/export/starexec/sandbox2/solver/bin/starexec_run_c /export/starexec/sandbox2/benchmark/theBenchmark.c /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given C Problem could be proven: (0) C Problem (1) CToLLVMProof [EQUIVALENT, 175 ms] (2) LLVM problem (3) LLVMToTerminationGraphProof [EQUIVALENT, 1793 ms] (4) LLVM Symbolic Execution Graph (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] (6) AND (7) LLVM Symbolic Execution SCC (8) SCC2IRS [SOUND, 45 ms] (9) IntTRS (10) IntTRSCompressionProof [EQUIVALENT, 0 ms] (11) IntTRS (12) PolynomialOrderProcessor [EQUIVALENT, 10 ms] (13) YES (14) LLVM Symbolic Execution SCC (15) SCC2IRS [SOUND, 28 ms] (16) IntTRS (17) IntTRSCompressionProof [EQUIVALENT, 0 ms] (18) IntTRS (19) RankingReductionPairProof [EQUIVALENT, 6 ms] (20) YES ---------------------------------------- (0) Obligation: c file /export/starexec/sandbox2/benchmark/theBenchmark.c ---------------------------------------- (1) CToLLVMProof (EQUIVALENT) Compiled c-file /export/starexec/sandbox2/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: "test_fun" 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 %x_ref = alloca *i32, align 8 %y_ref = alloca *i32, align 8 store %x, %1 store %y, %2 %3 = alloca i8, numElementsLit: 4 %4 = bitcast *i8 %3 to *i32 store %4, %x_ref %5 = alloca i8, numElementsLit: 4 %6 = bitcast *i8 %5 to *i32 store %6, %y_ref %7 = load %1 %8 = load %x_ref store %7, %8 %9 = load %2 %10 = load %y_ref store %9, %10 br %11 11: %12 = load %x_ref %13 = load %12 %14 = icmp sgt %13 0 br %14, %15, %19 15: %16 = load %y_ref %17 = load %16 %18 = icmp sgt %17 0 br %19 19: %20 = phi [0, %11], [%18, %15] br %20, %21, %50 21: %22 = load %x_ref %23 = load %22 %24 = load %y_ref %25 = load %24 %26 = icmp sgt %23 %25 br %26, %27, %38 27: br %28 28: %29 = load %x_ref %30 = load %29 %31 = icmp sgt %30 0 br %31, %32, %37 32: %33 = load %x_ref %34 = load %33 %35 = sub %34 1 %36 = load %x_ref store %35, %36 br %28 37: br %49 38: br %39 39: %40 = load %y_ref %41 = load %40 %42 = icmp sgt %41 0 br %42, %43, %48 43: %44 = load %y_ref %45 = load %44 %46 = sub %45 1 %47 = load %y_ref store %46, %47 br %39 48: br %49 49: br %11 50: %51 = load %x_ref %52 = load %51 %53 = load %y_ref %54 = load %53 %55 = add %52 %54 ret %55 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 0: %1 = alloca i32, align 4 store 0, %1 %2 = call i32 @__VERIFIER_nondet_int() %3 = call i32 @__VERIFIER_nondet_int() %4 = call i32 @test_fun(i32 %2, i32 %3) ret %4 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 2 SCCs. ---------------------------------------- (6) Complex Obligation (AND) ---------------------------------------- (7) Obligation: SCC ---------------------------------------- (8) SCC2IRS (SOUND) Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: Generated rules. Obtained 12 rulesP rules: f_381(v98, v99, v100, v101, v102, v103, v104, v105, 1, 0, v108, v109, v110, v111, v112, v113, v114, v115, v116, v117, 3, 7, 4, 8) -> f_384(v98, v99, v100, v101, v102, v103, v104, v105, 1, 0, v109, v108, v110, v111, v112, v113, v114, v115, v116, v117, 3, 7, 4, 8) :|: 0 = 0 f_384(v98, v99, v100, v101, v102, v103, v104, v105, 1, 0, v109, v108, v110, v111, v112, v113, v114, v115, v116, v117, 