8.11/3.37 YES 8.11/3.38 proof of /export/starexec/sandbox2/benchmark/theBenchmark.c 8.11/3.38 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 8.11/3.38 8.11/3.38 8.11/3.38 Termination of the given C Problem could be proven: 8.11/3.38 8.11/3.38 (0) C Problem 8.11/3.38 (1) CToLLVMProof [EQUIVALENT, 175 ms] 8.11/3.38 (2) LLVM problem 8.11/3.38 (3) LLVMToTerminationGraphProof [EQUIVALENT, 893 ms] 8.11/3.38 (4) LLVM Symbolic Execution Graph 8.11/3.38 (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] 8.11/3.38 (6) LLVM Symbolic Execution SCC 8.11/3.38 (7) SCC2IRS [SOUND, 79 ms] 8.11/3.38 (8) IntTRS 8.11/3.38 (9) IntTRSCompressionProof [EQUIVALENT, 0 ms] 8.11/3.38 (10) IntTRS 8.11/3.38 (11) RankingReductionPairProof [EQUIVALENT, 19 ms] 8.11/3.38 (12) YES 8.11/3.38 8.11/3.38 8.11/3.38 ---------------------------------------- 8.11/3.38 8.11/3.38 (0) 8.11/3.38 Obligation: 8.11/3.38 c file /export/starexec/sandbox2/benchmark/theBenchmark.c 8.11/3.38 ---------------------------------------- 8.11/3.38 8.11/3.38 (1) CToLLVMProof (EQUIVALENT) 8.11/3.38 Compiled c-file /export/starexec/sandbox2/benchmark/theBenchmark.c to LLVM. 8.11/3.38 ---------------------------------------- 8.11/3.38 8.11/3.38 (2) 8.11/3.38 Obligation: 8.11/3.38 LLVM Problem 8.11/3.38 8.11/3.38 Aliases: 8.11/3.38 8.11/3.38 Data layout: 8.11/3.38 8.11/3.38 "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" 8.11/3.38 8.11/3.38 Machine: 8.11/3.38 8.11/3.38 "x86_64-pc-linux-gnu" 8.11/3.38 8.11/3.38 Type definitions: 8.11/3.38 8.11/3.38 Global variables: 8.11/3.38 8.11/3.38 Function declarations and definitions: 8.11/3.38 8.11/3.38 *BasicFunctionTypename: "__VERIFIER_nondet_int" returnParam: i32 parameters: () variableLength: true visibilityType: DEFAULT callingConvention: ccc 8.11/3.38 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 8.11/3.38 0: 8.11/3.38 %1 = alloca i32, align 4 8.11/3.38 %x = alloca i32, align 4 8.11/3.38 %y = alloca i32, align 4 8.11/3.38 %z = alloca i32, align 4 8.11/3.38 %old_x = alloca i32, align 4 8.11/3.38 store 0, %1 8.11/3.38 %2 = call i32 (...)* @__VERIFIER_nondet_int() 8.11/3.38 store %2, %x 8.11/3.38 %3 = call i32 (...)* @__VERIFIER_nondet_int() 8.11/3.38 store %3, %y 8.11/3.38 %4 = call i32 (...)* @__VERIFIER_nondet_int() 8.11/3.38 store %4, %z 8.11/3.38 br %5 8.11/3.38 5: 8.11/3.38 %6 = load %x 8.11/3.38 %7 = icmp sgt %6 0 8.11/3.38 br %7, %8, %12 8.11/3.38 8: 8.11/3.38 %9 = load %x 8.11/3.38 %10 = load %y 8.11/3.38 %11 = icmp slt %9 %10 8.11/3.38 br %12 8.11/3.38 12: 8.11/3.38 %13 = phi [0, %5], [%11, %8] 8.11/3.38 br %13, %14, %24 8.11/3.38 14: 8.11/3.38 %15 = load %x 8.11/3.38 store %15, %old_x 8.11/3.38 %16 = call i32 (...)* @__VERIFIER_nondet_int() 8.11/3.38 store %16, %x 8.11/3.38 %17 = load %x 8.11/3.38 %18 = load %old_x 8.11/3.38 %19 = mul 2 %18 8.11/3.38 %20 = icmp sle %17 %19 8.11/3.38 br %20, %21, %22 8.11/3.38 21: 8.11/3.38 br %24 8.11/3.38 22: 8.11/3.38 %23 = load %z 8.11/3.38 store %23, %y 8.11/3.38 br %5 8.11/3.38 24: 8.11/3.38 ret 0 8.11/3.38 8.11/3.38 8.11/3.38 Analyze Termination of all function calls matching the pattern: 8.11/3.38 main() 8.11/3.38 ---------------------------------------- 8.11/3.38 8.11/3.38 (3) LLVMToTerminationGraphProof (EQUIVALENT) 8.11/3.38 Constructed symbolic execution graph for LLVM program and proved memory safety. 8.11/3.38 ---------------------------------------- 8.11/3.38 8.11/3.38 (4) 8.11/3.38 Obligation: 8.11/3.38 SE Graph 8.11/3.38 ---------------------------------------- 8.11/3.38 8.11/3.38 (5) SymbolicExecutionGraphToSCCProof (SOUND) 8.11/3.38 Splitted symbolic execution graph to 1 SCC. 8.11/3.38 ---------------------------------------- 8.11/3.38 8.11/3.38 (6) 8.11/3.38 Obligation: 8.11/3.38 SCC 8.11/3.38 ---------------------------------------- 8.11/3.38 8.11/3.38 (7) SCC2IRS (SOUND) 8.11/3.38 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 8.11/3.38 Generated rules. Obtained 23 rulesP rules: 8.11/3.38 f_191(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v151, v153, v155, 0, v157, v158, v159, v160, v161, 3, 2, 