14.32/4.98 YES 14.32/5.00 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 14.32/5.00 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 14.32/5.00 14.32/5.00 14.32/5.00 Termination of the given C Problem could be proven: 14.32/5.00 14.32/5.00 (0) C Problem 14.32/5.00 (1) CToLLVMProof [EQUIVALENT, 169 ms] 14.32/5.00 (2) LLVM problem 14.32/5.00 (3) LLVMToTerminationGraphProof [EQUIVALENT, 2188 ms] 14.32/5.00 (4) LLVM Symbolic Execution Graph 14.32/5.00 (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] 14.32/5.00 (6) LLVM Symbolic Execution SCC 14.32/5.00 (7) SCC2IRS [SOUND, 87 ms] 14.32/5.00 (8) IntTRS 14.32/5.00 (9) TerminationGraphProcessor [EQUIVALENT, 32 ms] 14.32/5.00 (10) IntTRS 14.32/5.00 (11) IntTRSCompressionProof [EQUIVALENT, 0 ms] 14.32/5.00 (12) IntTRS 14.32/5.00 (13) RankingReductionPairProof [EQUIVALENT, 11 ms] 14.32/5.00 (14) YES 14.32/5.00 14.32/5.00 14.32/5.00 ---------------------------------------- 14.32/5.00 14.32/5.00 (0) 14.32/5.00 Obligation: 14.32/5.00 c file /export/starexec/sandbox/benchmark/theBenchmark.c 14.32/5.00 ---------------------------------------- 14.32/5.00 14.32/5.00 (1) CToLLVMProof (EQUIVALENT) 14.32/5.00 Compiled c-file /export/starexec/sandbox/benchmark/theBenchmark.c to LLVM. 14.32/5.00 ---------------------------------------- 14.32/5.00 14.32/5.00 (2) 14.32/5.00 Obligation: 14.32/5.00 LLVM Problem 14.32/5.00 14.32/5.00 Aliases: 14.32/5.00 14.32/5.00 Data layout: 14.32/5.00 14.32/5.00 "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" 14.32/5.00 14.32/5.00 Machine: 14.32/5.00 14.32/5.00 "x86_64-pc-linux-gnu" 14.32/5.00 14.32/5.00 Type definitions: 14.32/5.00 14.32/5.00 Global variables: 14.32/5.00 14.32/5.00 Function declarations and definitions: 14.32/5.00 14.32/5.00 *BasicFunctionTypename: "__VERIFIER_nondet_int" returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 14.32/5.00 *BasicFunctionTypename: "mlog" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: (x i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc 14.32/5.00 0: 14.32/5.00 %1 = alloca i32, align 4 14.32/5.00 %x_ref = alloca *i32, align 8 14.32/5.00 %res = alloca *i32, align 8 14.32/5.00 store %x, %1 14.32/5.00 %2 = alloca i8, numElementsLit: 4 14.32/5.00 %3 = bitcast *i8 %2 to *i32 14.32/5.00 store %3, %x_ref 14.32/5.00 %4 = alloca i8, numElementsLit: 4 14.32/5.00 %5 = bitcast *i8 %4 to *i32 14.32/5.00 store %5, %res 14.32/5.00 %6 = load %1 14.32/5.00 %7 = load %x_ref 14.32/5.00 store %6, %7 14.32/5.00 %8 = load %res 14.32/5.00 store 0, %8 14.32/5.00 br %9 14.32/5.00 9: 14.32/5.00 %10 = load %x_ref 14.32/5.00 %11 = load %10 14.32/5.00 %12 = icmp sgt %11 1 14.32/5.00 br %12, %13, %21 14.32/5.00 13: 14.32/5.00 %14 = load %x_ref 14.32/5.00 %15 = load %14 14.32/5.00 %16 = sdiv %15 2 14.32/5.00 %17 = load %x_ref 14.32/5.00 store %16, %17 14.32/5.00 %18 = load %res 14.32/5.00 %19 = load %18 14.32/5.00 %20 = add %19 1 14.32/5.00 store %20, %18 14.32/5.00 br %9 14.32/5.00 21: 14.32/5.00 %22 = load %res 