23.92/8.40 YES 23.92/8.42 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 23.92/8.42 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 23.92/8.42 23.92/8.42 23.92/8.42 Termination of the given C Problem could be proven: 23.92/8.42 23.92/8.42 (0) C Problem 23.92/8.42 (1) CToLLVMProof [EQUIVALENT, 172 ms] 23.92/8.42 (2) LLVM problem 23.92/8.42 (3) LLVMToTerminationGraphProof [EQUIVALENT, 5261 ms] 23.92/8.42 (4) LLVM Symbolic Execution Graph 23.92/8.42 (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] 23.92/8.42 (6) LLVM Symbolic Execution SCC 23.92/8.42 (7) SCC2IRS [SOUND, 61 ms] 23.92/8.42 (8) IntTRS 23.92/8.42 (9) IntTRSCompressionProof [EQUIVALENT, 0 ms] 23.92/8.42 (10) IntTRS 23.92/8.42 (11) PolynomialOrderProcessor [EQUIVALENT, 10 ms] 23.92/8.42 (12) YES 23.92/8.42 23.92/8.42 23.92/8.42 ---------------------------------------- 23.92/8.42 23.92/8.42 (0) 23.92/8.42 Obligation: 23.92/8.42 c file /export/starexec/sandbox/benchmark/theBenchmark.c 23.92/8.42 ---------------------------------------- 23.92/8.42 23.92/8.42 (1) CToLLVMProof (EQUIVALENT) 23.92/8.42 Compiled c-file /export/starexec/sandbox/benchmark/theBenchmark.c to LLVM. 23.92/8.42 ---------------------------------------- 23.92/8.42 23.92/8.42 (2) 23.92/8.42 Obligation: 23.92/8.42 LLVM Problem 23.92/8.42 23.92/8.42 Aliases: 23.92/8.42 23.92/8.42 Data layout: 23.92/8.42 23.92/8.42 "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" 23.92/8.42 23.92/8.42 Machine: 23.92/8.42 23.92/8.42 "x86_64-pc-linux-gnu" 23.92/8.42 23.92/8.42 Type definitions: 23.92/8.42 23.92/8.42 Global variables: 23.92/8.42 23.92/8.42 Function declarations and definitions: 23.92/8.42 23.92/8.42 *BasicFunctionTypename: "__VERIFIER_nondet_int" returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 23.92/8.42 *BasicFunctionTypename: "iterate" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: (bound i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc 23.92/8.42 0: 23.92/8.42 %1 = alloca i32, align 4 23.92/8.42 %i = alloca i32, align 4 23.92/8.42 %sum = alloca i32, align 4 23.92/8.42 store %bound, %1 23.92/8.42 store 0, %sum 23.92/8.42 store 0, %i 23.92/8.42 br %2 23.92/8.42 2: 23.92/8.42 %3 = load %i 23.92/8.42 %4 = load %1 23.92/8.42 %5 = icmp slt %3 %4 23.92/8.42 br %5, %6, %13 23.92/8.42 6: 23.92/8.42 %7 = load %i 23.92/8.42 %8 = load %sum 23.92/8.42 %9 = add %8 %7 23.92/8.42 store %9, %sum 23.92/8.42 br %10 23.92/8.42 10: 23.92/8.42 %11 = load %i 23.92/8.42 %12 = add %11 1 23.92/8.42 store %12, %i 23.92/8.42 br %2 23.92/8.42 13: 23.92/8.42 %14 = load %sum 23.92/8.42 ret %14 23.92/8.42 23.92/8.42 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 23.92/8.42 0: 23.92/8.42 %1 = alloca i32, align 4 23.92/8.42 store 0, %1 23.92/8.42 %2 = call i32 @__VERIFIER_nondet_int() 23.92/8.42 %3 = call i32 @iterate(i32 %2) 23.92/8.42 ret %3 23.92/8.42 23.92/8.42 23.92/8.42 Analyze Termination of all function calls matching the pattern: 23.92/8.42 main() 23.92/8.42 ---------------------------------------- 23.92/8.42 23.92/8.42 (3) LLVMToTerminationGraphProof (EQUIVALENT) 23.92/8.42 Constructed symbolic execution graph for LLVM program and proved memory safety. 