20.12/6.96 YES 20.12/6.97 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 20.12/6.97 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 20.12/6.97 20.12/6.97 20.12/6.97 Termination of the given C Problem could be proven: 20.12/6.97 20.12/6.97 (0) C Problem 20.12/6.97 (1) CToLLVMProof [EQUIVALENT, 175 ms] 20.12/6.97 (2) LLVM problem 20.12/6.97 (3) LLVMToTerminationGraphProof [EQUIVALENT, 3808 ms] 20.12/6.97 (4) LLVM Symbolic Execution Graph 20.12/6.97 (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] 20.12/6.97 (6) LLVM Symbolic Execution SCC 20.12/6.97 (7) SCC2IRS [SOUND, 94 ms] 20.12/6.97 (8) IntTRS 20.12/6.97 (9) IntTRSCompressionProof [EQUIVALENT, 0 ms] 20.12/6.97 (10) IntTRS 20.12/6.97 (11) RankingReductionPairProof [EQUIVALENT, 26 ms] 20.12/6.97 (12) YES 20.12/6.97 20.12/6.97 20.12/6.97 ---------------------------------------- 20.12/6.97 20.12/6.97 (0) 20.12/6.97 Obligation: 20.12/6.97 c file /export/starexec/sandbox/benchmark/theBenchmark.c 20.12/6.97 ---------------------------------------- 20.12/6.97 20.12/6.97 (1) CToLLVMProof (EQUIVALENT) 20.12/6.97 Compiled c-file /export/starexec/sandbox/benchmark/theBenchmark.c to LLVM. 20.12/6.97 ---------------------------------------- 20.12/6.97 20.12/6.97 (2) 20.12/6.97 Obligation: 20.12/6.97 LLVM Problem 20.12/6.97 20.12/6.97 Aliases: 20.12/6.97 20.12/6.97 Data layout: 20.12/6.97 20.12/6.97 "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" 20.12/6.97 20.12/6.97 Machine: 20.12/6.97 20.12/6.97 "x86_64-pc-linux-gnu" 20.12/6.97 20.12/6.97 Type definitions: 20.12/6.97 20.12/6.97 Global variables: 20.12/6.97 20.12/6.97 Function declarations and definitions: 20.12/6.97 20.12/6.97 *BasicFunctionTypename: "__VERIFIER_nondet_int" returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 20.12/6.97 *BasicFunctionTypename: "f" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: (i i32, x i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc 20.12/6.97 0: 20.12/6.97 %1 = alloca i32, align 4 20.12/6.97 %2 = alloca i32, align 4 20.12/6.97 %3 = alloca i32, align 4 20.12/6.97 store %i, %2 20.12/6.97 store %x, %3 20.12/6.97 %4 = load %2 20.12/6.97 %5 = icmp eq %4 0 20.12/6.97 br %5, %6, %8 20.12/6.97 6: 20.12/6.97 %7 = load %3 20.12/6.97 store %7, %1 20.12/6.97 br %14 20.12/6.97 8: 20.12/6.97 %9 = load %2 20.12/6.97 %10 = sub %9 1 20.12/6.97 %11 = load %3 20.12/6.97 %12 = load %2 20.12/6.97 %13 = call i32 @g(i32 %10, i32 %11, i32 %12) 20.12/6.97 store %13, %1 20.12/6.97 br %14 20.12/6.97 14: 20.12/6.97 %15 = load %1 20.12/6.97 ret %15 20.12/6.97 20.12/6.97 *BasicFunctionTypename: "g" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: (a i32, b i32, c i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc 20.12/6.97 0: 20.12/6.97 %1 = alloca i32, align 4 20.12/6.97 %2 = alloca i32, align 4 20.12/6.97 %3 = alloca i32, align 4 20.12/6.97 store %a, %1 20.12/6.97 store %b, %2 20.12/6.97 store %c, %3 20.12/6.97 %4 = load %1 20.12/6.97 %5 = load %2 20.12/6.97 %6 = load %3 20.12/6.97 %7 = add %5 %6 20.12/6.97 %8 = call i32 @f(i32 %4, i32 %7) 20.12/6.97 ret %8 20.12/6.97 20.12/6.97 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 20.12/6.97 0: 20.12/6.97 %1 = alloca i32, align 4 20.12/6.97 %i = alloca i32, align 4 20.12/6.97 %x = alloca i32, align 4 20.12/6.97 store 0, %1 20.12/6.97 %2 = call i32 @__VERIFIER_nondet_int() 20.12/6.97 store %2, %i 20.12/6.97 %3 = call i32 @__VERIFIER_nondet_int() 20.12/6.97 store %3, %x 20.12/6.97 %4 = load %i 20.12/6.97 %5 = icmp sge %4 0 20.12/6.97 br %5, %6, %13 20.12/6.97 6: 20.12/6.97 %7 = load %x 20.12/6.97 %8 = icmp sge %7 0 20.12/6.97 br %8, %9, %13 20.12/6.97 9: 20.12/6.97 %10 = load %i 20.12/6.97 %11 = load %x 20.12/6.97 %12 = call i32 @f(i32 %10, i32 %11) 20.12/6.97 br %13 20.12/6.97 13: 20.12/6.97 ret 0 20.12/6.97 20.12/6.97 20.12/6.97 Analyze Termination of all function calls matching the pattern: 20.12/6.97 main() 20.12/6.97 ---------------------------------------- 20.12/6.97 20.12/6.97 (3) LLVMToTerminationGraphProof (EQUIVALENT) 20.12/6.97 Constructed symbolic execution graph for LLVM program and proved memory safety. 