/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given C Problem could be proven: (0) C Problem (1) CToLLVMProof [EQUIVALENT, 175 ms] (2) LLVM problem (3) LLVMToTerminationGraphProof [EQUIVALENT, 3737 ms] (4) LLVM Symbolic Execution Graph (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] (6) LLVM Symbolic Execution SCC (7) SCC2IRS [SOUND, 96 ms] (8) IntTRS (9) IntTRSCompressionProof [EQUIVALENT, 0 ms] (10) IntTRS (11) RankingReductionPairProof [EQUIVALENT, 17 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: "f" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: (i i32, x i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc 0: %1 = alloca i32, align 4 %2 = alloca i32, align 4 %3 = alloca i32, align 4 store %i, %2 store %x, %3 %4 = load %2 %5 = icmp eq %4 0 br %5, %6, %8 6: %7 = load %3 store %7, %1 br %14 8: %9 = load %2 %10 = sub %9 1 %11 = load %3 %12 = load %2 %13 = call i32 @g(i32 %10, i32 %11, i32 %12) store %13, %1 br %14 14: %15 = load %1 ret %15 *BasicFunctionTypename: "g" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: (a i32, b i32, c i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc 0: %1 = alloca i32, align 4 %2 = alloca i32, align 4 %3 = alloca i32, align 4 store %a, %1 store %b, %2 store %c, %3 %4 = load %1 %5 = load %2 %6 = load %3 %7 = add %5 %6 %8 = call i32 @f(i32 %4, i32 %7) ret %8 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 0: %1 = alloca i32, align 4 %i = alloca i32, align 4 %x = alloca i32, align 4 store 0, %1 %2 = call i32 @__VERIFIER_nondet_int() store %2, %i %3 = call i32 @__VERIFIER_nondet_int() store %3, %x %4 = load %i %5 = icmp sge %4 0 br %5, %6, %13 6: %7 = load %x %8 = icmp sge %7 0 br %8, %9, %13 9: %10 = load %i %11 = load %x %12 = call i32 @f(i32 %10, i32 %11) br %13 13: 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 28 rulesP rules: f_261(v98, v99, v109, v100, v101, v102, v103, v104, v105, v110, 0, v107, v108, 3, 1, 4) -> f_262(v98, v99, v109, v111, v100, v101, v102, v103, v104, v105, v110, v112, 0, v107, v108, 3, 1, 4) :|: 1 <= v111 && v112 = 3 + v111 && 4 <= v112 f_262(v98, v99, v109, v111, v100, v101, v102, v103, v104, v105, v110, v112, 0, v107, v108, 3, 1, 4) -> f_263(v98, v99, v109, v111, v113, v100, v101, v102, v103, v104, v105, v110, v112, v114, 0, v107, v108, 3, 1, 4) :|: 1 <= v113 && v114 = 3 + v113 && 4 <= v114 f_263(v98, v99, v109, v111, v113, v100, v101, v102, v103, v104, v105, v110, v112, v114, 0, v107, v108, 3, 1, 4) -> f_264(v98, v99, v109, v111, v113, v100, v101, v102, v103, v104, v105, v110, v112, v114, 0, v107, v108, 3, 1, 4) :|: TRUE f_264(v98, v99, v109, v111, v113, v100, v101, v102, v103, v104, v105, v110, v112, v114, 0, v107, v108, 3, 1, 4) -> f_265(v98, v99, v109, v111, v113, v100, v101, v102, v103, v104, v105, v110, v112, v114, 0, v107, v108, 3, 1, 4) :|: TRUE f_265(v98, v99, v109, v111, v113, v100, v101, v102, v103, v104, v105, v110, v112, v114, 