/export/starexec/sandbox/solver/bin/starexec_run_c /export/starexec/sandbox/benchmark/theBenchmark.c /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.c # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given C Problem could be proven: (0) C Problem (1) CToLLVMProof [EQUIVALENT, 178 ms] (2) LLVM problem (3) LLVMToTerminationGraphProof [EQUIVALENT, 7790 ms] (4) LLVM Symbolic Execution Graph (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] (6) LLVM Symbolic Execution SCC (7) SCC2IRS [SOUND, 152 ms] (8) IntTRS (9) IntTRSCompressionProof [EQUIVALENT, 0 ms] (10) IntTRS (11) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (12) IntTRS (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IntTRS (15) RankingReductionPairProof [EQUIVALENT, 7 ms] (16) 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 %z = 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 = call i32 @__VERIFIER_nondet_int() store %4, %z %5 = call i32 @random() %6 = call i32 @random() %7 = call i32 @average(i32 %5, i32 %6) %8 = load %1 ret %8 *BasicFunctionTypename: "average" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: (x i32, y i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc 0: %1 = alloca i32, align 4 %2 = alloca i32, align 4 %3 = alloca i32, align 4 store %x, %2 store %y, %3 %4 = load %2 %5 = icmp sgt %4 0 br %5, %6, %12 6: %7 = load %2 %8 = sub %7 1 %9 = load %3 %10 = add %9 1 %11 = call i32 @average(i32 %8, i32 %10) store %11, %1 br %23 12: %13 = load %3 %14 = icmp sgt %13 2 br %14, %15, %22 15: %16 = load %2 %17 = add %16 1 %18 = load %3 %19 = sub %18 2 %20 = call i32 @average(i32 %17, i32 %19) %21 = add 1 %20 store %21, %1 br %23 22: store 1, %1 br %23 23: %24 = load %1 ret %24 *BasicFunctionTypename: "random" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 0: %1 = alloca i32, align 4 %x = alloca i32, align 4 %2 = call i32 @__VERIFIER_nondet_int() store %2, %x %3 = load %x %4 = icmp slt %3 0 br %4, %5, %8 5: %6 = load %x %7 = sub 0 %6 store %7, %1 br %10 8: %9 = load %x store %9, %1 br %10 10: %11 = load %1 ret %11 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 30 rulesP rules: f_254(v19, v41, v71, v1, v2, v3, v4, v5, v6, v7, v8, v72, 0, v9, v11, v13, 3, 1, 4) -> f_255(v19, v41, v71, v73, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, 0, v9, v11, v13, 3, 1, 4) :|: 1 <= v73 && v74 = 3 + v73 && 4 <= v74 f_255(v19, v41, v71, v73, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, 0, v9, v11, v13, 3, 1, 4) -> f_256(v19, v41, v71, v73, v75, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, 0, v9, v11, v13, 3, 1, 4) :|: 1 <= v75 && v76 = 3 + v75 && 4 <= v76 f_256(v19, v41, v71, v73, v75, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, 0, v9, v11, v13, 3, 1, 4) -> f_257(v19, v41, v71, v73, v75, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, 0, v9, v11, v13, 3, 1, 4) :|: TRUE f_257(v19, v41, v71, v73, v75, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, 0, v9, v11, v13, 3, 1, 4) -> f_258(v19, v41, v71, v73, v75, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, 0, v9, v11, v13, 3, 1, 