23.92/8.42 ---------------------------------------- 23.92/8.42 23.92/8.42 (4) 23.92/8.42 Obligation: 23.92/8.42 SE Graph 23.92/8.42 ---------------------------------------- 23.92/8.42 23.92/8.42 (5) SymbolicExecutionGraphToSCCProof (SOUND) 23.92/8.42 Splitted symbolic execution graph to 1 SCC. 23.92/8.42 ---------------------------------------- 23.92/8.42 23.92/8.42 (6) 23.92/8.42 Obligation: 23.92/8.42 SCC 23.92/8.42 ---------------------------------------- 23.92/8.42 23.92/8.42 (7) SCC2IRS (SOUND) 23.92/8.42 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 23.92/8.42 Generated rules. Obtained 15 rulesP rules: 23.92/8.42 f_216(v85, v86, v87, v88, v93, 1, v89, v91, v92, v94, v95, v96, v97, v98, 0, 3, 4) -> f_217(v85, v86, v87, v88, v93, 1, v89, v91, v92, v94, v95, v96, v97, v98, 0, 3, 4) :|: 0 = 0 23.92/8.42 f_217(v85, v86, v87, v88, v93, 1, v89, v91, v92, v94, v95, v96, v97, v98, 0, 3, 4) -> f_218(v85, v86, v87, v88, v93, 1, v89, v91, v92, v94, v95, v96, v97, v98, 0, 3, 2, 4) :|: v93 < v85 && 2 <= v85 23.92/8.42 f_218(v85, v86, v87, v88, v93, 1, v89, v91, v92, v94, v95, v96, v97, v98, 0, 3, 2, 4) -> f_220(v85, v86, v87, v88, v93, 1, v89, v91, v92, v94, v95, v96, v97, v98, 0, 3, 2, 4) :|: 0 = 0 23.92/8.42 f_220(v85, v86, v87, v88, v93, 1, v89, v91, v92, v94, v95, v96, v97, v98, 0, 3, 2, 4) -> f_222(v85, v86, v87, v88, v93, 1, v89, v91, v92, v94, v95, v96, v97, v98, 0, 3, 2, 4) :|: TRUE 23.92/8.42 f_222(v85, v86, v87, v88, v93, 1, v89, v91, v92, v94, v95, v96, v97, v98, 0, 3, 2, 4) -> f_224(v85, v86, v87, v88, v93, 1, v91, v92, v89, v94, v95, v96, v97, v98, 0, 3, 2, 4) :|: 0 = 0 23.92/8.42 f_224(v85, v86, v87, v88, v93, 1, v91, v92, v89, v94, v95, v96, v97, v98, 0, 3, 2, 4) -> f_226(v85, v86, v87, v88, v93, 1, v92, v89, v94, v95, v96, v97, v98, 0, 3, 2, 4) :|: 0 = 0 23.92/8.42 f_226(v85, v86, v87, v88, v93, 1, v92, v89, v94, v95, v96, v97, v98, 0, 3, 2, 4) -> f_228(v85, v86, v87, v88, v93, 1, v92, v100, v89, v94, v95, v96, v97, v98, 0, 3, 2, 4) :|: v100 = v92 + v93 && 1 <= v100 23.92/8.42 f_228(v85, v86, v87, v88, v93, 1, v92, v100, v89, v94, v95, v96, v97, v98, 0, 3, 2, 4) -> f_229(v85, v86, v87, v88, v93, 1, v92, v100, v89, v94, v95, v96, v97, v98, 0, 3, 2, 4) :|: TRUE 23.92/8.42 f_229(v85, v86, v87, v88, v93, 1, v92, v100, v89, v94, v95, v96, v97, v98, 0, 3, 2, 4) -> f_230(v85, v86, v87, v88, v93, 1, v92, v100, v89, v94, v95, v96, v97, v98, 0, 3, 2, 4) :|: TRUE 23.92/8.42 f_230(v85, v86, v87, v88, v93, 1, v92, v100, v89, v94, v95, v96, v97, v98, 0, 3, 2, 4) -> f_231(v85, v86, v87, v88, v93, 1, v92, v100, v94, v95, v96, v97, v98, 0, 3, 2, 4) :|: 0 = 0 23.92/8.42 f_231(v85, v86, v87, v88, v93, 1, v92, v100, v94, v95, v96, v97, v98, 0, 3, 2, 4) -> f_232(v85, v86, v87, v88, v93, 1, v92, v100, v102, v94, v95, v96, v97, v98, 0, 3, 2, 4) :|: v102 = 1 + v93 && 2 <= v102 