0, v107, v108, 3, 1, 4) -> f_266(v98, v99, v109, v111, v113, v100, v101, v102, v103, v104, v105, v110, v112, v114, 0, v107, v108, 3, 1, 4) :|: 0 = 0 f_266(v98, v99, v109, v111, v113, v100, v101, v102, v103, v104, v105, v110, v112, v114, 0, v107, v108, 3, 1, 4) -> f_268(v98, v99, v109, v111, v113, v100, v101, v102, v103, v104, v105, v110, v112, v114, 0, v107, v108, 3, 1, 4) :|: v98 != 0 && 1 <= v107 f_268(v98, v99, v109, v111, v113, v100, v101, v102, v103, v104, v105, v110, v112, v114, 0, v107, v108, 3, 1, 4) -> f_270(v98, v99, v109, v111, v113, 0, v100, v101, v102, v103, v104, v105, v110, v112, v114, v107, v108, 3, 1, 4) :|: 0 = 0 f_270(v98, v99, v109, v111, v113, 0, v100, v101, v102, v103, v104, v105, v110, v112, v114, v107, v108, 3, 1, 4) -> f_272(v98, v99, v109, v111, v113, 0, v100, v101, v102, v103, v104, v105, v110, v112, v114, v107, v108, 3, 1, 4) :|: TRUE f_272(v98, v99, v109, v111, v113, 0, v100, v101, v102, v103, v104, v105, v110, v112, v114, v107, v108, 3, 1, 4) -> f_274(v98, v99, v109, v111, v113, 0, v100, v101, v102, v103, v104, v105, v110, v112, v114, v107, v108, 3, 1, 4) :|: 0 = 0 f_274(v98, v99, v109, v111, v113, 0, v100, v101, v102, v103, v104, v105, v110, v112, v114, v107, v108, 3, 1, 4) -> f_276(v98, v99, v109, v111, v113, 0, v118, v100, v101, v102, v103, v104, v105, v110, v112, v114, v107, v108, 3, 1, 4) :|: 1 + v118 = v98 && 0 <= v118 f_276(v98, v99, v109, v111, v113, 0, v118, v100, v101, v102, v103, v104, v105, v110, v112, v114, v107, v108, 3, 1, 4) -> f_278(v98, v99, v109, v111, v113, 0, v118, v100, v101, v102, v103, v104, v105, v110, v112, v114, v107, v108, 3, 1, 4) :|: 0 = 0 f_278(v98, v99, v109, v111, v113, 0, v118, v100, v101, v102, v103, v104, v105, v110, v112, v114, v107, v108, 3, 1, 4) -> f_280(v98, v99, v109, v111, v113, 0, v118, v100, v101, v102, v103, v104, v105, v110, v112, v114, v107, v108, 3, 1, 4) :|: 0 = 0 f_280(v98, v99, v109, v111, v113, 0, v118, v100, v101, v102, v103, v104, v105, v110, v112, v114, v107, v108, 3, 1, 4) -> f_282(v118, v99, v98, v100, v101, v102, v103, v104, v105, v109, v110, v111, v112, v113, v114, 0, v107, v108, 3, 1, 4) :|: 0 = 0 f_282(v118, v99, v98, v100, v101, v102, v103, v104, v105, v109, v110, v111, v112, v113, v114, 0, v107, v108, 3, 1, 4) -> f_284(v118, v99, v98, v100, v101, v102, v103, v104, v105, v109, v110, v111, v112, v113, v114, 0, v107, v108, 3, 1, 4) :|: TRUE f_284(v118, v99, v98, v100, v101, v102, v103, v104, v105, v109, v110, v111, v112, v113, v114, 0, v107, v108, 3, 1, 4) -> f_286(v118, v99, v98, v138, v100, v101, v102, v103, v104, v105, v109, v110, v111, v112, v113, v114, v139, 0, v107, v108, 3, 1, 4) :|: 1 <= v138 && v139 = 3 + v138 && 4 <= v139 f_286(v118, v99, v98, v138, v100, v101, v102, v103, v104, v105, v109, v110, v111, v112, v113, v114, v139, 0, v107, v108, 3, 1, 4) -> f_287(v118, v99, v98, v138, v140, v100, v101, v102, v103, v104, v105, v109, v110, v111, v112, v113, v114, v139, v141, 