4) :|: TRUE f_258(v19, v41, v71, v73, v75, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, 0, v9, v11, v13, 3, 1, 4) -> f_259(v19, v41, v71, v73, v75, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, 0, v9, v11, v13, 3, 1, 4) :|: 0 = 0 f_259(v19, v41, v71, v73, v75, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, 0, v9, v11, v13, 3, 1, 4) -> f_260(v19, v41, v71, v73, v75, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, 0, v9, v11, v13, 3, 1, 4) :|: 0 < v19 f_259(v19, v41, v71, v73, v75, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, 0, v9, v11, v13, 3, 1, 4) -> f_261(0, v41, v71, v73, v75, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, v9, v11, v13, 3, 1, 4) :|: v19 <= 0 f_260(v19, v41, v71, v73, v75, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, 0, v9, v11, v13, 3, 1, 4) -> f_262(v19, v41, v71, v73, v75, 1, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, 0, v9, v11, v13, 3, 4) :|: 0 = 0 f_262(v19, v41, v71, v73, v75, 1, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, 0, v9, v11, v13, 3, 4) -> f_264(v19, v41, v71, v73, v75, 1, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, 0, v9, v11, v13, 3, 4) :|: TRUE f_264(v19, v41, v71, v73, v75, 1, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, 0, v9, v11, v13, 3, 4) -> f_266(v19, v41, v71, v73, v75, 1, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, 0, v9, v11, v13, 3, 4) :|: 0 = 0 f_266(v19, v41, v71, v73, v75, 1, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, 0, v9, v11, v13, 3, 4) -> f_268(v19, v41, v71, v73, v75, 1, v79, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, 0, v9, v11, v13, 3, 4) :|: 1 + v79 = v19 && 0 <= v79 f_268(v19, v41, v71, v73, v75, 1, v79, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, 0, v9, v11, v13, 3, 4) -> f_271(v19, v41, v71, v73, v75, 1, v79, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, 0, v9, v11, v13, 3, 4) :|: 0 = 0 f_271(v19, v41, v71, v73, v75, 1, v79, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, 0, v9, v11, v13, 3, 4) -> f_274(v19, v41, v71, v73, v75, 1, v79, v80, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, 0, v9, v11, v13, 3, 4) :|: v80 = 1 + v41 && 1 <= v80 f_274(v19, v41, v71, v73, v75, 1, v79, v80, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, 0, v9, v11, v13, 3, 4) -> f_277(v79, v80, v1, v2, v3, v4, v5, v6, v7, v8, v71, v72, v73, v74, v75, v76, 0, v9, v11, v13, v19, v41, 1, 3, 4) :|: 0 = 0 f_277(v79, v80, v1, v2, v3, v4, v5, v6, v7, v8, v71, v72, v73, v74, v75, v76, 0, v9, v11, v13, v19, v41, 1, 3, 4) -> f_280(v79, v80, v1, v2, v3, v4, v5, v6, v7, v8, v71, v72, v73, v74, v75, v76, 0, v9, v11, v13, v19, v41, 3, 1, 4) :|: TRUE f_280(v79, v80, v1, v2, v3, v4, v5, v6, v7, v8, v71, v72, v73, v74, v75, v76, 0, v9, v11, v13, v19, v41, 3, 1, 4) -> f_252(v79, v80, v1, v2, v3, v4, v5, v6, v7, v8, 0, v9, v11, v13, 3, 1, 4) :|: TRUE f_252(v19, v41, v1, v2, v3, v4, v5, v6, v7, v8, 0, v9, v11, v13, 3, 1, 4) -> f_254(v19, v41, v71, v1, v2, v3, v4, v5, v6, v7, v8, v72, 0, v9, v11, v13, 3, 1, 4) :|: 1 <= v71 && v72 = 3 + v71 && 4 <= v72 