20.12/6.97 ---------------------------------------- 20.12/6.97 20.12/6.97 (4) 20.12/6.97 Obligation: 20.12/6.97 SE Graph 20.12/6.97 ---------------------------------------- 20.12/6.97 20.12/6.97 (5) SymbolicExecutionGraphToSCCProof (SOUND) 20.12/6.97 Splitted symbolic execution graph to 1 SCC. 20.12/6.97 ---------------------------------------- 20.12/6.97 20.12/6.97 (6) 20.12/6.97 Obligation: 20.12/6.97 SCC 20.12/6.97 ---------------------------------------- 20.12/6.97 20.12/6.97 (7) SCC2IRS (SOUND) 20.12/6.97 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 20.12/6.97 Generated rules. Obtained 28 rulesP rules: 20.12/6.97 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 20.12/6.97 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 20.12/6.97 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 20.12/6.97 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 20.12/6.97 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 20.12/6.97 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 20.12/6.97 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 20.12/6.97 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 20.12/6.97 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 20.12/6.97 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 20.12/6.97 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 20.12/6.97 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 20.12/6.97 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 20.12/6.97 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 20.12/6.97 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 20.12/6.97 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 20.12/6.97 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 20.12/6.97 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 20.12/6.97 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 20.12/6.97 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 20.12/6.97 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 20.12/6.97 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 20.12/6.97 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 20.12/6.97 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 20.12/6.97 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 20.12/6.97 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 20.12/6.97 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 20.12/6.97 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 20.12/6.97 Combined rules. Obtained 1 rulesP rules: 20.12/6.97 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 20.12/6.97 Filtered unneeded arguments: 20.12/6.97 f_261(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16) -> f_261(x1, x2, x12) 20.12/6.97 Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: 20.12/6.97 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 20.12/6.97 20.12/6.97 ---------------------------------------- 20.12/6.97 20.12/6.97 (8) 20.12/6.97 Obligation: 20.12/6.97 Rules: 20.12/6.97 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 20.12/6.97 20.12/6.97 ---------------------------------------- 20.12/6.97 20.12/6.97 (9) IntTRSCompressionProof (EQUIVALENT) 20.12/6.97 Compressed rules. 20.12/6.97 ---------------------------------------- 20.12/6.97 20.12/6.97 (10) 20.12/6.97 Obligation: 20.12/6.97 Rules: 20.12/6.97 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 20.12/6.97 20.12/6.97 ---------------------------------------- 20.12/6.97 20.12/6.97 (11) RankingReductionPairProof (EQUIVALENT) 20.12/6.97 Interpretation: 20.12/6.97 [ f_261 ] = f_261_1 20.12/6.97 20.12/6.97 The following rules are decreasing: 20.12/6.97 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 20.12/6.97 20.12/6.97 The following rules are bounded: 20.12/6.97 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 20.12/6.97 20.12/6.97 20.12/6.97 ---------------------------------------- 20.12/6.97 20.12/6.97 (12) 20.12/6.97 YES 20.92/7.10 EOF