/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given C Problem could be proven: (0) C Problem (1) CToLLVMProof [EQUIVALENT, 176 ms] (2) LLVM problem (3) LLVMToTerminationGraphProof [EQUIVALENT, 1997 ms] (4) LLVM Symbolic Execution Graph (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] (6) AND (7) LLVM Symbolic Execution SCC (8) SCC2IRS [SOUND, 50 ms] (9) IntTRS (10) IntTRSCompressionProof [EQUIVALENT, 0 ms] (11) IntTRS (12) PolynomialOrderProcessor [EQUIVALENT, 9 ms] (13) YES (14) LLVM Symbolic Execution SCC (15) SCC2IRS [SOUND, 0 ms] (16) IntTRS (17) IntTRSCompressionProof [EQUIVALENT, 0 ms] (18) IntTRS (19) RankingReductionPairProof [EQUIVALENT, 21 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: "__VERIFIER_nondet_int" returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 0: %1 = alloca i32, align 4 %n = alloca i32, align 4 %m = alloca i32, align 4 %i = alloca i32, align 4 store 0, %1 %2 = call i32 @__VERIFIER_nondet_int() store %2, %n %3 = call i32 @__VERIFIER_nondet_int() store %3, %m %4 = load %m %5 = icmp sgt %4 0 br %5, %6, %28 6: %7 = load %n %8 = load %m %9 = icmp sgt %7 %8 br %9, %10, %28 10: %11 = load %n store %11, %i br %12 12: %13 = load %i %14 = icmp sgt %13 0 br %14, %15, %27 15: %16 = load %i %17 = load %m %18 = icmp slt %16 %17 br %18, %19, %22 19: %20 = load %i %21 = add %20 -1 store %21, %i br %26 22: %23 = load %m %24 = load %i %25 = sub %24 %23 store %25, %i br %26 26: br %12 27: br %28 28: 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 14 rulesP rules: f_244(v211, v212, v213, v214, v215, v216, 1, v218, v219, v220, v221, v222, v223, v224, v225, 0, 3, 2, 4) -> f_245(v211, v212, v213, v214, v215, v216, 1, v221, v218, v219, v220, v222, v223, v224, v225, 0, 3, 2, 4) :|: 0 = 0 f_245(v211, v212, v213, v214, v215, v216, 1, v221, v218, v219, v220, v222, v223, v224, v225, 0, 3, 2, 4) -> f_246(v211, v212, v213, v214, v215, v216, 1, v221, v218, v219, v220, v222, v223, v224, v225, 0, 3, 2, 5, 4) :|: 0 < v221 && 2 <= v218 && 2 <= v220 && 5 <= v219 && 3 <= v216 f_246(v211, v212, v213, v214, v215, v216, 1, v221, v218, v219, v220, v222, v223, v224, v225, 0, 3, 2, 5, 4) -> f_248(v211, v212, v213, v214, v215, v216, 1, v221, v218, v219, v220, v222, v223, v224, v225, 0, 3, 2, 5, 4) :|: 0 = 0 f_248(v211, v212, v213, v214, v215, v216, 1, v221, v218, v219, v220, v222, v223, v224, v225, 0, 3, 2, 5, 4) -> f_250(v211, v212, v213, v214, v215, v216, 1, v221, v218, v219, v220, v222, v223, v224, v225, 0, 3, 2, 5, 4) :|: TRUE f_250(v211, v212, v213, v214, v215, v216, 1, v221, v218, v219, v220, v222, v223, v224, v225, 0, 3, 2, 5, 4) -> f_252(v211, v212, v213, v214, v215, v216, 1, v221, v219, v220, v218, v222, v223, v224, v225, 0, 3, 2, 5, 4) :|: 0 = 0 f_252(v211, v212, v213, v214, v215, v216, 1, v221, v219, v220, v218, v222, v223, v224, v225, 0, 