/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given C Problem could be proven: (0) C Problem (1) CToLLVMProof [EQUIVALENT, 170 ms] (2) LLVM problem (3) LLVMToTerminationGraphProof [EQUIVALENT, 3015 ms] (4) LLVM Symbolic Execution Graph (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] (6) LLVM Symbolic Execution SCC (7) SCC2IRS [SOUND, 91 ms] (8) IntTRS (9) IntTRSCompressionProof [EQUIVALENT, 0 ms] (10) IntTRS (11) CaseAnalysis [EQUIVALENT, 21 ms] (12) AND (13) IntTRS (14) IntTRSCompressionProof [EQUIVALENT, 0 ms] (15) IntTRS (16) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (17) YES (18) IntTRS (19) IntTRSCompressionProof [EQUIVALENT, 0 ms] (20) IntTRS (21) RankingReductionPairProof [EQUIVALENT, 0 ms] (22) 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 %x = alloca i32, align 4 %y = alloca i32, align 4 %z = alloca i32, align 4 store 0, %1 %2 = call i32 @__VERIFIER_nondet_int() store %2, %x %3 = call i32 @__VERIFIER_nondet_int() store %3, %y %4 = call i32 @__VERIFIER_nondet_int() store %4, %z %5 = call i32 @random() %6 = call i32 @random() Unnamed Call-Instruction = call BasicVoidType @loop(i32 %5, i32 %6) %7 = load %1 ret %7 *BasicFunctionTypename: "loop" linkageType: EXTERNALLY_VISIBLE returnParam: BasicVoidType parameters: (a i32, b i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc 0: %1 = alloca i32, align 4 %2 = alloca i32, align 4 store %a, %1 store %b, %2 %3 = load %1 %4 = icmp sgt %3 0 br %4, %5, %13 5: %6 = load %1 %7 = load %2 %8 = add %6 %7 store %8, %1 %9 = load %2 %10 = sub %9 1 store %10, %2 %11 = load %1 %12 = load %2 Unnamed Call-Instruction = call BasicVoidType @loop(i32 %11, i32 %12) br %13 13: ret void *BasicFunctionTypename: "random" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 0: %1 = alloca i32, align 4 %x = alloca i32, align 4 %2 = call i32 @__VERIFIER_nondet_int() store %2, %x %3 = load %x %4 = icmp slt %3 0 br %4, %5, %8 5: %6 = load %x %7 = sub 0 %6 store %7, %1 br %10 8: %9 = load %x store %9, %1 br %10 10: %11 = load %1 ret %11 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 1 SCC. ---------------------------------------- (6) Obligation: SCC ---------------------------------------- (7) SCC2IRS (SOUND) Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: Generated rules. Obtained 20 rulesP rules: f_337(v283, v284, v297, v285, v286, v287, v288, v289, v290, v291, v292, v298, 0, v294, v295, v296, 3, 1, 4) -> f_338(v283, v284, v297, v299, v285, v286, v287, v288, v289, v290, v291, v292, v298, v300, 0, v294, v295, v296, 3, 1, 4) :|: 1 <= v299 && v300 = 3 + v299 && 4 <= v300 f_338(v283, v284, v297, v299, v285, v286, v287, v288, v289, v290, v291, v292, v298, v300, 0, v294, v295, v296, 3, 1, 4) -> f_339(v283, v284, v297, v299, v285, v286, v287, v288, v289, v290, v291, v292, v298, v300, 0, v294, v295, v296, 3, 1, 4) :|: TRUE f_339(v283, v284, v297, v299, v285, v286, v287, v288, v289, v290, v291, v292, v298, v300, 0, v294, v295, v296, 3, 1, 4) -> f_340(v283, v284, v297, v299, v285, v286, v287, v288, v289, v290, v291, v292, v298, v300, 0, v294, v295, v296, 3, 1, 4) :|: TRUE f_340(v283, v284, v297, v299, v285, v286, v287, v288, v289, v290, v291, v292, v298, v300, 0, v294, v295, v296, 3, 1, 4) -> f_341(v283, v284, v297, v299, v285, v286, v287, v288, v289, v290, v291, v292, v298, v300, 0, v294, v295, v296, 3, 1, 4) :|: 0 = 0 f_341(v283, v284, v297, v299, v285, v286, v287, v288, v289, v290, v291, v292, v298, v300, 0, v294, v295, v296, 3, 1, 4) -> f_342(v283, v284, v297, v299, v285, v286, v287, v288, v289, v290, v291, v292, v298, v300, 0, v294, v295, v296, 3, 1, 4) :|: 0 < v283 f_342(v283, v284, v297, v299, v285, v286, v287, v288, v289, v290, v291, v292, v298, v300, 0, v294, v295, v296, 3, 1, 