25.90/7.78 YES 26.81/8.26 proof of /export/starexec/sandbox2/benchmark/theBenchmark.c 26.81/8.26 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 26.81/8.26 26.81/8.26 26.81/8.26 Termination of the given C Problem could be proven: 26.81/8.26 26.81/8.26 (0) C Problem 26.81/8.26 (1) CToLLVMProof [EQUIVALENT, 175 ms] 26.81/8.26 (2) LLVM problem 26.81/8.26 (3) LLVMToTerminationGraphProof [EQUIVALENT, 1607 ms] 26.81/8.26 (4) LLVM Symbolic Execution Graph 26.81/8.26 (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] 26.81/8.26 (6) AND 26.81/8.26 (7) LLVM Symbolic Execution SCC 26.81/8.26 (8) SCC2IRS [SOUND, 75 ms] 26.81/8.26 (9) IntTRS 26.81/8.26 (10) IRS2T2 [EQUIVALENT, 0 ms] 26.81/8.26 (11) T2IntSys 26.81/8.26 (12) T2 [EQUIVALENT, 1053 ms] 26.81/8.26 (13) YES 26.81/8.26 (14) LLVM Symbolic Execution SCC 26.81/8.26 (15) SCC2IRS [SOUND, 66 ms] 26.81/8.26 (16) IntTRS 26.81/8.26 (17) IntTRSCompressionProof [EQUIVALENT, 1 ms] 26.81/8.26 (18) IntTRS 26.81/8.26 (19) PolynomialOrderProcessor [EQUIVALENT, 15 ms] 26.81/8.26 (20) YES 26.81/8.26 26.81/8.26 26.81/8.26 ---------------------------------------- 26.81/8.26 26.81/8.26 (0) 26.81/8.26 Obligation: 26.81/8.26 c file /export/starexec/sandbox2/benchmark/theBenchmark.c 26.81/8.26 ---------------------------------------- 26.81/8.26 26.81/8.26 (1) CToLLVMProof (EQUIVALENT) 26.81/8.26 Compiled c-file /export/starexec/sandbox2/benchmark/theBenchmark.c to LLVM. 26.81/8.26 ---------------------------------------- 26.81/8.26 26.81/8.26 (2) 26.81/8.26 Obligation: 26.81/8.26 LLVM Problem 26.81/8.26 26.81/8.26 Aliases: 26.81/8.26 26.81/8.26 Data layout: 26.81/8.26 26.81/8.26 "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" 26.81/8.26 26.81/8.26 Machine: 26.81/8.26 26.81/8.26 "x86_64-pc-linux-gnu" 26.81/8.26 26.81/8.26 Type definitions: 26.81/8.26 26.81/8.26 Global variables: 26.81/8.26 26.81/8.26 Function declarations and definitions: 26.81/8.26 26.81/8.26 *BasicFunctionTypename: "__VERIFIER_nondet_int" returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 26.81/8.26 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 26.81/8.26 0: 26.81/8.26 %1 = alloca i32, align 4 26.81/8.26 %j = alloca i32, align 4 26.81/8.26 %N = alloca i32, align 4 26.81/8.26 %i = alloca i32, align 4 26.81/8.26 store 0, %1 26.81/8.26 %2 = call i32 @__VERIFIER_nondet_int() 26.81/8.26 store %2, %j 26.81/8.26 %3 = call i32 @__VERIFIER_nondet_int() 26.81/8.26 store %3, %N 26.81/8.26 %4 = load %N 26.81/8.26 store %4, %i 26.81/8.26 br %5 26.81/8.26 5: 26.81/8.26 %6 = load %i 26.81/8.26 %7 = icmp sgt %6 0 26.81/8.26 br %7, %8, %19 26.81/8.26 8: 26.81/8.26 %9 = load %j 26.81/8.26 %10 = icmp sgt %9 0 26.81/8.26 br %10, %11, %14 26.81/8.26 11: 26.81/8.26 %12 = load %j 26.81/8.26 %13 = add %12 -1 26.81/8.26 store %13, %j 26.81/8.26 br %18 26.81/8.26 14: 26.81/8.26 %15 = load %N 26.81/8.26 store %15, %j 26.81/8.26 %16 = load %i 26.81/8.26 %17 = add %16 -1 26.81/8.26 store %17, %i 26.81/8.26 br %18 26.81/8.26 18: 26.81/8.26 br %5 26.81/8.26 19: 26.81/8.26 ret 0 26.81/8.26 26.81/8.26 26.81/8.26 Analyze Termination of all function calls matching the pattern: 26.81/8.26 main() 26.81/8.26 ---------------------------------------- 26.81/8.26 26.81/8.26 (3) LLVMToTerminationGraphProof (EQUIVALENT) 26.81/8.26 Constructed symbolic execution graph for LLVM program and proved memory safety. 