/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given C Problem could be proven: (0) C Problem (1) CToLLVMProof [EQUIVALENT, 177 ms] (2) LLVM problem (3) LLVMToTerminationGraphProof [EQUIVALENT, 1508 ms] (4) LLVM Symbolic Execution Graph (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] (6) AND (7) LLVM Symbolic Execution SCC (8) SCC2IRS [SOUND, 32 ms] (9) IntTRS (10) IntTRSCompressionProof [EQUIVALENT, 0 ms] (11) IntTRS (12) RankingReductionPairProof [EQUIVALENT, 6 ms] (13) YES (14) LLVM Symbolic Execution SCC (15) SCC2IRS [SOUND, 70 ms] (16) IntTRS (17) IntTRSCompressionProof [EQUIVALENT, 0 ms] (18) IntTRS (19) RankingReductionPairProof [EQUIVALENT, 21 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: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 0: %1 = alloca i32, align 4 %i = alloca i32, align 4 %j = alloca i32, align 4 %c = alloca i32, align 4 store 0, %1 store 0, %c store 0, %i br %2 2: %3 = load %i %4 = icmp slt %3 100 br %4, %5, %11 5: %6 = load %c %7 = add %6 1 store %7, %c br %8 8: %9 = load %i %10 = add %9 1 store %10, %i br %2 11: store 5, %j br %12 12: %13 = load %j %14 = icmp slt %13 21 br %14, %15, %21 15: %16 = load %c %17 = add %16 1 store %17, %c br %18 18: %19 = load %j %20 = add %19 3 store %20, %j br %12 21: %22 = load %c ret %22 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 13 rulesP rules: f_270(v187, v188, v189, v190, 100, 0, 99, v198, 1, v196, v197, v194, v199, v200, v201, v202, 3, 5, 20, 101, 8, 23, 4) -> f_271(v187, v188, v189, v190, 100, 0, 99, v198, 1, v196, v197, v194, v199, v200, v201, v202, 3, 5, 17, 101, 8, 20, 4) :|: v198 < 21 && v194 <= 17 f_271(v187, v188, v189, v190, 100, 0, 99, v198, 1, v196, v197, v194, v199, v200, v201, v202, 3, 5, 17, 101, 8, 20, 4) -> f_273(v187, v188, v189, v190, 100, 0, 99, v198, 1, v196, v197, v194, v199, v200, v201, v202, 3, 5, 17, 101, 8, 20, 4) :|: 0 = 0 f_273(v187, v188, v189, v190, 100, 0, 99, v198, 1, v196, v197, v194, v199, v200, v201, v202, 3, 5, 17, 101, 8, 20, 4) -> f_275(v187, v188, v189, v190, 100, 0, 99, v198, 1, v196, v197, v194, v199, v200, v201, v202, 3, 5, 17, 101, 8, 20, 4) :|: TRUE f_275(v187, v188, v189, v190, 100, 0, 99, v198, 1, v196, v197, v194, v199, v200, v201, v202, 3, 5, 17, 101, 8, 20, 4) -> f_277(v187, v188, v189, v190, 100, 0, 99, v198, 1, v197, v194, v199, v200, v201, v202, 3, 5, 17, 101, 8, 20, 4) :|: 0 = 0 f_277(v187, v188, v189, v190, 100, 0, 99, v198, 1, v197, v194, v199, v200, v201, v202, 3, 5, 17, 101, 8, 20, 4) -> f_279(v187, v188, v189, v190, 100, 0, 99, v198, 1, v197, v210, v194, v199, v200, v201, v202, 3, 5, 17, 101, 8, 20, 4, 102) :|: v210 = 1 + v197 && 102 <= v210 f_279(v187, v188, v189, v190, 100, 0, 99, v198, 1, v197, v210, v194, v199, v200, v201, v202, 3, 5, 17, 101, 8, 20, 4, 102) -> f_280(v187, v188, v189, v190, 100, 0, 99, v198, 1, v197, v210, v194, v199, v200, v201, v202, 3, 5, 17, 101, 8, 20, 4, 102) :|: TRUE f_280(v187, v188, v189, v190, 100, 0, 99, v198, 1, v197, v210, v194, v199, v200, v201, v202, 3, 5, 17, 101, 8, 20, 4, 102) -> f_281(v187, v188, v189, v190, 100, 0, 99, v198, 1, v197, v210, v194, v199, v200, v201, v202, 3, 5, 17, 101, 8, 20, 4, 102) :|: TRUE f_281(v187, v188, v189, v190, 100, 0, 99, v198, 1, v197, v210, v194, v199, v200, v201, v202, 3, 5, 17, 101, 8, 20, 4, 102) -> f_282(v187, v188, v189, v190, 100, 0, 99, v198, 1, v197, v210, v199, v200, v201, v202, 3, 101, 8, 20, 4, 102) :|: 0 = 0 f_282(v187, v188, v189, v190, 100, 