28.88/8.95 YES 28.88/8.96 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 28.88/8.96 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 28.88/8.96 28.88/8.96 28.88/8.96 Termination of the given C Problem could be proven: 28.88/8.96 28.88/8.96 (0) C Problem 28.88/8.96 (1) CToLLVMProof [EQUIVALENT, 168 ms] 28.88/8.96 (2) LLVM problem 28.88/8.96 (3) LLVMToTerminationGraphProof [EQUIVALENT, 3591 ms] 28.88/8.96 (4) LLVM Symbolic Execution Graph 28.88/8.96 (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] 28.88/8.96 (6) AND 28.88/8.96 (7) LLVM Symbolic Execution SCC 28.88/8.96 (8) SCC2IRS [SOUND, 111 ms] 28.88/8.96 (9) IntTRS 28.88/8.96 (10) IRS2T2 [EQUIVALENT, 0 ms] 28.88/8.96 (11) T2IntSys 28.88/8.96 (12) T2 [EQUIVALENT, 1263 ms] 28.88/8.96 (13) YES 28.88/8.96 (14) LLVM Symbolic Execution SCC 28.88/8.96 (15) SCC2IRS [SOUND, 27 ms] 28.88/8.96 (16) IntTRS 28.88/8.96 (17) IntTRSCompressionProof [EQUIVALENT, 0 ms] 28.88/8.96 (18) IntTRS 28.88/8.96 (19) PolynomialOrderProcessor [EQUIVALENT, 12 ms] 28.88/8.96 (20) YES 28.88/8.96 (21) LLVM Symbolic Execution SCC 28.88/8.96 (22) SCC2IRS [SOUND, 45 ms] 28.88/8.96 (23) IntTRS 28.88/8.96 (24) TerminationGraphProcessor [EQUIVALENT, 17 ms] 28.88/8.96 (25) YES 28.88/8.96 28.88/8.96 28.88/8.96 ---------------------------------------- 28.88/8.96 28.88/8.96 (0) 28.88/8.96 Obligation: 28.88/8.96 c file /export/starexec/sandbox/benchmark/theBenchmark.c 28.88/8.96 ---------------------------------------- 28.88/8.96 28.88/8.96 (1) CToLLVMProof (EQUIVALENT) 28.88/8.96 Compiled c-file /export/starexec/sandbox/benchmark/theBenchmark.c to LLVM. 28.88/8.96 ---------------------------------------- 28.88/8.96 28.88/8.96 (2) 28.88/8.96 Obligation: 28.88/8.96 LLVM Problem 28.88/8.96 28.88/8.96 Aliases: 28.88/8.96 28.88/8.96 Data layout: 28.88/8.96 28.88/8.96 "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" 28.88/8.96 28.88/8.96 Machine: 28.88/8.96 28.88/8.96 "x86_64-pc-linux-gnu" 28.88/8.96 28.88/8.96 Type definitions: 28.88/8.96 28.88/8.96 Global variables: 28.88/8.96 28.88/8.96 Function declarations and definitions: 28.88/8.96 28.88/8.96 *BasicFunctionTypename: "__VERIFIER_nondet_int" returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 28.88/8.96 *BasicFunctionTypename: "test_fun" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: (x i32, y i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc 28.88/8.96 0: 28.88/8.96 %1 = alloca i32, align 4 28.88/8.96 %2 = alloca i32, align 4 28.88/8.96 %c = alloca i32, align 4 28.88/8.96 store %x, %1 28.88/8.96 store %y, %2 28.88/8.96 store 0, %c 28.88/8.96 br %3 28.88/8.96 3: 28.88/8.96 %4 = load %1 28.88/8.96 %5 = icmp sge %4 0 28.88/8.96 br %5, %6, %19 28.88/8.96 6: 28.88/8.96 store 1, %2 28.88/8.96 br %7 28.88/8.96 7: 28.88/8.96 %8 = load %1 28.88/8.96 %9 = load %2 28.88/8.96 %10 = icmp sgt %8 %9 28.88/8.96 br %10, %11, %16 28.88/8.96 11: 28.88/8.96 %12 = load %2 28.88/8.96 %13 = mul 2 %12 28.88/8.96 store %13, %2 28.88/8.96 %14 = load %c 28.88/8.96 %15 = add %14 1 28.88/8.96 store %15, %c 28.88/8.96 br %7 28.88/8.96 16: 28.88/8.96 %17 = load %1 28.88/8.96 %18 = sub %17 1 28.88/8.96 store %18, %1 28.88/8.96 br %3 28.88/8.96 19: 28.88/8.96 %20 = load %c 28.88/8.96 ret %20 28.88/8.96 28.88/8.96 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 28.88/8.96 0: 28.88/8.96 %1 = alloca i32, align 4 28.88/8.96 store 0, %1 28.88/8.96 %2 = call i32 @__VERIFIER_nondet_int() 28.88/8.96 %3 = call i32 @__VERIFIER_nondet_int() 28.88/8.96 %4 = call i32 @test_fun(i32 %2, i32 %3) 28.88/8.96 ret %4 28.88/8.96 28.88/8.96 28.88/8.96 Analyze Termination of all function calls matching the pattern: 28.88/8.96 main() 28.88/8.96 ---------------------------------------- 28.88/8.96 28.88/8.96 (3) LLVMToTerminationGraphProof (EQUIVALENT) 28.88/8.96 Constructed symbolic execution graph for LLVM program and proved memory safety. 