17.48/5.54 YES 17.48/5.56 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 17.48/5.56 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 17.48/5.56 17.48/5.56 17.48/5.56 Termination of the given C Problem could be proven: 17.48/5.56 17.48/5.56 (0) C Problem 17.48/5.56 (1) CToLLVMProof [EQUIVALENT, 170 ms] 17.48/5.56 (2) LLVM problem 17.48/5.56 (3) LLVMToTerminationGraphProof [EQUIVALENT, 1095 ms] 17.48/5.56 (4) LLVM Symbolic Execution Graph 17.48/5.56 (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] 17.48/5.56 (6) AND 17.48/5.56 (7) LLVM Symbolic Execution SCC 17.48/5.56 (8) SCC2IRS [SOUND, 89 ms] 17.48/5.56 (9) IntTRS 17.48/5.56 (10) IRS2T2 [EQUIVALENT, 0 ms] 17.48/5.56 (11) T2IntSys 17.48/5.56 (12) T2 [EQUIVALENT, 943 ms] 17.48/5.56 (13) YES 17.48/5.56 (14) LLVM Symbolic Execution SCC 17.48/5.56 (15) SCC2IRS [SOUND, 81 ms] 17.48/5.56 (16) IntTRS 17.48/5.56 (17) IntTRSCompressionProof [EQUIVALENT, 0 ms] 17.48/5.56 (18) IntTRS 17.48/5.56 (19) PolynomialOrderProcessor [EQUIVALENT, 14 ms] 17.48/5.56 (20) YES 17.48/5.56 17.48/5.56 17.48/5.56 ---------------------------------------- 17.48/5.56 17.48/5.56 (0) 17.48/5.56 Obligation: 17.48/5.56 c file /export/starexec/sandbox/benchmark/theBenchmark.c 17.48/5.56 ---------------------------------------- 17.48/5.56 17.48/5.56 (1) CToLLVMProof (EQUIVALENT) 17.48/5.56 Compiled c-file /export/starexec/sandbox/benchmark/theBenchmark.c to LLVM. 17.48/5.56 ---------------------------------------- 17.48/5.56 17.48/5.56 (2) 17.48/5.56 Obligation: 17.48/5.56 LLVM Problem 17.48/5.56 17.48/5.56 Aliases: 17.48/5.56 17.48/5.56 Data layout: 17.48/5.56 17.48/5.56 "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" 17.48/5.56 17.48/5.56 Machine: 17.48/5.56 17.48/5.56 "x86_64-pc-linux-gnu" 17.48/5.56 17.48/5.56 Type definitions: 17.48/5.56 17.48/5.56 Global variables: 17.48/5.56 17.48/5.56 Function declarations and definitions: 17.48/5.56 17.48/5.56 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 17.48/5.56 0: 17.48/5.56 %1 = alloca i32, align 4 17.48/5.56 %x1 = alloca *i32, align 8 17.48/5.56 %x2 = alloca *i32, align 8 17.48/5.56 store 0, %1 17.48/5.56 %2 = alloca i8, numElementsLit: 4 17.48/5.56 %3 = bitcast *i8 %2 to *i32 17.48/5.56 store %3, %x1 17.48/5.56 %4 = alloca i8, numElementsLit: 4 17.48/5.56 %5 = bitcast *i8 %4 to *i32 17.48/5.56 store %5, %x2 17.48/5.56 br %6 17.48/5.56 6: 17.48/5.56 %7 = load %x1 17.48/5.56 %8 = load %7 17.48/5.56 %9 = icmp sle %8 10 17.48/5.56 br %9, %10, %26 17.48/5.56 10: 17.48/5.56 %11 = load %x2 17.48/5.56 store 10, %11 17.48/5.56 br %12 17.48/5.56 12: 17.48/5.56 %13 = load %x2 17.48/5.56 %14 = load %13 17.48/5.56 %15 = icmp sgt %14 1 17.48/5.56 br %15, %16, %21 17.48/5.56 16: 17.48/5.56 %17 = load %x2 17.48/5.56 %18 = load %17 17.48/5.56 %19 = sub %18 1 17.48/5.56 %20 = load %x2 17.48/5.56 store %19, %20 17.48/5.56 br %12 17.48/5.56 21: 17.48/5.56 %22 = load %x1 17.48/5.56 %23 = load %22 17.48/5.56 %24 = add %23 1 17.48/5.56 %25 = load %x1 17.48/5.56 store %24, %25 17.48/5.56 br %6 17.48/5.56 26: 17.48/5.56 %27 = load %1 17.48/5.56 ret %27 17.48/5.56 17.48/5.56 17.48/5.56 Analyze Termination of all function calls matching the pattern: 17.48/5.56 main() 17.48/5.56 ---------------------------------------- 17.48/5.56 17.48/5.56 (3) LLVMToTerminationGraphProof (EQUIVALENT) 17.48/5.56 Constructed symbolic execution graph for LLVM program and proved memory safety. 17.48/5.56 ---------------------------------------- 17.48/5.56 17.48/5.56 (4) 17.48/5.56 Obligation: 17.48/5.56 SE Graph 17.48/5.56 ---------------------------------------- 17.48/5.56 17.48/5.56 (5) SymbolicExecutionGraphToSCCProof (SOUND) 17.48/5.56 Splitted symbolic execution graph to 2 SCCs. 17.48/5.56 ---------------------------------------- 17.48/5.56 17.48/5.56 (6) 17.48/5.56 Complex Obligation (AND) 17.48/5.56 17.48/5.56 ---------------------------------------- 17.48/5.56 17.48/5.56 (7) 17.48/5.56 Obligation: 17.48/5.56 SCC 17.48/5.56 ---------------------------------------- 17.48/5.56 17.48/5.56 (8) SCC2IRS (SOUND) 17.48/5.56 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 17.48/5.56 Generated rules. Obtained 37 rulesP rules: 17.48/5.56 f_197(v49, v50, v51, v52, v53, v54, 1, 0, 2, v65, v58, v59, v60, v61, v62, 3, 7, 10, 4, 8, 11) -> f_198(v49, v50, v51, v52, v53, v65, 1, 0, 2, v54, v58, v59, v60, v61, v62, 3, 7, 10, 4, 8, 11) :|: 0 = 0 17.48/5.56 f_198(v49, v50, v51, v52, v53, v65, 1, 0, 2, v54, v58, v59, v60, v61, v62, 3, 7, 10, 4, 8, 11) -> f_199(v49, v50, v51, v52, v53, v65, 1, 0, 2, v54, v58, v59, v60, v61, v62, 3, 7, 9, 4, 8, 10) :|: v65 <= 10 && v54 <= 9 17.48/5.56 f_199(v49, v50, v51, v52, v53, v65, 1, 0, 2, v54, v58, v59, v60, v61, v62, 3, 7, 9, 4, 8, 10) -> f_201(v49, v50, v51, v52, v53, v65, 1, 0, 2, v54, v58, v59, v60, v61, v62, 3, 7, 9, 4, 8, 10) :|: 0 = 0 17.48/5.56 f_201(v49, v50, v51, v52, v53, v65, 1, 0, 2, v54, v58, v59, v60, v61, v62, 3, 7, 9, 4, 8, 10) -> f_203(v49, v50, v51, v52, v53, v65, 1, 0, 2, v54, v58, v59, v60, v61, v62, 3, 7, 9, 4, 8, 10) :|: TRUE 17.48/5.56 f_203(v49, v50, v51, v52, v53, v65, 1, 0, 2, v54, v58, v59, v60, v61, v62, 3, 7, 9, 4, 8, 10) -> f_205(v49, v50, v51, v52, v53, v65, 1, 0, 2, v54, v58, v59, v60, v61, v62, 3, 7, 9, 4, 8, 10) :|: 0 = 0 17.48/5.56 f_205(v49, v50, v51, v52, v53, v65, 1, 0, 2, v54, v58, v59, v60, v61, v62, 3, 7, 9, 4, 8, 10) -> f_207(v49, v50, v51, v52, v53, v65, 1, 0, 2, v54, v58, v59, v60, v61, v62, 10, 3, 7, 9, 4, 8) :|: TRUE 17.48/5.56 f_207(v49, v50, v51, v52, v53, v65, 1, 0, 2, v54, v58, v59, v60, v61, v62, 10, 3, 7, 9, 4, 8) -> f_208(v49, v50, v51, v52, v53, v65, 1, 0, 2, v54, v58, v59, v60, v61, v62, 10, 3, 7, 9, 4, 8) :|: TRUE 17.48/5.56 f_208(v49, v50, v51, v52, v53, v65, 1, 0, 2, v54, v58, v59, v60, v61, v62, 10, 3, 7, 9, 4, 8) -> f_209(v49, v50, v51, v52, v53, v65, 1, 0, 2, v54, v58, v59, v60, v61, v62, 10, 3, 7, 9, 4, 8) :|: 0 = 0 17.48/5.56 f_209(v49, v50, v51, v52, v53, v65, 1, 0, 2, v54, v58, v59, v60, v61, v62, 10, 3, 7, 9, 4, 8) -> f_210(v49, v50, v51, v52, v53, v65, 1, 10, 0, 2, v54, v58, v59, v60, v61, v62, 3, 7, 9, 4, 8) :|: 0 = 0 17.48/5.56 f_210(v49, v50, v51, v52, v53, v65, 1, 10, 0, 2, v54, v58, v59, v60, v61, v62, 3, 7, 9, 4, 8) -> f_211(v49, v50, v51, v52, v53, v65, 1, 10, 2, v54, v58, v59, v60, v61, v62, 0, 3, 7, 9, 4, 8) :|: 0 = 0 17.48/5.56 f_211(v49, v50, v51, v52, v53, v65, 1, 10, 2, v54, v58, v59, v60, v61, v62, 0, 3, 7, 9, 4, 8) -> f_212(v49, v50, v51, v52, v53, v65, 1, 10, 2, v54, v58, v59, v60, v61, v62, 0, 3, 7, 9, 4, 8) :|: TRUE 17.48/5.56 f_212(v49, v50, v51, v52, v53, v65, 1, 10, 2, v54, v58, v59, v60, v61, v62, 0, 3, 7, 9, 4, 8) -> f_223(v49, v50, v51, v52, v53, v65, 1, 10, 2, 1, v54, v58, v59, v60, v61, v62, 0, 3, 7, 10, 9, 2, 4, 8) :|: TRUE 17.48/5.56 f_223(v127, v128, v129, v130, v131, v132, 1, v134, v135, v136, v137, v138, v139, v140, v141, v142, 0, 3, 7, 10, 9, 2, 4, 8) -> f_234(v127, v128, v129, v130, v131, v132, 1, v134, v135, v136, v137, v138, v139, v140, v141, v142, 0, 3, 7, 10, 8, 2, 9, 4) :|: TRUE 17.48/5.56 f_234(v171, v172, v173, v174, v175, v176, 1, v178, v179, v180, v181, v182, v183, v184, v185, v186, 0, 3, 7, 10, 8, 2, 9, 4) -> f_245(v171, v172, v173, v174, v175, v176, 1, v178, v179, v180, v181, v182, v183, v184, v185, v186, 0, 3, 7, 10, 2, 9, 4, 8) :|: TRUE 17.48/5.56 f_245(v215, v216, v217, v218, v219, v220, 1, v222, v223, v224, v225, v226, v227, v228, v229, v230, 0, 3, 7, 10, 2, 9, 4, 8) -> f_246(v215, v216, v217, v218, v219, v220, 1, v222, v223, v224, v225, v226, v227, v228, v229, v230, 0, 3, 7, 10, 2, 9, 4, 8) :|: 0 = 0 17.48/5.56 f_246(v215, v216, v217, v218, v219, v220, 1, v222, v223, v224, v225, v226, v227, v228, v229, v230, 0, 3, 7, 10, 2, 9, 4, 8) -> f_247(v215, v216, v217, v218, v219, v220, 1, v222, v224, v225, v226, v227, v228, v229, v230, 0, 3, 7, 10, 2, 9, 4, 8) :|: 0 = 0 17.48/5.56 f_247(v215, v216, v217, v218, v219, v220, 1, v222, v224, v225, v226, v227, v228, v229, v230, 0, 3, 7, 10, 2, 9, 4, 8) -> f_248(v215, v216, v217, v218, v219, v220, 1, v222, v232, v225, v226, v227, v228, v229, v230, 0, 3, 7, 10, 2, 9, 4, 8) :|: 1 + v232 = v222 && 1 <= v232 && v232 <= 9 17.48/5.56 f_248(v215, v216, v217, v218, v219, v220, 