8.10/3.30 YES 8.10/3.31 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 8.10/3.31 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 8.10/3.31 8.10/3.31 8.10/3.31 Termination of the given C Problem could be proven: 8.10/3.31 8.10/3.31 (0) C Problem 8.10/3.31 (1) CToLLVMProof [EQUIVALENT, 169 ms] 8.10/3.31 (2) LLVM problem 8.10/3.31 (3) LLVMToTerminationGraphProof [EQUIVALENT, 884 ms] 8.10/3.31 (4) LLVM Symbolic Execution Graph 8.10/3.31 (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] 8.10/3.31 (6) LLVM Symbolic Execution SCC 8.10/3.31 (7) SCC2IRS [SOUND, 47 ms] 8.10/3.31 (8) IntTRS 8.10/3.31 (9) IntTRSCompressionProof [EQUIVALENT, 0 ms] 8.10/3.31 (10) IntTRS 8.10/3.31 (11) PolynomialOrderProcessor [EQUIVALENT, 10 ms] 8.10/3.31 (12) YES 8.10/3.31 8.10/3.31 8.10/3.31 ---------------------------------------- 8.10/3.31 8.10/3.31 (0) 8.10/3.31 Obligation: 8.10/3.31 c file /export/starexec/sandbox/benchmark/theBenchmark.c 8.10/3.31 ---------------------------------------- 8.10/3.31 8.10/3.31 (1) CToLLVMProof (EQUIVALENT) 8.10/3.31 Compiled c-file /export/starexec/sandbox/benchmark/theBenchmark.c to LLVM. 8.10/3.31 ---------------------------------------- 8.10/3.31 8.10/3.31 (2) 8.10/3.31 Obligation: 8.10/3.31 LLVM Problem 8.10/3.31 8.10/3.31 Aliases: 8.10/3.31 8.10/3.31 Data layout: 8.10/3.31 8.10/3.31 "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" 8.10/3.31 8.10/3.31 Machine: 8.10/3.31 8.10/3.31 "x86_64-pc-linux-gnu" 8.10/3.31 8.10/3.31 Type definitions: 8.10/3.31 8.10/3.31 Global variables: 8.10/3.31 8.10/3.31 Function declarations and definitions: 8.10/3.31 8.10/3.31 *BasicFunctionTypename: "__VERIFIER_nondet_int" returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 8.10/3.31 *BasicFunctionTypename: "test_fun" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: (x i32, y i32, r i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc 8.10/3.31 0: 8.10/3.31 %1 = alloca i32, align 4 8.10/3.31 %2 = alloca i32, align 4 8.10/3.31 %3 = alloca i32, align 4 8.10/3.31 store %x, %1 8.10/3.31 store %y, %2 8.10/3.31 store %r, %3 8.10/3.31 store 1, %3 8.10/3.31 br %4 8.10/3.31 4: 8.10/3.31 %5 = load %2 8.10/3.31 %6 = icmp sgt %5 0 8.10/3.31 br %6, %7, %13 8.10/3.31 7: 8.10/3.31 %8 = load %3 8.10/3.31 %9 = load %1 8.10/3.31 %10 = mul %8 %9 8.10/3.31 store %10, %3 8.10/3.31 %11 = load %2 8.10/3.31 %12 = sub %11 1 8.10/3.31 store %12, %2 8.10/3.31 br %4 8.10/3.31 13: 8.10/3.31 %14 = load %3 8.10/3.31 ret %14 8.10/3.31 8.10/3.31 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 8.10/3.31 0: 8.10/3.31 %1 = alloca i32, align 4 8.10/3.31 store 0, %1 8.10/3.31 %2 = call i32 @__VERIFIER_nondet_int() 8.10/3.31 %3 = call i32 @__VERIFIER_nondet_int() 8.10/3.31 %4 = call i32 @__VERIFIER_nondet_int() 8.10/3.31 %5 = call i32 @test_fun(i32 %2, i32 %3, i32 %4) 8.10/3.31 ret %5 8.10/3.31 8.10/3.31 8.10/3.31 Analyze Termination of all function calls matching the pattern: 8.10/3.31 main() 8.10/3.31 ---------------------------------------- 8.10/3.31 8.10/3.31 (3) LLVMToTerminationGraphProof (EQUIVALENT) 8.10/3.31 Constructed symbolic execution graph for LLVM program and proved memory safety. 