/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given C Problem could be proven: (0) C Problem (1) CToLLVMProof [EQUIVALENT, 178 ms] (2) LLVM problem (3) LLVMToTerminationGraphProof [EQUIVALENT, 1392 ms] (4) LLVM Symbolic Execution Graph (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] (6) AND (7) LLVM Symbolic Execution SCC (8) SCC2IRS [SOUND, 86 ms] (9) IntTRS (10) IntTRSCompressionProof [EQUIVALENT, 0 ms] (11) IntTRS (12) RankingReductionPairProof [EQUIVALENT, 26 ms] (13) YES (14) LLVM Symbolic Execution SCC (15) SCC2IRS [SOUND, 42 ms] (16) IntTRS (17) IntTRSCompressionProof [EQUIVALENT, 0 ms] (18) IntTRS (19) RankingReductionPairProof [EQUIVALENT, 8 ms] (20) 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: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 0: %1 = alloca i32, align 4 %x = alloca i32, align 4 %y = alloca i32, align 4 store 0, %1 store 0, %x store 0, %y br %2 2: %3 = load %x %4 = icmp sle %3 50 br %4, %5, %8 5: %6 = load %y %7 = add %6 1 store %7, %y br %11 8: %9 = load %y %10 = add %9 -1 store %10, %y br %11 11: %12 = load %y %13 = icmp slt %12 0 br %13, %14, %15 14: br %18 15: %16 = load %x %17 = add %16 1 store %17, %x br %2 18: 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 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 16 rulesP rules: f_305(v237, v238, v239, v240, 0, 50, 51, v246, v245, v244, v247, v248, v249, 3, 1, 4) -> f_307(v237, v238, v239, v240, 0, 50, 51, v246, v245, v244, v247, v248, v249, 3, 1, 4) :|: 0 <= v246 && 1 <= v244 f_307(v237, v238, v239, v240, 0, 50, 51, v246, v245, v244, v247, v248, v249, 3, 1, 4) -> f_309(v237, v238, v239, v240, 0, 50, 51, v246, v245, v244, v247, v248, v249, 3, 1, 4) :|: 0 = 0 f_309(v237, v238, v239, v240, 0, 50, 51, v246, v245, v244, v247, v248, v249, 3, 1, 4) -> f_311(v237, v238, v239, v240, 0, 50, 51, v246, v245, v244, v247, v248, v249, 3, 1, 4) :|: TRUE f_311(v237, v238, v239, v240, 0, 50, 51, v246, v245, v244, v247, v248, v249, 3, 1, 4) -> f_313(v237, v238, v239, v240, 0, 50, 51, v246, v244, v247, v248, v249, 3, 1, 4) :|: 0 = 0 f_313(v237, v238, v239, v240, 0, 50, 51, v246, v244, v247, v248, v249, 3, 1, 4) -> f_314(v237, v238, v239, v240, 0, 50, 51, v246, v253, v244, v247, v248, v249, 3, 1, 4, 52) :|: v253 = 1 + v240 && 52 <= v253 f_314(v237, v238, v239, v240, 0, 50, 51, v246, v253, v244, v247, v248, v249, 3, 1, 4, 52) -> f_315(v237, v238, v239, v240, 0, 50, 51, v246, v253, v244, v247, v248, v249, 3, 1, 4, 52) :|: TRUE f_315(v237, v238, v239, v240, 0, 50, 51, v246, v253, v244, v247, v248, v249, 3, 1, 4, 52) -> f_316(v237, v238, v239, v240, 0, 50, 