26.81/8.26 ---------------------------------------- 26.81/8.26 26.81/8.26 (4) 26.81/8.26 Obligation: 26.81/8.26 SE Graph 26.81/8.26 ---------------------------------------- 26.81/8.26 26.81/8.26 (5) SymbolicExecutionGraphToSCCProof (SOUND) 26.81/8.26 Splitted symbolic execution graph to 2 SCCs. 26.81/8.26 ---------------------------------------- 26.81/8.26 26.81/8.26 (6) 26.81/8.26 Complex Obligation (AND) 26.81/8.26 26.81/8.26 ---------------------------------------- 26.81/8.26 26.81/8.26 (7) 26.81/8.26 Obligation: 26.81/8.26 SCC 26.81/8.26 ---------------------------------------- 26.81/8.26 26.81/8.26 (8) SCC2IRS (SOUND) 26.81/8.26 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 26.81/8.26 Generated rules. Obtained 33 rulesP rules: 26.81/8.26 f_305(v793, v794, v795, v796, v797, v798, v799, 1, v801, v802, v803, v804, v805, v806, v807, 0, 3, 2, 4) -> f_306(v793, v794, v795, v796, v797, v798, v799, 1, v801, v802, v803, v804, v805, v806, v807, 0, 3, 2, 4) :|: 0 = 0 26.81/8.26 f_306(v793, v794, v795, v796, v797, v798, v799, 1, v801, v802, v803, v804, v805, v806, v807, 0, 3, 2, 4) -> f_307(v793, v794, v795, v796, v797, v798, v799, 1, v801, v802, v803, v804, v805, v806, v807, 0, 3, 2, 4) :|: 0 = 0 26.81/8.26 f_307(v793, v794, v795, v796, v797, v798, v799, 1, v801, v802, v803, v804, v805, v806, v807, 0, 3, 2, 4) -> f_308(v793, v794, v795, v796, v797, v798, v799, 1, v801, v802, v803, v804, v805, v806, v807, 0, 3, 2, 4) :|: TRUE 26.81/8.26 f_308(v793, v794, v795, v796, v797, v798, v799, 1, v801, v802, v803, v804, v805, v806, v807, 0, 3, 2, 4) -> f_309(v793, v794, v795, v796, v797, v798, v799, 1, v803, v802, v801, v804, v805, v806, v807, 0, 3, 2, 4) :|: 0 = 0 26.81/8.26 f_309(v793, v794, v795, v796, v797, v798, v799, 1, v803, v802, v801, v804, v805, v806, v807, 0, 3, 2, 4) -> f_310(v793, v794, v795, v796, v797, v798, v799, 1, v803, v802, v801, v804, v805, v806, v807, 0, 3, 2, 4) :|: 0 < v803 && 2 <= v801 26.81/8.26 f_309(v793, v794, v795, v796, v797, v798, v799, 1, v803, v802, v801, v804, v805, v806, v807, 0, 3, 2, 4) -> f_311(v793, v794, v795, v796, v797, v798, v799, 1, 0, v802, v804, v805, v806, v807, 3, 2, 4) :|: v803 <= 0 && v801 = 1 && v803 = 0 && 0 = 0 26.81/8.26 f_310(v793, v794, v795, v796, v797, v798, v799, 1, v803, v802, v801, v804, v805, v806, v807, 0, 3, 2, 4) -> f_312(v793, v794, v795, v796, v797, v798, v799, 1, v803, v802, v801, v804, v805, v806, v807, 0, 3, 2, 4) :|: 0 = 0 26.81/8.26 f_312(v793, v794, v795, v796, v797, v798, v799, 1, v803, v802, v801, v804, v805, v806, v807, 0, 3, 2, 4) -> f_314(v793, v794, v795, v796, v797, v798, v799, 1, v803, v802, v801, v804, v805, v806, v807, 0, 3, 2, 4) :|: TRUE 26.81/8.26 f_314(v793, v794, v795, v796, v797, v798, v799, 1, v803, v802, v801, v804, v805, v806, v807, 0, 3, 2, 4) -> f_315(v793, v794, v795, v796, v797, v798, v799, 1, v803, v802, v801, v803, v804, v805, v806, v807, 0, 3, 2, 4) :|: TRUE 26.81/8.26 f_315(v894, v895, v896, v897, v898, v899, v900, 1, v902, v903, v904, v905, v906, v907, v908, v909, 0, 3, 2, 4) -> f_317(v894, v895, v896, v897, v898, v899, v900, 1, v902, v903, v905, v906, v907, v908, v909, 0, 3, 