14.32/5.00 %23 = load %22 14.32/5.00 ret %23 14.32/5.00 14.32/5.00 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 14.32/5.00 0: 14.32/5.00 %1 = alloca i32, align 4 14.32/5.00 store 0, %1 14.32/5.00 %2 = call i32 @__VERIFIER_nondet_int() 14.32/5.00 %3 = call i32 @mlog(i32 %2) 14.32/5.00 ret %3 14.32/5.00 14.32/5.00 14.32/5.00 Analyze Termination of all function calls matching the pattern: 14.32/5.00 main() 14.32/5.00 ---------------------------------------- 14.32/5.00 14.32/5.00 (3) LLVMToTerminationGraphProof (EQUIVALENT) 14.32/5.00 Constructed symbolic execution graph for LLVM program and proved memory safety. 14.32/5.00 ---------------------------------------- 14.32/5.00 14.32/5.00 (4) 14.32/5.00 Obligation: 14.32/5.00 SE Graph 14.32/5.00 ---------------------------------------- 14.32/5.00 14.32/5.00 (5) SymbolicExecutionGraphToSCCProof (SOUND) 14.32/5.00 Splitted symbolic execution graph to 1 SCC. 14.32/5.00 ---------------------------------------- 14.32/5.00 14.32/5.00 (6) 14.32/5.00 Obligation: 14.32/5.00 SCC 14.32/5.00 ---------------------------------------- 14.32/5.00 14.32/5.00 (7) SCC2IRS (SOUND) 14.32/5.00 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 14.32/5.00 Generated rules. Obtained 16 rulesP rules: 14.32/5.00 f_292(v137, v138, v139, v140, v141, v142, v143, 1, v145, v146, v147, v148, v149, v150, v151, v152, v153, v154, 0, 3, 7, 2, 4, 8) -> f_293(v137, v138, v139, v140, v141, v142, v145, 1, v143, v146, v147, v148, v149, v150, v151, v152, v153, v154, 0, 3, 7, 2, 4, 8) :|: 0 = 0 14.32/5.00 f_293(v137, v138, v139, v140, v141, v142, v145, 1, v143, v146, v147, v148, v149, v150, v151, v152, v153, v154, 0, 3, 7, 2, 4, 8) -> f_294(v137, v138, v139, v140, v141, v142, v145, 1, v143, v146, v147, v148, v149, v150, v151, v152, v153, v154, 0, 3, 7, 2, 4, 8) :|: 1 < v145 14.32/5.00 f_294(v137, v138, v139, v140, v141, v142, v145, 1, v143, v146, v147, v148, v149, v150, v151, v152, v153, v154, 0, 3, 7, 2, 4, 8) -> f_296(v137, v138, v139, v140, v141, v142, v145, 1, v143, v146, v147, v148, v149, v150, v151, v152, v153, v154, 0, 3, 7, 2, 4, 8) :|: 0 = 0 14.32/5.00 f_296(v137, v138, v139, v140, v141, v142, v145, 1, v143, v146, v147, v148, v149, v150, v151, v152, v153, v154, 0, 3, 7, 2, 4, 8) -> f_298(v137, v138, v139, v140, v141, v142, v145, 1, v143, v146, v147, v148, v149, v150, v151, v152, v153, v154, 0, 3, 7, 2, 4, 8) :|: TRUE 14.32/5.00 f_298(v137, v138, v139, v140, v141, v142, v145, 1, v143, v146, v147, v148, v149, v150, v151, v152, v153, v154, 0, 3, 7, 2, 4, 8) -> f_300(v137, v138, v139, v140, v141, v142, v145, 1, v143, v146, v147, v148, v149, v150, v151, v152, v153, v154, 0, 3, 7, 2, 4, 8) :|: 0 = 0 14.32/5.00 f_300(v137, v138, v139, v140, v141, v142, v145, 1, v143, v146, v147, v148, v149, v150, v151, v152, v153, v154, 0, 3, 7, 2, 4, 8) -> f_302(v137, v138, v139, v140, v141, v142, v145, 1, v146, v147, v148, v149, v150, v151, v152, v153, v154, 0, 3, 7, 2, 4, 8) :|: 0 = 0 14.32/5.00 f_302(v137, v138, v139, v140, v141, v142, v145, 