8.10/3.31 ---------------------------------------- 8.10/3.31 8.10/3.31 (4) 8.10/3.31 Obligation: 8.10/3.31 SE Graph 8.10/3.31 ---------------------------------------- 8.10/3.31 8.10/3.31 (5) SymbolicExecutionGraphToSCCProof (SOUND) 8.10/3.31 Splitted symbolic execution graph to 1 SCC. 8.10/3.31 ---------------------------------------- 8.10/3.31 8.10/3.31 (6) 8.10/3.31 Obligation: 8.10/3.31 SCC 8.10/3.31 ---------------------------------------- 8.10/3.31 8.10/3.31 (7) SCC2IRS (SOUND) 8.10/3.31 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 8.10/3.31 Generated rules. Obtained 13 rulesP rules: 8.10/3.31 f_156(v43, v44, v45, v46, v47, v48, v53, 1, v51, v52, v49, v54, v55, v56, v57, v58, 0, 3, 4) -> f_157(v43, v44, v45, v46, v47, v48, v53, 1, v51, v52, v49, v54, v55, v56, v57, v58, 0, 3, 2, 4) :|: 0 < v53 && 2 <= v49 && 2 <= v44 8.10/3.31 f_157(v43, v44, v45, v46, v47, v48, v53, 1, v51, v52, v49, v54, v55, v56, v57, v58, 0, 3, 2, 4) -> f_159(v43, v44, v45, v46, v47, v48, v53, 1, v51, v52, v49, v54, v55, v56, v57, v58, 0, 3, 2, 4) :|: 0 = 0 8.10/3.31 f_159(v43, v44, v45, v46, v47, v48, v53, 1, v51, v52, v49, v54, v55, v56, v57, v58, 0, 3, 2, 4) -> f_161(v43, v44, v45, v46, v47, v48, v53, 1, v51, v52, v49, v54, v55, v56, v57, v58, 0, 3, 2, 4) :|: TRUE 8.10/3.31 f_161(v43, v44, v45, v46, v47, v48, v53, 1, v51, v52, v49, v54, v55, v56, v57, v58, 0, 3, 2, 4) -> f_163(v43, v44, v45, v46, v47, v48, v53, 1, v52, v49, v54, v55, v56, v57, v58, 0, 3, 2, 4) :|: 0 = 0 8.10/3.31 f_163(v43, v44, v45, v46, v47, v48, v53, 1, v52, v49, v54, v55, v56, v57, v58, 0, 3, 2, 4) -> f_165(v43, v44, v45, v46, v47, v48, v53, 1, v52, v49, v54, v55, v56, v57, v58, 0, 3, 2, 4) :|: 0 = 0 8.10/3.31 f_165(v43, v44, v45, v46, v47, v48, v53, 1, v52, v49, v54, v55, v56, v57, v58, 0, 3, 2, 4) -> f_167(v43, v44, v45, v46, v47, v48, v53, 1, v52, v60, v49, v54, v55, v56, v57, v58, 0, 3, 2, 4) :|: v60 = v52 * v43 8.10/3.31 f_167(v43, v44, v45, v46, v47, v48, v53, 1, v52, v60, v49, v54, v55, v56, v57, v58, 0, 3, 2, 4) -> f_168(v43, v44, v45, v46, v47, v48, v53, 1, v52, v60, v49, v54, v55, v56, v57, v58, 0, 3, 2, 4) :|: TRUE 8.10/3.31 f_168(v43, v44, v45, v46, v47, v48, v53, 1, v52, v60, v49, v54, v55, v56, v57, v58, 0, 3, 2, 4) -> f_169(v43, v44, v45, v46, v47, v48, v53, 1, v52, v60, v54, v55, v56, v57, v58, 0, 3, 2, 4) :|: 0 = 0 8.10/3.31 f_169(v43, v44, v45, v46, v47, v48, v53, 1, v52, v60, v54, v55, v56, v57, v58, 0, 3, 2, 4) -> f_170(v43, v44, v45, v46, v47, v48, v53, 1, v52, v60, v62, v54, v55, v56, v57, v58, 0, 3, 2, 4) :|: 1 + v62 = v53 && 0 <= v62 8.10/3.31 f_170(v43, v44, v45, v46, v47, v48, v53, 1, v52, v60, v62, v54, v55, v56, v57, v58, 0, 3, 2, 4) -> f_171(v43, v44, v45, v46, v47, v48, v53, 