10.12/3.97 YES 10.12/3.98 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 10.12/3.98 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 10.12/3.98 10.12/3.98 10.12/3.98 Termination of the given C Problem could be proven: 10.12/3.98 10.12/3.98 (0) C Problem 10.12/3.98 (1) CToLLVMProof [EQUIVALENT, 175 ms] 10.12/3.98 (2) LLVM problem 10.12/3.98 (3) LLVMToTerminationGraphProof [EQUIVALENT, 909 ms] 10.12/3.98 (4) LLVM Symbolic Execution Graph 10.12/3.98 (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] 10.12/3.98 (6) LLVM Symbolic Execution SCC 10.12/3.98 (7) SCC2IRS [SOUND, 0 ms] 10.12/3.98 (8) IntTRS 10.12/3.98 (9) IntTRSCompressionProof [EQUIVALENT, 0 ms] 10.12/3.98 (10) IntTRS 10.12/3.98 (11) RankingReductionPairProof [EQUIVALENT, 9 ms] 10.12/3.98 (12) YES 10.12/3.98 10.12/3.98 10.12/3.98 ---------------------------------------- 10.12/3.98 10.12/3.98 (0) 10.12/3.98 Obligation: 10.12/3.98 c file /export/starexec/sandbox/benchmark/theBenchmark.c 10.12/3.98 ---------------------------------------- 10.12/3.98 10.12/3.98 (1) CToLLVMProof (EQUIVALENT) 10.12/3.98 Compiled c-file /export/starexec/sandbox/benchmark/theBenchmark.c to LLVM. 10.12/3.98 ---------------------------------------- 10.12/3.98 10.12/3.98 (2) 10.12/3.98 Obligation: 10.12/3.98 LLVM Problem 10.12/3.98 10.12/3.98 Aliases: 10.12/3.98 10.12/3.98 Data layout: 10.12/3.98 10.12/3.98 "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" 10.12/3.98 10.12/3.98 Machine: 10.12/3.98 10.12/3.98 "x86_64-pc-linux-gnu" 10.12/3.98 10.12/3.98 Type definitions: 10.12/3.98 10.12/3.98 Global variables: 10.12/3.98 10.12/3.98 Function declarations and definitions: 10.12/3.98 10.12/3.98 *BasicFunctionTypename: "__VERIFIER_nondet_int" returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 10.12/3.98 *BasicFunctionTypename: "test_fun" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: (x i32, y i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc 10.12/3.98 0: 10.12/3.98 %1 = alloca i32, align 4 10.12/3.98 %2 = alloca i32, align 4 10.12/3.98 %3 = alloca i32, align 4 10.12/3.98 store %x, %2 10.12/3.98 store %y, %3 10.12/3.98 %4 = load %2 10.12/3.98 %5 = icmp sle %4 0 10.12/3.98 br %5, %6, %8 10.12/3.98 6: 10.12/3.98 %7 = load %3 10.12/3.98 store %7, %1 10.12/3.98 br %19 10.12/3.98 8: 10.12/3.98 br %9 10.12/3.98 9: 10.12/3.98 %10 = load %2 10.12/3.98 %11 = load %3 10.12/3.98 %12 = icmp sgt %10 %11 10.12/3.98 br %12, %13, %17 10.12/3.98 13: 10.12/3.98 %14 = load %3 10.12/3.98 %15 = load %2 10.12/3.98 %16 = add %14 %15 10.12/3.98 store %16, %3 