51, v246, v253, v244, v247, v248, v249, 3, 1, 4, 52) :|: TRUE f_316(v237, v238, v239, v240, 0, 50, 51, v246, v253, v244, v247, v248, v249, 3, 1, 4, 52) -> f_317(v237, v238, v239, v253, 0, 50, 51, v246, v240, v244, v247, v248, v249, 3, 1, 4, 52) :|: 0 = 0 f_317(v237, v238, v239, v253, 0, 50, 51, v246, v240, v244, v247, v248, v249, 3, 1, 4, 52) -> f_318(v237, v238, v239, v253, 0, 50, 51, v246, v240, v244, v247, v248, v249, 3, 1, 4, 52) :|: 0 = 0 f_318(v237, v238, v239, v253, 0, 50, 51, v246, v240, v244, v247, v248, v249, 3, 1, 4, 52) -> f_319(v237, v238, v239, v253, 0, 50, 51, v246, v240, v244, v247, v248, v249, 3, 1, 4, 52) :|: TRUE f_319(v237, v238, v239, v253, 0, 50, 51, v246, v240, v244, v247, v248, v249, 3, 1, 4, 52) -> f_320(v237, v238, v239, v253, 0, 50, 51, v246, v240, v247, v248, v249, 3, 1, 4, 52) :|: 0 = 0 f_320(v237, v238, v239, v253, 0, 50, 51, v246, v240, v247, v248, v249, 3, 1, 4, 52) -> f_321(v237, v238, v239, v253, 0, 50, 51, v246, v240, v261, v247, v248, v249, 3, 1, 4, 52, 49) :|: 1 + v261 = v246 && 0 <= 1 + v261 && v261 <= 49 f_321(v237, v238, v239, v253, 0, 50, 51, v246, v240, v261, v247, v248, v249, 3, 1, 4, 52, 49) -> f_322(v237, v238, v239, v253, 0, 50, 51, v246, v240, v261, v247, v248, v249, 3, 1, 4, 52, 49) :|: TRUE f_322(v237, v238, v239, v253, 0, 50, 51, v246, v240, v261, v247, v248, v249, 3, 1, 4, 52, 49) -> f_323(v237, v238, v239, v253, 0, 50, 51, v246, v240, v261, v247, v248, v249, 3, 1, 4, 52, 49) :|: TRUE f_323(v237, v238, v239, v253, 0, 50, 51, v246, v240, v261, v247, v248, v249, 3, 1, 4, 52, 49) -> f_304(v237, v238, v239, v253, 0, 50, 51, v246, v240, v261, v247, v248, v249, 3, 1, 4) :|: TRUE f_304(v237, v238, v239, v240, 0, 50, 51, v244, v245, v246, v247, v248, v249, 3, 1, 4) -> f_305(v237, v238, v239, v240, 0, 50, 51, v246, v245, v244, v247, v248, v249, 3, 1, 4) :|: 0 = 0 Combined rules. Obtained 1 rulesP rules: f_305(v237:0, v238:0, v239:0, v240:0, 0, 50, 51, 1 + v261:0, v245:0, v244:0, v247:0, v248:0, v249:0, 3, 1, 4) -> f_305(v237:0, v238:0, v239:0, 1 + v240:0, 0, 50, 51, v261:0, v240:0, 1 + v261:0, v247:0, v248:0, v249:0, 3, 1, 4) :|: v244:0 > 0 && v261:0 > -2 && v240:0 > 50 && v261:0 < 50 Filtered unneeded arguments: f_305(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16) -> f_305(x4, x8, x10) Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: f_305(v240:0, sum~cons_1~v261:0, v244:0) -> f_305(1 + v240:0, v261:0, 1 + v261:0) :|: v261:0 > -2 && v244:0 > 0 && v261:0 < 50 && v240:0 > 50 && sum~cons_1~v261:0 = 1 + v261:0 ---------------------------------------- (9) Obligation: Rules: f_305(v240:0, sum~cons_1~v261:0, v244:0) -> f_305(1 + v240:0, v261:0, 1 + v261:0) :|: v261:0 > -2 && v244:0 > 0 && v261:0 < 50 && v240:0 > 50 && sum~cons_1~v261:0 = 1 + v261:0 ---------------------------------------- (10) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (11) Obligation: Rules: f_305(v240:0:0, sum~cons_1~v261:0:0, v244:0:0) -> f_305(1 + v240:0:0, v261:0:0, 1 + v261:0:0) :|: v261:0:0 < 50 && v240:0:0 > 50 && v244:0:0 > 0 && v261:0:0 > -2 && sum~cons_1~v261:0:0 = 1 + v261:0:0 ---------------------------------------- (12) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f_305 ] = f_305_2 The following rules are decreasing: f_305(v240:0:0, sum~cons_1~v261:0:0, v244:0:0) -> f_305(1 + v240:0:0, v261:0:0, 1 + v261:0:0) :|: v261:0:0 < 50 && v240:0:0 > 50 && v244:0:0 > 0 && v261:0:0 > -2 && sum~cons_1~v261:0:0 = 1 + v261:0:0 The following rules are bounded: f_305(v240:0:0, sum~cons_1~v261:0:0, v244:0:0) -> f_305(1 + v240:0:0, v261:0:0, 1 + v261:0:0) :|: v261:0:0 < 50 && v240:0:0 > 50 && v244:0:0 > 0 && v261:0:0 > -2 && sum~cons_1~v261:0:0 = 1 + v261:0:0 ---------------------------------------- (13) YES ---------------------------------------- (14) Obligation: SCC ---------------------------------------- (15) SCC2IRS (SOUND) Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: Generated rules. Obtained 16 rulesP rules: f_208(v71, v72, v73, v76, 1, v74, 0, v78, v79, v80, 3, 50, 51, 4) -> f_209(v71, v72, v73, v76, 1, v74, 0, v78, v79, v80, 3, 49, 50, 4) :|: v76 <= 50 && v74 <= 49 f_209(v71, v72, v73, v76, 1, v74, 0, v78, v79, v80, 3, 49, 50, 4) -> f_211(v71, v72, v73, v76, 1, v74, 0, v78, v79, v80, 3, 49, 50, 4) :|: 0 = 0 f_211(v71, v72, v73, v76, 1, v74, 0, v78, v79, v80, 3, 49, 50, 4) -> f_213(v71, v72, v73, v76, 1, v74, 0, v78, v79, v80, 3, 49, 50, 4) :|: TRUE f_213(v71, v72, v73, v76, 1, v74, 0, v78, v79, v80, 3, 49, 50, 4) -> f_215(v71, v72, v73, v76, 1, 0, v74, v78, v79, v80, 3, 49, 50, 4) :|: 0 = 0 f_215(v71, v72, v73, v76, 1, 0, v74, v78, v79, v80, 3, 49, 50, 4) -> f_217(v71, v72, v73, v76, 1, v81, 0, v74, v78, v79, v80, 3, 49, 50, 4, 2, 51) :|: v81 = 1 + v76 && 2 <= v81 && v81 <= 51 f_217(v71, v72, v73, v76, 1, v81, 0, v74, v78, v79, v80, 3, 49, 50, 4, 2, 51) -> f_219(v71, v72, v73, v76, 1, v81, 0, v74, v78, v79, v80, 3, 49, 50, 4, 2, 51) :|: TRUE f_219(v71, v72, v73, v76, 1, v81, 0, v74, v78, v79, v80, 3, 49, 50, 4, 2, 51) -> f_221(v71, v72, v73, v76, 1, v81, 0, v74, v78, v79, v80, 3, 49, 50, 4, 2, 51) :|: TRUE f_221(v71, v72, v73, v76, 1, v81, 0, v74, v78, v79, v80, 3, 49, 50, 4, 2, 51) -> f_223(v71, v72, v73, v76, 1, v81, 0, v74, v78, v79, v80, 3, 49, 