3, 7, 4, 8) -> f_387(v98, v99, v100, v101, v102, v103, v104, v105, 1, 0, v109, v108, v110, v111, v112, v113, v114, v115, v116, v117, 3, 7, 2, 4, 8) :|: 0 < v109 && 2 <= v108 && 2 <= v99 f_387(v98, v99, v100, v101, v102, v103, v104, v105, 1, 0, v109, v108, v110, v111, v112, v113, v114, v115, v116, v117, 3, 7, 2, 4, 8) -> f_391(v98, v99, v100, v101, v102, v103, v104, v105, 1, 0, v109, v108, v110, v111, v112, v113, v114, v115, v116, v117, 3, 7, 2, 4, 8) :|: 0 = 0 f_391(v98, v99, v100, v101, v102, v103, v104, v105, 1, 0, v109, v108, v110, v111, v112, v113, v114, v115, v116, v117, 3, 7, 2, 4, 8) -> f_395(v98, v99, v100, v101, v102, v103, v104, v105, 1, 0, v109, v108, v110, v111, v112, v113, v114, v115, v116, v117, 3, 7, 2, 4, 8) :|: TRUE f_395(v98, v99, v100, v101, v102, v103, v104, v105, 1, 0, v109, v108, v110, v111, v112, v113, v114, v115, v116, v117, 3, 7, 2, 4, 8) -> f_399(v98, v99, v100, v101, v102, v103, v104, v105, 1, 0, v109, v108, v110, v111, v112, v113, v114, v115, v116, v117, 3, 7, 2, 4, 8) :|: 0 = 0 f_399(v98, v99, v100, v101, v102, v103, v104, v105, 1, 0, v109, v108, v110, v111, v112, v113, v114, v115, v116, v117, 3, 7, 2, 4, 8) -> f_403(v98, v99, v100, v101, v102, v103, v104, v105, 1, 0, v109, v110, v111, v112, v113, v114, v115, v116, v117, 3, 7, 2, 4, 8) :|: 0 = 0 f_403(v98, v99, v100, v101, v102, v103, v104, v105, 1, 0, v109, v110, v111, v112, v113, v114, v115, v116, v117, 3, 7, 2, 4, 8) -> f_407(v98, v99, v100, v101, v102, v103, v104, v105, 1, 0, v109, v119, v110, v111, v112, v113, v114, v115, v116, v117, 3, 7, 2, 4, 8) :|: 1 + v119 = v109 && 0 <= v119 f_407(v98, v99, v100, v101, v102, v103, v104, v105, 1, 0, v109, v119, v110, v111, v112, v113, v114, v115, v116, v117, 3, 7, 2, 4, 8) -> f_411(v98, v99, v100, v101, v102, v103, v104, v105, 1, 0, v109, v119, v110, v111, v112, v113, v114, v115, v116, v117, 3, 7, 2, 4, 8) :|: 0 = 0 f_411(v98, v99, v100, v101, v102, v103, v104, v105, 1, 0, v109, v119, v110, v111, v112, v113, v114, v115, v116, v117, 3, 7, 2, 4, 8) -> f_415(v98, v99, v100, v101, v102, v103, v104, v105, 1, 0, v109, v119, v110, v111, v112, v113, v114, v115, v116, v117, 3, 7, 2, 4, 8) :|: TRUE f_415(v98, v99, v100, v101, v102, v103, v104, v105, 1, 0, v109, v119, v110, v111, v112, v113, v114, v115, v116, v117, 3, 7, 2, 4, 8) -> f_418(v98, v99, v100, v101, v102, v103, v104, v105, 1, 0, v109, v119, v110, v111, v112, v113, v114, v115, v116, v117, 3, 7, 2, 4, 8) :|: TRUE f_418(v98, v99, v100, v101, v102, v103, v104, v105, 1, 0, v109, v119, v110, v111, v112, v113, v114, v115, v116, v117, 3, 7, 2, 4, 8) -> f_379(v98, v99, v100, v101, v102, v103, v104, v105, 1, 0, v109, v119, v110, v111, v112, v113, v114, v115, v116, v117, 3, 7, 4, 8) :|: TRUE f_379(v98, v99, v100, v101, v102, v103, v104, v105, 1, 0, v108, v109, v110, v111, v112, v113, v114, v115, v116, v117, 3, 7, 4, 8) -> f_381(v98, v99, v100, v101, v102, v103, v104, v105, 1, 0, v108, v109, v110, v111, v112, v113, v114, v115, v116, v117, 3, 7, 4, 8) :|: 0 = 0 Combined rules. Obtained 1 rulesP rules: f_381(v98:0, v99:0, v100:0, v101:0, v102:0, v103:0, v104:0, v105:0, 1, 0, v108:0, 1 + v119:0, v110:0, v111:0, v112:0, v113:0, v114:0, v115:0, v116:0, v117:0, 3, 7, 4, 8) -> f_381(v98:0, v99:0, v100:0, v101:0, v102:0, v103:0, v104:0, v105:0, 