23.92/8.42 f_232(v85, v86, v87, v88, v93, 1, v92, v100, v102, v94, v95, v96, v97, v98, 0, 3, 2, 4) -> f_233(v85, v86, v87, v88, v93, 1, v92, v100, v102, v94, v95, v96, v97, v98, 0, 3, 2, 4) :|: TRUE 23.92/8.42 f_233(v85, v86, v87, v88, v93, 1, v92, v100, v102, v94, v95, v96, v97, v98, 0, 3, 2, 4) -> f_234(v85, v86, v87, v88, v93, 1, v92, v100, v102, v94, v95, v96, v97, v98, 0, 3, 2, 4) :|: TRUE 23.92/8.42 f_234(v85, v86, v87, v88, v93, 1, v92, v100, v102, v94, v95, v96, v97, v98, 0, 3, 2, 4) -> f_215(v85, v86, v87, v88, v93, 1, v92, v100, v102, v94, v95, v96, v97, v98, 0, 3, 4) :|: TRUE 23.92/8.42 f_215(v85, v86, v87, v88, v89, 1, v91, v92, v93, v94, v95, v96, v97, v98, 0, 3, 4) -> f_216(v85, v86, v87, v88, v93, 1, v89, v91, v92, v94, v95, v96, v97, v98, 0, 3, 4) :|: 0 = 0 23.92/8.42 Combined rules. Obtained 1 rulesP rules: 23.92/8.42 f_216(v85:0, v86:0, v87:0, v88:0, v93:0, 1, v89:0, v91:0, v92:0, v94:0, v95:0, v96:0, v97:0, v98:0, 0, 3, 4) -> f_216(v85:0, v86:0, v87:0, v88:0, 1 + v93:0, 1, v93:0, v92:0, v92:0 + v93:0, v94:0, v95:0, v96:0, v97:0, v98:0, 0, 3, 4) :|: v85:0 > 1 && v93:0 < v85:0 && v93:0 > 0 && v92:0 + v93:0 > 0 23.92/8.42 Filtered unneeded arguments: 23.92/8.42 f_216(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17) -> f_216(x1, x5, x9) 23.92/8.42 Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: 23.92/8.42 f_216(v85:0, v93:0, v92:0) -> f_216(v85:0, 1 + v93:0, v92:0 + v93:0) :|: v93:0 < v85:0 && v85:0 > 1 && v92:0 + v93:0 > 0 && v93:0 > 0 23.92/8.42 23.92/8.42 ---------------------------------------- 23.92/8.42 23.92/8.42 (8) 23.92/8.42 Obligation: 23.92/8.42 Rules: 23.92/8.42 f_216(v85:0, v93:0, v92:0) -> f_216(v85:0, 1 + v93:0, v92:0 + v93:0) :|: v93:0 < v85:0 && v85:0 > 1 && v92:0 + v93:0 > 0 && v93:0 > 0 23.92/8.42 23.92/8.42 ---------------------------------------- 23.92/8.42 23.92/8.42 (9) IntTRSCompressionProof (EQUIVALENT) 23.92/8.42 Compressed rules. 23.92/8.42 ---------------------------------------- 23.92/8.42 23.92/8.42 (10) 23.92/8.42 Obligation: 23.92/8.42 Rules: 23.92/8.42 f_216(v85:0:0, v93:0:0, v92:0:0) -> f_216(v85:0:0, 1 + v93:0:0, v92:0:0 + v93:0:0) :|: v92:0:0 + v93:0:0 > 0 && v93:0:0 > 0 && v85:0:0 > 1 && v93:0:0 < v85:0:0 23.92/8.42 23.92/8.42 ---------------------------------------- 23.92/8.42 23.92/8.42 (11) PolynomialOrderProcessor (EQUIVALENT) 23.92/8.42 Found the following polynomial interpretation: 23.92/8.42 [f_216(x, x1, x2)] = x - x1 23.92/8.42 23.92/8.42 The following rules are decreasing: 23.92/8.42 f_216(v85:0:0, v93:0:0, v92:0:0) -> f_216(v85:0:0, 1 + v93:0:0, v92:0:0 + v93:0:0) :|: v92:0:0 + v93:0:0 > 0 && v93:0:0 > 0 && v85:0:0 > 1 && v93:0:0 < v85:0:0 23.92/8.42 The following rules are bounded: 23.92/8.42 f_216(v85:0:0, v93:0:0, v92:0:0) -> f_216(v85:0:0, 1 + v93:0:0, v92:0:0 + v93:0:0) :|: v92:0:0 + v93:0:0 > 0 && v93:0:0 > 0 && v85:0:0 > 1 && v93:0:0 < v85:0:0 23.92/8.42 23.92/8.42 ---------------------------------------- 23.92/8.42 23.92/8.42 (12) 23.92/8.42 YES 24.99/8.71 EOF