9.79/3.80 YES 9.79/3.84 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 9.79/3.84 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.79/3.84 9.79/3.84 9.79/3.84 Termination of the given C Problem could be proven: 9.79/3.84 9.79/3.84 (0) C Problem 9.79/3.84 (1) CToLLVMProof [EQUIVALENT, 172 ms] 9.79/3.84 (2) LLVM problem 9.79/3.84 (3) LLVMToTerminationGraphProof [EQUIVALENT, 1286 ms] 9.79/3.84 (4) LLVM Symbolic Execution Graph 9.79/3.84 (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] 9.79/3.84 (6) LLVM Symbolic Execution SCC 9.79/3.84 (7) SCC2IRS [SOUND, 61 ms] 9.79/3.84 (8) IntTRS 9.79/3.84 (9) IntTRSCompressionProof [EQUIVALENT, 0 ms] 9.79/3.84 (10) IntTRS 9.79/3.84 (11) RankingReductionPairProof [EQUIVALENT, 22 ms] 9.79/3.84 (12) YES 9.79/3.84 9.79/3.84 9.79/3.84 ---------------------------------------- 9.79/3.84 9.79/3.84 (0) 9.79/3.84 Obligation: 9.79/3.84 c file /export/starexec/sandbox/benchmark/theBenchmark.c 9.79/3.84 ---------------------------------------- 9.79/3.84 9.79/3.84 (1) CToLLVMProof (EQUIVALENT) 9.79/3.84 Compiled c-file /export/starexec/sandbox/benchmark/theBenchmark.c to LLVM. 9.79/3.84 ---------------------------------------- 9.79/3.84 9.79/3.84 (2) 9.79/3.84 Obligation: 9.79/3.84 LLVM Problem 9.79/3.84 9.79/3.84 Aliases: 9.79/3.84 9.79/3.84 Data layout: 9.79/3.84 9.79/3.84 "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" 9.79/3.84 9.79/3.84 Machine: 9.79/3.84 9.79/3.84 "x86_64-pc-linux-gnu" 9.79/3.84 9.79/3.84 Type definitions: 9.79/3.84 9.79/3.84 Global variables: 9.79/3.84 9.79/3.84 Function declarations and definitions: 9.79/3.84 9.79/3.84 *BasicFunctionTypename: "__VERIFIER_nondet_int" returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 9.79/3.84 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 9.79/3.84 0: 9.79/3.84 %1 = alloca i32, align 4 9.79/3.84 %x = alloca i32, align 4 9.79/3.84 %c = alloca i32, align 4 9.79/3.84 store 0, %1 9.79/3.84 %2 = call i32 @__VERIFIER_nondet_int() 9.79/3.84 store %2, %x 9.79/3.84 %3 = call i32 @__VERIFIER_nondet_int() 9.79/3.84 store %3, %c 9.79/3.84 %4 = load %c 9.79/3.84 %5 = icmp slt %4 2 9.79/3.84 br %5, %6, %7 9.79/3.84 6: 9.79/3.84 store 0, %1 9.79/3.84 br %20 9.79/3.84 7: 9.79/3.84 br %8 9.79/3.84 8: 9.79/3.84 %9 = load %x 9.79/3.84 %10 = load %c 9.79/3.84 %11 = add %9 %10 9.79/3.84 %12 = icmp sge %11 0 9.79/3.84 br %12, %13, %19 9.79/3.84 13: 9.79/3.84 %14 = load %x 9.79/3.84 %15 = load %c 9.79/3.84 %16 = sub %14 %15 9.79/3.84 store %16, %x 9.79/3.84 %17 = load %c 9.79/3.84 %18 = add %17 1 9.79/3.84 store %18, %c 9.79/3.84 br %8 9.79/3.84 19: 9.79/3.84 store 0, %1 9.79/3.84 br %20 9.79/3.84 20: 9.79/3.84 %21 = load %1 9.79/3.84 ret %21 9.79/3.84 9.79/3.84 9.79/3.84 Analyze Termination of all function calls matching the pattern: 9.79/3.84 main() 9.79/3.84 ---------------------------------------- 9.79/3.84 9.79/3.84 (3) LLVMToTerminationGraphProof (EQUIVALENT) 9.79/3.84 Constructed symbolic execution graph for LLVM program and proved memory safety. 