1, v146, v147, v148, v149, v150, v151, v152, v153, v154, 0, 3, 7, 2, 4, 8) -> f_304(v137, v138, v139, v140, v141, v142, v145, 1, v156, v146, v147, v148, v149, v150, v151, v152, v153, v154, 0, 3, 7, 2, 4, 8) :|: v156 = v145 / 2 14.32/5.00 f_304(v137, v138, v139, v140, v141, v142, v145, 1, v156, v146, v147, v148, v149, v150, v151, v152, v153, v154, 0, 3, 7, 2, 4, 8) -> f_306(v137, v138, v139, v140, v141, v142, v145, 1, v156, v146, v147, v148, v149, v150, v151, v152, v153, v154, 0, 3, 7, 2, 4, 8) :|: 0 = 0 14.32/5.00 f_306(v137, v138, v139, v140, v141, v142, v145, 1, v156, v146, v147, v148, v149, v150, v151, v152, v153, v154, 0, 3, 7, 2, 4, 8) -> f_307(v137, v138, v139, v140, v141, v142, v145, 1, v156, v146, v147, v148, v149, v150, v151, v152, v153, v154, 0, 3, 7, 2, 4, 8) :|: TRUE 14.32/5.00 f_307(v137, v138, v139, v140, v141, v142, v145, 1, v156, v146, v147, v148, v149, v150, v151, v152, v153, v154, 0, 3, 7, 2, 4, 8) -> f_308(v137, v138, v139, v140, v141, v142, v145, 1, v156, v146, v147, v148, v149, v150, v151, v152, v153, v154, 0, 3, 7, 2, 4, 8) :|: 0 = 0 14.32/5.00 f_308(v137, v138, v139, v140, v141, v142, v145, 1, v156, v146, v147, v148, v149, v150, v151, v152, v153, v154, 0, 3, 7, 2, 4, 8) -> f_309(v137, v138, v139, v140, v141, v142, v145, 1, v156, v147, v148, v149, v150, v151, v152, v153, v154, 0, 3, 7, 2, 4, 8) :|: 0 = 0 14.32/5.00 f_309(v137, v138, v139, v140, v141, v142, v145, 1, v156, v147, v148, v149, v150, v151, v152, v153, v154, 0, 3, 7, 2, 4, 8) -> f_310(v137, v138, v139, v140, v141, v142, v145, 1, v156, v147, v158, v148, v149, v150, v151, v152, v153, v154, 0, 3, 7, 2, 4, 8) :|: v158 = 1 + v147 && 2 <= v158 14.32/5.00 f_310(v137, v138, v139, v140, v141, v142, v145, 1, v156, v147, v158, v148, v149, v150, v151, v152, v153, v154, 0, 3, 7, 2, 4, 8) -> f_311(v137, v138, v139, v140, v141, v142, v145, 1, v156, v147, v158, v148, v149, v150, v151, v152, v153, v154, 0, 3, 7, 2, 4, 8) :|: TRUE 14.32/5.00 f_311(v137, v138, v139, v140, v141, v142, v145, 1, v156, v147, v158, v148, v149, v150, v151, v152, v153, v154, 0, 3, 7, 2, 4, 8) -> f_312(v137, v138, v139, v140, v141, v142, v145, 1, v156, v147, v158, v148, v149, v150, v151, v152, v153, v154, 0, 3, 7, 2, 4, 8) :|: TRUE 14.32/5.00 f_312(v137, v138, v139, v140, v141, v142, v145, 1, v156, v147, v158, v148, v149, v150, v151, v152, v153, v154, 0, 3, 7, 2, 4, 8) -> f_291(v137, v138, v139, v140, v141, v142, v145, 1, v156, v147, v158, v148, v149, v150, v151, v152, v153, v154, 0, 3, 7, 2, 4, 8) :|: TRUE 14.32/5.00 f_291(v137, v138, v139, v140, v141, v142, v143, 1, v145, v146, v147, v148, v149, v150, v151, v152, v153, v154, 0, 3, 7, 2, 4, 8) -> f_292(v137, v138, v139, v140, v141, v142, v143, 1, v145, v146, v147, v148, v149, v150, v151, v152, v153, v154, 0, 3, 7, 2, 4, 8) :|: 0 = 0 14.32/5.00 Combined rules. Obtained 1 rulesP rules: 14.32/5.00 f_292(v137:0, v138:0, v139:0, v140:0, v141:0, v142:0, v143:0, 1, v145:0, v146:0, v147:0, v148:0, v149:0, v150:0, v151:0, v152:0, v153:0, v154:0, 