0, v107, v108, 3, 1, 4) :|: 1 <= v140 && v141 = 3 + v140 && 4 <= v141 f_287(v118, v99, v98, v138, v140, v100, v101, v102, v103, v104, v105, v109, v110, v111, v112, v113, v114, v139, v141, 0, v107, v108, 3, 1, 4) -> f_288(v118, v99, v98, v138, v140, v142, v100, v101, v102, v103, v104, v105, v109, v110, v111, v112, v113, v114, v139, v141, v143, 0, v107, v108, 3, 1, 4) :|: 1 <= v142 && v143 = 3 + v142 && 4 <= v143 f_288(v118, v99, v98, v138, v140, v142, v100, v101, v102, v103, v104, v105, v109, v110, v111, v112, v113, v114, v139, v141, v143, 0, v107, v108, 3, 1, 4) -> f_289(v118, v99, v98, v138, v140, v142, v100, v101, v102, v103, v104, v105, v109, v110, v111, v112, v113, v114, v139, v141, v143, 0, v107, v108, 3, 1, 4) :|: TRUE f_289(v118, v99, v98, v138, v140, v142, v100, v101, v102, v103, v104, v105, v109, v110, v111, v112, v113, v114, v139, v141, v143, 0, v107, v108, 3, 1, 4) -> f_290(v118, v99, v98, v138, v140, v142, v100, v101, v102, v103, v104, v105, v109, v110, v111, v112, v113, v114, v139, v141, v143, 0, v107, v108, 3, 1, 4) :|: TRUE f_290(v118, v99, v98, v138, v140, v142, v100, v101, v102, v103, v104, v105, v109, v110, v111, v112, v113, v114, v139, v141, v143, 0, v107, v108, 3, 1, 4) -> f_291(v118, v99, v98, v138, v140, v142, v100, v101, v102, v103, v104, v105, v109, v110, v111, v112, v113, v114, v139, v141, v143, 0, v107, v108, 3, 1, 4) :|: TRUE f_291(v118, v99, v98, v138, v140, v142, v100, v101, v102, v103, v104, v105, v109, v110, v111, v112, v113, v114, v139, v141, v143, 0, v107, v108, 3, 1, 4) -> f_292(v118, v99, v98, v138, v140, v142, v100, v101, v102, v103, v104, v105, v109, v110, v111, v112, v113, v114, v139, v141, v143, 0, v107, v108, 3, 1, 4) :|: 0 = 0 f_292(v118, v99, v98, v138, v140, v142, v100, v101, v102, v103, v104, v105, v109, v110, v111, v112, v113, v114, v139, v141, v143, 0, v107, v108, 3, 1, 4) -> f_293(v118, v99, v98, v138, v140, v142, v100, v101, v102, v103, v104, v105, v109, v110, v111, v112, v113, v114, v139, v141, v143, 0, v107, v108, 3, 1, 4) :|: 0 = 0 f_293(v118, v99, v98, v138, v140, v142, v100, v101, v102, v103, v104, v105, v109, v110, v111, v112, v113, v114, v139, v141, v143, 0, v107, v108, 3, 1, 4) -> f_294(v118, v99, v98, v138, v140, v142, v100, v101, v102, v103, v104, v105, v109, v110, v111, v112, v113, v114, v139, v141, v143, 0, v107, v108, 3, 1, 4) :|: 0 = 0 f_294(v118, v99, v98, v138, v140, v142, v100, v101, v102, v103, v104, v105, v109, v110, v111, v112, v113, v114, v139, v141, v143, 0, v107, v108, 3, 1, 4) -> f_295(v118, v99, v98, v138, v140, v142, v147, v100, v101, v102, v103, v104, v105, v109, v110, v111, v112, v113, v114, v139, v141, v143, 0, v107, v108, 3, 1, 4) :|: v147 = v99 + v98 && 1 <= v147 f_295(v118, v99, v98, v138, v140, v142, v147, v100, v101, v102, v103, v104, v105, v109, v110, v111, v112, v113, v114, v139, v141, v143, 0, v107, v108, 3, 1, 