1, v222, v232, v225, v226, v227, v228, v229, v230, 0, 3, 7, 10, 2, 9, 4, 8) -> f_249(v215, v216, v217, v218, v219, v220, 1, v222, v232, v225, v226, v227, v228, v229, v230, 0, 3, 7, 10, 2, 9, 4, 8) :|: 0 = 0 17.48/5.56 f_249(v215, v216, v217, v218, v219, v220, 1, v222, v232, v225, v226, v227, v228, v229, v230, 0, 3, 7, 10, 2, 9, 4, 8) -> f_250(v215, v216, v217, v218, v219, v220, 1, v222, v232, v225, v226, v227, v228, v229, v230, 0, 3, 7, 10, 2, 9, 4, 8) :|: TRUE 17.48/5.56 f_250(v215, v216, v217, v218, v219, v220, 1, v222, v232, v225, v226, v227, v228, v229, v230, 0, 3, 7, 10, 2, 9, 4, 8) -> f_251(v215, v216, v217, v218, v219, v220, 1, v222, v232, v225, v226, v227, v228, v229, v230, 0, 3, 7, 10, 2, 9, 4, 8) :|: TRUE 17.48/5.56 f_251(v215, v216, v217, v218, v219, v220, 1, v222, v232, v225, v226, v227, v228, v229, v230, 0, 3, 7, 10, 2, 9, 4, 8) -> f_252(v215, v216, v217, v218, v219, v220, 1, v222, v232, v225, v226, v227, v228, v229, v230, 0, 3, 7, 10, 2, 9, 4, 8) :|: 0 = 0 17.48/5.56 f_252(v215, v216, v217, v218, v219, v220, 1, v222, v232, v225, v226, v227, v228, v229, v230, 0, 3, 7, 10, 2, 9, 4, 8) -> f_253(v215, v216, v217, v218, v219, v220, 1, v232, v222, v225, v226, v227, v228, v229, v230, 0, 3, 7, 10, 2, 9, 4, 8) :|: 0 = 0 17.48/5.56 f_253(v215, v216, v217, v218, v219, v220, 1, v232, v222, v225, v226, v227, v228, v229, v230, 0, 3, 7, 10, 2, 9, 4, 8) -> f_254(v215, v216, v217, v218, v219, v220, 1, v232, v222, v225, v226, v227, v228, v229, v230, 0, 3, 7, 10, 9, 4, 8, 2) :|: 1 < v232 && 3 <= v222 17.48/5.56 f_253(v215, v216, v217, v218, v219, v220, 1, v232, v222, v225, v226, v227, v228, v229, v230, 0, 3, 7, 10, 2, 9, 4, 8) -> f_255(v215, v216, v217, v218, v219, v220, 1, 2, v225, v226, v227, v228, v229, v230, 0, 3, 7, 10, 9, 4, 8) :|: v232 <= 1 && v222 = 2 && v232 = 1 && 0 = 0 17.48/5.56 f_254(v215, v216, v217, v218, v219, v220, 1, v232, v222, v225, v226, v227, v228, v229, v230, 0, 3, 7, 10, 9, 4, 8, 2) -> f_256(v215, v216, v217, v218, v219, v220, 1, v232, v222, v225, v226, v227, v228, v229, v230, 0, 3, 7, 10, 9, 4, 8, 2) :|: 0 = 0 17.48/5.56 f_256(v215, v216, v217, v218, v219, v220, 1, v232, v222, v225, v226, v227, v228, v229, v230, 0, 3, 7, 10, 9, 4, 8, 2) -> f_258(v215, v216, v217, v218, v219, v220, 1, v232, v222, v225, v226, v227, v228, v229, v230, 0, 3, 7, 10, 9, 4, 8, 2) :|: TRUE 17.48/5.56 f_258(v215, v216, v217, v218, v219, v220, 1, v232, v222, v225, v226, v227, v228, v229, v230, 0, 3, 7, 10, 9, 4, 8, 2) -> f_245(v215, v216, v217, v218, v219, v220, 1, v232, v222, v232, v225, v226, v227, v228, v229, v230, 0, 3, 7, 10, 2, 9, 4, 8) :|: TRUE 17.48/5.56 f_255(v215, v216, v217, v218, v219, v220, 1, 2, v225, v226, v227, v228, v229, v230, 0, 3, 7, 10, 9, 4, 8) -> f_257(v215, v216, v217, v218, v219, v220, 