4) -> f_344(v283, v284, v297, v299, 1, v285, v286, v287, v288, v289, v290, v291, v292, v298, v300, 0, v294, v295, v296, 3, 4) :|: 0 = 0 f_344(v283, v284, v297, v299, 1, v285, v286, v287, v288, v289, v290, v291, v292, v298, v300, 0, v294, v295, v296, 3, 4) -> f_346(v283, v284, v297, v299, 1, v285, v286, v287, v288, v289, v290, v291, v292, v298, v300, 0, v294, v295, v296, 3, 4) :|: TRUE f_346(v283, v284, v297, v299, 1, v285, v286, v287, v288, v289, v290, v291, v292, v298, v300, 0, v294, v295, v296, 3, 4) -> f_348(v283, v284, v297, v299, 1, v285, v286, v287, v288, v289, v290, v291, v292, v298, v300, 0, v294, v295, v296, 3, 4) :|: 0 = 0 f_348(v283, v284, v297, v299, 1, v285, v286, v287, v288, v289, v290, v291, v292, v298, v300, 0, v294, v295, v296, 3, 4) -> f_351(v283, v284, v297, v299, 1, v285, v286, v287, v288, v289, v290, v291, v292, v298, v300, 0, v294, v295, v296, 3, 4) :|: 0 = 0 f_351(v283, v284, v297, v299, 1, v285, v286, v287, v288, v289, v290, v291, v292, v298, v300, 0, v294, v295, v296, 3, 4) -> f_354(v283, v284, v297, v299, 1, v337, v285, v286, v287, v288, v289, v290, v291, v292, v298, v300, 0, v294, v295, v296, 3, 4) :|: v337 = v283 + v284 f_354(v283, v284, v297, v299, 1, v337, v285, v286, v287, v288, v289, v290, v291, v292, v298, v300, 0, v294, v295, v296, 3, 4) -> f_357(v283, v284, v297, v299, 1, v337, v285, v286, v287, v288, v289, v290, v291, v292, v298, v300, 0, v294, v295, v296, 3, 4) :|: TRUE f_357(v283, v284, v297, v299, 1, v337, v285, v286, v287, v288, v289, v290, v291, v292, v298, v300, 0, v294, v295, v296, 3, 4) -> f_358(v283, v284, v297, v299, 1, v337, v285, v286, v287, v288, v289, v290, v291, v292, v298, v300, 0, v294, v295, v296, 3, 4) :|: 0 = 0 f_358(v283, v284, v297, v299, 1, v337, v285, v286, v287, v288, v289, v290, v291, v292, v298, v300, 0, v294, v295, v296, 3, 4) -> f_359(v283, v284, v297, v299, 1, v337, v339, v285, v286, v287, v288, v289, v290, v291, v292, v298, v300, 0, v294, v295, v296, 3, 4) :|: 1 + v339 = v284 f_359(v283, v284, v297, v299, 1, v337, v339, v285, v286, v287, v288, v289, v290, v291, v292, v298, v300, 0, v294, v295, v296, 3, 4) -> f_360(v283, v284, v297, v299, 1, v337, v339, v285, v286, v287, v288, v289, v290, v291, v292, v298, v300, 0, v294, v295, v296, 3, 4) :|: TRUE f_360(v283, v284, v297, v299, 1, v337, v339, v285, v286, v287, v288, v289, v290, v291, v292, v298, v300, 0, v294, v295, v296, 3, 4) -> f_361(v283, v284, v297, v299, 1, v337, v339, v285, v286, v287, v288, v289, v290, v291, v292, v298, v300, 0, v294, v295, v296, 3, 4) :|: 0 = 0 f_361(v283, v284, v297, v299, 1, v337, v339, v285, v286, v287, v288, v289, v290, v291, v292, v298, v300, 0, v294, v295, v296, 3, 4) -> f_362(v283, v284, v297, v299, 1, v337, v339, v285, v286, v287, v288, v289, v290, v291, v292, v298, v300, 0, v294, v295, v296, 3, 4) :|: 0 = 0 f_362(v283, v284, v297, v299, 1, v337, v339, v285, v286, v287, v288, v289, v290, v291, v292, v298, v300, 0, v294, v295, v296, 3, 4) -> f_363(v337, v339, v285, v286, v287, v288, v289, v290, v291, v292, v297, v298, v299, v300, 0, v294, v295, v296, v283, v284, 1, 3, 4) :|: 0 = 0 f_363(v337, v339, v285, v286, v287, v288, v289, v290, v291, v292, v297, v298, v299, v300, 0, v294, v295, v296, v283, v284, 1, 3, 4) -> f_364(v337, v339, v285, v286, v287, v288, v289, v290, v291, v292, v297, v298, v299, v300, 0, v294, v295, v296, 3, 1, 4) :|: TRUE f_364(v337, v339, v285, v286, v287, v288, v289, v290, v291, v292, v297, v298, v299, v300, 0, v294, v295, v296, 3, 1, 4) -> f_336(v337, v339, v285, v286, v287, v288, v289, v290, v291, v292, 0, v294, v295, v296, 3, 1, 4) :|: TRUE f_336(v283, v284, v285, v286, v287, v288, v289, v290, v291, v292, 0, v294, v295, v296, 3, 1, 4) -> f_337(v283, v284, v297, v285, v286, v287, v288, v289, v290, v291, v292, v298, 