7.82/3.04 YES 7.82/3.05 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 7.82/3.05 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 7.82/3.05 7.82/3.05 7.82/3.05 Termination of the given C Problem could be proven: 7.82/3.05 7.82/3.05 (0) C Problem 7.82/3.05 (1) CToLLVMProof [EQUIVALENT, 171 ms] 7.82/3.05 (2) LLVM problem 7.82/3.05 (3) LLVMToTerminationGraphProof [EQUIVALENT, 685 ms] 7.82/3.05 (4) LLVM Symbolic Execution Graph 7.82/3.05 (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] 7.82/3.05 (6) LLVM Symbolic Execution SCC 7.82/3.05 (7) SCC2IRS [SOUND, 42 ms] 7.82/3.05 (8) IntTRS 7.82/3.05 (9) IntTRSCompressionProof [EQUIVALENT, 0 ms] 7.82/3.05 (10) IntTRS 7.82/3.05 (11) RankingReductionPairProof [EQUIVALENT, 21 ms] 7.82/3.05 (12) YES 7.82/3.05 7.82/3.05 7.82/3.05 ---------------------------------------- 7.82/3.05 7.82/3.05 (0) 7.82/3.05 Obligation: 7.82/3.05 c file /export/starexec/sandbox/benchmark/theBenchmark.c 7.82/3.05 ---------------------------------------- 7.82/3.05 7.82/3.05 (1) CToLLVMProof (EQUIVALENT) 7.82/3.05 Compiled c-file /export/starexec/sandbox/benchmark/theBenchmark.c to LLVM. 7.82/3.05 ---------------------------------------- 7.82/3.05 7.82/3.05 (2) 7.82/3.05 Obligation: 7.82/3.05 LLVM Problem 7.82/3.05 7.82/3.05 Aliases: 7.82/3.05 7.82/3.05 Data layout: 7.82/3.05 7.82/3.05 "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" 7.82/3.05 7.82/3.05 Machine: 7.82/3.05 7.82/3.05 "x86_64-pc-linux-gnu" 7.82/3.05 7.82/3.05 Type definitions: 7.82/3.05 7.82/3.05 Global variables: 7.82/3.05 7.82/3.05 Function declarations and definitions: 7.82/3.05 7.82/3.05 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 7.82/3.05 0: 7.82/3.05 %1 = alloca i32, align 4 7.82/3.05 %i = alloca i32, align 4 7.82/3.05 %c = alloca i32, align 4 7.82/3.05 store 0, %1 7.82/3.05 store 0, %i 7.82/3.05 store 0, %c 7.82/3.05 br %2 7.82/3.05 2: 7.82/3.05 %3 = load %i 7.82/3.05 %4 = icmp sgt %3 10 7.82/3.05 br %4, %5, %6 7.82/3.05 5: 7.82/3.05 br %11 7.82/3.05 6: 7.82/3.05 %7 = load %i 7.82/3.05 %8 = add %7 1 7.82/3.05 store %8, %i 7.82/3.05 %9 = load %c 7.82/3.05 %10 = add %9 1 7.82/3.05 store %10, %c 7.82/3.05 br %2 7.82/3.05 11: 7.82/3.05 %12 = load %c 7.82/3.05 ret %12 7.82/3.05 7.82/3.05 7.82/3.05 Analyze Termination of all function calls matching the pattern: 7.82/3.05 main() 7.82/3.05 ---------------------------------------- 7.82/3.05 7.82/3.05 (3) LLVMToTerminationGraphProof (EQUIVALENT) 7.82/3.05 Constructed symbolic execution graph for LLVM program and proved memory safety. 7.82/3.05 ---------------------------------------- 7.82/3.05 7.82/3.05 (4) 7.82/3.05 Obligation: 7.82/3.05 SE Graph 7.82/3.05 ---------------------------------------- 7.82/3.05 7.82/3.05 (5) SymbolicExecutionGraphToSCCProof (SOUND) 7.82/3.05 Splitted symbolic execution graph to 1 SCC. 7.82/3.05 ---------------------------------------- 7.82/3.05 7.82/3.05 (6) 7.82/3.05 Obligation: 7.82/3.05 SCC 7.82/3.05 ---------------------------------------- 7.82/3.05 7.82/3.05 (7) SCC2IRS (SOUND) 7.82/3.05 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 7.82/3.05 Generated rules. Obtained 12 rulesP rules: 7.82/3.05 f_147(v55, v56, v57, v60, 0, v58, v61, v62, v63, 3, 1, 4) -> f_149(v55, v56, v57, v60, 0, v58, v61, v62, v63, 3, 1, 9, 10, 4) :|: v60 <= 10 && v58 <= 9 7.82/3.05 f_149(v55, v56, v57, v60, 0, v58, v61, v62, v63, 3, 1, 9, 10, 4) -> f_151(v55, v56, v57, v60, 0, v58, v61, v62, v63, 3, 1, 