f_261(0, v41, v71, v73, v75, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, v9, v11, v13, 3, 1, 4) -> f_263(0, v41, v71, v73, v75, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, v9, v11, v13, 3, 1, 4) :|: 0 = 0 f_263(0, v41, v71, v73, v75, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, v9, v11, v13, 3, 1, 4) -> f_265(0, v41, v71, v73, v75, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, v9, v11, v13, 3, 1, 4) :|: TRUE f_265(0, v41, v71, v73, v75, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, v9, v11, v13, 3, 1, 4) -> f_267(0, v41, v71, v73, v75, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, v9, v11, v13, 3, 1, 4) :|: 0 = 0 f_267(0, v41, v71, v73, v75, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, v9, v11, v13, 3, 1, 4) -> f_269(0, v41, v71, v73, v75, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, v9, v11, v13, 3, 1, 4) :|: 2 < v41 f_269(0, v41, v71, v73, v75, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, v9, v11, v13, 3, 1, 4) -> f_272(0, v41, v71, v73, v75, 1, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, v9, v11, v13, 3, 4) :|: 0 = 0 f_272(0, v41, v71, v73, v75, 1, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, v9, v11, v13, 3, 4) -> f_275(0, v41, v71, v73, v75, 1, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, v9, v11, v13, 3, 4) :|: TRUE f_275(0, v41, v71, v73, v75, 1, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, v9, v11, v13, 3, 4) -> f_278(0, v41, v71, v73, v75, 1, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, v9, v11, v13, 3, 4) :|: 0 = 0 f_278(0, v41, v71, v73, v75, 1, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, v9, v11, v13, 3, 4) -> f_281(0, v41, v71, v73, v75, 1, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, v9, v11, v13, 3, 4) :|: 0 = 0 f_281(0, v41, v71, v73, v75, 1, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, v9, v11, v13, 3, 4) -> f_283(0, v41, v71, v73, v75, 1, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, v9, v11, v13, 3, 4) :|: 0 = 0 f_283(0, v41, v71, v73, v75, 1, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, v9, v11, v13, 3, 4) -> f_285(0, v41, v71, v73, v75, 1, v95, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, v9, v11, v13, 3, 2, 4) :|: 2 + v95 = v41 && 1 <= v95 f_285(0, v41, v71, v73, v75, 1, v95, v1, v2, v3, v4, v5, v6, v7, v8, v72, v74, v76, v9, v11, v13, 3, 2, 4) -> f_289(1, v95, v1, v2, v3, v4, v5, v6, v7, v8, v71, v72, v73, v74, v75, v76, 0, v9, v11, v13, v41, 3, 2, 4) :|: 0 = 0 f_289(1, v95, v1, v2, v3, v4, v5, v6, v7, v8, v71, v72, v73, v74, v75, v76, 0, v9, v11, v13, v41, 3, 2, 4) -> f_293(1, v95, v1, v2, v3, v4, v5, v6, v7, v8, v71, v72, v73, v74, v75, v76, 0, v9, v11, v13, v41, 3, 2, 4) :|: TRUE f_293(1, v95, v1, v2, v3, v4, v5, v6, v7, v8, v71, v72, v73, v74, v75, v76, 0, v9, v11, v13, v41, 3, 2, 4) -> f_252(1, v95, v1, v2, v3, v4, v5, v6, v7, v8, 0, v9, v11, v13, 3, 1, 4) :|: TRUE Combined rules. Obtained 2 rulesP rules: f_254(v19:0, 2 + v95:0, v71:0, v1:0, v2:0, v3:0, v4:0, v5:0, v6:0, v7:0, v8:0, v72:0, 0, v9:0, v11:0, v13:0, 3, 1, 