3, 2, 5, 4) -> f_254(v211, v212, v213, v214, v215, v216, 1, v221, v219, v220, v218, v222, v223, v224, v225, 0, 3, 2, 5, 4) :|: 0 = 0 f_254(v211, v212, v213, v214, v215, v216, 1, v221, v219, v220, v218, v222, v223, v224, v225, 0, 3, 2, 5, 4) -> f_255(v211, v212, v213, v214, v215, v216, 1, v221, v219, v220, v218, v222, v223, v224, v225, 0, 3, 2, 5, 4) :|: 0 = 0 f_255(v211, v212, v213, v214, v215, v216, 1, v221, v219, v220, v218, v222, v223, v224, v225, 0, 3, 2, 5, 4) -> f_256(v211, v212, v213, v214, v215, v216, 1, v221, v219, v220, v218, v222, v223, v224, v225, 0, 3, 2, 5, 4) :|: TRUE f_256(v211, v212, v213, v214, v215, v216, 1, v221, v219, v220, v218, v222, v223, v224, v225, 0, 3, 2, 5, 4) -> f_257(v211, v212, v213, v214, v215, v216, 1, v221, v219, v220, v222, v223, v224, v225, 0, 3, 2, 5, 4) :|: 0 = 0 f_257(v211, v212, v213, v214, v215, v216, 1, v221, v219, v220, v222, v223, v224, v225, 0, 3, 2, 5, 4) -> f_258(v211, v212, v213, v214, v215, v216, 1, v221, v219, v220, v270, v222, v223, v224, v225, 0, 3, 2, 5, 4) :|: 1 + v270 = v221 && 0 <= v270 f_258(v211, v212, v213, v214, v215, v216, 1, v221, v219, v220, v270, v222, v223, v224, v225, 0, 3, 2, 5, 4) -> f_259(v211, v212, v213, v214, v215, v216, 1, v221, v219, v220, v270, v222, v223, v224, v225, 0, 3, 2, 5, 4) :|: TRUE f_259(v211, v212, v213, v214, v215, v216, 1, v221, v219, v220, v270, v222, v223, v224, v225, 0, 3, 2, 5, 4) -> f_260(v211, v212, v213, v214, v215, v216, 1, v221, v219, v220, v270, v222, v223, v224, v225, 0, 3, 2, 5, 4) :|: TRUE f_260(v211, v212, v213, v214, v215, v216, 1, v221, v219, v220, v270, v222, v223, v224, v225, 0, 3, 2, 5, 4) -> f_243(v211, v212, v213, v214, v215, v216, 1, v221, v219, v220, v270, v222, v223, v224, v225, 0, 3, 2, 4) :|: TRUE f_243(v211, v212, v213, v214, v215, v216, 1, v218, v219, v220, v221, v222, v223, v224, v225, 0, 3, 2, 4) -> f_244(v211, v212, v213, v214, v215, v216, 1, v218, v219, v220, v221, v222, v223, v224, v225, 0, 3, 2, 4) :|: TRUE Combined rules. Obtained 1 rulesP rules: f_244(v211:0, v212:0, v213:0, v214:0, v215:0, v216:0, 1, v218:0, v219:0, v220:0, 1 + v270:0, v222:0, v223:0, v224:0, v225:0, 0, 3, 2, 4) -> f_244(v211:0, v212:0, v213:0, v214:0, v215:0, v216:0, 1, 1 + v270:0, v219:0, v220:0, v270:0, v222:0, v223:0, v224:0, v225:0, 0, 3, 2, 4) :|: v218:0 > 1 && v270:0 > -1 && v220:0 > 1 && v219:0 > 4 && v216:0 > 2 Filtered unneeded arguments: f_244(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) -> f_244(x6, x8, x9, x10, x11) Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: f_244(v216:0, v218:0, v219:0, v220:0, sum~cons_1~v270:0) -> f_244(v216:0, 1 + v270:0, v219:0, v220:0, v270:0) :|: v270:0 > -1 && v218:0 > 1 && v220:0 > 1 && v216:0 > 2 && v219:0 > 4 && sum~cons_1~v270:0 = 1 + v270:0 ---------------------------------------- (9) Obligation: Rules: f_244(v216:0, v218:0, v219:0, v220:0, sum~cons_1~v270:0) -> f_244(v216:0, 1 + v270:0, v219:0, v220:0, v270:0) :|: v270:0 > -1 && v218:0 > 1 && v220:0 > 1 && v216:0 > 2 && v219:0 > 4 && sum~cons_1~v270:0 = 1 + v270:0 ---------------------------------------- (10) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (11) Obligation: Rules: f_244(v216:0:0, v218:0:0, v219:0:0, v220:0:0, sum~cons_1~v270:0:0) -> f_244(v216:0:0, 1 + v270:0:0, v219:0:0, v220:0:0, v270:0:0) :|: v216:0:0 > 2 && v219:0:0 > 4 && v220:0:0 > 1 && v218:0:0 > 1 && v270:0:0 > -1 && sum~cons_1~v270:0:0 = 1 + v270:0:0 ---------------------------------------- (12) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f_244(x, x1, x2, x3, x4)] = x4 The following rules are decreasing: f_244(v216:0:0, v218:0:0, v219:0:0, v220:0:0, sum~cons_1~v270:0:0) -> f_244(v216:0:0, 1 + v270:0:0, v219:0:0, v220:0:0, v270:0:0) :|: v216:0:0 > 2 && v219:0:0 > 4 && v220:0:0 > 1 && v218:0:0 > 1 && v270:0:0 > -1 && sum~cons_1~v270:0:0 = 1 + v270:0:0 The following rules are bounded: f_244(v216:0:0, v218:0:0, v219:0:0, v220:0:0, sum~cons_1~v270:0:0) -> f_244(v216:0:0, 1 + v270:0:0, v219:0:0, v220:0:0, v270:0:0) :|: v216:0:0 > 2 && v219:0:0 > 4 && v220:0:0 > 1 && v218:0:0 > 1 && v270:0:0 > -1 && sum~cons_1~v270:0:0 = 1 + v270:0:0 ---------------------------------------- (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_182(v32, v33, v34, v35, v36, v37, 1, v41, v39, 0, v42, v43, v44, v45, 3, 2, 4) -> f_183(v32, v33, v34, v35, v36, v37, 1, v41, v39, 0, v42, v43, v44, v45, 3, 2, 4) :|: 0 < v41 && 2 <= v39 f_183(v32, v33, v34, v35, v36, v37, 1, v41, v39, 0, v42, v43, v44, v45, 3, 2, 4) -> f_185(v32, v33, v34, v35, v36, v37, 1, v41, v39, 0, v42, v43, v44, v45, 3, 2, 4) :|: 0 = 0 f_185(v32, v33, v34, v35, v36, v37, 1, v41, v39, 0, v42, v43, v44, v45, 3, 2, 4) -> f_187(v32, v33, v34, v35, v36, v37, 1, v41, v39, 0, v42, v43, v44, v45, 3, 2, 4) :|: TRUE f_187(v32, v33, v34, v35, v36, v37, 1, v41, v39, 0, v42, v43, v44, v45, 3, 2, 4) -> f_189(v32, v33, v34, v35, v36, v37, 1, v41, 0, v39, v42, v43, v44, v45, 3, 2, 4) :|: 0 = 0 f_189(v32, v33, v34, v35, v36, v37, 1, v41, 0, v39, v42, v43, v44, v45, 3, 2, 4) -> f_191(v32, v33, v34, v35, v36, v37, 1, v41, 0, v39, v42, v43, v44, v45, 3, 2, 4) :|: 0 = 0 f_191(v32, v33, v34, v35, v36, v37, 1, v41, 0, v39, v42, v43, v44, v45, 3, 2, 4) -> f_193(v32, v33, v34, v35, v36, v37, 1, v41, 0, v39, v42, v43, v44, v45, 3, 2, 4) :|: v37 <= v41 f_193(v32, v33, v34, v35, v36, v37, 1, v41, 0, v39, v42, v43, v44, v45, 3, 2, 4) -> f_195(v32, v33, v34, v35, v36, v37, 1, v41, 0, v39, v42, v43, v44, v45, 3, 2, 4) :|: 0 = 0 f_195(v32, v33, v34, v35, v36, v37, 1, v41, 0, v39, v42, v43, v44, v45, 3, 2, 4) -> f_197(v32, v33, v34, v35, v36, v37, 1, v41, 0, v39, v42, v43, v44, v45, 3, 2, 4) :|: TRUE f_197(v32, v33, v34, v35, v36, v37, 