9.79/3.84 ---------------------------------------- 9.79/3.84 9.79/3.84 (4) 9.79/3.84 Obligation: 9.79/3.84 SE Graph 9.79/3.84 ---------------------------------------- 9.79/3.84 9.79/3.84 (5) SymbolicExecutionGraphToSCCProof (SOUND) 9.79/3.84 Splitted symbolic execution graph to 1 SCC. 9.79/3.84 ---------------------------------------- 9.79/3.84 9.79/3.84 (6) 9.79/3.84 Obligation: 9.79/3.84 SCC 9.79/3.84 ---------------------------------------- 9.79/3.84 9.79/3.84 (7) SCC2IRS (SOUND) 9.79/3.84 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 9.79/3.84 Generated rules. Obtained 15 rulesP rules: 9.79/3.84 f_178(v47, v48, v49, v50, v51, 0, v57, v54, v55, 1, v53, v58, v59, v60, v61, 3, 2, 4) -> f_179(v47, v48, v49, v50, v51, 0, v57, v58, v55, 1, v53, v54, v59, v60, v61, 3, 2, 4) :|: 0 = 0 9.79/3.84 f_179(v47, v48, v49, v50, v51, 0, v57, v58, v55, 1, v53, v54, v59, v60, v61, 3, 2, 4) -> f_180(v47, v48, v49, v50, v51, 0, v57, v58, v62, 1, v53, v54, v59, v60, v61, 3, 2, 4) :|: v62 = v57 + v58 9.79/3.84 f_180(v47, v48, v49, v50, v51, 0, v57, v58, v62, 1, v53, v54, v59, v60, v61, 3, 2, 4) -> f_181(v47, v48, v49, v50, v51, 0, v57, v58, v62, 1, v53, v54, v59, v60, v61, 3, 2, 4) :|: 0 <= v62 9.79/3.84 f_181(v47, v48, v49, v50, v51, 0, v57, v58, v62, 1, v53, v54, v59, v60, v61, 3, 2, 4) -> f_183(v47, v48, v49, v50, v51, 0, v57, v58, v62, 1, v53, v54, v59, v60, v61, 3, 2, 4) :|: 0 = 0 9.79/3.84 f_183(v47, v48, v49, v50, v51, 0, v57, v58, v62, 1, v53, v54, v59, v60, v61, 3, 2, 4) -> f_185(v47, v48, v49, v50, v51, 0, v57, v58, v62, 1, v53, v54, v59, v60, v61, 3, 2, 4) :|: TRUE 9.79/3.84 f_185(v47, v48, v49, v50, v51, 0, v57, v58, v62, 1, v53, v54, v59, v60, v61, 3, 2, 4) -> f_187(v47, v48, v49, v50, v51, 0, v57, v58, v62, 1, v54, v59, v60, v61, 3, 2, 4) :|: 0 = 0 9.79/3.84 f_187(v47, v48, v49, v50, v51, 0, v57, v58, v62, 1, v54, v59, v60, v61, 3, 2, 4) -> f_189(v47, v48, v49, v50, v51, 0, v57, v58, v62, 1, v54, v59, v60, v61, 3, 2, 4) :|: 0 = 0 9.79/3.84 f_189(v47, v48, v49, v50, v51, 0, v57, v58, v62, 1, v54, v59, v60, v61, 3, 2, 4) -> f_191(v47, v48, v49, v50, v51, 0, v57, v58, v62, 1, v66, v54, v59, v60, v61, 3, 2, 4) :|: v66 + v58 = v57 9.79/3.84 f_191(v47, v48, v49, v50, v51, 0, v57, v58, v62, 1, v66, v54, v59, v60, v61, 3, 2, 4) -> f_193(v47, v48, v49, v50, v51, 0, v57, v58, v62, 1, v66, v54, v59, v60, v61, 3, 2, 4) :|: TRUE 9.79/3.84 f_193(v47, v48, v49, v50, v51, 0, v57, v58, v62, 1, v66, v54, v59, v60, v61, 3, 2, 4) -> f_194(v47, v48, v49, v50, v51, 0, v57, v58, v62, 1, v66, v59, v60, v61, 3, 2, 4) :|: 0 = 0 9.79/3.84 f_194(v47, v48, v49, v50, v51, 0, v57, v58, v62, 1, v66, v59, v60, v61, 3, 2, 4) -> f_195(v47, v48, v49, v50, v51, 0, v57, v58, v62, 1, v66, v68, v59, v60, v61, 3, 2, 4) :|: v68 = 1 + v58 && 4 <= v68 9.79/3.84 f_195(v47, v48, v49, v50, v51, 0, v57, v58, v62, 