1, 0, 2, v225, v226, v227, v228, v229, v230, 3, 7, 10, 9, 4, 8) :|: 0 = 0 17.48/5.56 f_257(v215, v216, v217, v218, v219, v220, 1, 0, 2, v225, v226, v227, v228, v229, v230, 3, 7, 10, 9, 4, 8) -> f_259(v215, v216, v217, v218, v219, v220, 1, 0, 2, v225, v226, v227, v228, v229, v230, 3, 7, 10, 9, 4, 8) :|: TRUE 17.48/5.56 f_259(v215, v216, v217, v218, v219, v220, 1, 0, 2, v225, v226, v227, v228, v229, v230, 3, 7, 10, 9, 4, 8) -> f_260(v215, v216, v217, v218, v219, v220, 1, 0, 2, v225, v226, v227, v228, v229, v230, 3, 7, 10, 9, 4, 8) :|: 0 = 0 17.48/5.56 f_260(v215, v216, v217, v218, v219, v220, 1, 0, 2, v225, v226, v227, v228, v229, v230, 3, 7, 10, 9, 4, 8) -> f_261(v215, v216, v217, v218, v219, v220, 1, 0, 2, v226, v227, v228, v229, v230, 3, 7, 10, 4, 8) :|: 0 = 0 17.48/5.56 f_261(v215, v216, v217, v218, v219, v220, 1, 0, 2, v226, v227, v228, v229, v230, 3, 7, 10, 4, 8) -> f_262(v215, v216, v217, v218, v219, v220, 1, 0, 2, v276, v226, v227, v228, v229, v230, 3, 7, 10, 4, 8, 11) :|: v276 = 1 + v220 && v276 <= 11 17.48/5.56 f_262(v215, v216, v217, v218, v219, v220, 1, 0, 2, v276, v226, v227, v228, v229, v230, 3, 7, 10, 4, 8, 11) -> f_263(v215, v216, v217, v218, v219, v220, 1, 0, 2, v276, v226, v227, v228, v229, v230, 3, 7, 10, 4, 8, 11) :|: 0 = 0 17.48/5.56 f_263(v215, v216, v217, v218, v219, v220, 1, 0, 2, v276, v226, v227, v228, v229, v230, 3, 7, 10, 4, 8, 11) -> f_264(v215, v216, v217, v218, v219, v220, 1, 0, 2, v276, v226, v227, v228, v229, v230, 3, 7, 10, 4, 8, 11) :|: TRUE 17.48/5.56 f_264(v215, v216, v217, v218, v219, v220, 1, 0, 2, v276, v226, v227, v228, v229, v230, 3, 7, 10, 4, 8, 11) -> f_265(v215, v216, v217, v218, v219, v220, 1, 0, 2, v276, v226, v227, v228, v229, v230, 3, 7, 10, 4, 8, 11) :|: TRUE 17.48/5.56 f_265(v215, v216, v217, v218, v219, v220, 1, 0, 2, v276, v226, v227, v228, v229, v230, 3, 7, 10, 4, 8, 11) -> f_196(v215, v216, v217, v218, v219, v220, 1, 0, 2, v276, v226, v227, v228, v229, v230, 3, 7, 10, 4, 8, 11) :|: TRUE 17.48/5.56 f_196(v49, v50, v51, v52, v53, v54, 1, 0, 2, v65, v58, v59, v60, v61, v62, 3, 7, 10, 4, 8, 11) -> f_197(v49, v50, v51, v52, v53, v54, 1, 0, 2, v65, v58, v59, v60, v61, v62, 3, 7, 10, 4, 8, 11) :|: 0 = 0 17.48/5.56 Combined rules. Obtained 2 rulesP rules: 17.48/5.56 f_253(v215:0, v216:0, v217:0, v218:0, v219:0, v220:0, 1, 1, 2, v225:0, v226:0, v227:0, v228:0, v229:0, v230:0, 0, 3, 7, 10, 2, 9, 4, 8) -> f_253(v215:0, v216:0, v217:0, v218:0, v219:0, 1 + v220:0, 1, 9, 10, v220:0, v226:0, v227:0, v228:0, v229:0, v230:0, 0, 3, 7, 10, 2, 9, 4, 8) :|: v220:0 < 10 && v220:0 < 11 17.48/5.56 f_253(v215:0, v216:0, v217:0, v218:0, v219:0, v220:0, 1, 1 + v232:1, v222:0, v225:0, v226:0, v227:0, v228:0, v229:0, v230:0, 