14.02/4.72 YES 14.02/4.73 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 14.02/4.73 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 14.02/4.73 14.02/4.73 14.02/4.73 Termination of the given C Problem could be proven: 14.02/4.73 14.02/4.73 (0) C Problem 14.02/4.73 (1) CToLLVMProof [EQUIVALENT, 172 ms] 14.02/4.73 (2) LLVM problem 14.02/4.73 (3) LLVMToTerminationGraphProof [EQUIVALENT, 1188 ms] 14.02/4.73 (4) LLVM Symbolic Execution Graph 14.02/4.73 (5) SymbolicExecutionGraphToSCCProof [SOUND, 4 ms] 14.02/4.73 (6) AND 14.02/4.73 (7) LLVM Symbolic Execution SCC 14.02/4.73 (8) SCC2IRS [SOUND, 30 ms] 14.02/4.73 (9) IntTRS 14.02/4.73 (10) IntTRSCompressionProof [EQUIVALENT, 0 ms] 14.02/4.73 (11) IntTRS 14.02/4.73 (12) RankingReductionPairProof [EQUIVALENT, 17 ms] 14.02/4.73 (13) YES 14.02/4.73 (14) LLVM Symbolic Execution SCC 14.02/4.73 (15) SCC2IRS [SOUND, 12 ms] 14.02/4.73 (16) IntTRS 14.02/4.73 (17) IntTRSCompressionProof [EQUIVALENT, 0 ms] 14.02/4.73 (18) IntTRS 14.02/4.73 (19) RankingReductionPairProof [EQUIVALENT, 9 ms] 14.02/4.73 (20) YES 14.02/4.73 14.02/4.73 14.02/4.73 ---------------------------------------- 14.02/4.73 14.02/4.73 (0) 14.02/4.73 Obligation: 14.02/4.73 c file /export/starexec/sandbox/benchmark/theBenchmark.c 14.02/4.73 ---------------------------------------- 14.02/4.73 14.02/4.73 (1) CToLLVMProof (EQUIVALENT) 14.02/4.73 Compiled c-file /export/starexec/sandbox/benchmark/theBenchmark.c to LLVM. 14.02/4.73 ---------------------------------------- 14.02/4.73 14.02/4.73 (2) 14.02/4.73 Obligation: 14.02/4.73 LLVM Problem 14.02/4.73 14.02/4.73 Aliases: 14.02/4.73 14.02/4.73 Data layout: 14.02/4.73 14.02/4.73 "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" 14.02/4.73 14.02/4.73 Machine: 14.02/4.73 14.02/4.73 "x86_64-pc-linux-gnu" 14.02/4.73 14.02/4.73 Type definitions: 14.02/4.73 14.02/4.73 Global variables: 14.02/4.73 14.02/4.73 Function declarations and definitions: 14.02/4.73 14.02/4.73 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 14.02/4.73 0: 14.02/4.73 %1 = alloca i32, align 4 14.02/4.73 %i = alloca i32, align 4 14.02/4.73 %j = alloca i32, align 4 14.02/4.73 %c = alloca i32, align 4 14.02/4.73 store 0, %1 14.02/4.73 store 0, %c 14.02/4.73 store 0, %i 14.02/4.73 br %2 14.02/4.73 2: 14.02/4.73 %3 = load %i 14.02/4.73 %4 = icmp slt %3 100 14.02/4.73 br %4, %5, %11 14.02/4.73 5: 14.02/4.73 %6 = load %c 14.02/4.73 %7 = add %6 1 14.02/4.73 store %7, %c 14.02/4.73 br %8 14.02/4.73 8: 14.02/4.73 %9 = load %i 14.02/4.73 %10 = add %9 1 14.02/4.73 store %10, %i 14.02/4.73 br %2 14.02/4.73 11: 14.02/4.73 store 5, %j 14.02/4.73 br %12 14.02/4.73 12: 14.02/4.73 %13 = load %j 14.02/4.73 %14 = icmp slt %13 21 14.02/4.73 br %14, %15, %21 14.02/4.73 15: 14.02/4.73 %16 = load %c 14.02/4.73 %17 = add %16 1 14.02/4.73 store %17, %c 14.02/4.73 br %18 14.02/4.73 18: 14.02/4.73 %19 = load %j 14.02/4.73 %20 = add %19 3 14.02/4.73 store %20, %j 14.02/4.73 br %12 14.02/4.73 21: 14.02/4.73 %22 = load %c 14.02/4.73 ret %22 14.02/4.73 14.02/4.73 14.02/4.73 Analyze Termination of all function calls matching the pattern: 14.02/4.73 main() 14.02/4.73 ---------------------------------------- 14.02/4.73 14.02/4.73 (3) LLVMToTerminationGraphProof (EQUIVALENT) 14.02/4.73 Constructed symbolic execution graph for LLVM program and proved memory safety. 14.02/4.73 ---------------------------------------- 14.02/4.73 14.02/4.73 (4) 14.02/4.73 Obligation: 14.02/4.73 SE Graph 14.02/4.73 ---------------------------------------- 14.02/4.73 14.02/4.73 (5) SymbolicExecutionGraphToSCCProof (SOUND) 14.02/4.73 Splitted symbolic execution graph to 2 SCCs. 14.02/4.73 ---------------------------------------- 14.02/4.73 14.02/4.73 (6) 14.02/4.73 Complex Obligation (AND) 14.02/4.73 14.02/4.73 ---------------------------------------- 14.02/4.73 14.02/4.73 (7) 14.02/4.73 Obligation: 14.02/4.73 SCC 14.02/4.73 ---------------------------------------- 14.02/4.73 14.02/4.73 (8) SCC2IRS (SOUND) 14.02/4.73 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 14.02/4.73 Generated rules. Obtained 13 rulesP rules: 14.02/4.73 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 14.02/4.73 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 14.02/4.73 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 14.02/4.73 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 14.02/4.73 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 14.02/4.73 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 14.02/4.73 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 14.02/4.73 