4) -> f_296(v118, v147, v100, v101, v102, v103, v104, v105, v109, v110, v111, v112, v113, v114, v138, v139, v140, v141, v142, v143, 0, v107, v108, v98, v99, 3, 1, 4) :|: 0 = 0 f_296(v118, v147, v100, v101, v102, v103, v104, v105, v109, v110, v111, v112, v113, v114, v138, v139, v140, v141, v142, v143, 0, v107, v108, v98, v99, 3, 1, 4) -> f_297(v118, v147, v100, v101, v102, v103, v104, v105, v109, v110, v111, v112, v113, v114, v138, v139, v140, v141, v142, v143, 0, v107, v108, v98, v99, 3, 1, 4) :|: TRUE f_297(v118, v147, v100, v101, v102, v103, v104, v105, v109, v110, v111, v112, v113, v114, v138, v139, v140, v141, v142, v143, 0, v107, v108, v98, v99, 3, 1, 4) -> f_260(v118, v147, v100, v101, v102, v103, v104, v105, 0, v107, v108, 3, 1, 4) :|: TRUE f_260(v98, v99, v100, v101, v102, v103, v104, v105, 0, v107, v108, 3, 1, 4) -> f_261(v98, v99, v109, v100, v101, v102, v103, v104, v105, v110, 0, v107, v108, 3, 1, 4) :|: 1 <= v109 && v110 = 3 + v109 && 4 <= v110 Combined rules. Obtained 1 rulesP rules: f_261(1 + v118:0, v99:0, v109:0, v100:0, v101:0, v102:0, v103:0, v104:0, v105:0, v110:0, 0, v107:0, v108:0, 3, 1, 4) -> f_261(v118:0, v99:0 + (1 + v118:0), v109:1, v100:0, v101:0, v102:0, v103:0, v104:0, v105:0, 3 + v109:1, 0, v107:0, v108:0, 3, 1, 4) :|: v113:0 > 0 && v111:0 > 0 && v107:0 > 0 && v118:0 > -1 && v138:0 > 0 && v140:0 > 0 && v142:0 > 0 && v99:0 + (1 + v118:0) > 0 && v109:1 > 0 Filtered unneeded arguments: f_261(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16) -> f_261(x1, x2, x12) Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: f_261(sum~cons_1~v118:0, v99:0, v107:0) -> f_261(v118:0, v99:0 + (1 + v118:0), v107:0) :|: v118:0 > -1 && v99:0 + (1 + v118:0) > 0 && v107:0 > 0 && sum~cons_1~v118:0 = 1 + v118:0 ---------------------------------------- (8) Obligation: Rules: f_261(sum~cons_1~v118:0, v99:0, v107:0) -> f_261(v118:0, v99:0 + (1 + v118:0), v107:0) :|: v118:0 > -1 && v99:0 + (1 + v118:0) > 0 && v107:0 > 0 && sum~cons_1~v118:0 = 1 + v118:0 ---------------------------------------- (9) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (10) Obligation: Rules: f_261(sum~cons_1~v118:0:0, v99:0:0, v107:0:0) -> f_261(v118:0:0, v99:0:0 + (1 + v118:0:0), v107:0:0) :|: v118:0:0 > -1 && v99:0:0 + (1 + v118:0:0) > 0 && v107:0:0 > 0 && sum~cons_1~v118:0:0 = 1 + v118:0:0 ---------------------------------------- (11) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f_261 ] = f_261_1 The following rules are decreasing: f_261(sum~cons_1~v118:0:0, v99:0:0, v107:0:0) -> f_261(v118:0:0, v99:0:0 + (1 + v118:0:0), v107:0:0) :|: v118:0:0 > -1 && v99:0:0 + (1 + v118:0:0) > 0 && v107:0:0 > 0 && sum~cons_1~v118:0:0 = 1 + v118:0:0 The following rules are bounded: f_261(sum~cons_1~v118:0:0, v99:0:0, v107:0:0) -> f_261(v118:0:0, v99:0:0 + (1 + v118:0:0), v107:0:0) :|: v118:0:0 > -1 && v99:0:0 + (1 + v118:0:0) > 0 && v107:0:0 > 0 && sum~cons_1~v118:0:0 = 1 + v118:0:0 ---------------------------------------- (12) YES