4) -> f_192(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v151, v153, v155, 0, v157, v158, v159, v160, v161, 3, 2, 4) :|: 0 = 0 8.11/3.38 f_192(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v151, v153, v155, 0, v157, v158, v159, v160, v161, 3, 2, 4) -> f_193(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v151, v153, v155, 0, v157, v158, v159, v160, v161, 3, 2, 4) :|: TRUE 8.11/3.38 f_193(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v151, v153, v155, 0, v157, v158, v159, v160, v161, 3, 2, 4) -> f_194(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v153, v151, v155, 0, v157, v158, v159, v160, v161, 3, 2, 4) :|: 0 = 0 8.11/3.38 f_194(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v153, v151, v155, 0, v157, v158, v159, v160, v161, 3, 2, 4) -> f_195(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v151, v155, 0, v157, v158, v159, v160, v161, 3, 2, 4) :|: 0 = 0 8.11/3.38 f_195(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v151, v155, 0, v157, v158, v159, v160, v161, 3, 2, 4) -> f_196(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v151, v155, 0, v157, v158, v159, v160, v161, 3, 2, 4) :|: v154 < v150 && 4 <= v150 8.11/3.38 f_196(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v151, v155, 0, v157, v158, v159, v160, v161, 3, 2, 4) -> f_198(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v151, v155, 0, v157, v158, v159, v160, v161, 3, 2, 4) :|: 0 = 0 8.11/3.38 f_198(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v151, v155, 0, v157, v158, v159, v160, v161, 3, 2, 4) -> f_200(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v151, v155, 0, v157, v158, v159, v160, v161, 3, 2, 4) :|: 0 = 0 8.11/3.38 f_200(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v151, v155, 0, v157, v158, v159, v160, v161, 3, 2, 4) -> f_202(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v151, v155, 0, v157, v158, v159, v160, v161, 3, 2, 4) :|: TRUE 8.11/3.38 f_202(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v151, v155, 0, v157, v158, v159, v160, v161, 3, 2, 4) -> f_204(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v151, v155, 0, v157, v158, v159, v160, v161, 3, 2, 4) :|: 0 = 0 8.11/3.38 f_204(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v151, v155, 0, v157, v158, v159, v160, v161, 3, 2, 4) -> f_205(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v151, v155, 0, v157, v158, v159, v160, v161, 3, 2, 4) :|: TRUE 8.11/3.38 f_205(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v151, v155, 0, v157, v158, v159, v160, v161, 3, 2, 4) -> f_206(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v224, v151, v155, 0, v157, v158, v159, v160, v161, 3, 2, 4) :|: TRUE 8.11/3.38 f_206(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v224, v151, v155, 0, v157, v158, v159, v160, v161, 3, 2, 4) -> f_207(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v224, v151, v155, 0, v157, v158, v159, v160, v161, 3, 2, 4) :|: TRUE 8.11/3.38 f_207(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v224, v151, v155, 0, v157, v158, v159, v160, v161, 3, 2, 4) -> f_208(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v224, v151, v155, 0, v157, v158, v159, v160, v161, 3, 2, 4) :|: 0 = 0 8.11/3.38 f_208(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v224, v151, v155, 0, v157, v158, v159, v160, v161, 3, 2, 4) -> f_209(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v224, v155, 0, v157, v158, v159, v160, v161, 3, 2, 4) :|: 0 = 0 8.11/3.38 f_209(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v224, v155, 0, v157, v158, v159, v160, v161, 3, 2, 4) -> f_210(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v224, v226, 0, v157, v158, v159, v160, v161, 3, 2, 4, 6) :|: v226 = 2 * v154 && 6 <= v226 8.11/3.38 f_210(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v224, v226, 0, v157, v158, v159, v160, v161, 3, 2, 4, 6) -> f_212(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v224, v226, 0, v157, v158, v159, v160, v161, 3, 2, 4, 7, 6) :|: v226 < v224 && 7 <= v224 8.11/3.38 f_212(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v224, v226, 