9.00/3.75 YES 9.27/3.77 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 9.27/3.77 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.27/3.77 9.27/3.77 9.27/3.77 Termination of the given C Problem could be proven: 9.27/3.77 9.27/3.77 (0) C Problem 9.27/3.77 (1) CToLLVMProof [EQUIVALENT, 175 ms] 9.27/3.77 (2) LLVM problem 9.27/3.77 (3) LLVMToTerminationGraphProof [EQUIVALENT, 1197 ms] 9.27/3.77 (4) LLVM Symbolic Execution Graph 9.27/3.77 (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] 9.27/3.77 (6) LLVM Symbolic Execution SCC 9.27/3.77 (7) SCC2IRS [SOUND, 111 ms] 9.27/3.77 (8) IntTRS 9.27/3.77 (9) IntTRSCompressionProof [EQUIVALENT, 0 ms] 9.27/3.77 (10) IntTRS 9.27/3.77 (11) PolynomialOrderProcessor [EQUIVALENT, 8 ms] 9.27/3.77 (12) YES 9.27/3.77 9.27/3.77 9.27/3.77 ---------------------------------------- 9.27/3.77 9.27/3.77 (0) 9.27/3.77 Obligation: 9.27/3.77 c file /export/starexec/sandbox/benchmark/theBenchmark.c 9.27/3.77 ---------------------------------------- 9.27/3.77 9.27/3.77 (1) CToLLVMProof (EQUIVALENT) 9.27/3.77 Compiled c-file /export/starexec/sandbox/benchmark/theBenchmark.c to LLVM. 9.27/3.77 ---------------------------------------- 9.27/3.77 9.27/3.77 (2) 9.27/3.77 Obligation: 9.27/3.77 LLVM Problem 9.27/3.77 9.27/3.77 Aliases: 9.27/3.77 9.27/3.77 Data layout: 9.27/3.77 9.27/3.77 "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" 9.27/3.77 9.27/3.77 Machine: 9.27/3.77 9.27/3.77 "x86_64-pc-linux-gnu" 9.27/3.77 9.27/3.77 Type definitions: 9.27/3.77 9.27/3.77 Global variables: 9.27/3.77 9.27/3.77 Function declarations and definitions: 9.27/3.77 9.27/3.77 *BasicFunctionTypename: "__VERIFIER_nondet_int" returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 9.27/3.77 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 9.27/3.77 0: 9.27/3.77 %1 = alloca i32, align 4 9.27/3.77 %i = alloca i32, align 4 9.27/3.77 %j = alloca i32, align 4 9.27/3.77 %k = alloca i32, align 4 9.27/3.77 %ell = alloca i32, align 4 9.27/3.77 store 0, %1 9.27/3.77 %2 = call i32 @__VERIFIER_nondet_int() 9.27/3.77 store %2, %i 9.27/3.77 %3 = call i32 @__VERIFIER_nondet_int() 9.27/3.77 store %3, %j 9.27/3.77 %4 = call i32 @__VERIFIER_nondet_int() 9.27/3.77 store %4, %k 9.27/3.77 br %5 9.27/3.77 5: 9.27/3.77 %6 = load %i 9.27/3.77 %7 = icmp sle %6 100 9.27/3.77 br %7, %8, %12 9.27/3.77 8: 9.27/3.77 %9 = load %j 9.27/3.77 %10 = load %k 9.27/3.77 %11 = icmp sle %9 %10 9.27/3.77 br %12 9.27/3.77 12: 9.27/3.77 %13 = phi [0, %5], [%11, %8] 9.27/3.77 br %13, %14, %21 9.27/3.77 14: 9.27/3.77 %15 = load %i 9.27/3.77 store %15, %ell 9.27/3.77 %16 = load %j 9.27/3.77 store %16, %i 9.27/3.77 %17 = load %ell 9.27/3.77 %18 = add %17 1 9.27/3.77 store %18, %j 9.27/3.77 %19 = load %k 9.27/3.77 %20 = add %19 -1 9.27/3.77 store %20, %k 9.27/3.77 br %5 9.27/3.77 21: 9.27/3.77 ret 0 9.27/3.77 9.27/3.77 9.27/3.77 Analyze Termination of all function calls matching the pattern: 9.27/3.77 main() 9.27/3.77 ---------------------------------------- 9.27/3.77 9.27/3.77 (3) LLVMToTerminationGraphProof (EQUIVALENT) 9.27/3.77 Constructed symbolic execution graph for LLVM program and proved memory safety. 9.27/3.77 ---------------------------------------- 9.27/3.77 9.27/3.77 (4) 9.27/3.77 Obligation: 9.27/3.77 SE Graph 9.27/3.77 ---------------------------------------- 9.27/3.77 9.27/3.77 (5) SymbolicExecutionGraphToSCCProof (SOUND) 9.27/3.77 Splitted symbolic execution graph to 1 SCC. 9.27/3.77 ---------------------------------------- 9.27/3.77 9.27/3.77 (6) 9.27/3.77 Obligation: 9.27/3.77 SCC 9.27/3.77 ---------------------------------------- 9.27/3.77 9.27/3.77 (7) SCC2IRS (SOUND) 9.27/3.77 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 9.27/3.77 Generated rules. Obtained 22 rulesP rules: 9.27/3.77 f_208(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v294, v291, v295, v296, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) -> f_209(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v294, v291, v295, v296, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) :|: v293 <= 100 9.27/3.77 f_209(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v294, v291, v295, v296, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) -> f_211(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v294, v291, v295, v296, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) :|: 