28.88/8.96 ---------------------------------------- 28.88/8.96 28.88/8.96 (4) 28.88/8.96 Obligation: 28.88/8.96 SE Graph 28.88/8.96 ---------------------------------------- 28.88/8.96 28.88/8.96 (5) SymbolicExecutionGraphToSCCProof (SOUND) 28.88/8.96 Splitted symbolic execution graph to 3 SCCs. 28.88/8.96 ---------------------------------------- 28.88/8.96 28.88/8.96 (6) 28.88/8.96 Complex Obligation (AND) 28.88/8.96 28.88/8.96 ---------------------------------------- 28.88/8.96 28.88/8.96 (7) 28.88/8.96 Obligation: 28.88/8.96 SCC 28.88/8.96 ---------------------------------------- 28.88/8.96 28.88/8.96 (8) SCC2IRS (SOUND) 28.88/8.96 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 28.88/8.96 Generated rules. Obtained 38 rulesP rules: 28.88/8.96 f_454(v553, v554, v555, v556, v557, v558, 1, v560, v562, v563, v564, v565, v566, v567, v568, v569, v570, 0, 3, 2, 4) -> f_455(v553, v554, v555, v556, v557, v558, 1, v560, v572, v563, v564, v565, v566, v567, v568, v569, v570, 0, 3, 2, 4) :|: v572 = 2 * v560 && 2 <= v572 28.88/8.96 f_455(v553, v554, v555, v556, v557, v558, 1, v560, v572, v563, v564, v565, v566, v567, v568, v569, v570, 0, 3, 2, 4) -> f_456(v553, v554, v555, v556, v557, v558, 1, v560, v572, v563, v564, v565, v566, v567, v568, v569, v570, 0, 3, 2, 4) :|: TRUE 28.88/8.96 f_456(v553, v554, v555, v556, v557, v558, 1, v560, v572, v563, v564, v565, v566, v567, v568, v569, v570, 0, 3, 2, 4) -> f_457(v553, v554, v555, v556, v557, v558, 1, v560, v572, v564, v565, v566, v567, v568, v569, v570, 0, 3, 2, 4) :|: 0 = 0 28.88/8.96 f_457(v553, v554, v555, v556, v557, v558, 1, v560, v572, v564, v565, v566, v567, v568, v569, v570, 0, 3, 2, 4) -> f_458(v553, v554, v555, v556, v557, v558, 1, v560, v572, v564, v574, v565, v566, v567, v568, v569, v570, 0, 3, 2, 4) :|: v574 = 1 + v564 && 2 <= v574 28.88/8.96 f_458(v553, v554, v555, v556, v557, v558, 1, v560, v572, v564, v574, v565, v566, v567, v568, v569, v570, 0, 3, 2, 4) -> f_459(v553, v554, v555, v556, v557, v558, 1, v560, v572, v564, v574, v565, v566, v567, v568, v569, v570, 0, 3, 2, 4) :|: TRUE 28.88/8.96 f_459(v553, v554, v555, v556, v557, v558, 1, v560, v572, v564, v574, v565, v566, v567, v568, v569, v570, 0, 3, 2, 4) -> f_460(v553, v554, v555, v556, v557, v558, 1, v560, v572, v564, v574, v565, v566, v567, v568, v569, v570, 0, 3, 2, 4) :|: TRUE 28.88/8.96 f_460(v553, v554, v555, v556, v557, v558, 1, v560, v572, v564, v574, v565, v566, v567, v568, v569, v570, 0, 3, 2, 4) -> f_461(v553, v554, v555, v556, v557, v558, 1, v560, v572, v564, v574, v565, v566, v567, v568, v569, v570, 0, 3, 2, 4) :|: 0 = 0 28.88/8.96 f_461(v553, v554, v555, v556, v557, v558, 1, v560, v572, v564, v574, v565, v566, v567, v568, v569, v570, 0, 3, 2, 4) -> f_462(v553, v554, v555, v556, v557, v558, 1, v572, v560, v564, v574, v565, v566, v567, v568, v569, v570, 0, 3, 2, 4) :|: 0 = 0 28.88/8.96 f_462(v553, v554, v555, v556, v557, v558, 1, v572, v560, v564, v574, v565, v566, v567, v568, v569, v570, 0, 3, 2, 4) -> f_463(v553, v554, v555, v556, v557, v558, 1, v572, v560, v564, v574, v565, v566, v567, v568, v569, v570, 0, 3, 2, 4) :|: v572 < v558 && 3 <= v558 && 4 <= v565 && 4 <= v553 28.88/8.96 f_462(v553, v554, v555, v556, v557, v558, 1, v572, v560, v564, v574, v565, v566, v567, v568, v569, v570, 0, 3, 2, 4) -> f_464(v553, v554, v555, v556, v557, v558, 1, v572, v560, v564, v574, v565, v566, v567, v568, v569, v570, 0, 3, 2, 4) :|: v558 <= v572 28.88/8.96 f_463(v553, v554, v555, v556, v557, v558, 1, v572, v560, v564, v574, v565, v566, v567, v568, v569, v570, 0, 3, 2, 4) -> f_465(v553, v554, v555, v556, v557, v558, 1, v572, v560, v564, v574, v565, v566, v567, v568, v569, v570, 0, 3, 2, 4) :|: 0 = 0 28.88/8.96 f_465(v553, v554, v555, v556, v557, v558, 1, v572, v560, v564, v574, v565, v566, v567, v568, v569, v570, 0, 3, 2, 4) -> f_467(v553, v554, v555, v556, v557, v558, 1, v572, v560, v564, v574, v565, v566, v567, v568, v569, v570, 0, 3, 2, 4) :|: TRUE 28.88/8.96 f_467(v553, v554, v555, v556, v557, v558, 1, v572, v560, v564, v574, v565, v566, v567, v568, v569, v570, 