0, 99, v198, 1, v197, v210, v199, v200, v201, v202, 3, 101, 8, 20, 4, 102) -> f_283(v187, v188, v189, v190, 100, 0, 99, v198, 1, v197, v210, v212, v199, v200, v201, v202, 3, 101, 8, 20, 4, 102, 11, 23) :|: v212 = 3 + v198 && 11 <= v212 && v212 <= 23 f_283(v187, v188, v189, v190, 100, 0, 99, v198, 1, v197, v210, v212, v199, v200, v201, v202, 3, 101, 8, 20, 4, 102, 11, 23) -> f_284(v187, v188, v189, v190, 100, 0, 99, v198, 1, v197, v210, v212, v199, v200, v201, v202, 3, 101, 8, 20, 4, 102, 11, 23) :|: TRUE f_284(v187, v188, v189, v190, 100, 0, 99, v198, 1, v197, v210, v212, v199, v200, v201, v202, 3, 101, 8, 20, 4, 102, 11, 23) -> f_285(v187, v188, v189, v190, 100, 0, 99, v198, 1, v197, v210, v212, v199, v200, v201, v202, 3, 101, 8, 20, 4, 102, 11, 23) :|: TRUE f_285(v187, v188, v189, v190, 100, 0, 99, v198, 1, v197, v210, v212, v199, v200, v201, v202, 3, 101, 8, 20, 4, 102, 11, 23) -> f_269(v187, v188, v189, v190, 100, 0, 99, v198, 1, v197, v210, v212, v199, v200, v201, v202, 3, 5, 20, 101, 8, 23, 4) :|: TRUE f_269(v187, v188, v189, v190, 100, 0, 99, v194, 1, v196, v197, v198, v199, v200, v201, v202, 3, 5, 20, 101, 8, 23, 4) -> f_270(v187, v188, v189, v190, 100, 0, 99, v198, 1, v196, v197, v194, v199, v200, v201, v202, 3, 5, 20, 101, 8, 23, 4) :|: 0 = 0 Combined rules. Obtained 1 rulesP rules: f_270(v187:0, v188:0, v189:0, v190:0, 100, 0, 99, v198:0, 1, v196:0, v197:0, v194:0, v199:0, v200:0, v201:0, v202:0, 3, 5, 20, 101, 8, 23, 4) -> f_270(v187:0, v188:0, v189:0, v190:0, 100, 0, 99, 3 + v198:0, 1, v197:0, 1 + v197:0, v198:0, v199:0, v200:0, v201:0, v202:0, 3, 5, 20, 101, 8, 23, 4) :|: v194:0 < 18 && v198:0 < 21 && v197:0 > 100 && v198:0 > 7 Filtered unneeded arguments: f_270(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23) -> f_270(x8, x11, x12) Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: f_270(v198:0, v197:0, v194:0) -> f_270(3 + v198:0, 1 + v197:0, v198:0) :|: v198:0 < 21 && v194:0 < 18 && v198:0 > 7 && v197:0 > 100 ---------------------------------------- (9) Obligation: Rules: f_270(v198:0, v197:0, v194:0) -> f_270(3 + v198:0, 1 + v197:0, v198:0) :|: v198:0 < 21 && v194:0 < 18 && v198:0 > 7 && v197:0 > 100 ---------------------------------------- (10) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (11) Obligation: Rules: f_270(v198:0:0, v197:0:0, v194:0:0) -> f_270(3 + v198:0:0, 1 + v197:0:0, v198:0:0) :|: v198:0:0 > 7 && v197:0:0 > 100 && v194:0:0 < 18 && v198:0:0 < 21 ---------------------------------------- (12) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f_270 ] = -1/3*f_270_1 The following rules are decreasing: f_270(v198:0:0, v197:0:0, v194:0:0) -> f_270(3 + v198:0:0, 1 + v197:0:0, v198:0:0) :|: v198:0:0 > 7 && v197:0:0 > 100 && v194:0:0 < 18 && v198:0:0 < 21 The following rules are bounded: f_270(v198:0:0, v197:0:0, v194:0:0) -> f_270(3 + v198:0:0, 1 + v197:0:0, v198:0:0) :|: v198:0:0 > 7 && v197:0:0 > 100 && v194:0:0 < 18 && v198:0:0 < 21 ---------------------------------------- (13) YES ---------------------------------------- (14) Obligation: SCC ---------------------------------------- (15) SCC2IRS (SOUND) Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: Generated rules. Obtained 13 rulesP rules: f_206(v69, v70, v71, v72, v75, 1, v73, v76, v77, v78, v79, 0, 3, 99, 100, 4) -> f_207(v69, v70, v71, v72, v75, 1, v73, v76, v77, v78, v79, 0, 3, 98, 99, 4) :|: v75 < 100 && v73 <= 98 f_207(v69, v70, v71, v72, v75, 1, v73, v76, v77, v78, v79, 