8.74/3.39 YES 8.74/3.42 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 8.74/3.42 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 8.74/3.42 8.74/3.42 8.74/3.42 Termination of the given C Problem could be proven: 8.74/3.42 8.74/3.42 (0) C Problem 8.74/3.42 (1) CToLLVMProof [EQUIVALENT, 175 ms] 8.74/3.42 (2) LLVM problem 8.74/3.42 (3) LLVMToTerminationGraphProof [EQUIVALENT, 991 ms] 8.74/3.42 (4) LLVM Symbolic Execution Graph 8.74/3.42 (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] 8.74/3.42 (6) LLVM Symbolic Execution SCC 8.74/3.42 (7) SCC2IRS [SOUND, 43 ms] 8.74/3.42 (8) IntTRS 8.74/3.42 (9) IntTRSCompressionProof [EQUIVALENT, 0 ms] 8.74/3.42 (10) IntTRS 8.74/3.42 (11) PolynomialOrderProcessor [EQUIVALENT, 17 ms] 8.74/3.42 (12) YES 8.74/3.42 8.74/3.42 8.74/3.42 ---------------------------------------- 8.74/3.42 8.74/3.42 (0) 8.74/3.42 Obligation: 8.74/3.42 c file /export/starexec/sandbox/benchmark/theBenchmark.c 8.74/3.42 ---------------------------------------- 8.74/3.42 8.74/3.42 (1) CToLLVMProof (EQUIVALENT) 8.74/3.42 Compiled c-file /export/starexec/sandbox/benchmark/theBenchmark.c to LLVM. 8.74/3.42 ---------------------------------------- 8.74/3.42 8.74/3.42 (2) 8.74/3.42 Obligation: 8.74/3.42 LLVM Problem 8.74/3.42 8.74/3.42 Aliases: 8.74/3.42 8.74/3.42 Data layout: 8.74/3.42 8.74/3.42 "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" 8.74/3.42 8.74/3.42 Machine: 8.74/3.42 8.74/3.42 "x86_64-pc-linux-gnu" 8.74/3.42 8.74/3.42 Type definitions: 8.74/3.42 8.74/3.42 Global variables: 8.74/3.42 8.74/3.42 Function declarations and definitions: 8.74/3.42 8.74/3.42 *BasicFunctionTypename: "__VERIFIER_nondet_int" returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 8.74/3.42 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 8.74/3.42 0: 8.74/3.42 %1 = alloca i32, align 4 8.74/3.42 %x = alloca i32, align 4 8.74/3.42 %a = alloca i32, align 4 8.74/3.42 %b = alloca i32, align 4 8.74/3.42 store 0, %1 8.74/3.42 %2 = call i32 @__VERIFIER_nondet_int() 8.74/3.42 store %2, %x 8.74/3.42 %3 = call i32 @__VERIFIER_nondet_int() 8.74/3.42 store %3, %a 8.74/3.42 %4 = call i32 @__VERIFIER_nondet_int() 8.74/3.42 store %4, %b 8.74/3.42 %5 = load %a 8.74/3.42 %6 = load %b 8.74/3.42 %7 = icmp ne %5 %6 8.74/3.42 br %7, %8, %9 8.74/3.42 8: 8.74/3.42 store 0, %1 8.74/3.42 br %21 8.74/3.42 9: 8.74/3.42 br %10 8.74/3.42 10: 8.74/3.42 %11 = load %x 8.74/3.42 %12 = icmp sge %11 0 8.74/3.42 br %12, %13, %20 8.74/3.42 13: 8.74/3.42 %14 = load %x 8.74/3.42 %15 = load %a 8.74/3.42 %16 = add %14 %15 8.74/3.42 %17 = load %b 8.74/3.42 %18 = sub %16 %17 8.74/3.42 %19 = sub %18 1 8.74/3.42 store %19, %x 8.74/3.42 br %10 8.74/3.42 20: 8.74/3.42 store 0, %1 8.74/3.42 br %21 8.74/3.42 21: 8.74/3.42 %22 = load %1 8.74/3.42 ret %22 8.74/3.42 8.74/3.42 8.74/3.42 Analyze Termination of all function calls matching the pattern: 8.74/3.42 main() 8.74/3.42 ---------------------------------------- 8.74/3.42 8.74/3.42 (3) LLVMToTerminationGraphProof (EQUIVALENT) 8.74/3.42 Constructed symbolic execution graph for LLVM program and proved memory safety. 