0, 3, 7, 10, 2, 9, 4, 8) -> f_253(v215:0, v216:0, v217:0, v218:0, v219:0, v220:0, 1, v232:1, 1 + v232:1, v225:0, v226:0, v227:0, v228:0, v229:0, v230:0, 0, 3, 7, 10, 2, 9, 4, 8) :|: v232:1 > 0 && v232:1 < 10 && v222:0 > 2 17.48/5.56 Filtered unneeded arguments: 17.48/5.56 f_253(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23) -> f_253(x6, x8, x9) 17.48/5.56 Removed division, modulo operations, cleaned up constraints. Obtained 2 rules.P rules: 17.48/5.56 f_253(v220:0, cons_1, cons_2) -> f_253(1 + v220:0, 9, 10) :|: v220:0 < 10 && v220:0 < 11 && cons_1 = 1 && cons_2 = 2 17.48/5.56 f_253(v220:0, sum~cons_1~v232:1, v222:0) -> f_253(v220:0, v232:1, 1 + v232:1) :|: v232:1 < 10 && v222:0 > 2 && v232:1 > 0 && sum~cons_1~v232:1 = 1 + v232:1 17.48/5.56 17.48/5.56 ---------------------------------------- 17.48/5.56 17.48/5.56 (9) 17.48/5.56 Obligation: 17.48/5.56 Rules: 17.48/5.56 f_253(v220:0, cons_1, cons_2) -> f_253(1 + v220:0, 9, 10) :|: v220:0 < 10 && v220:0 < 11 && cons_1 = 1 && cons_2 = 2 17.48/5.56 f_253(x, x1, x2) -> f_253(x, x3, 1 + x3) :|: x3 < 10 && x2 > 2 && x3 > 0 && x1 = 1 + x3 17.48/5.56 17.48/5.56 ---------------------------------------- 17.48/5.56 17.48/5.56 (10) IRS2T2 (EQUIVALENT) 17.48/5.56 Transformed input IRS into an integer transition system.Used the following mapping from defined symbols to location IDs: 17.48/5.56 17.48/5.56 (f_253_3,1) 17.48/5.56 17.48/5.56 ---------------------------------------- 17.48/5.56 17.48/5.56 (11) 17.48/5.56 Obligation: 17.48/5.56 START: 0; 17.48/5.56 17.48/5.56 FROM: 0; 17.48/5.56 TO: 1; 17.48/5.56 17.48/5.56 FROM: 1; 17.48/5.56 oldX0 := x0; 17.48/5.56 oldX1 := x1; 17.48/5.56 oldX2 := x2; 17.48/5.56 assume(oldX0 < 10 && oldX0 < 11 && oldX1 = 1 && oldX2 = 2); 17.48/5.56 x0 := 1 + oldX0; 17.48/5.56 x1 := 9; 17.48/5.56 x2 := 10; 17.48/5.56 TO: 1; 17.48/5.56 17.48/5.56 FROM: 1; 17.48/5.56 oldX0 := x0; 17.48/5.56 oldX1 := x1; 17.48/5.56 oldX2 := x2; 17.48/5.56 oldX3 := oldX1 - 1; 17.48/5.56 assume(oldX3 < 10 && oldX2 > 2 && oldX3 > 0 && oldX1 = 1 + oldX3); 17.48/5.56 x0 := oldX0; 17.48/5.56 x1 := oldX1 - 1; 17.48/5.56 x2 := 1 + oldX3; 17.48/5.56 TO: 1; 17.48/5.56 17.48/5.56 17.48/5.56 ---------------------------------------- 17.48/5.56 17.48/5.56 (12) T2 (EQUIVALENT) 17.48/5.56 Initially, performed program simplifications using lexicographic rank functions: 17.48/5.56 * Removed transitions 1, 4, 5 using the following rank functions: 17.48/5.56 - Rank function 1: 17.48/5.56 RF for loc. 5: 1-18*x0+2*x1 17.48/5.56 RF for loc. 6: -18*x0+2*x1 17.48/5.56 Bound for (chained) transitions 4: -178 17.48/5.56 - Rank function 2: 17.48/5.56 RF for loc. 5: 1+2*x1 17.48/5.56 RF for loc. 6: 2*x1 17.48/5.56 Bound for (chained) transitions 5: 