50, 4, 2, 51) :|: 0 = 0 f_223(v71, v72, v73, v76, 1, v81, 0, v74, v78, v79, v80, 3, 49, 50, 4, 2, 51) -> f_225(v71, v72, v73, v76, 1, v81, 0, v74, v78, v79, v80, 3, 49, 50, 4, 2, 51) :|: 0 = 0 f_225(v71, v72, v73, v76, 1, v81, 0, v74, v78, v79, v80, 3, 49, 50, 4, 2, 51) -> f_227(v71, v72, v73, v76, 1, v81, 0, v74, v78, v79, v80, 3, 49, 50, 4, 2, 51) :|: TRUE f_227(v71, v72, v73, v76, 1, v81, 0, v74, v78, v79, v80, 3, 49, 50, 4, 2, 51) -> f_229(v71, v72, v73, v76, 1, v81, 0, v78, v79, v80, 3, 50, 4, 2, 51) :|: 0 = 0 f_229(v71, v72, v73, v76, 1, v81, 0, v78, v79, v80, 3, 50, 4, 2, 51) -> f_231(v71, v72, v73, v76, 1, v81, 0, v78, v79, v80, 3, 50, 4, 2, 51) :|: v81 = 1 + v76 f_231(v71, v72, v73, v76, 1, v81, 0, v78, v79, v80, 3, 50, 4, 2, 51) -> f_233(v71, v72, v73, v76, 1, v81, 0, v78, v79, v80, 3, 50, 4, 2, 51) :|: TRUE f_233(v71, v72, v73, v76, 1, v81, 0, v78, v79, v80, 3, 50, 4, 2, 51) -> f_235(v71, v72, v73, v76, 1, v81, 0, v78, v79, v80, 3, 50, 4, 2, 51) :|: TRUE f_235(v71, v72, v73, v76, 1, v81, 0, v78, v79, v80, 3, 50, 4, 2, 51) -> f_207(v71, v72, v73, v76, 1, v81, 0, v78, v79, v80, 3, 50, 51, 4) :|: TRUE f_207(v71, v72, v73, v74, 1, v76, 0, v78, v79, v80, 3, 50, 51, 4) -> f_208(v71, v72, v73, v76, 1, v74, 0, v78, v79, v80, 3, 50, 51, 4) :|: 0 = 0 Combined rules. Obtained 1 rulesP rules: f_208(v71:0, v72:0, v73:0, v76:0, 1, v74:0, 0, v78:0, v79:0, v80:0, 3, 50, 51, 4) -> f_208(v71:0, v72:0, v73:0, 1 + v76:0, 1, v76:0, 0, v78:0, v79:0, v80:0, 3, 50, 51, 4) :|: v74:0 < 50 && v76:0 < 51 && v76:0 > 0 Filtered unneeded arguments: f_208(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> f_208(x4, x6) Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: f_208(v76:0, v74:0) -> f_208(1 + v76:0, v76:0) :|: v76:0 < 51 && v76:0 > 0 && v74:0 < 50 ---------------------------------------- (16) Obligation: Rules: f_208(v76:0, v74:0) -> f_208(1 + v76:0, v76:0) :|: v76:0 < 51 && v76:0 > 0 && v74:0 < 50 ---------------------------------------- (17) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (18) Obligation: Rules: f_208(v76:0:0, v74:0:0) -> f_208(1 + v76:0:0, v76:0:0) :|: v76:0:0 < 51 && v76:0:0 > 0 && v74:0:0 < 50 ---------------------------------------- (19) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f_208 ] = -1*f_208_1 The following rules are decreasing: f_208(v76:0:0, v74:0:0) -> f_208(1 + v76:0:0, v76:0:0) :|: v76:0:0 < 51 && v76:0:0 > 0 && v74:0:0 < 50 The following rules are bounded: f_208(v76:0:0, v74:0:0) -> f_208(1 + v76:0:0, v76:0:0) :|: v76:0:0 < 51 && v76:0:0 > 0 && v74:0:0 < 50 ---------------------------------------- (20) YES