10.12/3.98 br %9 10.12/3.98 17: 10.12/3.98 %18 = load %3 10.12/3.98 store %18, %1 10.12/3.98 br %19 10.12/3.98 19: 10.12/3.98 %20 = load %1 10.12/3.98 ret %20 10.12/3.98 10.12/3.98 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 10.12/3.98 0: 10.12/3.98 %1 = alloca i32, align 4 10.12/3.98 store 0, %1 10.12/3.98 %2 = call i32 @__VERIFIER_nondet_int() 10.12/3.98 %3 = call i32 @__VERIFIER_nondet_int() 10.12/3.98 %4 = call i32 @test_fun(i32 %2, i32 %3) 10.12/3.98 ret %4 10.12/3.98 10.12/3.98 10.12/3.98 Analyze Termination of all function calls matching the pattern: 10.12/3.98 main() 10.12/3.98 ---------------------------------------- 10.12/3.98 10.12/3.98 (3) LLVMToTerminationGraphProof (EQUIVALENT) 10.12/3.98 Constructed symbolic execution graph for LLVM program and proved memory safety. 10.12/3.98 ---------------------------------------- 10.12/3.98 10.12/3.98 (4) 10.12/3.98 Obligation: 10.12/3.98 SE Graph 10.12/3.98 ---------------------------------------- 10.12/3.98 10.12/3.98 (5) SymbolicExecutionGraphToSCCProof (SOUND) 10.12/3.98 Splitted symbolic execution graph to 1 SCC. 10.12/3.98 ---------------------------------------- 10.12/3.98 10.12/3.98 (6) 10.12/3.98 Obligation: 10.12/3.98 SCC 10.12/3.98 ---------------------------------------- 10.12/3.98 10.12/3.98 (7) SCC2IRS (SOUND) 10.12/3.98 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 10.12/3.98 Generated rules. Obtained 11 rulesP rules: 10.12/3.98 f_178(v39, v40, v41, v42, v43, 0, v45, 1, v47, v48, v49, v50, v51, v52, 3, 4) -> f_179(v39, v40, v41, v42, v43, 0, v47, 1, v45, v48, v49, v50, v51, v52, 3, 4) :|: 0 = 0 10.12/3.98 f_179(v39, v40, v41, v42, v43, 0, v47, 1, v45, v48, v49, v50, v51, v52, 3, 4) -> f_180(v39, v40, v41, v42, v43, 0, v47, 1, v45, v48, v49, v50, v51, v52, 3, 4) :|: v47 < v39 && 1 + v45 <= 0 10.12/3.98 f_180(v39, v40, v41, v42, v43, 0, v47, 1, v45, v48, v49, v50, v51, v52, 3, 4) -> f_182(v39, v40, v41, v42, v43, 0, v47, 1, v45, v48, v49, v50, v51, v52, 3, 4) :|: 0 = 0 10.12/3.98 f_182(v39, v40, v41, v42, v43, 0, v47, 1, v45, v48, v49, v50, v51, v52, 3, 4) -> f_184(v39, v40, v41, v42, v43, 0, v47, 1, v45, v48, v49, v50, v51, v52, 3, 4) :|: TRUE 10.12/3.98 f_184(v39, v40, v41, v42, v43, 0, v47, 1, v45, v48, v49, v50, v51, v52, 3, 4) -> f_186(v39, v40, v41, v42, v43, 0, v47, 1, v48, v49, v50, v51, v52, 3, 4) :|: 0 = 0 10.12/3.98 f_186(v39, v40, v41, v42, v43, 0, v47, 1, v48, v49, v50, v51, v52, 3, 4) -> f_188(v39, v40, v41, v42, v43, 0, v47, 1, v48, v49, v50, v51, v52, 3, 4) :|: 0 = 0 10.12/3.98 f_188(v39, v40, v41, v42, v43, 0, v47, 