1, 0, 1 + v119:0, v119:0, v110:0, v111:0, v112:0, v113:0, v114:0, v115:0, v116:0, v117:0, 3, 7, 4, 8) :|: v108:0 > 1 && v119:0 > -1 && v99:0 > 1 Filtered unneeded arguments: f_381(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24) -> f_381(x2, x11, x12) Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: f_381(v99:0, v108:0, sum~cons_1~v119:0) -> f_381(v99:0, 1 + v119:0, v119:0) :|: v119:0 > -1 && v99:0 > 1 && v108:0 > 1 && sum~cons_1~v119:0 = 1 + v119:0 ---------------------------------------- (9) Obligation: Rules: f_381(v99:0, v108:0, sum~cons_1~v119:0) -> f_381(v99:0, 1 + v119:0, v119:0) :|: v119:0 > -1 && v99:0 > 1 && v108:0 > 1 && sum~cons_1~v119:0 = 1 + v119:0 ---------------------------------------- (10) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (11) Obligation: Rules: f_381(v99:0:0, v108:0:0, sum~cons_1~v119:0:0) -> f_381(v99:0:0, 1 + v119:0:0, v119:0:0) :|: v119:0:0 > -1 && v99:0:0 > 1 && v108:0:0 > 1 && sum~cons_1~v119:0:0 = 1 + v119:0:0 ---------------------------------------- (12) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f_381(x, x1, x2)] = x2 The following rules are decreasing: f_381(v99:0:0, v108:0:0, sum~cons_1~v119:0:0) -> f_381(v99:0:0, 1 + v119:0:0, v119:0:0) :|: v119:0:0 > -1 && v99:0:0 > 1 && v108:0:0 > 1 && sum~cons_1~v119:0:0 = 1 + v119:0:0 The following rules are bounded: f_381(v99:0:0, v108:0:0, sum~cons_1~v119:0:0) -> f_381(v99:0:0, 1 + v119:0:0, v119:0:0) :|: v119:0:0 > -1 && v99:0:0 > 1 && v108:0:0 > 1 && sum~cons_1~v119:0:0 = 1 + v119:0:0 ---------------------------------------- (13) YES ---------------------------------------- (14) Obligation: SCC ---------------------------------------- (15) SCC2IRS (SOUND) Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: Generated rules. Obtained 12 rulesP rules: f_377(v77, v78, v79, v80, v81, v82, v83, v84, 1, v86, v87, v88, v89, v90, v91, v92, v93, v94, v95, 0, 3, 7, 2, 4, 8) -> f_380(v77, v78, v79, v80, v81, v82, v83, v84, 1, v87, v86, v88, v89, v90, v91, v92, v93, v94, v95, 0, 3, 7, 2, 4, 8) :|: 0 = 0 f_380(v77, v78, v79, v80, v81, v82, v83, v84, 1, v87, v86, v88, v89, v90, v91, v92, v93, v94, v95, 0, 3, 7, 2, 4, 8) -> f_382(v77, v78, v79, v80, v81, v82, v83, v84, 1, v87, v86, v88, v89, v90, v91, v92, v93, v94, v95, 0, 3, 7, 2, 4, 8) :|: 0 < v87 && 2 <= v86 f_382(v77, v78, v79, v80, v81, v82, v83, v84, 1, v87, v86, v88, v89, v90, v91, v92, v93, v94, v95, 0, 3, 7, 2, 4, 8) -> f_385(v77, v78, v79, v80, v81, v82, v83, v84, 1, v87, v86, v88, v89, v90, v91, v92, v93, v94, v95, 0, 3, 7, 2, 4, 8) :|: 0 = 0 f_385(v77, v78, v79, v80, v81, v82, v83, v84, 1, v87, v86, v88, v89, v90, v91, v92, v93, v94, v95, 0, 3, 7, 2, 4, 8) -> f_389(v77, v78, v79, v80, v81, v82, v83, v84, 1, v87, v86, v88, v89, v90, v91, v92, v93, v94, v95, 0, 3, 7, 2, 4, 8) :|: TRUE f_389(v77, v78, v79, v80, v81, v82, v83, v84, 1, v87, v86, v88, v89, v90, v91, v92, v93, v94, v95, 0, 3, 7, 2, 4, 8) -> f_393(v77, v78, v79, v80, v81, v82, v83, v84, 1, v87, v86, v88, v89, v90, v91, v92, v93, v94, v95, 0, 3, 7, 2, 4, 8) :|: 0 = 0 f_393(v77, v78, v79, v80, v81, v82, v83, v84, 1, v87, v86, v88, v89, v90, v91, v92, v93, v94, v95, 0, 3, 7, 2, 4, 8) -> f_397(v77, v78, v79, v80, v81, v82, v83, v84, 