0, 3, 2, 4) -> f_453(v553, v554, v555, v556, v557, v558, 1, v572, v560, v572, v564, v574, v565, v566, v567, v568, v569, v570, 0, 3, 2, 4) :|: TRUE 28.88/8.96 f_453(v553, v554, v555, v556, v557, v558, 1, v560, v561, v562, v563, v564, v565, v566, v567, v568, v569, v570, 0, 3, 2, 4) -> f_454(v553, v554, v555, v556, v557, v558, 1, v560, v562, v563, v564, v565, v566, v567, v568, v569, v570, 0, 3, 2, 4) :|: 0 = 0 28.88/8.96 f_464(v553, v554, v555, v556, v557, v558, 1, v572, v560, v564, v574, v565, v566, v567, v568, v569, v570, 0, 3, 2, 4) -> f_466(v553, v554, v555, v556, v557, v558, 1, v572, 0, v560, v564, v574, v565, v566, v567, v568, v569, v570, 3, 2, 4) :|: 0 = 0 28.88/8.96 f_466(v553, v554, v555, v556, v557, v558, 1, v572, 0, v560, v564, v574, v565, v566, v567, v568, v569, v570, 3, 2, 4) -> f_468(v553, v554, v555, v556, v557, v558, 1, v572, 0, v560, v564, v574, v565, v566, v567, v568, v569, v570, 3, 2, 4) :|: TRUE 28.88/8.96 f_468(v553, v554, v555, v556, v557, v558, 1, v572, 0, v560, v564, v574, v565, v566, v567, v568, v569, v570, 3, 2, 4) -> f_487(v553, v554, v555, v556, v557, v558, 1, v572, 0, v560, v572, v564, v574, v565, v566, v567, v568, v569, v570, 3, 2, 4) :|: TRUE 28.88/8.96 f_487(v771, v772, v773, v774, v775, v776, 1, v778, 0, v780, v781, v782, v783, v784, v785, v786, v787, v788, v789, 3, 2, 4) -> f_488(v771, v772, v773, v774, v775, v776, 1, v778, 0, v780, v781, v782, v783, v785, v786, v787, v788, v789, 3, 2, 4) :|: 0 = 0 28.88/8.96 f_488(v771, v772, v773, v774, v775, v776, 1, v778, 0, v780, v781, v782, v783, v785, v786, v787, v788, v789, 3, 2, 4) -> f_489(v771, v772, v773, v774, v775, v776, 1, v778, 0, v780, v781, v782, v783, v790, v785, v786, v787, v788, v789, 3, 2, 4) :|: 1 + v790 = v776 && 0 <= 1 + v790 28.88/8.96 f_489(v771, v772, v773, v774, v775, v776, 1, v778, 0, v780, v781, v782, v783, v790, v785, v786, v787, v788, v789, 3, 2, 4) -> f_490(v771, v772, v773, v774, v775, v776, 1, v778, 0, v780, v781, v782, v783, v790, v785, v786, v787, v788, v789, 3, 2, 4) :|: TRUE 28.88/8.96 f_490(v771, v772, v773, v774, v775, v776, 1, v778, 0, v780, v781, v782, v783, v790, v785, v786, v787, v788, v789, 3, 2, 4) -> f_491(v771, v772, v773, v774, v775, v776, 1, v778, 0, v780, v781, v782, v783, v790, v785, v786, v787, v788, v789, 3, 2, 4) :|: TRUE 28.88/8.96 f_491(v771, v772, v773, v774, v775, v776, 1, v778, 0, v780, v781, v782, v783, v790, v785, v786, v787, v788, v789, 3, 2, 4) -> f_492(v771, v772, v773, v774, v775, v790, 1, v776, v778, 0, v780, v781, v782, v783, v785, v786, v787, v788, v789, 3, 2, 4) :|: 0 = 0 28.88/8.96 f_492(v771, v772, v773, v774, v775, v790, 1, v776, v778, 0, v780, v781, v782, v783, v785, v786, v787, v788, v789, 3, 2, 4) -> f_493(v771, v772, v773, v774, v775, v790, 1, v776, v778, 0, v780, v781, v782, v783, v785, v786, v787, v788, v789, 3, 2, 4) :|: 0 <= v790 && 1 <= v776 28.88/8.96 f_493(v771, v772, v773, v774, v775, v790, 1, v776, v778, 0, v780, v781, v782, v783, v785, v786, v787, v788, v789, 3, 2, 4) -> f_495(v771, v772, v773, v774, v775, v790, 1, v776, v778, 0, v780, v781, v782, v783, v785, v786, v787, v788, v789, 3, 2, 4) :|: 0 = 0 28.88/8.96 f_495(v771, v772, v773, v774, v775, v790, 1, v776, v778, 0, v780, v781, v782, v783, v785, v786, v787, v788, v789, 3, 2, 4) -> f_497(v771, v772, v773, v774, v775, v790, 1, v776, v778, 0, v780, v781, v782, v783, v785, v786, v787, v788, v789, 3, 2, 4) :|: TRUE 28.88/8.96 f_497(v771, v772, v773, v774, v775, v790, 1, v776, v778, 0, v780, v781, v782, v783, v785, v786, v787, v788, v789, 3, 2, 4) -> f_499(v771, v772, v773, v774, v775, v790, 1, v776, v778, 0, v780, v781, v782, v783, v785, v786, v787, v788, v789, 3, 2, 4) :|: TRUE 28.88/8.96 f_499(v771, v772, v773, v774, v775, v790, 1, v776, v778, 0, v780, v781, v782, v783, v785, v786, v787, v788, v789, 3, 2, 4) -> f_501(v771, v772, v773, v774, v775, v790, 1, v776, v778, 0, v780, v781, v782, v783, v785, v786, v787, v788, v789, 3, 2, 4) :|: TRUE 28.88/8.96 