YES proof of /export/starexec/sandbox/benchmark/theBenchmark.c # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given C Problem could be proven: (0) C Problem (1) CToLLVMProof [EQUIVALENT, 155 ms] (2) LLVM problem (3) LLVMToTerminationGraphProof [EQUIVALENT, 744 ms] (4) LLVM Symbolic Execution Graph (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] (6) LLVM Symbolic Execution SCC (7) SCC2IRS [SOUND, 0 ms] (8) IntTRS (9) IntTRSCompressionProof [EQUIVALENT, 0 ms] (10) IntTRS (11) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (12) YES ---------------------------------------- (0) Obligation: c file /export/starexec/sandbox/benchmark/theBenchmark.c ---------------------------------------- (1) CToLLVMProof (EQUIVALENT) Compiled c-file /export/starexec/sandbox/benchmark/theBenchmark.c to LLVM. ---------------------------------------- (2) Obligation: LLVM Problem Aliases: Data layout: "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" Machine: "x86_64-pc-linux-gnu" Type definitions: Global variables: Function declarations and definitions: *BasicFunctionTypename: "__VERIFIER_nondet_int" returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 0: %1 = alloca i32, align 4 %x = alloca i32, align 4 %y = alloca i32, align 4 store 0, %1 %2 = call i32 @__VERIFIER_nondet_int() store %2, %x %3 = call i32 @__VERIFIER_nondet_int() store %3, %y %4 = load %x %5 = icmp sgt %4 0 br %5, %6, %16 6: br %7 7: %8 = load %x %9 = load %y %10 = icmp sgt %8 %9 br %10, %11, %15 11: %12 = load %x %13 = load %y %14 = add %12 %13 store %14, %y br %7 15: br %16 16: ret 0 Analyze Termination of all function calls matching the pattern: main() ---------------------------------------- (3) LLVMToTerminationGraphProof (EQUIVALENT) Constructed symbolic execution graph for LLVM program and proved memory safety. ---------------------------------------- (4) Obligation: SE Graph ---------------------------------------- (5) SymbolicExecutionGraphToSCCProof (SOUND) Splitted symbolic execution graph to 1 SCC. ---------------------------------------- (6) Obligation: SCC ---------------------------------------- (7) SCC2IRS (SOUND) Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: Generated rules. Obtained 11 rulesP rules: f_133(v37, v38, v39, v40, v41, 1, v43, v44, v45, v46, v47, 0, 3, 4) -> f_134(v37, v38, v39, v40, v41, 1, v44, v43, v45, v46, v47, 0, 3, 4) :|: 0 = 0 f_134(v37, v38, v39, v40, v41, 1, v44, v43, v45, v46, v47, 0, 3, 4) -> f_135(v37, v38, v39, v40, v41, 1, v44, v43, v45, v46, v47, 0, 3, 4) :|: v44 < v40 && 1 + v43 <= 0 f_135(v37, v38, v39, v40, v41, 1, v44, v43, v45, v46, v47, 0, 3, 4) -> f_137(v37, v38, v39, v40, v41, 1, v44, v43, v45, v46, v47, 0, 3, 4) :|: 0 = 0 f_137(v37, v38, v39, v40, v41, 1, v44, v43, v45, v46, v47, 0, 3, 4) -> f_139(v37, v38, v39, v40, v41, 1, v44, v43, v45, v46, v47, 0, 3, 4) :|: TRUE f_139(v37, v38, v39, v40, v41, 1, v44, v43, v45, v46, v47, 0, 3, 4) -> f_141(v37, v38, v39, v40, v41, 1, v44, v43, v45, v46, v47, 0, 3, 4) :|: 0 = 0 f_141(v37, v38, v39, v40, v41, 1, v44, v43, v45, v46, v47, 0, 3, 4) -> f_143(v37, v38, v39, v40, v41, 1, v44, v45, v46, v47, 0, 3, 4) :|: 0 = 0 f_143(v37, v38, v39, v40, v41, 1, v44, v45, v46, v47, 0, 3, 4) -> f_144(v37, v38, v39, v40, v41, 1, v44, v53, v45, v46, v47, 0, 3, 4) :|: v53 = v40 + v44 f_144(v37, v38, v39, v40, v41, 1, v44, v53, v45, v46, v47, 0, 3, 4) -> f_145(v37, v38, v39, v40, v41, 1, v44, v53, v45, v46, v47, 0, 3, 4) :|: TRUE f_145(v37, v38, v39, v40, v41, 1, v44, v53, v45, v46, v47, 0, 3, 4) -> f_146(v37, v38, v39, v40, v41, 