0, 3, 7, 2, 4, 8) -> f_292(v137:0, v138:0, v139:0, v140:0, v141:0, v142:0, v145:0, 1, v156:0, v147:0, 1 + v147:0, v148:0, v149:0, v150:0, v151:0, v152:0, v153:0, v154:0, 0, 3, 7, 2, 4, 8) :|: v145:0 > 1 && v147:0 > 0 && v156:0 = v145:0 / 2 14.32/5.00 Filtered unneeded arguments: 14.32/5.00 f_292(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24) -> f_292(x9, x11) 14.32/5.00 Removed division, modulo operations, cleaned up constraints. Obtained 3 rules.P rules: 14.32/5.00 f_292(v145:0, v147:0) -> f_292'(v145:0, v147:0) :|: v145:0 > 1 && v147:0 > 0 14.32/5.00 f_292'(v145:0, v147:0) -> f_292(div, 1 + v147:0) :|: v147:0 > 0 && v145:0 > 1 && v145:0 < 0 && v145:0 - 2 * div <= 0 && v145:0 - 2 * div > -2 14.32/5.00 f_292'(v145:0, v147:0) -> f_292(div, 1 + v147:0) :|: v145:0 > 1 && v147:0 > 0 && v145:0 - 2 * div < 2 && v145:0 - 2 * div >= 0 14.32/5.00 14.32/5.00 ---------------------------------------- 14.32/5.00 14.32/5.00 (8) 14.32/5.00 Obligation: 14.32/5.00 Rules: 14.32/5.00 f_292(v145:0, v147:0) -> f_292'(v145:0, v147:0) :|: v145:0 > 1 && v147:0 > 0 14.32/5.00 f_292'(x, x1) -> f_292(x2, 1 + x1) :|: x1 > 0 && x > 1 && x < 0 && x - 2 * x2 <= 0 && x - 2 * x2 > -2 14.32/5.00 f_292'(x3, x4) -> f_292(x5, 1 + x4) :|: x3 > 1 && x4 > 0 && x3 - 2 * x5 < 2 && x3 - 2 * x5 >= 0 14.32/5.00 14.32/5.00 ---------------------------------------- 14.32/5.00 14.32/5.00 (9) TerminationGraphProcessor (EQUIVALENT) 14.32/5.00 Constructed the termination graph and obtained one non-trivial SCC. 14.32/5.00 14.32/5.00 ---------------------------------------- 14.32/5.00 14.32/5.00 (10) 14.32/5.00 Obligation: 14.32/5.00 Rules: 14.32/5.00 f_292(v145:0, v147:0) -> f_292'(v145:0, v147:0) :|: v145:0 > 1 && v147:0 > 0 14.32/5.00 f_292'(x3, x4) -> f_292(x5, 1 + x4) :|: x3 > 1 && x4 > 0 && x3 - 2 * x5 < 2 && x3 - 2 * x5 >= 0 14.32/5.00 14.32/5.00 ---------------------------------------- 14.32/5.00 14.32/5.00 (11) IntTRSCompressionProof (EQUIVALENT) 14.32/5.00 Compressed rules. 14.32/5.00 ---------------------------------------- 14.32/5.00 14.32/5.00 (12) 14.32/5.00 Obligation: 14.32/5.00 Rules: 14.32/5.00 f_292(v145:0:0, v147:0:0) -> f_292(x5:0, 1 + v147:0:0) :|: v145:0:0 - 2 * x5:0 >= 0 && v145:0:0 - 2 * x5:0 < 2 && v147:0:0 > 0 && v145:0:0 > 1 14.32/5.00 14.32/5.00 ---------------------------------------- 14.32/5.00 14.32/5.00 (13) RankingReductionPairProof (EQUIVALENT) 14.32/5.00 Interpretation: 14.32/5.00 [ f_292 ] = f_292_1 14.32/5.00 14.32/5.00 The following rules are decreasing: 14.32/5.00 f_292(v145:0:0, v147:0:0) -> f_292(x5:0, 1 + v147:0:0) :|: v145:0:0 - 2 * x5:0 >= 0 && v145:0:0 - 2 * x5:0 < 2 && v147:0:0 > 0 && v145:0:0 > 1 14.32/5.00 14.32/5.00 The following rules are bounded: 14.32/5.00 f_292(v145:0:0, v147:0:0) -> f_292(x5:0, 1 + v147:0:0) :|: v145:0:0 - 2 * x5:0 >= 0 && v145:0:0 - 2 * x5:0 < 2 && v147:0:0 > 0 && v145:0:0 > 1 14.32/5.00 14.32/5.00 14.32/5.00 ---------------------------------------- 14.32/5.00 14.32/5.00 (14) 14.32/5.00 YES 14.32/5.05 EOF