8.13/3.20 YES 8.13/3.23 proof of /export/starexec/sandbox2/benchmark/theBenchmark.c 8.13/3.23 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 8.13/3.23 8.13/3.23 8.13/3.23 Termination of the given C Problem could be proven: 8.13/3.23 8.13/3.23 (0) C Problem 8.13/3.23 (1) CToLLVMProof [EQUIVALENT, 175 ms] 8.13/3.23 (2) LLVM problem 8.13/3.23 (3) LLVMToTerminationGraphProof [EQUIVALENT, 879 ms] 8.13/3.23 (4) LLVM Symbolic Execution Graph 8.13/3.23 (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] 8.13/3.23 (6) LLVM Symbolic Execution SCC 8.13/3.23 (7) SCC2IRS [SOUND, 55 ms] 8.13/3.23 (8) IntTRS 8.13/3.23 (9) IntTRSCompressionProof [EQUIVALENT, 0 ms] 8.13/3.23 (10) IntTRS 8.13/3.23 (11) PolynomialOrderProcessor [EQUIVALENT, 7 ms] 8.13/3.23 (12) YES 8.13/3.23 8.13/3.23 8.13/3.23 ---------------------------------------- 8.13/3.23 8.13/3.23 (0) 8.13/3.23 Obligation: 8.13/3.23 c file /export/starexec/sandbox2/benchmark/theBenchmark.c 8.13/3.23 ---------------------------------------- 8.13/3.23 8.13/3.23 (1) CToLLVMProof (EQUIVALENT) 8.13/3.23 Compiled c-file /export/starexec/sandbox2/benchmark/theBenchmark.c to LLVM. 8.13/3.23 ---------------------------------------- 8.13/3.23 8.13/3.23 (2) 8.13/3.23 Obligation: 8.13/3.23 LLVM Problem 8.13/3.23 8.13/3.23 Aliases: 8.13/3.23 8.13/3.23 Data layout: 8.13/3.23 8.13/3.23 "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" 8.13/3.23 8.13/3.23 Machine: 8.13/3.23 8.13/3.23 "x86_64-pc-linux-gnu" 8.13/3.23 8.13/3.23 Type definitions: 8.13/3.23 8.13/3.23 Global variables: 8.13/3.23 8.13/3.23 Function declarations and definitions: 8.13/3.23 8.13/3.23 *BasicFunctionTypename: "__VERIFIER_nondet_int" returnParam: i32 parameters: () variableLength: true visibilityType: DEFAULT callingConvention: ccc 8.13/3.23 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 8.13/3.23 0: 8.13/3.23 %1 = alloca i32, align 4 8.13/3.23 %x = alloca i32, align 4 8.13/3.23 %y = alloca i32, align 4 8.13/3.23 store 0, %1 8.13/3.23 %2 = call i32 (...)* @__VERIFIER_nondet_int() 8.13/3.23 store %2, %x 8.13/3.23 %3 = call i32 (...)* @__VERIFIER_nondet_int() 8.13/3.23 store %3, %y 8.13/3.23 br %4 8.13/3.23 4: 8.13/3.23 %5 = load %x 8.13/3.23 %6 = icmp sgt %5 0 8.13/3.23 br %6, %7, %11 8.13/3.23 7: 8.13/3.23 %8 = load %x 8.13/3.23 %9 = load %y 8.13/3.23 %10 = icmp slt %8 %9 8.13/3.23 br %11 8.13/3.23 11: 8.13/3.23 %12 = phi [0, %4], [%10, %7] 8.13/3.23 br %12, %13, %18 8.13/3.23 13: 8.13/3.23 %14 = load %x 8.13/3.23 %15 = mul 2 %14 8.13/3.23 store %15, %x 8.13/3.23 %16 = load %y 8.13/3.23 %17 = add %16 1 8.13/3.23 store %17, %y 8.13/3.23 br %4 8.13/3.23 18: 8.13/3.23 ret 0 8.13/3.23 8.13/3.23 8.13/3.23 Analyze Termination of all function calls matching the pattern: 8.13/3.23 main() 8.13/3.23 ---------------------------------------- 8.13/3.23 8.13/3.23 (3) LLVMToTerminationGraphProof (EQUIVALENT) 8.13/3.23 Constructed symbolic execution graph for LLVM program and proved memory safety. 