9, 10, 4) :|: 0 = 0 7.82/3.05 f_151(v55, v56, v57, v60, 0, v58, v61, v62, v63, 3, 1, 9, 10, 4) -> f_153(v55, v56, v57, v60, 0, v58, v61, v62, v63, 3, 1, 9, 10, 4) :|: TRUE 7.82/3.05 f_153(v55, v56, v57, v60, 0, v58, v61, v62, v63, 3, 1, 9, 10, 4) -> f_155(v55, v56, v57, v60, 0, v58, v61, v62, v63, 3, 1, 9, 10, 4) :|: 0 = 0 7.82/3.05 f_155(v55, v56, v57, v60, 0, v58, v61, v62, v63, 3, 1, 9, 10, 4) -> f_157(v55, v56, v57, v60, 0, v64, v58, v61, v62, v63, 3, 1, 9, 10, 4, 2, 11) :|: v64 = 1 + v60 && 2 <= v64 && v64 <= 11 7.82/3.05 f_157(v55, v56, v57, v60, 0, v64, v58, v61, v62, v63, 3, 1, 9, 10, 4, 2, 11) -> f_158(v55, v56, v57, v60, 0, v64, v58, v61, v62, v63, 3, 1, 9, 10, 4, 2, 11) :|: TRUE 7.82/3.05 f_158(v55, v56, v57, v60, 0, v64, v58, v61, v62, v63, 3, 1, 9, 10, 4, 2, 11) -> f_159(v55, v56, v57, v60, 0, v64, v61, v62, v63, 3, 1, 10, 4, 2, 11) :|: 0 = 0 7.82/3.05 f_159(v55, v56, v57, v60, 0, v64, v61, v62, v63, 3, 1, 10, 4, 2, 11) -> f_160(v55, v56, v57, v60, 0, v64, v61, v62, v63, 3, 1, 10, 4, 2, 11) :|: v64 = 1 + v60 7.82/3.05 f_160(v55, v56, v57, v60, 0, v64, v61, v62, v63, 3, 1, 10, 4, 2, 11) -> f_161(v55, v56, v57, v60, 0, v64, v61, v62, v63, 3, 1, 10, 4, 2, 11) :|: TRUE 7.82/3.05 f_161(v55, v56, v57, v60, 0, v64, v61, v62, v63, 3, 1, 10, 4, 2, 11) -> f_162(v55, v56, v57, v60, 0, v64, v61, v62, v63, 3, 1, 10, 4, 2, 11) :|: TRUE 7.82/3.05 f_162(v55, v56, v57, v60, 0, v64, v61, v62, v63, 3, 1, 10, 4, 2, 11) -> f_146(v55, v56, v57, v60, 0, v64, v61, v62, v63, 3, 1, 4) :|: TRUE 7.82/3.05 f_146(v55, v56, v57, v58, 0, v60, v61, v62, v63, 3, 1, 4) -> f_147(v55, v56, v57, v60, 0, v58, v61, v62, v63, 3, 1, 4) :|: 0 = 0 7.82/3.05 Combined rules. Obtained 1 rulesP rules: 7.82/3.05 f_147(v55:0, v56:0, v57:0, v60:0, 0, v58:0, v61:0, v62:0, v63:0, 3, 1, 4) -> f_147(v55:0, v56:0, v57:0, 1 + v60:0, 0, v60:0, v61:0, v62:0, v63:0, 3, 1, 4) :|: v58:0 < 10 && v60:0 < 11 && v60:0 > 0 7.82/3.05 Filtered unneeded arguments: 7.82/3.05 f_147(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) -> f_147(x4, x6) 7.82/3.05 Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: 7.82/3.05 f_147(v60:0, v58:0) -> f_147(1 + v60:0, v60:0) :|: v60:0 < 11 && v60:0 > 0 && v58:0 < 10 7.82/3.05 7.82/3.05 ---------------------------------------- 7.82/3.05 7.82/3.05 (8) 7.82/3.05 Obligation: 7.82/3.05 Rules: 7.82/3.05 f_147(v60:0, v58:0) -> f_147(1 + v60:0, v60:0) :|: v60:0 < 11 && v60:0 > 0 && v58:0 < 10 7.82/3.05 7.82/3.05 ---------------------------------------- 7.82/3.05 7.82/3.05 (9) IntTRSCompressionProof (EQUIVALENT) 7.82/3.05 Compressed rules. 7.82/3.05 ---------------------------------------- 7.82/3.05 7.82/3.05 (10) 7.82/3.05 Obligation: 7.82/3.05 Rules: 7.82/3.05 f_147(v60:0:0, v58:0:0) -> f_147(1 + v60:0:0, v60:0:0) :|: v60:0:0 < 11 && v60:0:0 > 0 && v58:0:0 < 10 7.82/3.05 7.82/3.05 ---------------------------------------- 7.82/3.05 7.82/3.05 (11) RankingReductionPairProof (EQUIVALENT) 7.82/3.05 Interpretation: 7.82/3.05 [ f_147 ] = -1*f_147_1 7.82/3.05 7.82/3.05 The following rules are decreasing: 7.82/3.05 f_147(v60:0:0, v58:0:0) -> f_147(1 + v60:0:0, v60:0:0) :|: v60:0:0 < 11 && v60:0:0 > 0 && v58:0:0 < 10 7.82/3.05 7.82/3.05 The following rules are bounded: 7.82/3.05 f_147(v60:0:0, v58:0:0) -> f_147(1 + v60:0:0, v60:0:0) :|: v60:0:0 < 11 && v60:0:0 > 0 && v58:0:0 < 10 7.82/3.05 7.82/3.05 7.82/3.05 ---------------------------------------- 7.82/3.05 7.82/3.05 (12) 7.82/3.05 YES 7.82/3.09 EOF