, align 4 41.50/12.02 %res1 = alloca i32, align 4 41.50/12.02 %res2 = alloca i32, align 4 41.50/12.02 store 0, %1 41.50/12.02 %2 = call i32 @__VERIFIER_nondet_int() 41.50/12.02 store %2, %m 41.50/12.02 %3 = load %m 41.50/12.02 %4 = icmp slt %3 0 41.50/12.02 br %4, %5, %6 41.50/12.02 5: 41.50/12.02 store 0, %1 41.50/12.02 br %29 41.50/12.02 6: 41.50/12.02 %7 = call i32 @__VERIFIER_nondet_int() 41.50/12.02 store %7, %n 41.50/12.02 %8 = load %n 41.50/12.02 %9 = icmp slt %8 0 41.50/12.02 br %9, %10, %11 41.50/12.02 10: 41.50/12.02 store 0, %1 41.50/12.02 br %29 41.50/12.02 11: 41.50/12.02 %12 = load %m 41.50/12.02 %13 = load %n 41.50/12.02 %14 = call i32 @mult(i32 %12, i32 %13) 41.50/12.02 store %14, %res1 41.50/12.02 %15 = load %n 41.50/12.02 %16 = load %m 41.50/12.02 %17 = call i32 @mult(i32 %15, i32 %16) 41.50/12.02 store %17, %res2 41.50/12.02 %18 = load %res1 41.50/12.02 %19 = icmp eq %18 0 41.50/12.02 br %19, %26, %20 41.50/12.02 20: 41.50/12.02 %21 = load %m 41.50/12.02 %22 = icmp sgt %21 0 41.50/12.02 br %22, %26, %23 41.50/12.02 23: 41.50/12.02 %24 = load %n 41.50/12.02 %25 = icmp sgt %24 0 41.50/12.02 br %25, %26, %27 41.50/12.02 26: 41.50/12.02 store 0, %1 41.50/12.02 br %29 41.50/12.02 27: 41.50/12.02 br %28 41.50/12.02 28: 41.50/12.02 Unnamed Call-Instruction = call BasicVoidType (...)* @__VERIFIER_error() noreturn 41.50/12.02 unreachable 41.50/12.02 29: 41.50/12.02 %30 = load %1 41.50/12.02 ret %30 41.50/12.02 41.50/12.02 41.50/12.02 Analyze Termination of all function calls matching the pattern: 41.50/12.02 main() 41.50/12.02 ---------------------------------------- 41.50/12.02 41.50/12.02 (3) LLVMToTerminationGraphProof (EQUIVALENT) 41.50/12.02 Constructed symbolic execution graph for LLVM program and proved memory safety. 41.50/12.02 ---------------------------------------- 41.50/12.02 41.50/12.02 (4) 41.50/12.02 Obligation: 41.50/12.02 SE Graph 41.50/12.02 ---------------------------------------- 41.50/12.02 41.50/12.02 (5) SymbolicExecutionGraphToSCCProof (SOUND) 41.50/12.02 Splitted symbolic execution graph to 1 SCC. 41.50/12.02 ---------------------------------------- 41.50/12.02 41.50/12.02 (6) 41.50/12.02 Obligation: 41.50/12.02 SCC 41.50/12.02 ---------------------------------------- 41.50/12.02 41.50/12.02 (7) SCC2IRS (SOUND) 41.50/12.02 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 41.50/12.02 Generated rules. Obtained 19 rulesP rules: 41.50/12.02 f_357(v155, v156, v158, v159, 3, 0, 1, 4) -> f_358(v155, v156, v158, v160, v159, v161, 3, 0, 1, 4) :|: 1 <= v160 && v161 = 3 + v160 && 4 <= v161 41.50/12.02 f_358(v155, v156, v158, v160, v159, v161, 3, 0, 1, 4) -> f_359(v155, v156, v158, v160, v162, v159, v161, v163, 3, 0, 1, 4) :|: 1 <= v162 && v163 = 3 + v162 && 4 <= v163 41.50/12.02 f_359(v155, v156, v158, v160, v162, v159, v161, v163, 3, 0, 1, 4) -> f_360(v155, v156, v158, v160, v162, v159, v161, v163, 3, 0, 1, 4) :|: TRUE 41.50/12.02 f_360(v155, v156, v158, v160, v162, v159, v161, v163, 3, 0, 1, 4) -> f_361(v155, v156, v158, v160, v162, v159, v161, v163, 3, 0, 1, 4) :|: TRUE 41.50/12.02 f_361(v155, v156, v158, v160, v162, v159, v161, v163, 3, 0, 1, 4) -> f_362(v155, v156, v158, v160, v162, v159, v161, v163, 3, 0, 1, 4) :|: 0 = 0 41.50/12.02 f_362(v155, v156, v158, v160, v162, v159, v161, v163, 3, 0, 1, 4) -> f_363(v155, v156, v158, v160, v162, 0, v159, v161, v163, 3, 1, 4) :|: 0 = 0 41.50/12.02 f_363(v155, v156, v158, v160, v162, 0, v159, v161, v163, 3, 1, 4) -> f_364(v155, v156, v158, v160, v162, 0, v159, v161, v163, 3, 1, 4) :|: TRUE 41.50/12.02 f_364(v155, v156, v158, v160, v162, 0, v159, v161, v163, 3, 1, 