1, v44, v53, v45, v46, v47, 0, 3, 4) :|: TRUE f_146(v37, v38, v39, v40, v41, 1, v44, v53, v45, v46, v47, 0, 3, 4) -> f_132(v37, v38, v39, v40, v41, 1, v44, v53, v45, v46, v47, 0, 3, 4) :|: v41 < v40 && 1 <= v37 && 1 <= v38 && 1 <= v39 && 1 <= v40 && 4 <= v45 && 4 <= v46 && 4 <= v47 && v37 <= v45 && v38 <= v46 && v39 <= v47 f_132(v37, v38, v39, v40, v41, 1, v43, v44, v45, v46, v47, 0, 3, 4) -> f_133(v37, v38, v39, v40, v41, 1, v43, v44, v45, v46, v47, 0, 3, 4) :|: 0 = 0 Combined rules. Obtained 1 rulesP rules: f_133(v37:0, v38:0, v39:0, v40:0, v41:0, 1, v43:0, v44:0, v45:0, v46:0, v47:0, 0, 3, 4) -> f_133(v37:0, v38:0, v39:0, v40:0, v41:0, 1, v44:0, v40:0 + v44:0, v45:0, v46:0, v47:0, 0, 3, 4) :|: v37:0 > 0 && v41:0 < v40:0 && v38:0 > 0 && v43:0 < 0 && v44:0 < v40:0 && v39:0 > 0 && v40:0 > 0 && v45:0 > 3 && v46:0 > 3 && v47:0 > 3 && v45:0 >= v37:0 && v47:0 >= v39:0 && v46:0 >= v38:0 Filtered unneeded arguments: f_133(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> f_133(x1, x2, x3, x4, x5, x7, x8, x9, x10, x11) Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: f_133(v37:0, v38:0, v39:0, v40:0, v41:0, v43:0, v44:0, v45:0, v46:0, v47:0) -> f_133(v37:0, v38:0, v39:0, v40:0, v41:0, v44:0, v40:0 + v44:0, v45:0, v46:0, v47:0) :|: v41:0 < v40:0 && v37:0 > 0 && v38:0 > 0 && v43:0 < 0 && v44:0 < v40:0 && v39:0 > 0 && v40:0 > 0 && v45:0 > 3 && v46:0 > 3 && v47:0 > 3 && v45:0 >= v37:0 && v46:0 >= v38:0 && v47:0 >= v39:0 ---------------------------------------- (8) Obligation: Rules: f_133(v37:0, v38:0, v39:0, v40:0, v41:0, v43:0, v44:0, v45:0, v46:0, v47:0) -> f_133(v37:0, v38:0, v39:0, v40:0, v41:0, v44:0, v40:0 + v44:0, v45:0, v46:0, v47:0) :|: v41:0 < v40:0 && v37:0 > 0 && v38:0 > 0 && v43:0 < 0 && v44:0 < v40:0 && v39:0 > 0 && v40:0 > 0 && v45:0 > 3 && v46:0 > 3 && v47:0 > 3 && v45:0 >= v37:0 && v46:0 >= v38:0 && v47:0 >= v39:0 ---------------------------------------- (9) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (10) Obligation: Rules: f_133(v37:0:0, v38:0:0, v39:0:0, v40:0:0, v41:0:0, v43:0:0, v44:0:0, v45:0:0, v46:0:0, v47:0:0) -> f_133(v37:0:0, v38:0:0, v39:0:0, v40:0:0, v41:0:0, v44:0:0, v40:0:0 + v44:0:0, v45:0:0, v46:0:0, v47:0:0) :|: v46:0:0 >= v38:0:0 && v47:0:0 >= v39:0:0 && v45:0:0 >= v37:0:0 && v47:0:0 > 3 && v46:0:0 > 3 && v45:0:0 > 3 && v40:0:0 > 0 && v39:0:0 > 0 && v44:0:0 < v40:0:0 && v43:0:0 < 0 && v38:0:0 > 0 && v37:0:0 > 0 && v41:0:0 < v40:0:0 ---------------------------------------- (11) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f_133(x, x1, x2, x3, x4, x5, x6, x7, x8, x9)] = x3 - x6 The following rules are decreasing: f_133(v37:0:0, v38:0:0, v39:0:0, v40:0:0, v41:0:0, v43:0:0, v44:0:0, v45:0:0, v46:0:0, v47:0:0) -> f_133(v37:0:0, v38:0:0, v39:0:0, v40:0:0, v41:0:0, v44:0:0, v40:0:0 + v44:0:0, v45:0:0, v46:0:0, v47:0:0) :|: v46:0:0 >= v38:0:0 && v47:0:0 >= v39:0:0 && v45:0:0 >= v37:0:0 && v47:0:0 > 3 && v46:0:0 > 3 && v45:0:0 > 3 && v40:0:0 > 0 && v39:0:0 > 0 && v44:0:0 < v40:0:0 && v43:0:0 < 0 && v38:0:0 > 0 && v37:0:0 > 0 && v41:0:0 < v40:0:0 The following rules are bounded: f_133(v37:0:0, v38:0:0, v39:0:0, v40:0:0, v41:0:0, v43:0:0, v44:0:0, v45:0:0, v46:0:0, v47:0:0) -> f_133(v37:0:0, v38:0:0, v39:0:0, v40:0:0, v41:0:0, v44:0:0, v40:0:0 + v44:0:0, v45:0:0, v46:0:0, v47:0:0) :|: v46:0:0 >= v38:0:0 && v47:0:0 >= v39:0:0 && v45:0:0 >= v37:0:0 && v47:0:0 > 3 && v46:0:0 > 3 && v45:0:0 > 3 && v40:0:0 > 0 && v39:0:0 > 0 && v44:0:0 < v40:0:0 && v43:0:0 < 0 && v38:0:0 > 0 && v37:0:0 > 0 && v41:0:0 < v40:0:0 ---------------------------------------- (12) YES