4 17.48/5.56 - Rank function 3: 17.48/5.56 RF for loc. 5: 0 17.48/5.56 RF for loc. 6: -1 17.48/5.56 Bound for (chained) transitions 1: 0 17.48/5.57 17.48/5.57 ---------------------------------------- 17.48/5.57 17.48/5.57 (13) 17.48/5.57 YES 17.48/5.57 17.48/5.57 ---------------------------------------- 17.48/5.57 17.48/5.57 (14) 17.48/5.57 Obligation: 17.48/5.57 SCC 17.48/5.57 ---------------------------------------- 17.48/5.57 17.48/5.57 (15) SCC2IRS (SOUND) 17.48/5.57 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 17.48/5.57 Generated rules. Obtained 12 rulesP rules: 17.48/5.57 f_177(v49, v50, v51, v52, v53, v54, 1, v56, v57, v58, v59, v60, v61, v62, 0, 3, 7, 10, 2, 9, 4, 8) -> f_178(v49, v50, v51, v52, v53, v54, 1, v57, v56, v58, v59, v60, v61, v62, 0, 3, 7, 10, 2, 9, 4, 8) :|: 0 = 0 17.48/5.57 f_178(v49, v50, v51, v52, v53, v54, 1, v57, v56, v58, v59, v60, v61, v62, 0, 3, 7, 10, 2, 9, 4, 8) -> f_179(v49, v50, v51, v52, v53, v54, 1, v57, v56, v58, v59, v60, v61, v62, 0, 3, 7, 10, 2, 9, 4, 8) :|: 1 < v57 && 3 <= v56 17.48/5.57 f_179(v49, v50, v51, v52, v53, v54, 1, v57, v56, v58, v59, v60, v61, v62, 0, 3, 7, 10, 2, 9, 4, 8) -> f_181(v49, v50, v51, v52, v53, v54, 1, v57, v56, v58, v59, v60, v61, v62, 0, 3, 7, 10, 2, 9, 4, 8) :|: 0 = 0 17.48/5.57 f_181(v49, v50, v51, v52, v53, v54, 1, v57, v56, v58, v59, v60, v61, v62, 0, 3, 7, 10, 2, 9, 4, 8) -> f_183(v49, v50, v51, v52, v53, v54, 1, v57, v56, v58, v59, v60, v61, v62, 0, 3, 7, 10, 2, 9, 4, 8) :|: TRUE 17.48/5.57 f_183(v49, v50, v51, v52, v53, v54, 1, v57, v56, v58, v59, v60, v61, v62, 0, 3, 7, 10, 2, 9, 4, 8) -> f_185(v49, v50, v51, v52, v53, v54, 1, v57, v56, v58, v59, v60, v61, v62, 0, 3, 7, 10, 2, 9, 4, 8) :|: 0 = 0 17.48/5.57 f_185(v49, v50, v51, v52, v53, v54, 1, v57, v56, v58, v59, v60, v61, v62, 0, 3, 7, 10, 2, 9, 4, 8) -> f_187(v49, v50, v51, v52, v53, v54, 1, v57, v58, v59, v60, v61, v62, 0, 3, 7, 10, 2, 9, 4, 8) :|: 0 = 0 17.48/5.57 f_187(v49, v50, v51, v52, v53, v54, 1, v57, v58, v59, v60, v61, v62, 0, 3, 7, 10, 2, 9, 4, 8) -> f_189(v49, v50, v51, v52, v53, v54, 1, v57, v64, v58, v59, v60, v61, v62, 0, 3, 7, 10, 2, 9, 4, 8) :|: 1 + v64 = v57 && 1 <= v64 && v64 <= 8 17.48/5.57 f_189(v49, v50, v51, v52, v53, v54, 1, v57, v64, v58, v59, v60, v61, v62, 0, 3, 7, 10, 2, 9, 4, 8) -> f_191(v49, v50, v51, v52, v53, v54, 1, v57, v64, v58, v59, v60, v61, v62, 0, 3, 7, 10, 2, 9, 4, 8) :|: 0 = 0 17.48/5.57 f_191(v49, v50, v51, v52, v53, v54, 1, v57, v64, v58, v59, v60, v61, v62, 0, 3, 7, 10, 2, 9, 4, 8) -> f_193(v49, v50, v51, v52, v53, v54, 1, v57, v64, v58, v59, v60, v61, v62, 0, 3, 7, 10, 2, 9, 4, 8) :|: TRUE 17.48/5.57 f_193(v49, v50, v51, v52, v53, v54, 1, v57, v64, v58, v59, v60, v61, v62, 0, 3, 7, 10, 2, 9, 