0 = 0 9.27/3.77 f_211(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v294, v291, v295, v296, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) -> f_213(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v294, v291, v295, v296, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) :|: TRUE 9.27/3.77 f_213(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v294, v291, v295, v296, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) -> f_215(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v295, v294, v291, v296, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) :|: 0 = 0 9.27/3.77 f_215(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v295, v294, v291, v296, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) -> f_217(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v295, v296, v291, v294, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) :|: 0 = 0 9.27/3.77 f_217(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v295, v296, v291, v294, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) -> f_218(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v295, v296, v291, v294, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) :|: v295 <= v296 9.27/3.77 f_218(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v295, v296, v291, v294, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) -> f_220(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v295, v296, v291, v294, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) :|: 0 = 0 9.27/3.77 f_220(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v295, v296, v291, v294, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) -> f_222(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v295, v296, v291, v294, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) :|: 0 = 0 9.27/3.77 f_222(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v295, v296, v291, v294, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) -> f_224(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v295, v296, v291, v294, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) :|: TRUE 9.27/3.77 f_224(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v295, v296, v291, v294, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) -> f_226(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v295, v296, v291, v294, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) :|: 0 = 0 9.27/3.77 f_226(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v295, v296, v291, v294, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) -> f_227(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v295, v296, v291, v294, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) :|: TRUE 9.27/3.77 f_227(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v295, v296, v291, v294, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) -> f_228(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v295, v296, v291, v294, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) :|: 0 = 0 9.27/3.77 f_228(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v295, v296, v291, v294, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) -> f_229(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v295, v296, v291, v294, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) :|: TRUE 9.27/3.77 f_229(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v295, v296, v291, v294, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) -> f_230(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v295, v296, v294, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) :|: 0 = 0 9.27/3.77 f_230(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v295, v296, v294, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) -> f_231(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v295, v296, v407, v294, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) :|: v407 = 1 + v293 && v407 <= 101 9.27/3.77 f_231(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v295, v296, v407, v294, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) -> f_232(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v295, v296, v407, v294, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) :|: TRUE 9.27/3.77 f_232(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v295, v296, v407, v294, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) -> f_233(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v295, v296, v407, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) :|: 0 = 0 9.27/3.77 f_233(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v295, v296, v407, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) -> f_234(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v295, v296, v407, v409, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) :|: 1 + v409 = v296 9.27/3.77 f_234(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v295, v296, v407, v409, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) -> f_235(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v295, v296, v407, v409, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) :|: TRUE 9.27/3.77 f_235(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v295, v296, v407, v409, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) -> f_236(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v295, v296, v407, v409, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) :|: TRUE 9.27/3.77 f_236(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v295, v296, v407, v409, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) -> f_207(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v295, v296, v407, v409, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) :|: TRUE 9.27/3.77 f_207(v283, v284, v285, v286, v287, v288, v289, v290, v291, 1, v293, v294, v295, v296, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) -> f_208(v283, v284, v285, v286, v287, v288, v289, v290, v293, 1, v294, v291, v295, v296, v297, v298, v299, v300, v301, 0, 3, 100, 101, 4) :|: 0 = 0 9.27/3.77 Combined rules. Obtained 1 rulesP rules: 9.27/3.77 f_208(v283:0, v284:0, v285:0, v286:0, v287:0, v288:0, v289:0, v290:0, v293:0, 1, v294:0, v291:0, v295:0, 1 + v409:0, v297:0, v298:0, v299:0, v300:0, v301:0, 0, 3, 100, 101, 4) -> f_208(v283:0, v284:0, v285:0, v286:0, v287:0, v288:0, v289:0, v290:0, v295:0, 1, 1 + v409:0, v293:0, 1 + v293:0, v409:0, v297:0, v298:0, v299:0, v300:0, v301:0, 0, 3, 100, 101, 4) :|: v293:0 < 101 && v295:0 <= 1 + v409:0 9.27/3.77 Filtered unneeded arguments: 9.27/3.77 f_208(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_208(x9, x13, x14) 9.27/3.77 Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: 9.27/3.77 f_208(v293:0, v295:0, sum~cons_1~v409:0) -> f_208(v295:0, 1 + v293:0, v409:0) :|: v293:0 < 101 && v295:0 <= 1 + v409:0 && sum~cons_1~v409:0 = 1 + v409:0 9.27/3.77 9.27/3.77 ---------------------------------------- 9.27/3.77 9.27/3.77 (8) 9.27/3.77 Obligation: 9.27/3.77 Rules: 9.27/3.77 f_208(v293:0, v295:0, sum~cons_1~v409:0) -> f_208(v295:0, 1 + v293:0, v409:0) :|: v293:0 < 101 && v295:0 <= 1 + v409:0 && sum~cons_1~v409:0 = 1 + v409:0 9.27/3.77 9.27/3.77 ---------------------------------------- 9.27/3.77 9.27/3.77 (9) IntTRSCompressionProof (EQUIVALENT) 9.27/3.77 Compressed rules. 9.27/3.77 ---------------------------------------- 9.27/3.77 9.27/3.77 (10) 9.27/3.77 Obligation: 9.27/3.77 Rules: 9.27/3.77 f_208(v293:0:0, v295:0:0, sum~cons_1~v409:0:0) -> f_208(v295:0:0, 1 + v293:0:0, v409:0:0) :|: v293:0:0 < 101 && v295:0:0 <= 1 + v409:0:0 && sum~cons_1~v409:0:0 = 1 + v409:0:0 9.27/3.77 9.27/3.77 ---------------------------------------- 9.27/3.77 9.27/3.77 (11) PolynomialOrderProcessor (EQUIVALENT) 9.27/3.77 Found the following polynomial interpretation: 9.27/3.77 [f_208(x, x1, x2)] = 100 - x - x1 + x2 9.27/3.77 9.27/3.77 The following rules are decreasing: 9.27/3.77 f_208(v293:0:0, v295:0:0, sum~cons_1~v409:0:0) -> f_208(v295:0:0, 1 + v293:0:0, v409:0:0) :|: v293:0:0 < 101 && v295:0:0 <= 1 + v409:0:0 && sum~cons_1~v409:0:0 = 1 + v409:0:0 9.27/3.77 The following rules are bounded: 9.27/3.77 f_208(v293:0:0, v295:0:0, sum~cons_1~v409:0:0) -> f_208(v295:0:0, 1 + v293:0:0, v409:0:0) :|: v293:0:0 < 101 && v295:0:0 <= 1 + v409:0:0 && sum~cons_1~v409:0:0 = 1 + v409:0:0 9.27/3.77 9.27/3.77 ---------------------------------------- 9.27/3.77 9.27/3.77 (12) 9.27/3.77 YES 9.53/3.85 EOF