f_501(v771, v772, v773, v774, v775, v790, 1, v776, v778, 0, v780, v781, v782, v783, v785, v786, v787, v788, v789, 3, 2, 4) -> f_478(v771, v772, v773, v774, v775, v790, 1, v776, v778, 0, v780, v781, v782, v783, v785, v786, v787, v788, v789, 3, 2, 4) :|: TRUE 28.88/8.96 f_478(v691, v692, v693, v694, v695, v696, 1, v698, v699, 0, v701, v702, v703, v704, v705, v706, v707, v708, v709, 3, 2, 4) -> f_479(v691, v692, v693, v694, v695, v696, 1, v699, 0, v701, v702, v703, v704, v698, v705, v706, v707, v708, v709, 3, 2, 4) :|: 0 = 0 28.88/8.96 f_479(v691, v692, v693, v694, v695, v696, 1, v699, 0, v701, v702, v703, v704, v698, v705, v706, v707, v708, v709, 3, 2, 4) -> f_480(v691, v692, v693, v694, v695, v696, 1, 0, v701, v702, v703, v704, v698, v705, v706, v707, v708, v709, 3, 2, 4) :|: 0 = 0 28.88/8.96 f_480(v691, v692, v693, v694, v695, v696, 1, 0, v701, v702, v703, v704, v698, v705, v706, v707, v708, v709, 3, 2, 4) -> f_481(v691, v692, v693, v694, v695, v696, 1, 0, v701, v702, v703, v704, v698, v705, v706, v707, v708, v709, 3, 2, 4) :|: 1 < v696 && 3 <= v698 && 3 <= v691 && 4 <= v702 && 2 <= v701 28.88/8.96 f_480(v691, v692, v693, v694, v695, v696, 1, 0, v701, v702, v703, v704, v698, v705, v706, v707, v708, v709, 3, 2, 4) -> f_482(v691, v692, v693, v694, v695, v696, 1, 0, v701, v702, v703, v704, v698, v705, v706, v707, v708, v709, 3, 2, 4) :|: v696 <= 1 && v698 <= 2 28.88/8.96 f_481(v691, v692, v693, v694, v695, v696, 1, 0, v701, v702, v703, v704, v698, v705, v706, v707, v708, v709, 3, 2, 4) -> f_483(v691, v692, v693, v694, v695, v696, 1, v701, v702, v703, v704, v698, v705, v706, v707, v708, v709, 0, 3, 2, 4) :|: 0 = 0 28.88/8.96 f_483(v691, v692, v693, v694, v695, v696, 1, v701, v702, v703, v704, v698, v705, v706, v707, v708, v709, 0, 3, 2, 4) -> f_485(v691, v692, v693, v694, v695, v696, 1, v701, v702, v703, v704, v698, v705, v706, v707, v708, v709, 0, 3, 2, 4) :|: TRUE 28.88/8.96 f_485(v691, v692, v693, v694, v695, v696, 1, v701, v702, v703, v704, v698, v705, v706, v707, v708, v709, 0, 3, 2, 4) -> f_453(v691, v692, v693, v694, v695, v696, 1, 1, v701, v702, v703, v704, v698, v705, v706, v707, v708, v709, 0, 3, 2, 4) :|: TRUE 28.88/8.96 f_482(v691, v692, v693, v694, v695, v696, 1, 0, v701, v702, v703, v704, v698, v705, v706, v707, v708, v709, 3, 2, 4) -> f_484(v691, v692, v693, v694, v695, v696, 1, 0, v701, v702, v703, v704, v698, v705, v706, v707, v708, v709, 3, 2, 4) :|: 0 = 0 28.88/8.96 f_484(v691, v692, v693, v694, v695, v696, 1, 0, v701, v702, v703, v704, v698, v705, v706, v707, v708, v709, 3, 2, 4) -> f_486(v691, v692, v693, v694, v695, v696, 1, 0, v701, v702, v703, v704, v698, v705, v706, v707, v708, v709, 3, 2, 4) :|: TRUE 28.88/8.96 f_486(v691, v692, v693, v694, v695, v696, 1, 0, v701, v702, v703, v704, v698, v705, v706, v707, v708, v709, 3, 2, 4) -> f_487(v691, v692, v693, v694, v695, v696, 1, 1, 0, v701, v702, v703, v704, v698, v705, v706, v707, v708, v709, 3, 2, 4) :|: TRUE 28.88/8.96 Combined rules. Obtained 4 rulesP rules: 28.88/8.96 f_480(v691:0, v692:0, v693:0, v694:0, v695:0, 1 + v790:0, 1, 0, v701:0, v702:0, v703:0, v704:0, v698:0, v705:0, v706:0, v707:0, v708:0, v709:0, 3, 2, 4) -> f_480(v691:0, v692:0, v693:0, v694:0, v695:0, v790:0, 1, 0, v701:0, v702:0, v703:0, v704:0, 1 + v790:0, v705:0, v706:0, v707:0, v708:0, v709:0, 3, 2, 4) :|: v790:0 > -1 && v790:0 < 1 && v698:0 < 3 28.88/8.96 f_480(v691:0, v692:0, v693:0, v694:0, v695:0, v696:0, 1, 0, v701:0, v702:0, v703:0, v704:0, v698:0, v705:0, v706:0, v707:0, v708:0, v709:0, 3, 2, 4) -> f_454(v691:0, v692:0, v693:0, v694:0, v695:0, v696:0, 1, 1, v702:0, v703:0, v704:0, v698:0, v705:0, v706:0, v707:0, v708:0, v709:0, 0, 3, 2, 4) :|: v698:0 > 2 && v696:0 > 1 && v691:0 > 2 && v701:0 > 1 && v702:0 > 3 28.88/8.96 f_454(v553:0, v554:0, v555:0, v556:0, v557:0, 1 + v790:0, 1, v560:0, v562:0, v563:0, v564:0, v565:0, v566:0, v567:0, v568:0, v569:0, v570:0, 0, 3, 2, 4) -> f_480(v553:0, v554:0, v555:0, v556:0, v557:0, v790:0, 