8.13/3.23 ---------------------------------------- 8.13/3.23 8.13/3.23 (4) 8.13/3.23 Obligation: 8.13/3.23 SE Graph 8.13/3.23 ---------------------------------------- 8.13/3.23 8.13/3.23 (5) SymbolicExecutionGraphToSCCProof (SOUND) 8.13/3.23 Splitted symbolic execution graph to 1 SCC. 8.13/3.23 ---------------------------------------- 8.13/3.23 8.13/3.23 (6) 8.13/3.23 Obligation: 8.13/3.23 SCC 8.13/3.23 ---------------------------------------- 8.13/3.23 8.13/3.23 (7) SCC2IRS (SOUND) 8.13/3.23 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 8.13/3.23 Generated rules. Obtained 17 rulesP rules: 8.13/3.23 f_158(v126, v127, v128, v129, v130, v134, 1, v131, v133, v135, v136, v137, v138, 0, 3, 2, 4) -> f_159(v126, v127, v128, v129, v130, v134, 1, v131, v133, v135, v136, v137, v138, 0, 3, 2, 4) :|: 0 = 0 8.13/3.23 f_159(v126, v127, v128, v129, v130, v134, 1, v131, v133, v135, v136, v137, v138, 0, 3, 2, 4) -> f_160(v126, v127, v128, v129, v130, v134, 1, v131, v133, v135, v136, v137, v138, 0, 3, 2, 4) :|: TRUE 8.13/3.23 f_160(v126, v127, v128, v129, v130, v134, 1, v131, v133, v135, v136, v137, v138, 0, 3, 2, 4) -> f_161(v126, v127, v128, v129, v130, v134, 1, v133, v131, v135, v136, v137, v138, 0, 3, 2, 4) :|: 0 = 0 8.13/3.23 f_161(v126, v127, v128, v129, v130, v134, 1, v133, v131, v135, v136, v137, v138, 0, 3, 2, 4) -> f_162(v126, v127, v128, v129, v130, v134, 1, v135, v131, v133, v136, v137, v138, 0, 3, 2, 4) :|: 0 = 0 8.13/3.23 f_162(v126, v127, v128, v129, v130, v134, 1, v135, v131, v133, v136, v137, v138, 0, 3, 2, 4) -> f_163(v126, v127, v128, v129, v130, v134, 1, v135, v131, v133, v136, v137, v138, 0, 3, 2, 4) :|: v134 < v135 8.13/3.23 f_163(v126, v127, v128, v129, v130, v134, 1, v135, v131, v133, v136, v137, v138, 0, 3, 2, 4) -> f_165(v126, v127, v128, v129, v130, v134, 1, v135, v131, v133, v136, v137, v138, 0, 3, 2, 4) :|: 0 = 0 8.13/3.23 f_165(v126, v127, v128, v129, v130, v134, 1, v135, v131, v133, v136, v137, v138, 0, 3, 2, 4) -> f_167(v126, v127, v128, v129, v130, v134, 1, v135, v131, v133, v136, v137, v138, 0, 3, 2, 4) :|: 0 = 0 8.13/3.23 f_167(v126, v127, v128, v129, v130, v134, 1, v135, v131, v133, v136, v137, v138, 0, 3, 2, 4) -> f_169(v126, v127, v128, v129, v130, v134, 1, v135, v131, v133, v136, v137, v138, 0, 3, 2, 4) :|: TRUE 8.13/3.23 f_169(v126, v127, v128, v129, v130, v134, 1, v135, v131, v133, v136, v137, v138, 0, 3, 2, 4) -> f_171(v126, v127, v128, v129, v130, v134, 1, v135, v133, v136, v137, v138, 0, 3, 2, 4) :|: 0 = 0 8.13/3.23 f_171(v126, v127, v128, v129, v130, v134, 1, v135, v133, v136, v137, v138, 0, 3, 2, 4) -> f_172(v126, v127, v128, v129, v130, v134, 1, v135, v178, v133, v136, v137, v138, 0, 3, 2, 4) :|: v178 = 2 * v134 && 4 <= v178 8.13/3.23 f_172(v126, v127, v128, v129, v130, v134, 1, v135, v178, v133, v136, v137, v138, 0, 3, 2, 4) -> f_173(v126, v127, v128, v129, v130, v134, 1, v135, v178, v133, v136, v137, v138, 0, 3, 2, 4) :|: TRUE 8.13/3.23 f_173(v126, v127, v128, v129, v130, v134, 1, v135, v178, v133, v136, v137, v138, 0, 3, 2, 4) -> f_174(v126, v127, v128, v129, v130, v134, 1, v135, v178, v136, v137, v138, 0, 3, 2, 4) :|: 0 = 0 8.13/3.23 