0, 3, 98, 99, 4) -> f_209(v69, v70, v71, v72, v75, 1, v73, v76, v77, v78, v79, 0, 3, 98, 99, 4) :|: 0 = 0 f_209(v69, v70, v71, v72, v75, 1, v73, v76, v77, v78, v79, 0, 3, 98, 99, 4) -> f_211(v69, v70, v71, v72, v75, 1, v73, v76, v77, v78, v79, 0, 3, 98, 99, 4) :|: TRUE f_211(v69, v70, v71, v72, v75, 1, v73, v76, v77, v78, v79, 0, 3, 98, 99, 4) -> f_213(v69, v70, v71, v72, v75, 1, v73, v76, v77, v78, v79, 0, 3, 98, 99, 4) :|: 0 = 0 f_213(v69, v70, v71, v72, v75, 1, v73, v76, v77, v78, v79, 0, 3, 98, 99, 4) -> f_215(v69, v70, v71, v72, v75, 1, v81, v73, v76, v77, v78, v79, 0, 3, 98, 99, 4, 2, 100) :|: v81 = 1 + v75 && 2 <= v81 && v81 <= 100 f_215(v69, v70, v71, v72, v75, 1, v81, v73, v76, v77, v78, v79, 0, 3, 98, 99, 4, 2, 100) -> f_217(v69, v70, v71, v72, v75, 1, v81, v73, v76, v77, v78, v79, 0, 3, 98, 99, 4, 2, 100) :|: TRUE f_217(v69, v70, v71, v72, v75, 1, v81, v73, v76, v77, v78, v79, 0, 3, 98, 99, 4, 2, 100) -> f_219(v69, v70, v71, v72, v75, 1, v81, v73, v76, v77, v78, v79, 0, 3, 98, 99, 4, 2, 100) :|: TRUE f_219(v69, v70, v71, v72, v75, 1, v81, v73, v76, v77, v78, v79, 0, 3, 98, 99, 4, 2, 100) -> f_221(v69, v70, v71, v72, v75, 1, v81, v76, v77, v78, v79, 0, 3, 99, 4, 2, 100) :|: 0 = 0 f_221(v69, v70, v71, v72, v75, 1, v81, v76, v77, v78, v79, 0, 3, 99, 4, 2, 100) -> f_223(v69, v70, v71, v72, v75, 1, v81, v76, v77, v78, v79, 0, 3, 99, 4, 2, 100) :|: v81 = 1 + v75 f_223(v69, v70, v71, v72, v75, 1, v81, v76, v77, v78, v79, 0, 3, 99, 4, 2, 100) -> f_225(v69, v70, v71, v72, v75, 1, v81, v76, v77, v78, v79, 0, 3, 99, 4, 2, 100) :|: TRUE f_225(v69, v70, v71, v72, v75, 1, v81, v76, v77, v78, v79, 0, 3, 99, 4, 2, 100) -> f_227(v69, v70, v71, v72, v75, 1, v81, v76, v77, v78, v79, 0, 3, 99, 4, 2, 100) :|: TRUE f_227(v69, v70, v71, v72, v75, 1, v81, v76, v77, v78, v79, 0, 3, 99, 4, 2, 100) -> f_205(v69, v70, v71, v72, v75, 1, v81, v76, v77, v78, v79, 0, 3, 99, 100, 4) :|: TRUE f_205(v69, v70, v71, v72, v73, 1, v75, v76, v77, v78, v79, 0, 3, 99, 100, 4) -> f_206(v69, v70, v71, v72, v75, 1, v73, v76, v77, v78, v79, 0, 3, 99, 100, 4) :|: 0 = 0 Combined rules. Obtained 1 rulesP rules: f_206(v69:0, v70:0, v71:0, v72:0, v75:0, 1, v73:0, v76:0, v77:0, v78:0, v79:0, 0, 3, 99, 100, 4) -> f_206(v69:0, v70:0, v71:0, v72:0, 1 + v75:0, 1, v75:0, v76:0, v77:0, v78:0, v79:0, 0, 3, 99, 100, 4) :|: v73:0 < 99 && v75:0 < 100 && v75:0 > 0 Filtered unneeded arguments: f_206(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16) -> f_206(x5, x7) Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: f_206(v75:0, v73:0) -> f_206(1 + v75:0, v75:0) :|: v75:0 < 100 && v75:0 > 0 && v73:0 < 99 ---------------------------------------- (16) Obligation: Rules: f_206(v75:0, v73:0) -> f_206(1 + v75:0, v75:0) :|: v75:0 < 100 && v75:0 > 0 && v73:0 < 99 ---------------------------------------- (17) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (18) Obligation: Rules: f_206(v75:0:0, v73:0:0) -> f_206(1 + v75:0:0, v75:0:0) :|: v75:0:0 < 100 && v75:0:0 > 0 && v73:0:0 < 99 ---------------------------------------- (19) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f_206 ] = -1*f_206_1 The following rules are decreasing: f_206(v75:0:0, v73:0:0) -> f_206(1 + v75:0:0, v75:0:0) :|: v75:0:0 < 100 && v75:0:0 > 0 && v73:0:0 < 99 The following rules are bounded: f_206(v75:0:0, v73:0:0) -> f_206(1 + v75:0:0, v75:0:0) :|: v75:0:0 < 100 && v75:0:0 > 0 && v73:0:0 < 99 ---------------------------------------- (20) YES