1, 0, v560:0, 2 * v560:0, v564:0, 1 + v564:0, 1 + v790:0, v566:0, v567:0, v568:0, v569:0, v570:0, 3, 2, 4) :|: v790:0 > -1 && 2 * v560:0 > 1 && v564:0 > 0 && 2 * v560:0 >= 1 + v790:0 28.88/8.96 f_454(v553:0, v554:0, v555:0, v556:0, v557:0, v558:0, 1, v560:0, v562:0, v563:0, v564:0, v565:0, v566:0, v567:0, v568:0, v569:0, v570:0, 0, 3, 2, 4) -> f_454(v553:0, v554:0, v555:0, v556:0, v557:0, v558:0, 1, 2 * v560:0, 2 * v560:0, v564:0, 1 + v564:0, v565:0, v566:0, v567:0, v568:0, v569:0, v570:0, 0, 3, 2, 4) :|: 2 * v560:0 > 1 && v564:0 > 0 && v558:0 > 2 && v558:0 > 2 * v560:0 && v553:0 > 3 && v565:0 > 3 28.88/8.96 Filtered unneeded arguments: 28.88/8.96 f_480(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21) -> f_480(x1, x6, x9, x10, x12, x13) 28.88/8.96 f_454(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21) -> f_454(x1, x6, x8, x11, x12) 28.88/8.96 Removed division, modulo operations, cleaned up constraints. Obtained 4 rules.P rules: 28.88/8.96 f_480(v691:0, sum~cons_1~v790:0, v701:0, v702:0, v704:0, v698:0) -> f_480(v691:0, v790:0, v701:0, v702:0, v704:0, 1 + v790:0) :|: v790:0 < 1 && v698:0 < 3 && v790:0 > -1 && sum~cons_1~v790:0 = 1 + v790:0 28.88/8.96 f_480(v691:0, v696:0, v701:0, v702:0, v704:0, v698:0) -> f_454(v691:0, v696:0, 1, v704:0, v698:0) :|: v696:0 > 1 && v698:0 > 2 && v691:0 > 2 && v702:0 > 3 && v701:0 > 1 28.88/8.96 f_454(v553:0, sum~cons_1~v790:0, v560:0, v564:0, v565:0) -> f_480(v553:0, v790:0, v560:0, 2 * v560:0, 1 + v564:0, 1 + v790:0) :|: 2 * v560:0 > 1 && v790:0 > -1 && 2 * v560:0 >= 1 + v790:0 && v564:0 > 0 && sum~cons_1~v790:0 = 1 + v790:0 28.88/8.96 f_454(v553:0, v558:0, v560:0, v564:0, v565:0) -> f_454(v553:0, v558:0, 2 * v560:0, 1 + v564:0, v565:0) :|: v564:0 > 0 && 2 * v560:0 > 1 && v558:0 > 2 && v558:0 > 2 * v560:0 && v565:0 > 3 && v553:0 > 3 28.88/8.96 28.88/8.96 ---------------------------------------- 28.88/8.96 28.88/8.96 (9) 28.88/8.96 Obligation: 28.88/8.96 Rules: 28.88/8.96 f_480(v691:0, sum~cons_1~v790:0, v701:0, v702:0, v704:0, v698:0) -> f_480(v691:0, v790:0, v701:0, v702:0, v704:0, 1 + v790:0) :|: v790:0 < 1 && v698:0 < 3 && v790:0 > -1 && sum~cons_1~v790:0 = 1 + v790:0 28.88/8.96 f_480(x, x1, x2, x3, x4, x5) -> f_454(x, x1, 1, x4, x5) :|: x1 > 1 && x5 > 2 && x > 2 && x3 > 3 && x2 > 1 28.88/8.96 f_454(x6, x7, x8, x9, x10) -> f_480(x6, x11, x8, 2 * x8, 1 + x9, 1 + x11) :|: 2 * x8 > 1 && x11 > -1 && 2 * x8 >= 1 + x11 && x9 > 0 && x7 = 1 + x11 28.88/8.96 f_454(v553:0, v558:0, v560:0, v564:0, v565:0) -> f_454(v553:0, v558:0, 2 * v560:0, 1 + v564:0, v565:0) :|: v564:0 > 0 && 2 * v560:0 > 1 && v558:0 > 2 && v558:0 > 2 * v560:0 && v565:0 > 3 && v553:0 > 3 28.88/8.96 28.88/8.96 ---------------------------------------- 28.88/8.96 28.88/8.96 (10) IRS2T2 (EQUIVALENT) 28.88/8.96 Transformed input IRS into an integer transition system.Used the following mapping from defined symbols to location IDs: 28.88/8.96 28.88/8.96 (f_480_6,1) 28.88/8.96 (f_454_6,2) 28.88/8.96 28.88/8.96 ---------------------------------------- 28.88/8.96 28.88/8.96 (11) 28.88/8.96 Obligation: 28.88/8.96 START: 0; 28.88/8.96 28.88/8.96 FROM: 0; 28.88/8.96 TO: 1; 28.88/8.96 28.88/8.96 FROM: 0; 28.88/8.96 TO: 2; 28.88/8.96 28.88/8.96 FROM: 1; 28.88/8.96 oldX0 := x0; 28.88/8.96 oldX1 := x1; 28.88/8.96 oldX2 := x2; 28.88/8.96 oldX3 := x3; 28.88/8.96 oldX4 := x4; 28.88/8.96 oldX5 := x5; 28.88/8.96 oldX6 := oldX1 - 1; 28.88/8.96 assume(oldX6 < 1 && oldX5 < 3 && oldX6 > -1 && oldX1 = 1 + oldX6); 28.88/8.96 x0 := oldX0; 28.88/8.96 x1 := oldX1 - 1; 28.88/8.96 x2 := oldX2; 28.88/8.96 x3 := oldX3; 28.88/8.96 x4 := oldX4; 28.88/8.96 x5 := 1 + oldX6; 28.88/8.96 TO: 1; 28.88/8.96 28.88/8.96 FROM: 1; 28.88/8.96 oldX0 := x0; 28.88/8.96 oldX1 := x1; 28.88/8.96 oldX2 := x2; 28.88/8.96 oldX3 := x3; 28.88/8.96 oldX4 := x4; 28.88/8.96 oldX5 := x5; 28.88/8.96 oldX6 := nondet(); 28.88/8.96 assume(oldX1 > 1 && oldX5 > 2 && oldX0 > 2 && oldX3 > 3 && oldX2 > 1); 28.88/8.96 x0 := oldX0; 