8.74/3.42 ---------------------------------------- 8.74/3.42 8.74/3.42 (4) 8.74/3.42 Obligation: 8.74/3.42 SE Graph 8.74/3.42 ---------------------------------------- 8.74/3.42 8.74/3.42 (5) SymbolicExecutionGraphToSCCProof (SOUND) 8.74/3.42 Splitted symbolic execution graph to 1 SCC. 8.74/3.42 ---------------------------------------- 8.74/3.42 8.74/3.42 (6) 8.74/3.42 Obligation: 8.74/3.42 SCC 8.74/3.42 ---------------------------------------- 8.74/3.42 8.74/3.42 (7) SCC2IRS (SOUND) 8.74/3.42 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 8.74/3.42 Generated rules. Obtained 13 rulesP rules: 8.74/3.42 f_182(v48, v49, v50, v51, v52, v53, 0, v58, 1, v55, v57, v59, v60, v61, v62, 3, 4) -> f_183(v48, v49, v50, v51, v52, v53, 0, v58, 1, v55, v57, v59, v60, v61, v62, 3, 4) :|: 0 <= v58 && 1 <= v55 && 1 <= v52 8.74/3.42 f_183(v48, v49, v50, v51, v52, v53, 0, v58, 1, v55, v57, v59, v60, v61, v62, 3, 4) -> f_185(v48, v49, v50, v51, v52, v53, 0, v58, 1, v55, v57, v59, v60, v61, v62, 3, 4) :|: 0 = 0 8.74/3.42 f_185(v48, v49, v50, v51, v52, v53, 0, v58, 1, v55, v57, v59, v60, v61, v62, 3, 4) -> f_187(v48, v49, v50, v51, v52, v53, 0, v58, 1, v55, v57, v59, v60, v61, v62, 3, 4) :|: TRUE 8.74/3.42 f_187(v48, v49, v50, v51, v52, v53, 0, v58, 1, v55, v57, v59, v60, v61, v62, 3, 4) -> f_189(v48, v49, v50, v51, v52, v53, 0, v58, 1, v57, v55, v59, v60, v61, v62, 3, 4) :|: 0 = 0 8.74/3.42 f_189(v48, v49, v50, v51, v52, v53, 0, v58, 1, v57, v55, v59, v60, v61, v62, 3, 4) -> f_191(v48, v49, v50, v51, v52, v53, 0, v58, 1, v57, v55, v59, v60, v61, v62, 3, 4) :|: 0 = 0 8.74/3.42 f_191(v48, v49, v50, v51, v52, v53, 0, v58, 1, v57, v55, v59, v60, v61, v62, 3, 4) -> f_193(v48, v49, v50, v51, v52, v53, 0, v58, 1, v67, v55, v59, v60, v61, v62, 3, 4) :|: v67 = v58 + v53 8.74/3.42 f_193(v48, v49, v50, v51, v52, v53, 0, v58, 1, v67, v55, v59, v60, v61, v62, 3, 4) -> f_195(v48, v49, v50, v51, v52, v53, 0, v58, 1, v67, v55, v59, v60, v61, v62, 3, 4) :|: 0 = 0 8.74/3.42 f_195(v48, v49, v50, v51, v52, v53, 0, v58, 1, v67, v55, v59, v60, v61, v62, 3, 4) -> f_196(v48, v49, v50, v51, v52, v53, 0, v58, 1, v67, v59, v60, v61, v62, 3, 4) :|: v58 + v53 = v67 8.74/3.42 f_196(v48, v49, v50, v51, v52, v53, 0, v58, 1, v67, v59, v60, v61, v62, 3, 4) -> f_197(v48, v49, v50, v51, v52, v53, 0, v58, 1, v67, v68, v59, v60, v61, v62, 3, 4) :|: 1 + v68 = v58 && 0 <= 1 + v68 8.74/3.42 f_197(v48, v49, v50, v51, v52, v53, 0, v58, 1, v67, v68, v59, v60, v61, v62, 3, 4) -> f_198(v48, v49, v50, v51, v52, v53, 0, v58, 