4, 8) -> f_195(v49, v50, v51, v52, v53, v54, 1, v57, v64, v58, v59, v60, v61, v62, 0, 3, 7, 10, 2, 9, 4, 8) :|: TRUE 17.48/5.57 f_195(v49, v50, v51, v52, v53, v54, 1, v57, v64, v58, v59, v60, v61, v62, 0, 3, 7, 10, 2, 9, 4, 8) -> f_176(v49, v50, v51, v52, v53, v54, 1, v57, v64, v58, v59, v60, v61, v62, 0, 3, 7, 10, 2, 9, 4, 8) :|: TRUE 17.48/5.57 f_176(v49, v50, v51, v52, v53, v54, 1, v56, v57, v58, v59, v60, v61, v62, 0, 3, 7, 10, 2, 9, 4, 8) -> f_177(v49, v50, v51, v52, v53, v54, 1, v56, v57, v58, v59, v60, v61, v62, 0, 3, 7, 10, 2, 9, 4, 8) :|: 0 = 0 17.48/5.57 Combined rules. Obtained 1 rulesP rules: 17.48/5.57 f_177(v49:0, v50:0, v51:0, v52:0, v53:0, v54:0, 1, v56:0, 1 + v64:0, v58:0, v59:0, v60:0, v61:0, v62:0, 0, 3, 7, 10, 2, 9, 4, 8) -> f_177(v49:0, v50:0, v51:0, v52:0, v53:0, v54:0, 1, 1 + v64:0, v64:0, v58:0, v59:0, v60:0, v61:0, v62:0, 0, 3, 7, 10, 2, 9, 4, 8) :|: v56:0 > 2 && v64:0 > 0 && v64:0 < 9 17.72/5.57 Filtered unneeded arguments: 17.72/5.57 f_177(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) -> f_177(x8, x9) 17.72/5.57 Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: 17.72/5.57 f_177(v56:0, sum~cons_1~v64:0) -> f_177(1 + v64:0, v64:0) :|: v64:0 > 0 && v64:0 < 9 && v56:0 > 2 && sum~cons_1~v64:0 = 1 + v64:0 17.72/5.57 17.72/5.57 ---------------------------------------- 17.72/5.57 17.72/5.57 (16) 17.72/5.57 Obligation: 17.72/5.57 Rules: 17.72/5.57 f_177(v56:0, sum~cons_1~v64:0) -> f_177(1 + v64:0, v64:0) :|: v64:0 > 0 && v64:0 < 9 && v56:0 > 2 && sum~cons_1~v64:0 = 1 + v64:0 17.72/5.57 17.72/5.57 ---------------------------------------- 17.72/5.57 17.72/5.57 (17) IntTRSCompressionProof (EQUIVALENT) 17.72/5.57 Compressed rules. 17.72/5.57 ---------------------------------------- 17.72/5.57 17.72/5.57 (18) 17.72/5.57 Obligation: 17.72/5.57 Rules: 17.72/5.57 f_177(v56:0:0, sum~cons_1~v64:0:0) -> f_177(1 + v64:0:0, v64:0:0) :|: v64:0:0 > 0 && v64:0:0 < 9 && v56:0:0 > 2 && sum~cons_1~v64:0:0 = 1 + v64:0:0 17.72/5.57 17.72/5.57 ---------------------------------------- 17.72/5.57 17.72/5.57 (19) PolynomialOrderProcessor (EQUIVALENT) 17.72/5.57 Found the following polynomial interpretation: 17.72/5.57 [f_177(x, x1)] = x1 17.72/5.57 17.72/5.57 The following rules are decreasing: 17.72/5.57 f_177(v56:0:0, sum~cons_1~v64:0:0) -> f_177(1 + v64:0:0, v64:0:0) :|: v64:0:0 > 0 && v64:0:0 < 9 && v56:0:0 > 2 && sum~cons_1~v64:0:0 = 1 + v64:0:0 17.72/5.57 The following rules are bounded: 17.72/5.57 f_177(v56:0:0, sum~cons_1~v64:0:0) -> f_177(1 + v64:0:0, v64:0:0) :|: v64:0:0 > 0 && v64:0:0 < 9 && v56:0:0 > 2 && sum~cons_1~v64:0:0 = 1 + v64:0:0 17.72/5.57 17.72/5.57 ---------------------------------------- 17.72/5.57 17.72/5.57 (20) 17.72/5.57 YES 17.83/6.54 EOF