1, v48, v49, v50, v51, v52, 3, 4) -> f_190(v39, v40, v41, v42, v43, 0, v47, 1, v54, v48, v49, v50, v51, v52, 3, 4) :|: v54 = v47 + v39 10.12/3.98 f_190(v39, v40, v41, v42, v43, 0, v47, 1, v54, v48, v49, v50, v51, v52, 3, 4) -> f_192(v39, v40, v41, v42, v43, 0, v47, 1, v54, v48, v49, v50, v51, v52, 3, 4) :|: TRUE 10.12/3.98 f_192(v39, v40, v41, v42, v43, 0, v47, 1, v54, v48, v49, v50, v51, v52, 3, 4) -> f_194(v39, v40, v41, v42, v43, 0, v47, 1, v54, v48, v49, v50, v51, v52, 3, 4) :|: TRUE 10.12/3.98 f_194(v39, v40, v41, v42, v43, 0, v47, 1, v54, v48, v49, v50, v51, v52, 3, 4) -> f_177(v39, v40, v41, v42, v43, 0, v47, 1, v54, v48, v49, v50, v51, v52, 3, 4) :|: v40 < v39 && 1 <= v39 && 1 <= v41 && 1 <= v42 && 1 <= v43 && 1 <= v48 && 4 <= v49 && 4 <= v50 && 4 <= v51 && 4 <= v52 && v48 <= v49 && v41 <= v50 && v42 <= v51 && v43 <= v52 10.12/3.98 f_177(v39, v40, v41, v42, v43, 0, v45, 1, v47, v48, v49, v50, v51, v52, 3, 4) -> f_178(v39, v40, v41, v42, v43, 0, v45, 1, v47, v48, v49, v50, v51, v52, 3, 4) :|: 0 = 0 10.12/3.98 Combined rules. Obtained 1 rulesP rules: 10.12/3.98 f_178(v39:0, v40:0, v41:0, v42:0, v43:0, 0, v45:0, 1, v47:0, v48:0, v49:0, v50:0, v51:0, v52:0, 3, 4) -> f_178(v39:0, v40:0, v41:0, v42:0, v43:0, 0, v47:0, 1, v47:0 + v39:0, v48:0, v49:0, v50:0, v51:0, v52:0, 3, 4) :|: v39:0 > 0 && v40:0 < v39:0 && v41:0 > 0 && v42:0 > 0 && v43:0 > 0 && v48:0 > 0 && v45:0 < 0 && v47:0 < v39:0 && v49:0 > 3 && v50:0 > 3 && v51:0 > 3 && v52:0 > 3 && v49:0 >= v48:0 && v50:0 >= v41:0 && v52:0 >= v43:0 && v51:0 >= v42:0 10.12/3.98 Filtered unneeded arguments: 10.12/3.98 f_178(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16) -> f_178(x1, x2, x3, x4, x5, x7, x9, x10, x11, x12, x13, x14) 10.12/3.98 Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: 10.12/3.98 f_178(v39:0, v40:0, v41:0, v42:0, v43:0, v45:0, v47:0, v48:0, v49:0, v50:0, v51:0, v52:0) -> f_178(v39:0, v40:0, v41:0, v42:0, v43:0, v47:0, v47:0 + v39:0, v48:0, v49:0, v50:0, v51:0, v52:0) :|: v40:0 < v39:0 && v39:0 > 0 && v41:0 > 0 && v42:0 > 0 && v43:0 > 0 && v48:0 > 0 && v45:0 < 0 && v47:0 < v39:0 && v49:0 > 3 && v50:0 > 3 && v51:0 > 3 && v52:0 > 3 && v49:0 >= v48:0 && v50:0 >= v41:0 && v51:0 >= v42:0 && v52:0 >= v43:0 10.12/3.98 10.12/3.98 ---------------------------------------- 10.12/3.98 10.12/3.98 (8) 10.12/3.98 Obligation: 10.12/3.98 Rules: 10.12/3.98 f_178(v39:0, v40:0, v41:0, v42:0, v43:0, v45:0, v47:0, v48:0, v49:0, v50:0, v51:0, v52:0) -> f_178(v39:0, v40:0, v41:0, v42:0, v43:0, v47:0, v47:0 + v39:0, v48:0, v49:0, v50:0, v51:0, v52:0) :|: v40:0 < v39:0 && v39:0 > 0 && v41:0 > 0 && v42:0 > 0 && v43:0 > 0 && v48:0 > 0 && v45:0 < 0 && v47:0 < v39:0 && v49:0 > 3 && v50:0 > 3 && v51:0 > 3 && v52:0 > 3 && v49:0 >= v48:0 && v50:0 >= v41:0 && v51:0 >= v42:0 && v52:0 >= v43:0 10.12/3.98 10.12/3.98 ---------------------------------------- 10.12/3.98 10.12/3.98 (9) IntTRSCompressionProof (EQUIVALENT) 10.12/3.98 Compressed rules. 10.12/3.98 ---------------------------------------- 10.12/3.98 10.12/3.98 (10) 10.12/3.98 Obligation: 10.12/3.98 Rules: 10.12/3.98 f_178(v39:0:0, v40:0:0, v41:0:0, v42:0:0, v43:0:0, v45:0:0, v47:0:0, v48:0:0, v49:0:0, v50:0:0, v51:0:0, v52:0:0) -> f_178(v39:0:0, v40:0:0, v41:0:0, v42:0:0, v43:0:0, v47:0:0, v47:0:0 + v39:0:0, v48:0:0, v49:0:0, v50:0:0, v51:0:0, v52:0:0) :|: v51:0:0 >= v42:0:0 && v52:0:0 >= v43:0:0 && v50:0:0 >= v41:0:0 && v49:0:0 >= v48:0:0 && v52:0:0 > 3 && v51:0:0 > 3 && v50:0:0 > 3 && v49:0:0 > 3 && v47:0:0 < v39:0:0 && v45:0:0 < 0 && v48:0:0 > 0 && v43:0:0 > 0 && v42:0:0 > 0 && v41:0:0 > 0 && v39:0:0 > 0 && v40:0:0 < v39:0:0 10.12/3.98 10.12/3.98 ---------------------------------------- 10.12/3.98 10.12/3.98 (11) RankingReductionPairProof (EQUIVALENT) 10.12/3.98 Interpretation: 10.12/3.98 [ f_178 ] = -1*f_178_7 + f_178_1 10.12/3.98 10.12/3.98 The following rules are decreasing: 10.12/3.98 f_178(v39:0:0, v40:0:0, v41:0:0, v42:0:0, v43:0:0, v45:0:0, v47:0:0, v48:0:0, v49:0:0, v50:0:0, v51:0:0, v52:0:0) -> f_178(v39:0:0, v40:0:0, v41:0:0, v42:0:0, v43:0:0, v47:0:0, v47:0:0 + v39:0:0, v48:0:0, v49:0:0, v50:0:0, v51:0:0, v52:0:0) :|: v51:0:0 >= v42:0:0 && v52:0:0 >= v43:0:0 && v50:0:0 >= v41:0:0 && v49:0:0 >= v48:0:0 && v52:0:0 > 3 && v51:0:0 > 3 && v50:0:0 > 3 && v49:0:0 > 3 && v47:0:0 < v39:0:0 && v45:0:0 < 0 && v48:0:0 > 0 && v43:0:0 > 0 && v42:0:0 > 0 && v41:0:0 > 0 && v39:0:0 > 0 && v40:0:0 < v39:0:0 10.12/3.98 10.12/3.98 The following rules are bounded: 10.12/3.98 f_178(v39:0:0, v40:0:0, v41:0:0, v42:0:0, v43:0:0, v45:0:0, v47:0:0, v48:0:0, v49:0:0, v50:0:0, v51:0:0, v52:0:0) -> f_178(v39:0:0, v40:0:0, v41:0:0, v42:0:0, v43:0:0, v47:0:0, v47:0:0 + v39:0:0, v48:0:0, v49:0:0, v50:0:0, v51:0:0, v52:0:0) :|: v51:0:0 >= v42:0:0 && v52:0:0 >= v43:0:0 && v50:0:0 >= v41:0:0 && v49:0:0 >= v48:0:0 && v52:0:0 > 3 && v51:0:0 > 3 && v50:0:0 > 3 && v49:0:0 > 3 && v47:0:0 < v39:0:0 && v45:0:0 < 0 && v48:0:0 > 0 && v43:0:0 > 0 && v42:0:0 > 0 && v41:0:0 > 0 && v39:0:0 > 0 && v40:0:0 < v39:0:0 10.12/3.98 10.12/3.98 10.12/3.98 ---------------------------------------- 10.12/3.98 10.12/3.98 (12) 10.12/3.98 YES 11.47/4.02 EOF