1, v67, v68, v59, v60, v61, v62, 3, 4) :|: TRUE 8.74/3.42 f_198(v48, v49, v50, v51, v52, v53, 0, v58, 1, v67, v68, v59, v60, v61, v62, 3, 4) -> f_199(v48, v49, v50, v51, v52, v53, 0, v58, 1, v67, v68, v59, v60, v61, v62, 3, 4) :|: TRUE 8.74/3.42 f_199(v48, v49, v50, v51, v52, v53, 0, v58, 1, v67, v68, v59, v60, v61, v62, 3, 4) -> f_181(v48, v49, v50, v51, v52, v53, 0, v58, 1, v67, v68, v59, v60, v61, v62, 3, 4) :|: TRUE 8.74/3.42 f_181(v48, v49, v50, v51, v52, v53, 0, v55, 1, v57, v58, v59, v60, v61, v62, 3, 4) -> f_182(v48, v49, v50, v51, v52, v53, 0, v58, 1, v55, v57, v59, v60, v61, v62, 3, 4) :|: 0 = 0 8.74/3.42 Combined rules. Obtained 1 rulesP rules: 8.74/3.42 f_182(v48:0, v49:0, v50:0, v51:0, v52:0, v53:0, 0, 1 + v68:0, 1, v55:0, v57:0, v59:0, v60:0, v61:0, v62:0, 3, 4) -> f_182(v48:0, v49:0, v50:0, v51:0, v52:0, v53:0, 0, v68:0, 1, 1 + v68:0, 1 + v68:0 + v53:0, v59:0, v60:0, v61:0, v62:0, 3, 4) :|: v55:0 > 0 && v68:0 > -2 && v52:0 > 0 8.74/3.42 Filtered unneeded arguments: 8.74/3.42 f_182(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17) -> f_182(x5, x8, x10) 8.74/3.42 Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: 8.74/3.42 f_182(v52:0, sum~cons_1~v68:0, v55:0) -> f_182(v52:0, v68:0, 1 + v68:0) :|: v68:0 > -2 && v52:0 > 0 && v55:0 > 0 && sum~cons_1~v68:0 = 1 + v68:0 8.74/3.42 8.74/3.42 ---------------------------------------- 8.74/3.42 8.74/3.42 (8) 8.74/3.42 Obligation: 8.74/3.42 Rules: 8.74/3.42 f_182(v52:0, sum~cons_1~v68:0, v55:0) -> f_182(v52:0, v68:0, 1 + v68:0) :|: v68:0 > -2 && v52:0 > 0 && v55:0 > 0 && sum~cons_1~v68:0 = 1 + v68:0 8.74/3.42 8.74/3.42 ---------------------------------------- 8.74/3.42 8.74/3.42 (9) IntTRSCompressionProof (EQUIVALENT) 8.74/3.42 Compressed rules. 8.74/3.42 ---------------------------------------- 8.74/3.42 8.74/3.42 (10) 8.74/3.42 Obligation: 8.74/3.42 Rules: 8.74/3.42 f_182(v52:0:0, sum~cons_1~v68:0:0, v55:0:0) -> f_182(v52:0:0, v68:0:0, 1 + v68:0:0) :|: v68:0:0 > -2 && v52:0:0 > 0 && v55:0:0 > 0 && sum~cons_1~v68:0:0 = 1 + v68:0:0 8.74/3.42 8.74/3.42 ---------------------------------------- 8.74/3.42 8.74/3.42 (11) PolynomialOrderProcessor (EQUIVALENT) 8.74/3.42 Found the following polynomial interpretation: 8.74/3.42 [f_182(x, x1, x2)] = x1 8.74/3.42 8.74/3.42 The following rules are decreasing: 8.74/3.42 f_182(v52:0:0, sum~cons_1~v68:0:0, v55:0:0) -> f_182(v52:0:0, v68:0:0, 1 + v68:0:0) :|: v68:0:0 > -2 && v52:0:0 > 0 && v55:0:0 > 0 && sum~cons_1~v68:0:0 = 1 + v68:0:0 8.74/3.42 The following rules are bounded: 8.74/3.42 f_182(v52:0:0, sum~cons_1~v68:0:0, v55:0:0) -> f_182(v52:0:0, v68:0:0, 1 + v68:0:0) :|: v68:0:0 > -2 && v52:0:0 > 0 && v55:0:0 > 0 && sum~cons_1~v68:0:0 = 1 + v68:0:0 8.74/3.42 8.74/3.42 ---------------------------------------- 8.74/3.42 8.74/3.42 (12) 8.74/3.42 YES 9.24/3.46 EOF