1, v66, v68, v59, v60, v61, 3, 2, 4) -> f_196(v47, v48, v49, v50, v51, 0, v57, v58, v62, 1, v66, v68, v59, v60, v61, 3, 2, 4) :|: TRUE 9.79/3.84 f_196(v47, v48, v49, v50, v51, 0, v57, v58, v62, 1, v66, v68, v59, v60, v61, 3, 2, 4) -> f_197(v47, v48, v49, v50, v51, 0, v57, v58, v62, 1, v66, v68, v59, v60, v61, 3, 2, 4) :|: TRUE 9.79/3.84 f_197(v47, v48, v49, v50, v51, 0, v57, v58, v62, 1, v66, v68, v59, v60, v61, 3, 2, 4) -> f_177(v47, v48, v49, v50, v51, 0, v57, v58, v62, 1, v66, v68, v59, v60, v61, 3, 2, 4) :|: TRUE 9.79/3.84 f_177(v47, v48, v49, v50, v51, 0, v53, v54, v55, 1, v57, v58, v59, v60, v61, 3, 2, 4) -> f_178(v47, v48, v49, v50, v51, 0, v57, v54, v55, 1, v53, v58, v59, v60, v61, 3, 2, 4) :|: 0 = 0 9.79/3.84 Combined rules. Obtained 1 rulesP rules: 9.79/3.84 f_178(v47:0, v48:0, v49:0, v50:0, v51:0, 0, v66:0 + v58:0, v54:0, v55:0, 1, v53:0, v58:0, v59:0, v60:0, v61:0, 3, 2, 4) -> f_178(v47:0, v48:0, v49:0, v50:0, v51:0, 0, v66:0, v58:0, v66:0 + v58:0 + v58:0, 1, v66:0 + v58:0, 1 + v58:0, v59:0, v60:0, v61:0, 3, 2, 4) :|: v58:0 > 2 && v66:0 + v58:0 + v58:0 > -1 9.79/3.84 Filtered unneeded arguments: 9.79/3.84 f_178(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18) -> f_178(x7, x12) 9.79/3.84 Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: 9.79/3.84 f_178(sum~v66:0~v58:0, v58:0) -> f_178(v66:0, 1 + v58:0) :|: v58:0 > 2 && v66:0 + v58:0 + v58:0 > -1 && sum~v66:0~v58:0 = v66:0 + v58:0 9.79/3.84 9.79/3.84 ---------------------------------------- 9.79/3.84 9.79/3.84 (8) 9.79/3.84 Obligation: 9.79/3.84 Rules: 9.79/3.84 f_178(sum~v66:0~v58:0, v58:0) -> f_178(v66:0, 1 + v58:0) :|: v58:0 > 2 && v66:0 + v58:0 + v58:0 > -1 && sum~v66:0~v58:0 = v66:0 + v58:0 9.79/3.84 9.79/3.84 ---------------------------------------- 9.79/3.84 9.79/3.84 (9) IntTRSCompressionProof (EQUIVALENT) 9.79/3.84 Compressed rules. 9.79/3.84 ---------------------------------------- 9.79/3.84 9.79/3.84 (10) 9.79/3.84 Obligation: 9.79/3.84 Rules: 9.79/3.84 f_178(sum~v66:0:0~v58:0:0, v58:0:0) -> f_178(v66:0:0, 1 + v58:0:0) :|: v58:0:0 > 2 && v66:0:0 + v58:0:0 + v58:0:0 > -1 && sum~v66:0:0~v58:0:0 = v66:0:0 + v58:0:0 9.79/3.84 9.79/3.84 ---------------------------------------- 9.79/3.84 9.79/3.84 (11) RankingReductionPairProof (EQUIVALENT) 9.79/3.84 Interpretation: 9.79/3.84 [ f_178 ] = 1/2*f_178_2 + 1/2*f_178_1 9.79/3.84 9.79/3.84 The following rules are decreasing: 9.79/3.84 f_178(sum~v66:0:0~v58:0:0, v58:0:0) -> f_178(v66:0:0, 1 + v58:0:0) :|: v58:0:0 > 2 && v66:0:0 + v58:0:0 + v58:0:0 > -1 && sum~v66:0:0~v58:0:0 = v66:0:0 + v58:0:0 9.79/3.84 9.79/3.84 The following rules are bounded: 9.79/3.84 f_178(sum~v66:0:0~v58:0:0, v58:0:0) -> f_178(v66:0:0, 1 + v58:0:0) :|: v58:0:0 > 2 && v66:0:0 + v58:0:0 + v58:0:0 > -1 && sum~v66:0:0~v58:0:0 = v66:0:0 + v58:0:0 9.79/3.84 9.79/3.84 9.79/3.84 ---------------------------------------- 9.79/3.84 9.79/3.84 (12) 9.79/3.84 YES 10.84/3.93 EOF