4) -> f_365(v155, v156, v158, v160, v162, 0, v159, v161, v163, 3, 1, 4) :|: 0 = 0 41.50/12.02 f_365(v155, v156, v158, v160, v162, 0, v159, v161, v163, 3, 1, 4) -> f_367(v155, v156, v158, v160, v162, 0, v159, v161, v163, 3, 1, 4) :|: v156 != 0 41.50/12.02 f_367(v155, v156, v158, v160, v162, 0, v159, v161, v163, 3, 1, 4) -> f_369(v155, v156, v158, v160, v162, 0, v159, v161, v163, 3, 1, 4) :|: 0 = 0 41.50/12.02 f_369(v155, v156, v158, v160, v162, 0, v159, v161, v163, 3, 1, 4) -> f_371(v155, v156, v158, v160, v162, 0, v159, v161, v163, 3, 1, 4) :|: TRUE 41.50/12.02 f_371(v155, v156, v158, v160, v162, 0, v159, v161, v163, 3, 1, 4) -> f_373(v155, v156, v158, v160, v162, 0, v159, v161, v163, 3, 1, 4) :|: 0 = 0 41.50/12.02 f_373(v155, v156, v158, v160, v162, 0, v159, v161, v163, 3, 1, 4) -> f_375(v155, v156, v158, v160, v162, 0, v159, v161, v163, 3, 1, 4) :|: 0 = 0 41.50/12.02 f_375(v155, v156, v158, v160, v162, 0, v159, v161, v163, 3, 1, 4) -> f_377(v155, v156, v158, v160, v162, 0, v159, v161, v163, 3, 1, 4) :|: 0 = 0 41.50/12.02 f_377(v155, v156, v158, v160, v162, 0, v159, v161, v163, 3, 1, 4) -> f_379(v155, v156, v158, v160, v162, 0, v173, v159, v161, v163, 3, 1, 4) :|: 1 + v173 = v156 && 0 <= v173 41.50/12.02 f_379(v155, v156, v158, v160, v162, 0, v173, v159, v161, v163, 3, 1, 4) -> f_381(v155, v173, v158, v159, v160, v161, v162, v163, v156, 0, 3, 1, 4) :|: 0 = 0 41.50/12.02 f_381(v155, v173, v158, v159, v160, v161, v162, v163, v156, 0, 3, 1, 4) -> f_383(v155, v173, v158, v159, v160, v161, v162, v163, v156, 3, 1, 0, 4) :|: TRUE 41.50/12.02 f_383(v155, v173, v158, v159, v160, v161, v162, v163, v156, 3, 1, 0, 4) -> f_355(v155, v173, 0) :|: TRUE 41.50/12.02 f_355(v155, v156, 0) -> f_357(v155, v156, v158, v159, 3, 0, 1, 4) :|: 1 <= v158 && v159 = 3 + v158 && 4 <= v159 41.50/12.02 Combined rules. Obtained 1 rulesP rules: 41.50/12.02 f_357(v155:0, 1 + v173:0, v158:0, v159:0, 3, 0, 1, 4) -> f_357(v155:0, v173:0, v158:1, 3 + v158:1, 3, 0, 1, 4) :|: v162:0 > 0 && v160:0 > 0 && v173:0 > -1 && v158:1 > 0 41.50/12.02 Filtered unneeded arguments: 41.50/12.02 f_357(x1, x2, x3, x4, x5, x6, x7, x8) -> f_357(x2) 41.50/12.02 Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: 41.50/12.02 f_357(sum~cons_1~v173:0) -> f_357(v173:0) :|: v173:0 > -1 && sum~cons_1~v173:0 = 1 + v173:0 41.50/12.02 41.50/12.02 ---------------------------------------- 41.50/12.02 41.50/12.02 (8) 41.50/12.02 Obligation: 41.50/12.02 Rules: 41.50/12.02 f_357(sum~cons_1~v173:0) -> f_357(v173:0) :|: v173:0 > -1 && sum~cons_1~v173:0 = 1 + v173:0 41.50/12.02 41.50/12.02 ---------------------------------------- 41.50/12.02 41.50/12.02 (9) IntTRSCompressionProof (EQUIVALENT) 41.50/12.02 Compressed rules. 41.50/12.02 ---------------------------------------- 41.50/12.02 41.50/12.02 (10) 41.50/12.02 Obligation: 41.50/12.02 Rules: 41.50/12.02 f_357(sum~cons_1~v173:0:0) -> f_357(v173:0:0) :|: v173:0:0 > -1 && sum~cons_1~v173:0:0 = 1 + v173:0:0 41.50/12.02 41.50/12.02 ---------------------------------------- 41.50/12.02 41.50/12.02 (11) RankingReductionPairProof (EQUIVALENT) 41.50/12.02 Interpretation: 41.50/12.02 [ f_357 ] = f_357_1 41.50/12.02 41.50/12.02 The following rules are decreasing: 41.50/12.02 f_357(sum~cons_1~v173:0:0) -> f_357(v173:0:0) :|: v173:0:0 > -1 && sum~cons_1~v173:0:0 = 1 + v173:0:0 41.50/12.02 41.50/12.02 The following rules are bounded: 41.50/12.02 f_357(sum~cons_1~v173:0:0) -> f_357(v173:0:0) :|: v173:0:0 > -1 && sum~cons_1~v173:0:0 = 1 + v173:0:0 41.50/12.02 41.50/12.02 41.50/12.02 ---------------------------------------- 41.50/12.02 41.50/12.02 (12) 41.50/12.02 YES 41.91/14.59 EOF