f_174(v126, v127, v128, v129, v130, v134, 1, v135, v178, v136, v137, v138, 0, 3, 2, 4) -> f_175(v126, v127, v128, v129, v130, v134, 1, v135, v178, v180, v136, v137, v138, 0, 3, 2, 4) :|: v180 = 1 + v135 && 4 <= v180 8.13/3.23 f_175(v126, v127, v128, v129, v130, v134, 1, v135, v178, v180, v136, v137, v138, 0, 3, 2, 4) -> f_176(v126, v127, v128, v129, v130, v134, 1, v135, v178, v180, v136, v137, v138, 0, 3, 2, 4) :|: TRUE 8.13/3.23 f_176(v126, v127, v128, v129, v130, v134, 1, v135, v178, v180, v136, v137, v138, 0, 3, 2, 4) -> f_177(v126, v127, v128, v129, v130, v134, 1, v135, v178, v180, v136, v137, v138, 0, 3, 2, 4) :|: TRUE 8.13/3.23 f_177(v126, v127, v128, v129, v130, v134, 1, v135, v178, v180, v136, v137, v138, 0, 3, 2, 4) -> f_157(v126, v127, v128, v129, v130, v134, 1, v135, v178, v180, v136, v137, v138, 0, 3, 2, 4) :|: TRUE 8.13/3.23 f_157(v126, v127, v128, v129, v130, v131, 1, v133, v134, v135, v136, v137, v138, 0, 3, 2, 4) -> f_158(v126, v127, v128, v129, v130, v134, 1, v131, v133, v135, v136, v137, v138, 0, 3, 2, 4) :|: 0 = 0 8.13/3.23 Combined rules. Obtained 1 rulesP rules: 8.13/3.23 f_158(v126:0, v127:0, v128:0, v129:0, v130:0, v134:0, 1, v131:0, v133:0, v135:0, v136:0, v137:0, v138:0, 0, 3, 2, 4) -> f_158(v126:0, v127:0, v128:0, v129:0, v130:0, 2 * v134:0, 1, v134:0, v135:0, 1 + v135:0, v136:0, v137:0, v138:0, 0, 3, 2, 4) :|: v135:0 > v134:0 && v135:0 > 2 && 3 < 2 * v134:0 8.13/3.23 Filtered unneeded arguments: 8.13/3.23 f_158(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17) -> f_158(x6, x10) 8.13/3.23 Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: 8.13/3.23 f_158(v134:0, v135:0) -> f_158(2 * v134:0, 1 + v135:0) :|: v135:0 > 2 && 3 < 2 * v134:0 && v135:0 > v134:0 8.13/3.23 8.13/3.23 ---------------------------------------- 8.13/3.23 8.13/3.23 (8) 8.13/3.23 Obligation: 8.13/3.23 Rules: 8.13/3.23 f_158(v134:0, v135:0) -> f_158(2 * v134:0, 1 + v135:0) :|: v135:0 > 2 && 3 < 2 * v134:0 && v135:0 > v134:0 8.13/3.23 8.13/3.23 ---------------------------------------- 8.13/3.23 8.13/3.23 (9) IntTRSCompressionProof (EQUIVALENT) 8.13/3.23 Compressed rules. 8.13/3.23 ---------------------------------------- 8.13/3.23 8.13/3.23 (10) 8.13/3.23 Obligation: 8.13/3.23 Rules: 8.13/3.23 f_158(v134:0:0, v135:0:0) -> f_158(2 * v134:0:0, 1 + v135:0:0) :|: v135:0:0 > 2 && 3 < 2 * v134:0:0 && v135:0:0 > v134:0:0 8.13/3.23 8.13/3.23 ---------------------------------------- 8.13/3.23 8.13/3.23 (11) PolynomialOrderProcessor (EQUIVALENT) 8.13/3.23 Found the following polynomial interpretation: 8.13/3.23 [f_158(x, x1)] = -x + x1 8.13/3.23 8.13/3.23 The following rules are decreasing: 8.13/3.23 f_158(v134:0:0, v135:0:0) -> f_158(2 * v134:0:0, 1 + v135:0:0) :|: v135:0:0 > 2 && 3 < 2 * v134:0:0 && v135:0:0 > v134:0:0 8.13/3.23 The following rules are bounded: 8.13/3.23 f_158(v134:0:0, v135:0:0) -> f_158(2 * v134:0:0, 1 + v135:0:0) :|: v135:0:0 > 2 && 3 < 2 * v134:0:0 && v135:0:0 > v134:0:0 8.13/3.23 8.13/3.23 ---------------------------------------- 8.13/3.23 8.13/3.23 (12) 8.13/3.23 YES 9.09/3.27 EOF