4) -> f_254(1, v95:0, v71:1, v1:0, v2:0, v3:0, v4:0, v5:0, v6:0, v7:0, v8:0, 3 + v71:1, 0, v9:0, v11:0, v13:0, 3, 1, 4) :|: v75:0 > 0 && v73:0 > 0 && v19:0 < 1 && v95:0 > 0 && v71:1 > 0 f_254(1 + v79:0, v41:0, v71:0, v1:0, v2:0, v3:0, v4:0, v5:0, v6:0, v7:0, v8:0, v72:0, 0, v9:0, v11:0, v13:0, 3, 1, 4) -> f_254(v79:0, 1 + v41:0, v71:1, v1:0, v2:0, v3:0, v4:0, v5:0, v6:0, v7:0, v8:0, 3 + v71:1, 0, v9:0, v11:0, v13:0, 3, 1, 4) :|: v75:0 > 0 && v73:0 > 0 && v79:0 > -1 && v41:0 > -1 && v71:1 > 0 Filtered unneeded arguments: f_254(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) -> f_254(x1, x2) Removed division, modulo operations, cleaned up constraints. Obtained 2 rules.P rules: f_254(v19:0, sum~cons_2~v95:0) -> f_254(1, v95:0) :|: v19:0 < 1 && v95:0 > 0 && sum~cons_2~v95:0 = 2 + v95:0 f_254(sum~cons_1~v79:0, v41:0) -> f_254(v79:0, 1 + v41:0) :|: v79:0 > -1 && v41:0 > -1 && sum~cons_1~v79:0 = 1 + v79:0 ---------------------------------------- (8) Obligation: Rules: f_254(v19:0, sum~cons_2~v95:0) -> f_254(1, v95:0) :|: v19:0 < 1 && v95:0 > 0 && sum~cons_2~v95:0 = 2 + v95:0 f_254(sum~cons_1~v79:0, v41:0) -> f_254(v79:0, 1 + v41:0) :|: v79:0 > -1 && v41:0 > -1 && sum~cons_1~v79:0 = 1 + v79:0 ---------------------------------------- (9) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (10) Obligation: Rules: f_254(v19:0:0, sum~cons_2~v95:0:0) -> f_254(1, v95:0:0) :|: v19:0:0 < 1 && v95:0:0 > 0 && sum~cons_2~v95:0:0 = 2 + v95:0:0 f_254(sum~cons_1~v79:0:0, v41:0:0) -> f_254(v79:0:0, 1 + v41:0:0) :|: v79:0:0 > -1 && v41:0:0 > -1 && sum~cons_1~v79:0:0 = 1 + v79:0:0 ---------------------------------------- (11) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f_254(x, x1)] = x^2 + x1 The following rules are decreasing: f_254(v19:0:0, sum~cons_2~v95:0:0) -> f_254(1, v95:0:0) :|: v19:0:0 < 1 && v95:0:0 > 0 && sum~cons_2~v95:0:0 = 2 + v95:0:0 The following rules are bounded: f_254(v19:0:0, sum~cons_2~v95:0:0) -> f_254(1, v95:0:0) :|: v19:0:0 < 1 && v95:0:0 > 0 && sum~cons_2~v95:0:0 = 2 + v95:0:0 f_254(sum~cons_1~v79:0:0, v41:0:0) -> f_254(v79:0:0, 1 + v41:0:0) :|: v79:0:0 > -1 && v41:0:0 > -1 && sum~cons_1~v79:0:0 = 1 + v79:0:0 ---------------------------------------- (12) Obligation: Rules: f_254(sum~cons_1~v79:0:0, v41:0:0) -> f_254(v79:0:0, 1 + v41:0:0) :|: v79:0:0 > -1 && v41:0:0 > -1 && sum~cons_1~v79:0:0 = 1 + v79:0:0 ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: f_254(sum~cons_1~v79:0:0:0, v41:0:0:0) -> f_254(v79:0:0:0, 1 + v41:0:0:0) :|: v79:0:0:0 > -1 && v41:0:0:0 > -1 && sum~cons_1~v79:0:0:0 = 1 + v79:0:0:0 ---------------------------------------- (15) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f_254 ] = f_254_1 The following rules are decreasing: f_254(sum~cons_1~v79:0:0:0, v41:0:0:0) -> f_254(v79:0:0:0, 1 + v41:0:0:0) :|: v79:0:0:0 > -1 && v41:0:0:0 > -1 && sum~cons_1~v79:0:0:0 = 1 + v79:0:0:0 The following rules are bounded: f_254(sum~cons_1~v79:0:0:0, v41:0:0:0) -> f_254(v79:0:0:0, 1 + v41:0:0:0) :|: v79:0:0:0 > -1 && v41:0:0:0 > -1 && sum~cons_1~v79:0:0:0 = 1 + v79:0:0:0 ---------------------------------------- (16) YES