28.88/8.96 x1 := oldX1; 28.88/8.96 x2 := 1; 28.88/8.96 x3 := oldX4; 28.88/8.96 x4 := oldX5; 28.88/8.96 x5 := oldX6; 28.88/8.96 TO: 2; 28.88/8.96 28.88/8.96 FROM: 2; 28.88/8.96 oldX0 := x0; 28.88/8.96 oldX1 := x1; 28.88/8.96 oldX2 := x2; 28.88/8.96 oldX3 := x3; 28.88/8.96 oldX4 := x4; 28.88/8.96 oldX5 := x5; 28.88/8.96 oldX6 := oldX1 - 1; 28.88/8.96 assume(2 * oldX2 > 1 && oldX6 > -1 && 2 * oldX2 >= 1 + oldX6 && oldX3 > 0 && oldX1 = 1 + oldX6); 28.88/8.96 x0 := oldX0; 28.88/8.96 x1 := oldX1 - 1; 28.88/8.96 x2 := oldX2; 28.88/8.96 x3 := 2 * oldX2; 28.88/8.96 x4 := 1 + oldX3; 28.88/8.96 x5 := 1 + oldX6; 28.88/8.96 TO: 1; 28.88/8.96 28.88/8.96 FROM: 2; 28.88/8.96 oldX0 := x0; 28.88/8.96 oldX1 := x1; 28.88/8.96 oldX2 := x2; 28.88/8.96 oldX3 := x3; 28.88/8.96 oldX4 := x4; 28.88/8.96 oldX5 := x5; 28.88/8.96 oldX6 := nondet(); 28.88/8.96 assume(oldX3 > 0 && 2 * oldX2 > 1 && oldX1 > 2 && oldX1 > 2 * oldX2 && oldX4 > 3 && oldX0 > 3); 28.88/8.96 x0 := oldX0; 28.88/8.96 x1 := oldX1; 28.88/8.96 x2 := 2 * oldX2; 28.88/8.96 x3 := 1 + oldX3; 28.88/8.96 x4 := oldX4; 28.88/8.96 x5 := oldX6; 28.88/8.96 TO: 2; 28.88/8.96 28.88/8.96 28.88/8.96 ---------------------------------------- 28.88/8.96 28.88/8.96 (12) T2 (EQUIVALENT) 28.88/8.96 Initially, performed program simplifications using lexicographic rank functions: 28.88/8.96 * Removed transitions 2, 5, 6, 14, 17, 18 using the following rank functions: 28.88/8.96 - Rank function 1: 28.88/8.96 RF for loc. 6: 1+x1 28.88/8.96 RF for loc. 7: x1 28.88/8.96 RF for loc. 8: 1+x1 28.88/8.96 RF for loc. 12: x1 28.88/8.96 Bound for (chained) transitions 5: 2 28.88/8.96 Bound for (chained) transitions 6: 3 28.88/8.96 - Rank function 2: 28.88/8.96 RF for loc. 6: -2*oldX2 28.88/8.96 RF for loc. 7: 1+x1-2*x2 28.88/8.96 RF for loc. 8: -1-2*oldX2 28.88/8.96 RF for loc. 12: x1-2*x2 28.88/8.96 Bound for (chained) transitions 18: 1 28.88/8.96 - Rank function 3: 28.88/8.96 RF for loc. 6: -2 28.88/8.96 RF for loc. 7: 0 28.88/8.96 RF for loc. 8: -3 28.88/8.96 RF for loc. 12: -1 28.88/8.96 Bound for (chained) transitions 2: -2 28.88/8.96 Bound for (chained) transitions 14: 0 28.88/8.96 - Rank function 4: 28.88/8.96 RF for loc. 6: 0 28.88/8.96 RF for loc. 12: 1 28.88/8.96 Bound for (chained) transitions 17: 1 28.88/8.96 28.88/8.96 ---------------------------------------- 28.88/8.96 28.88/8.96 (13) 28.88/8.96 YES 28.88/8.96 28.88/8.96 ---------------------------------------- 28.88/8.96 28.88/8.96 (14) 28.88/8.96 Obligation: 28.88/8.96 SCC 28.88/8.96 ---------------------------------------- 28.88/8.96 28.88/8.96 (15) SCC2IRS (SOUND) 28.88/8.96 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 28.88/8.97 Generated rules. Obtained 13 rulesP rules: 28.88/8.97 f_323(v200, v201, v202, v203, v204, 1, v206, v207, v208, v209, v210, v211, v212, v213, v214, 0, 3, 2, 4) -> f_324(v200, v201, v202, v203, v204, 1, v207, v206, v208, v209, v210, v211, v212, v213, v214, 0, 3, 2, 4) :|: 0 = 0 28.88/8.97 f_324(v200, v201, v202, v203, v204, 1, v207, v206, v208, v209, v210, v211, v212, v213, v214, 0, 3, 2, 4) -> f_325(v200, v201, v202, v203, v204, 1, v207, v206, v208, v209, v210, v211, v212, v213, v214, 0, 3, 2, 4) :|: v207 < v200 && 3 <= v200 28.88/8.97 f_325(v200, v201, v202, v203, v204, 1, v207, v206, v208, v209, v210, v211, v212, v213, v214, 0, 3, 2, 4) -> f_327(v200, v201, v202, v203, v204, 1, v207, v206, v208, v209, v210, v211, v212, v213, v214, 0, 3, 2, 4) :|: 0 = 0 28.88/8.97 f_327(v200, v201, v202, v203, v204, 1, v207, v206, v208, v209, v210, v211, v212, v213, v214, 0, 3, 2, 4) -> f_329(v200, v201, v202, v203, v204, 1, v207, v206, v208, v209, v210, v211, v212, v213, v214, 0, 3, 2, 4) :|: TRUE 28.88/8.97 f_329(v200, v201, v202, v203, v204, 1, v207, v206, v208, v209, v210, v211, v212, v213, v214, 0, 3, 2, 4) -> f_331(v200, v201, v202, v203, v204, 1, v207, v208, v209, v210, v211, v212, v213, v214, 0, 3, 2, 4) :|: 0 = 0 28.88/8.97 f_331(v200, v201, v202, v203, v204, 