0, v157, v158, v159, v160, v161, 3, 2, 4, 7, 6) -> f_214(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v224, v226, 0, v157, v158, v159, v160, v161, 3, 2, 4, 7, 6) :|: 0 = 0 8.11/3.38 f_214(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v224, v226, 0, v157, v158, v159, v160, v161, 3, 2, 4, 7, 6) -> f_216(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v224, v226, 0, v157, v158, v159, v160, v161, 3, 2, 4, 7, 6) :|: TRUE 8.11/3.38 f_216(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v224, v226, 0, v157, v158, v159, v160, v161, 3, 2, 4, 7, 6) -> f_218(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v224, v226, 0, v157, v158, v159, v160, v161, 3, 2, 4, 7, 6) :|: 0 = 0 8.11/3.38 f_218(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v224, v226, 0, v157, v158, v159, v160, v161, 3, 2, 4, 7, 6) -> f_219(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v224, v226, 0, v157, v158, v159, v160, v161, 3, 2, 4, 7, 6) :|: TRUE 8.11/3.38 f_219(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v224, v226, 0, v157, v158, v159, v160, v161, 3, 2, 4, 7, 6) -> f_220(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v224, v226, 0, v157, v158, v159, v160, v161, 3, 2, 4, 7, 6) :|: TRUE 8.11/3.38 f_220(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v224, v226, 0, v157, v158, v159, v160, v161, 3, 2, 4, 7, 6) -> f_190(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v150, v224, v226, 0, v157, v158, v159, v160, v161, 3, 2, 4) :|: TRUE 8.11/3.38 f_190(v143, v144, v145, v146, v147, v148, v149, v150, v151, 1, v153, v154, v155, 0, v157, v158, v159, v160, v161, 3, 2, 4) -> f_191(v143, v144, v145, v146, v147, v148, v149, v150, v154, 1, v151, v153, v155, 0, v157, v158, v159, v160, v161, 3, 2, 4) :|: 0 = 0 8.11/3.38 Combined rules. Obtained 1 rulesP rules: 8.11/3.38 f_191(v143:0, v144:0, v145:0, v146:0, v147:0, v148:0, v149:0, v150:0, v154:0, 1, v151:0, v153:0, v155:0, 0, v157:0, v158:0, v159:0, v160:0, v161:0, 3, 2, 4) -> f_191(v143:0, v144:0, v145:0, v146:0, v147:0, v148:0, v149:0, v150:0, v224:0, 1, v154:0, v150:0, 2 * v154:0, 0, v157:0, v158:0, v159:0, v160:0, v161:0, 3, 2, 4) :|: v150:0 > 3 && v154:0 < v150:0 && 5 < 2 * v154:0 && v224:0 > 2 * v154:0 && v224:0 > 6 8.11/3.38 Filtered unneeded arguments: 8.11/3.38 f_191(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) -> f_191(x8, x9) 8.11/3.38 Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: 8.11/3.38 f_191(v150:0, v154:0) -> f_191(v150:0, v224:0) :|: v154:0 < v150:0 && v150:0 > 3 && 5 < 2 * v154:0 && v224:0 > 6 && v224:0 > 2 * v154:0 8.11/3.38 8.11/3.38 ---------------------------------------- 8.11/3.38 8.11/3.38 (8) 8.11/3.38 Obligation: 8.11/3.38 Rules: 8.11/3.38 f_191(v150:0, v154:0) -> f_191(v150:0, v224:0) :|: v154:0 < v150:0 && v150:0 > 3 && 5 < 2 * v154:0 && v224:0 > 6 && v224:0 > 2 * v154:0 8.11/3.38 8.11/3.38 ---------------------------------------- 8.11/3.38 8.11/3.38 (9) IntTRSCompressionProof (EQUIVALENT) 8.11/3.38 Compressed rules. 8.11/3.38 ---------------------------------------- 8.11/3.38 8.11/3.38 (10) 8.11/3.38 Obligation: 8.11/3.38 Rules: 8.11/3.38 f_191(v150:0:0, v154:0:0) -> f_191(v150:0:0, v224:0:0) :|: v224:0:0 > 6 && v224:0:0 > 2 * v154:0:0 && 5 < 2 * v154:0:0 && v150:0:0 > 3 && v154:0:0 < v150:0:0 8.11/3.38 8.11/3.38 ---------------------------------------- 8.11/3.38 8.11/3.38 (11) RankingReductionPairProof (EQUIVALENT) 8.11/3.38 Interpretation: 8.11/3.38 [ f_191 ] = -1/4*f_191_2 + 1/4*f_191_1 8.11/3.38 8.11/3.38 The following rules are decreasing: 8.11/3.38 f_191(v150:0:0, v154:0:0) -> f_191(v150:0:0, v224:0:0) :|: v224:0:0 > 6 && v224:0:0 > 2 * v154:0:0 && 5 < 2 * v154:0:0 && v150:0:0 > 3 && v154:0:0 < v150:0:0 8.11/3.38 8.11/3.38 The following rules are bounded: 8.11/3.38 f_191(v150:0:0, v154:0:0) -> f_191(v150:0:0, v224:0:0) :|: v224:0:0 > 6 && v224:0:0 > 2 * v154:0:0 && 5 < 2 * v154:0:0 && v150:0:0 > 3 && v154:0:0 < v150:0:0 8.11/3.38 8.11/3.38 8.11/3.38 ---------------------------------------- 8.11/3.38 8.11/3.38 (12) 8.11/3.38 YES 9.31/3.46 EOF