1, v87, v88, v89, v90, v91, v92, v93, v94, v95, 0, 3, 7, 2, 4, 8) :|: 0 = 0 f_397(v77, v78, v79, v80, v81, v82, v83, v84, 1, v87, v88, v89, v90, v91, v92, v93, v94, v95, 0, 3, 7, 2, 4, 8) -> f_401(v77, v78, v79, v80, v81, v82, v83, v84, 1, v87, v118, v88, v89, v90, v91, v92, v93, v94, v95, 0, 3, 7, 2, 4, 8) :|: 1 + v118 = v87 && 0 <= v118 f_401(v77, v78, v79, v80, v81, v82, v83, v84, 1, v87, v118, v88, v89, v90, v91, v92, v93, v94, v95, 0, 3, 7, 2, 4, 8) -> f_405(v77, v78, v79, v80, v81, v82, v83, v84, 1, v87, v118, v88, v89, v90, v91, v92, v93, v94, v95, 0, 3, 7, 2, 4, 8) :|: 0 = 0 f_405(v77, v78, v79, v80, v81, v82, v83, v84, 1, v87, v118, v88, v89, v90, v91, v92, v93, v94, v95, 0, 3, 7, 2, 4, 8) -> f_409(v77, v78, v79, v80, v81, v82, v83, v84, 1, v87, v118, v88, v89, v90, v91, v92, v93, v94, v95, 0, 3, 7, 2, 4, 8) :|: TRUE f_409(v77, v78, v79, v80, v81, v82, v83, v84, 1, v87, v118, v88, v89, v90, v91, v92, v93, v94, v95, 0, 3, 7, 2, 4, 8) -> f_413(v77, v78, v79, v80, v81, v82, v83, v84, 1, v87, v118, v88, v89, v90, v91, v92, v93, v94, v95, 0, 3, 7, 2, 4, 8) :|: TRUE f_413(v77, v78, v79, v80, v81, v82, v83, v84, 1, v87, v118, v88, v89, v90, v91, v92, v93, v94, v95, 0, 3, 7, 2, 4, 8) -> f_374(v77, v78, v79, v80, v81, v82, v83, v84, 1, v87, v118, v88, v89, v90, v91, v92, v93, v94, v95, 0, 3, 7, 2, 4, 8) :|: TRUE f_374(v77, v78, v79, v80, v81, v82, v83, v84, 1, v86, v87, v88, v89, v90, v91, v92, v93, v94, v95, 0, 3, 7, 2, 4, 8) -> f_377(v77, v78, v79, v80, v81, v82, v83, v84, 1, v86, v87, v88, v89, v90, v91, v92, v93, v94, v95, 0, 3, 7, 2, 4, 8) :|: 0 = 0 Combined rules. Obtained 1 rulesP rules: f_377(v77:0, v78:0, v79:0, v80:0, v81:0, v82:0, v83:0, v84:0, 1, v86:0, 1 + v118:0, v88:0, v89:0, v90:0, v91:0, v92:0, v93:0, v94:0, v95:0, 0, 3, 7, 2, 4, 8) -> f_377(v77:0, v78:0, v79:0, v80:0, v81:0, v82:0, v83:0, v84:0, 1, 1 + v118:0, v118:0, v88:0, v89:0, v90:0, v91:0, v92:0, v93:0, v94:0, v95:0, 0, 3, 7, 2, 4, 8) :|: v86:0 > 1 && v118:0 > -1 Filtered unneeded arguments: f_377(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25) -> f_377(x10, x11) Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: f_377(v86:0, sum~cons_1~v118:0) -> f_377(1 + v118:0, v118:0) :|: v86:0 > 1 && v118:0 > -1 && sum~cons_1~v118:0 = 1 + v118:0 ---------------------------------------- (16) Obligation: Rules: f_377(v86:0, sum~cons_1~v118:0) -> f_377(1 + v118:0, v118:0) :|: v86:0 > 1 && v118:0 > -1 && sum~cons_1~v118:0 = 1 + v118:0 ---------------------------------------- (17) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (18) Obligation: Rules: f_377(v86:0:0, sum~cons_1~v118:0:0) -> f_377(1 + v118:0:0, v118:0:0) :|: v86:0:0 > 1 && v118:0:0 > -1 && sum~cons_1~v118:0:0 = 1 + v118:0:0 ---------------------------------------- (19) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f_377 ] = f_377_2 The following rules are decreasing: f_377(v86:0:0, sum~cons_1~v118:0:0) -> f_377(1 + v118:0:0, v118:0:0) :|: v86:0:0 > 1 && v118:0:0 > -1 && sum~cons_1~v118:0:0 = 1 + v118:0:0 The following rules are bounded: f_377(v86:0:0, sum~cons_1~v118:0:0) -> f_377(1 + v118:0:0, v118:0:0) :|: v86:0:0 > 1 && v118:0:0 > -1 && sum~cons_1~v118:0:0 = 1 + v118:0:0 ---------------------------------------- (20) YES