0, v294, v295, v296, 3, 1, 4) :|: 1 <= v297 && v298 = 3 + v297 && 4 <= v298 Combined rules. Obtained 1 rulesP rules: f_337(v283:0, 1 + v339:0, v297:0, v285:0, v286:0, v287:0, v288:0, v289:0, v290:0, v291:0, v292:0, v298:0, 0, v294:0, v295:0, v296:0, 3, 1, 4) -> f_337(v283:0 + (1 + v339:0), v339:0, v297:1, v285:0, v286:0, v287:0, v288:0, v289:0, v290:0, v291:0, v292:0, 3 + v297:1, 0, v294:0, v295:0, v296:0, 3, 1, 4) :|: v299:0 > 0 && v283:0 > 0 && v297:1 > 0 Filtered unneeded arguments: f_337(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) -> f_337(x1, x2) Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: f_337(v283:0, sum~cons_1~v339:0) -> f_337(v283:0 + (1 + v339:0), v339:0) :|: v283:0 > 0 && sum~cons_1~v339:0 = 1 + v339:0 ---------------------------------------- (8) Obligation: Rules: f_337(v283:0, sum~cons_1~v339:0) -> f_337(v283:0 + (1 + v339:0), v339:0) :|: v283:0 > 0 && sum~cons_1~v339:0 = 1 + v339:0 ---------------------------------------- (9) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (10) Obligation: Rules: f_337(v283:0:0, sum~cons_1~v339:0:0) -> f_337(v283:0:0 + (1 + v339:0:0), v339:0:0) :|: v283:0:0 > 0 && sum~cons_1~v339:0:0 = 1 + v339:0:0 ---------------------------------------- (11) CaseAnalysis (EQUIVALENT) Found the following inductive condition: f_337(x, x1): -1 - 4*x1>=0 ---------------------------------------- (12) Complex Obligation (AND) ---------------------------------------- (13) Obligation: Rules: f_337(v283:0:0, sum~cons_1~v339:0:0) -> f_337(v283:0:0 + (1 + v339:0:0), v339:0:0) :|: v283:0:0 > 0 && sum~cons_1~v339:0:0 = 1 + v339:0:0 && -1 + -4 * sum~cons_1~v339:0:0 >= 0 ---------------------------------------- (14) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (15) Obligation: Rules: f_337(v283:0:0:0, sum~cons_1~v339:0:0:0) -> f_337(v283:0:0:0 + (1 + v339:0:0:0), v339:0:0:0) :|: 1 <= -4 * (1 + v339:0:0:0) && v283:0:0:0 > 0 && sum~cons_1~v339:0:0:0 = 1 + v339:0:0:0 ---------------------------------------- (16) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f_337(x, x1)] = -1 + x The following rules are decreasing: f_337(v283:0:0:0, sum~cons_1~v339:0:0:0) -> f_337(v283:0:0:0 + (1 + v339:0:0:0), v339:0:0:0) :|: 1 <= -4 * (1 + v339:0:0:0) && v283:0:0:0 > 0 && sum~cons_1~v339:0:0:0 = 1 + v339:0:0:0 The following rules are bounded: f_337(v283:0:0:0, sum~cons_1~v339:0:0:0) -> f_337(v283:0:0:0 + (1 + v339:0:0:0), v339:0:0:0) :|: 1 <= -4 * (1 + v339:0:0:0) && v283:0:0:0 > 0 && sum~cons_1~v339:0:0:0 = 1 + v339:0:0:0 ---------------------------------------- (17) YES ---------------------------------------- (18) Obligation: Rules: f_337(v283:0:0, sum~cons_1~v339:0:0) -> f_337(v283:0:0 + (1 + v339:0:0), v339:0:0) :|: v283:0:0 > 0 && sum~cons_1~v339:0:0 = 1 + v339:0:0 && -1 + -4 * sum~cons_1~v339:0:0 < 0 ---------------------------------------- (19) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (20) Obligation: Rules: f_337(v283:0:0:0, sum~cons_1~v339:0:0:0) -> f_337(v283:0:0:0 + (1 + v339:0:0:0), v339:0:0:0) :|: 1 > -4 * (1 + v339:0:0:0) && v283:0:0:0 > 0 && sum~cons_1~v339:0:0:0 = 1 + v339:0:0:0 ---------------------------------------- (21) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f_337 ] = f_337_2 The following rules are decreasing: f_337(v283:0:0:0, sum~cons_1~v339:0:0:0) -> f_337(v283:0:0:0 + (1 + v339:0:0:0), v339:0:0:0) :|: 1 > -4 * (1 + v339:0:0:0) && v283:0:0:0 > 0 && sum~cons_1~v339:0:0:0 = 1 + v339:0:0:0 The following rules are bounded: f_337(v283:0:0:0, sum~cons_1~v339:0:0:0) -> f_337(v283:0:0:0 + (1 + v339:0:0:0), v339:0:0:0) :|: 1 > -4 * (1 + v339:0:0:0) && v283:0:0:0 > 0 && sum~cons_1~v339:0:0:0 = 1 + v339:0:0:0 ---------------------------------------- (22) YES