1, v207, v208, v209, v210, v211, v212, v213, v214, 0, 3, 2, 4) -> f_333(v200, v201, v202, v203, v204, 1, v207, v216, v208, v209, v210, v211, v212, v213, v214, 0, 3, 2, 4) :|: v216 = 2 * v207 && 4 <= v216 28.88/8.97 f_333(v200, v201, v202, v203, v204, 1, v207, v216, v208, v209, v210, v211, v212, v213, v214, 0, 3, 2, 4) -> f_335(v200, v201, v202, v203, v204, 1, v207, v216, v208, v209, v210, v211, v212, v213, v214, 0, 3, 2, 4) :|: TRUE 28.88/8.97 f_335(v200, v201, v202, v203, v204, 1, v207, v216, v208, v209, v210, v211, v212, v213, v214, 0, 3, 2, 4) -> f_337(v200, v201, v202, v203, v204, 1, v207, v216, v209, v210, v211, v212, v213, v214, 0, 3, 2, 4) :|: 0 = 0 28.88/8.97 f_337(v200, v201, v202, v203, v204, 1, v207, v216, v209, v210, v211, v212, v213, v214, 0, 3, 2, 4) -> f_339(v200, v201, v202, v203, v204, 1, v207, v216, v209, v220, v210, v211, v212, v213, v214, 0, 3, 2, 4) :|: v220 = 1 + v209 && 2 <= v220 28.88/8.97 f_339(v200, v201, v202, v203, v204, 1, v207, v216, v209, v220, v210, v211, v212, v213, v214, 0, 3, 2, 4) -> f_341(v200, v201, v202, v203, v204, 1, v207, v216, v209, v220, v210, v211, v212, v213, v214, 0, 3, 2, 4) :|: TRUE 28.88/8.97 f_341(v200, v201, v202, v203, v204, 1, v207, v216, v209, v220, v210, v211, v212, v213, v214, 0, 3, 2, 4) -> f_343(v200, v201, v202, v203, v204, 1, v207, v216, v209, v220, v210, v211, v212, v213, v214, 0, 3, 2, 4) :|: TRUE 28.88/8.97 f_343(v200, v201, v202, v203, v204, 1, v207, v216, v209, v220, v210, v211, v212, v213, v214, 0, 3, 2, 4) -> f_322(v200, v201, v202, v203, v204, 1, v207, v216, v209, v220, v210, v211, v212, v213, v214, 0, 3, 2, 4) :|: TRUE 28.88/8.97 f_322(v200, v201, v202, v203, v204, 1, v206, v207, v208, v209, v210, v211, v212, v213, v214, 0, 3, 2, 4) -> f_323(v200, v201, v202, v203, v204, 1, v206, v207, v208, v209, v210, v211, v212, v213, v214, 0, 3, 2, 4) :|: 0 = 0 28.88/8.97 Combined rules. Obtained 1 rulesP rules: 28.88/8.97 f_323(v200:0, v201:0, v202:0, v203:0, v204:0, 1, v206:0, v207:0, v208:0, v209:0, v210:0, v211:0, v212:0, v213:0, v214:0, 0, 3, 2, 4) -> f_323(v200:0, v201:0, v202:0, v203:0, v204:0, 1, v207:0, 2 * v207:0, v209:0, 1 + v209:0, v210:0, v211:0, v212:0, v213:0, v214:0, 0, 3, 2, 4) :|: v200:0 > 2 && v207:0 < v200:0 && v209:0 > 0 && 3 < 2 * v207:0 28.88/8.97 Filtered unneeded arguments: 28.88/8.97 f_323(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) -> f_323(x1, x8, x10) 28.88/8.97 Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: 28.88/8.97 f_323(v200:0, v207:0, v209:0) -> f_323(v200:0, 2 * v207:0, 1 + v209:0) :|: v207:0 < v200:0 && v200:0 > 2 && 3 < 2 * v207:0 && v209:0 > 0 28.88/8.97 28.88/8.97 ---------------------------------------- 28.88/8.97 28.88/8.97 (16) 28.88/8.97 Obligation: 28.88/8.97 Rules: 28.88/8.97 f_323(v200:0, v207:0, v209:0) -> f_323(v200:0, 2 * v207:0, 1 + v209:0) :|: v207:0 < v200:0 && v200:0 > 2 && 3 < 2 * v207:0 && v209:0 > 0 28.88/8.97 28.88/8.97 ---------------------------------------- 28.88/8.97 28.88/8.97 (17) IntTRSCompressionProof (EQUIVALENT) 28.88/8.97 Compressed rules. 28.88/8.97 ---------------------------------------- 28.88/8.97 28.88/8.97 (18) 28.88/8.97 Obligation: 28.88/8.97 Rules: 28.88/8.97 f_323(v200:0:0, v207:0:0, v209:0:0) -> f_323(v200:0:0, 2 * v207:0:0, 1 + v209:0:0) :|: 3 < 2 * v207:0:0 && v209:0:0 > 0 && v200:0:0 > 2 && v207:0:0 < v200:0:0 28.88/8.97 28.88/8.97 ---------------------------------------- 28.88/8.97 28.88/8.97 (19) PolynomialOrderProcessor (EQUIVALENT) 28.88/8.97 Found the following polynomial interpretation: 28.88/8.97 [f_323(x, x1, x2)] = -2 + x - x1 + x2 28.88/8.97 28.88/8.97 The following rules are decreasing: 28.88/8.97 f_323(v200:0:0, v207:0:0, v209:0:0) -> f_323(v200:0:0, 2 * v207:0:0, 1 + v209:0:0) :|: 3 < 2 * v207:0:0 && v209:0:0 > 0 && v200:0:0 > 2 && v207:0:0 < v200:0:0 28.88/8.97 The following rules are bounded: 28.88/8.97 f_323(v200:0:0, v207:0:0, v209:0:0) -> f_323(v200:0:0, 2 * v207:0:0, 1 + v209:0:0) :|: 3 < 2 * v207:0:0 && v209:0:0 > 0 && v200:0:0 > 2 && v207:0:0 < v200:0:0 28.88/8.97 28.88/8.97 ---------------------------------------- 28.88/8.97 28.88/8.97 (20) 28.88/8.97 YES 28.88/8.97 28.88/8.97 ---------------------------------------- 28.88/8.97 28.88/8.97 (21) 28.88/8.97 Obligation: 28.88/8.97 SCC 28.88/8.97 ---------------------------------------- 28.88/8.97 28.88/8.97 (22) SCC2IRS (SOUND) 28.88/8.97 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 28.88/8.97 Generated rules. Obtained 15 rulesP rules: 28.88/8.97 f_194(v15, v16, v17, v18, v19, v23, 1, v20, 0, v24, v25, v26, v27, v28, 3, 4) -> f_196(1, v16, v17, v18, v19, 0, v24, v25, v26, v27, v28, 3, 4) :|: 0 <= v23 && v20 = 1 && v23 = 0 && 0 = 0 28.88/8.97 f_196(1, v16, v17, v18, v19, 0, v24, v25, v26, v27, v28, 3, 4) -> f_199(1, v16, v17, v18, v19, 0, v24, v25, v26, v27, v28, 3, 4) :|: 0 = 0 28.88/8.97 f_199(1, v16, v17, v18, v19, 0, v24, v25, v26, v27, v28, 3, 4) -> f_203(1, v16, v17, v18, v19, 0, v24, v25, v26, v27, v28, 3, 4) :|: TRUE 28.88/8.97 f_203(1, v16, v17, v18, v19, 0, v24, v25, v26, v27, v28, 3, 4) -> f_207(1, v16, v17, v18, v19, 0, v24, v25, v26, v27, v28, 3, 4) :|: TRUE 28.88/8.97 f_207(1, v16, v17, v18, v19, 0, v24, v25, v26, v27, v28, 3, 4) -> f_211(1, v16, v17, v18, v19, 0, v24, v25, v26, v27, v28, 3, 4) :|: TRUE 28.88/8.97 f_211(1, v16, v17, v18, v19, 0, v24, v25, v26, v27, v28, 3, 4) -> f_215(1, v16, v17, v18, v19, 0, v24, v25, v26, v27, v28, 3, 4) :|: 0 = 0 28.88/8.97 f_215(1, v16, v17, v18, v19, 0, v24, v25, v26, v27, v28, 3, 4) -> f_218(1, v16, v17, v18, v19, 0, v24, v25, v26, v27, v28, 3, 4) :|: 0 = 0 28.88/8.97 f_218(1, v16, v17, v18, v19, 0, v24, v25, v26, v27, v28, 3, 4) -> f_221(1, v16, v17, v18, v19, 0, v24, v25, v26, v27, v28, 3, 4) :|: 0 = 0 28.88/8.97 f_221(1, v16, v17, v18, v19, 0, v24, v25, v26, v27, v28, 3, 4) -> f_224(1, v16, v17, v18, v19, 0, v24, v25, v26, v27, v28, 3, 4) :|: TRUE 28.88/8.97 f_224(1, v16, v17, v18, v19, 0, v24, v25, v26, v27, v28, 3, 4) -> f_227(1, v16, v17, v18, v19, 0, v24, v25, v26, v27, v28, 3, 4) :|: 0 = 0 28.88/8.97 f_227(1, v16, v17, v18, v19, 0, v24, v25, v26, v27, v28, 3, 4) -> f_230(1, v16, v17, v18, v19, 0, -1, v24, v25, v26, v27, v28, 3, 4) :|: 0 = 0 28.88/8.97 f_230(1, v16, v17, v18, v19, 0, -1, v24, v25, v26, v27, v28, 3, 4) -> f_233(1, v16, v17, v18, v19, 0, -1, v24, v25, v26, v27, v28, 3, 4) :|: TRUE 28.88/8.97 f_233(1, v16, v17, v18, v19, 0, -1, v24, v25, v26, v27, v28, 3, 4) -> f_235(1, v16, v17, v18, v19, 0, -1, v24, v25, v26, v27, v28, 3, 4) :|: TRUE 28.88/8.97 f_235(1, v16, v17, v18, v19, 0, -1, v24, v25, v26, v27, v28, 3, 4) -> f_191(1, v16, v17, v18, v19, 0, 1, 0, -1, v24, v25, v26, v27, v28, 3, 4) :|: TRUE 28.88/8.97 f_191(v15, v16, v17, v18, v19, v20, 1, 0, v23, v24, v25, v26, v27, v28, 3, 4) -> f_194(v15, v16, v17, v18, v19, v23, 1, v20, 0, v24, v25, v26, v27, v28, 3, 4) :|: 0 = 0 28.88/8.97 Combined rules. Obtained 1 rulesP rules: 28.88/8.97 f_194(v15:0, v16:0, v17:0, v18:0, v19:0, 0, 1, 1, 0, v24:0, v25:0, v26:0, v27:0, v28:0, 3, 4) -> f_194(1, v16:0, v17:0, v18:0, v19:0, -1, 1, 0, 0, v24:0, v25:0, v26:0, v27:0, v28:0, 3, 4) :|: TRUE 28.88/8.97 Filtered unneeded arguments: 28.88/8.97 f_194(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16) -> f_194(x6, x8) 28.88/8.97 Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: 28.88/8.97 f_194(cons_0, cons_1) -> f_194(-1, 0) :|: TRUE && cons_0 = 0 && cons_1 = 1 28.88/8.97 28.88/8.97 ---------------------------------------- 28.88/8.97 28.88/8.97 (23) 28.88/8.97 Obligation: 28.88/8.97 Rules: 28.88/8.97 f_194(cons_0, cons_1) -> f_194(-1, 0) :|: TRUE && cons_0 = 0 && cons_1 = 1 28.88/8.97 28.88/8.97 ---------------------------------------- 28.88/8.97 28.88/8.97 (24) TerminationGraphProcessor (EQUIVALENT) 28.88/8.97 Constructed the termination graph and obtained no non-trivial SCC(s). 28.88/8.97 28.88/8.97 ---------------------------------------- 28.88/8.97 28.88/8.97 (25) 28.88/8.97 YES 29.23/9.03 EOF