1, v41, 0, v39, v42, v43, v44, v45, 3, 2, 4) -> f_199(v32, v33, v34, v35, v36, v37, 1, v41, 0, v39, v42, v43, v44, v45, 3, 2, 4) :|: 0 = 0 f_199(v32, v33, v34, v35, v36, v37, 1, v41, 0, v39, v42, v43, v44, v45, 3, 2, 4) -> f_201(v32, v33, v34, v35, v36, v37, 1, v41, 0, v42, v43, v44, v45, 3, 2, 4) :|: 0 = 0 f_201(v32, v33, v34, v35, v36, v37, 1, v41, 0, v42, v43, v44, v45, 3, 2, 4) -> f_203(v32, v33, v34, v35, v36, v37, 1, v41, 0, v63, v42, v43, v44, v45, 3, 2, 4) :|: v63 + v37 = v41 && 0 <= v63 f_203(v32, v33, v34, v35, v36, v37, 1, v41, 0, v63, v42, v43, v44, v45, 3, 2, 4) -> f_205(v32, v33, v34, v35, v36, v37, 1, v41, 0, v63, v42, v43, v44, v45, 3, 2, 4) :|: TRUE f_205(v32, v33, v34, v35, v36, v37, 1, v41, 0, v63, v42, v43, v44, v45, 3, 2, 4) -> f_207(v32, v33, v34, v35, v36, v37, 1, v41, 0, v63, v42, v43, v44, v45, 3, 2, 4) :|: TRUE f_207(v32, v33, v34, v35, v36, v37, 1, v41, 0, v63, v42, v43, v44, v45, 3, 2, 4) -> f_209(v32, v33, v34, v35, v36, v37, 1, v41, 0, v63, v42, v43, v44, v45, 3, 2, 4) :|: TRUE f_209(v32, v33, v34, v35, v36, v37, 1, v41, 0, v63, v42, v43, v44, v45, 3, 2, 4) -> f_181(v32, v33, v34, v35, v36, v37, 1, v41, 0, v63, v42, v43, v44, v45, 3, 2, 4) :|: 1 <= v32 && 1 <= v33 && 1 <= v34 && 1 <= v35 && 2 <= v36 && 1 <= v37 && 1 <= v41 && 0 <= v63 && 4 <= v42 && 4 <= v43 && 4 <= v44 && 4 <= v45 && v32 <= v42 && v33 <= v43 && v34 <= v44 && v35 <= v45 f_181(v32, v33, v34, v35, v36, v37, 1, v39, 0, v41, v42, v43, v44, v45, 3, 2, 4) -> f_182(v32, v33, v34, v35, v36, v37, 1, v41, v39, 0, v42, v43, v44, v45, 3, 2, 4) :|: 0 = 0 Combined rules. Obtained 1 rulesP rules: f_182(v32:0, v33:0, v34:0, v35:0, v36:0, v37:0, 1, v63:0 + v37:0, v39:0, 0, v42:0, v43:0, v44:0, v45:0, 3, 2, 4) -> f_182(v32:0, v33:0, v34:0, v35:0, v36:0, v37:0, 1, v63:0, v63:0 + v37:0, 0, v42:0, v43:0, v44:0, v45:0, 3, 2, 4) :|: v33:0 > 0 && v32:0 > 0 && v34:0 > 0 && v39:0 > 1 && v63:0 + v37:0 > 0 && v35:0 > 0 && v36:0 > 1 && v37:0 > 0 && v63:0 > -1 && v63:0 + v37:0 >= v37:0 && v42:0 > 3 && v43:0 > 3 && v44:0 > 3 && v45:0 > 3 && v42:0 >= v32:0 && v43:0 >= v33:0 && v45:0 >= v35:0 && v44:0 >= v34:0 Filtered unneeded arguments: f_182(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17) -> f_182(x1, x2, x3, x4, x5, x6, x8, x9, x11, x12, x13, x14) Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: f_182(v32:0, v33:0, v34:0, v35:0, v36:0, v37:0, sum~v63:0~v37:0, v39:0, v42:0, v43:0, v44:0, v45:0) -> f_182(v32:0, v33:0, v34:0, v35:0, v36:0, v37:0, v63:0, v63:0 + v37:0, v42:0, v43:0, v44:0, v45:0) :|: v32:0 > 0 && v33:0 > 0 && v34:0 > 0 && v39:0 > 1 && v63:0 + v37:0 > 0 && v35:0 > 0 && v36:0 > 1 && v37:0 > 0 && v63:0 > -1 && v63:0 + v37:0 >= v37:0 && v42:0 > 3 && v43:0 > 3 && v44:0 > 3 && v45:0 > 3 && v42:0 >= v32:0 && v43:0 >= v33:0 && v44:0 >= v34:0 && v45:0 >= v35:0 && sum~v63:0~v37:0 = v63:0 + v37:0 ---------------------------------------- (16) Obligation: Rules: f_182(v32:0, v33:0, v34:0, v35:0, v36:0, v37:0, sum~v63:0~v37:0, v39:0, v42:0, v43:0, v44:0, v45:0) -> f_182(v32:0, v33:0, v34:0, v35:0, v36:0, v37:0, v63:0, v63:0 + v37:0, v42:0, v43:0, v44:0, v45:0) :|: v32:0 > 0 && v33:0 > 0 && v34:0 > 0 && v39:0 > 1 && v63:0 + v37:0 > 0 && v35:0 > 0 && v36:0 > 1 && v37:0 > 0 && v63:0 > -1 && v63:0 + v37:0 >= v37:0 && v42:0 > 3 && v43:0 > 3 && v44:0 > 3 && v45:0 > 3 && v42:0 >= v32:0 && v43:0 >= v33:0 && v44:0 >= v34:0 && v45:0 >= v35:0 && sum~v63:0~v37:0 = v63:0 + v37:0 ---------------------------------------- (17) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (18) Obligation: Rules: f_182(v32:0:0, v33:0:0, v34:0:0, v35:0:0, v36:0:0, v37:0:0, sum~v63:0:0~v37:0:0, v39:0:0, v42:0:0, v43:0:0, v44:0:0, v45:0:0) -> f_182(v32:0:0, v33:0:0, v34:0:0, v35:0:0, v36:0:0, v37:0:0, v63:0:0, v63:0:0 + v37:0:0, v42:0:0, v43:0:0, v44:0:0, v45:0:0) :|: v44:0:0 >= v34:0:0 && v45:0:0 >= v35:0:0 && v43:0:0 >= v33:0:0 && v42:0:0 >= v32:0:0 && v45:0:0 > 3 && v44:0:0 > 3 && v43:0:0 > 3 && v42:0:0 > 3 && v63:0:0 + v37:0:0 >= v37:0:0 && v63:0:0 > -1 && v37:0:0 > 0 && v36:0:0 > 1 && v35:0:0 > 0 && v63:0:0 + v37:0:0 > 0 && v39:0:0 > 1 && v34:0:0 > 0 && v33:0:0 > 0 && v32:0:0 > 0 && sum~v63:0:0~v37:0:0 = v63:0:0 + v37:0:0 ---------------------------------------- (19) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f_182 ] = f_182_7 The following rules are decreasing: f_182(v32:0:0, v33:0:0, v34:0:0, v35:0:0, v36:0:0, v37:0:0, sum~v63:0:0~v37:0:0, v39:0:0, v42:0:0, v43:0:0, v44:0:0, v45:0:0) -> f_182(v32:0:0, v33:0:0, v34:0:0, v35:0:0, v36:0:0, v37:0:0, v63:0:0, v63:0:0 + v37:0:0, v42:0:0, v43:0:0, v44:0:0, v45:0:0) :|: v44:0:0 >= v34:0:0 && v45:0:0 >= v35:0:0 && v43:0:0 >= v33:0:0 && v42:0:0 >= v32:0:0 && v45:0:0 > 3 && v44:0:0 > 3 && v43:0:0 > 3 && v42:0:0 > 3 && v63:0:0 + v37:0:0 >= v37:0:0 && v63:0:0 > -1 && v37:0:0 > 0 && v36:0:0 > 1 && v35:0:0 > 0 && v63:0:0 + v37:0:0 > 0 && v39:0:0 > 1 && v34:0:0 > 0 && v33:0:0 > 0 && v32:0:0 > 0 && sum~v63:0:0~v37:0:0 = v63:0:0 + v37:0:0 The following rules are bounded: f_182(v32:0:0, v33:0:0, v34:0:0, v35:0:0, v36:0:0, v37:0:0, sum~v63:0:0~v37:0:0, v39:0:0, v42:0:0, v43:0:0, v44:0:0, v45:0:0) -> f_182(v32:0:0, v33:0:0, v34:0:0, v35:0:0, v36:0:0, v37:0:0, v63:0:0, v63:0:0 + v37:0:0, v42:0:0, v43:0:0, v44:0:0, v45:0:0) :|: v44:0:0 >= v34:0:0 && v45:0:0 >= v35:0:0 && v43:0:0 >= v33:0:0 && v42:0:0 >= v32:0:0 && v45:0:0 > 3 && v44:0:0 > 3 && v43:0:0 > 3 && v42:0:0 > 3 && v63:0:0 + v37:0:0 >= v37:0:0 && v63:0:0 > -1 && v37:0:0 > 0 && v36:0:0 > 1 && v35:0:0 > 0 && v63:0:0 + v37:0:0 > 0 && v39:0:0 > 1 && v34:0:0 > 0 && v33:0:0 > 0 && v32:0:0 > 0 && sum~v63:0:0~v37:0:0 = v63:0:0 + v37:0:0 ---------------------------------------- (20) YES