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 14.02/4.73 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 14.02/4.73 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 14.02/4.73 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 14.02/4.73 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 14.02/4.73 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 14.02/4.73 Combined rules. Obtained 1 rulesP rules: 14.02/4.73 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 14.02/4.73 Filtered unneeded arguments: 14.02/4.73 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) 14.02/4.73 Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: 14.02/4.73 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 14.02/4.73 14.02/4.73 ---------------------------------------- 14.02/4.73 14.02/4.73 (9) 14.02/4.73 Obligation: 14.02/4.73 Rules: 14.02/4.73 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 14.02/4.73 14.02/4.73 ---------------------------------------- 14.02/4.73 14.02/4.73 (10) IntTRSCompressionProof (EQUIVALENT) 14.02/4.73 Compressed rules. 14.02/4.73 ---------------------------------------- 14.02/4.73 14.02/4.73 (11) 14.02/4.73 Obligation: 14.02/4.73 Rules: 14.02/4.73 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 14.02/4.73 14.02/4.73 ---------------------------------------- 14.02/4.73 14.02/4.73 (12) RankingReductionPairProof (EQUIVALENT) 14.02/4.73 Interpretation: 14.02/4.73 [ f_270 ] = -1/3*f_270_1 14.02/4.73 14.02/4.73 The following rules are decreasing: 14.02/4.73 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 14.02/4.73 14.02/4.73 The following rules are bounded: 14.02/4.73 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 14.02/4.73 14.02/4.73 14.02/4.73 ---------------------------------------- 14.02/4.73 14.02/4.73 (13) 14.02/4.73 YES 14.02/4.73 14.02/4.73 ---------------------------------------- 14.02/4.73 14.02/4.73 (14) 14.02/4.73 Obligation: 14.02/4.73 SCC 14.02/4.73 ---------------------------------------- 14.02/4.73 14.02/4.73 (15) SCC2IRS (SOUND) 14.02/4.73 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 14.02/4.73 Generated rules. Obtained 13 rulesP rules: 14.02/4.73 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 14.02/4.73 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 14.02/4.73 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 14.02/4.73 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 14.02/4.73 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 14.02/4.73 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 14.02/4.73 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 14.02/4.73 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 14.02/4.73 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 14.02/4.73 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 14.02/4.73 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 14.02/4.73 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 14.02/4.73 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 14.02/4.73 Combined rules. Obtained 1 rulesP rules: 14.02/4.73 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 14.02/4.73 Filtered unneeded arguments: 14.02/4.73 f_206(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16) -> f_206(x5, x7) 14.02/4.73 Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: 14.02/4.73 f_206(v75:0, v73:0) -> f_206(1 + v75:0, v75:0) :|: v75:0 < 100 && v75:0 > 0 && v73:0 < 99 14.02/4.73 14.02/4.73 ---------------------------------------- 14.02/4.73 14.02/4.73 (16) 14.02/4.73 Obligation: 14.02/4.73 Rules: 14.02/4.73 f_206(v75:0, v73:0) -> f_206(1 + v75:0, v75:0) :|: v75:0 < 100 && v75:0 > 0 && v73:0 < 99 14.02/4.73 14.02/4.73 ---------------------------------------- 14.02/4.73 14.02/4.73 (17) IntTRSCompressionProof (EQUIVALENT) 14.02/4.73 Compressed rules. 14.02/4.73 ---------------------------------------- 14.02/4.73 14.02/4.73 (18) 14.02/4.73 Obligation: 14.02/4.73 Rules: 14.02/4.73 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 14.02/4.73 14.02/4.73 ---------------------------------------- 14.02/4.73 14.02/4.73 (19) RankingReductionPairProof (EQUIVALENT) 14.02/4.73 Interpretation: 14.02/4.73 [ f_206 ] = -1*f_206_1 14.02/4.73 14.02/4.73 The following rules are decreasing: 14.02/4.73 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 14.02/4.73 14.02/4.73 The following rules are bounded: 14.02/4.73 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 14.02/4.73 14.02/4.73 14.02/4.73 ---------------------------------------- 14.02/4.73 14.02/4.73 (20) 14.02/4.73 YES 14.55/4.83 EOF