1, v52, v60, v62, v54, v55, v56, v57, v58, 0, 3, 2, 4) :|: TRUE 8.10/3.31 f_171(v43, v44, v45, v46, v47, v48, v53, 1, v52, v60, v62, v54, v55, v56, v57, v58, 0, 3, 2, 4) -> f_172(v43, v44, v45, v46, v47, v48, v53, 1, v52, v60, v62, v54, v55, v56, v57, v58, 0, 3, 2, 4) :|: TRUE 8.10/3.31 f_172(v43, v44, v45, v46, v47, v48, v53, 1, v52, v60, v62, v54, v55, v56, v57, v58, 0, 3, 2, 4) -> f_155(v43, v44, v45, v46, v47, v48, v53, 1, v52, v60, v62, v54, v55, v56, v57, v58, 0, 3, 4) :|: TRUE 8.10/3.31 f_155(v43, v44, v45, v46, v47, v48, v49, 1, v51, v52, v53, v54, v55, v56, v57, v58, 0, 3, 4) -> f_156(v43, v44, v45, v46, v47, v48, v53, 1, v51, v52, v49, v54, v55, v56, v57, v58, 0, 3, 4) :|: 0 = 0 8.10/3.31 Combined rules. Obtained 1 rulesP rules: 8.10/3.31 f_156(v43:0, v44:0, v45:0, v46:0, v47:0, v48:0, 1 + v62:0, 1, v51:0, v52:0, v49:0, v54:0, v55:0, v56:0, v57:0, v58:0, 0, 3, 4) -> f_156(v43:0, v44:0, v45:0, v46:0, v47:0, v48:0, v62:0, 1, v52:0, v52:0 * v43:0, 1 + v62:0, v54:0, v55:0, v56:0, v57:0, v58:0, 0, 3, 4) :|: v49:0 > 1 && v62:0 > -1 && v44:0 > 1 8.10/3.31 Filtered unneeded arguments: 8.10/3.31 f_156(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) -> f_156(x2, x7, x11) 8.10/3.31 Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: 8.10/3.31 f_156(v44:0, sum~cons_1~v62:0, v49:0) -> f_156(v44:0, v62:0, 1 + v62:0) :|: v62:0 > -1 && v44:0 > 1 && v49:0 > 1 && sum~cons_1~v62:0 = 1 + v62:0 8.10/3.31 8.10/3.31 ---------------------------------------- 8.10/3.31 8.10/3.31 (8) 8.10/3.31 Obligation: 8.10/3.31 Rules: 8.10/3.31 f_156(v44:0, sum~cons_1~v62:0, v49:0) -> f_156(v44:0, v62:0, 1 + v62:0) :|: v62:0 > -1 && v44:0 > 1 && v49:0 > 1 && sum~cons_1~v62:0 = 1 + v62:0 8.10/3.31 8.10/3.31 ---------------------------------------- 8.10/3.31 8.10/3.31 (9) IntTRSCompressionProof (EQUIVALENT) 8.10/3.31 Compressed rules. 8.10/3.31 ---------------------------------------- 8.10/3.31 8.10/3.31 (10) 8.10/3.31 Obligation: 8.10/3.31 Rules: 8.10/3.31 f_156(v44:0:0, sum~cons_1~v62:0:0, v49:0:0) -> f_156(v44:0:0, v62:0:0, 1 + v62:0:0) :|: v62:0:0 > -1 && v44:0:0 > 1 && v49:0:0 > 1 && sum~cons_1~v62:0:0 = 1 + v62:0:0 8.10/3.31 8.10/3.31 ---------------------------------------- 8.10/3.31 8.10/3.31 (11) PolynomialOrderProcessor (EQUIVALENT) 8.10/3.31 Found the following polynomial interpretation: 8.10/3.31 [f_156(x, x1, x2)] = x1 8.10/3.31 8.10/3.31 The following rules are decreasing: 8.10/3.31 f_156(v44:0:0, sum~cons_1~v62:0:0, v49:0:0) -> f_156(v44:0:0, v62:0:0, 1 + v62:0:0) :|: v62:0:0 > -1 && v44:0:0 > 1 && v49:0:0 > 1 && sum~cons_1~v62:0:0 = 1 + v62:0:0 8.10/3.31 The following rules are bounded: 8.10/3.31 f_156(v44:0:0, sum~cons_1~v62:0:0, v49:0:0) -> f_156(v44:0:0, v62:0:0, 1 + v62:0:0) :|: v62:0:0 > -1 && v44:0:0 > 1 && v49:0:0 > 1 && sum~cons_1~v62:0:0 = 1 + v62:0:0 8.10/3.31 8.10/3.31 ---------------------------------------- 8.10/3.31 8.10/3.31 (12) 8.10/3.31 YES 9.36/3.34 EOF