2, 4) :|: 0 = 0 26.81/8.26 f_317(v894, v895, v896, v897, v898, v899, v900, 1, v902, v903, v905, v906, v907, v908, v909, 0, 3, 2, 4) -> f_319(v894, v895, v896, v897, v898, v899, v900, 1, v902, v903, v915, v906, v907, v908, v909, 0, 3, 2, 4) :|: 1 + v915 = v902 && 0 <= v915 26.81/8.26 f_319(v894, v895, v896, v897, v898, v899, v900, 1, v902, v903, v915, v906, v907, v908, v909, 0, 3, 2, 4) -> f_321(v894, v895, v896, v897, v898, v899, v900, 1, v902, v903, v915, v906, v907, v908, v909, 0, 3, 2, 4) :|: TRUE 26.81/8.26 f_321(v894, v895, v896, v897, v898, v899, v900, 1, v902, v903, v915, v906, v907, v908, v909, 0, 3, 2, 4) -> f_323(v894, v895, v896, v897, v898, v899, v900, 1, v902, v903, v915, v906, v907, v908, v909, 0, 3, 2, 4) :|: TRUE 26.81/8.26 f_323(v894, v895, v896, v897, v898, v899, v900, 1, v902, v903, v915, v906, v907, v908, v909, 0, 3, 2, 4) -> f_304(v894, v895, v896, v897, v898, v899, v900, 1, v902, v903, v915, v906, v907, v908, v909, 0, 3, 2, 4) :|: TRUE 26.81/8.26 f_304(v793, v794, v795, v796, v797, v798, v799, 1, v801, v802, v803, v804, v805, v806, v807, 0, 3, 2, 4) -> f_305(v793, v794, v795, v796, v797, v798, v799, 1, v801, v802, v803, v804, v805, v806, v807, 0, 3, 2, 4) :|: TRUE 26.81/8.26 f_311(v793, v794, v795, v796, v797, v798, v799, 1, 0, v802, v804, v805, v806, v807, 3, 2, 4) -> f_313(v793, v794, v795, v796, v797, v798, v799, 1, 0, v802, v804, v805, v806, v807, 3, 2, 4) :|: 0 = 0 26.81/8.26 f_313(v793, v794, v795, v796, v797, v798, v799, 1, 0, v802, v804, v805, v806, v807, 3, 2, 4) -> f_316(v793, v794, v795, v796, v797, v798, v799, 1, 0, v802, v804, v805, v806, v807, 3, 2, 4) :|: TRUE 26.81/8.26 f_316(v793, v794, v795, v796, v797, v798, v799, 1, 0, v802, v804, v805, v806, v807, 3, 2, 4) -> f_318(v793, v794, v795, v796, v797, v798, v799, 1, 0, v802, v804, v805, v806, v807, 3, 2, 4) :|: 0 = 0 26.81/8.26 f_318(v793, v794, v795, v796, v797, v798, v799, 1, 0, v802, v804, v805, v806, v807, 3, 2, 4) -> f_320(v793, v794, v795, v796, v797, v798, v799, 1, 0, v802, v804, v805, v806, v807, 3, 2, 4) :|: TRUE 26.81/8.26 f_320(v793, v794, v795, v796, v797, v798, v799, 1, 0, v802, v804, v805, v806, v807, 3, 2, 4) -> f_322(v793, v794, v795, v796, v797, v798, v799, 1, 0, v804, v805, v806, v807, 3, 2, 4) :|: 0 = 0 26.81/8.26 f_322(v793, v794, v795, v796, v797, v798, v799, 1, 0, v804, v805, v806, v807, 3, 2, 4) -> f_324(v793, v794, v795, v796, v797, v798, v799, 1, 0, v962, v804, v805, v806, v807, 3, 2, 4) :|: 1 + v962 = v799 && 0 <= v962 26.81/8.26 f_324(v793, v794, v795, v796, v797, v798, v799, 1, 0, v962, v804, v805, v806, v807, 3, 2, 4) -> f_325(v793, v794, v795, v796, v797, v798, v799, 1, 0, v962, v804, v805, v806, v807, 3, 2, 4) :|: TRUE 26.81/8.26 f_325(v793, v794, v795, v796, v797, v798, v799, 1, 0, v962, v804, v805, v806, v807, 3, 2, 4) -> f_326(v793, v794, v795, v796, v797, v798, v799, 1, 0, v962, v804, v805, v806, v807, 3, 2, 4) :|: TRUE 26.81/8.26 f_326(v793, v794, v795, v796, v797, v798, v799, 1, 0, v962, v804, v805, v806, v807, 3, 2, 4) -> f_327(v793, v794, v795, v796, v797, v798, v799, 1, 0, v962, v804, v805, v806, v807, 3, 4) :|: TRUE 26.81/8.26 f_327(v984, v985, v986, v987, v988, v989, v990, 1, 0, v993, v994, v995, v996, v997, 3, 4) -> f_328(v984, v985, v986, v987, v988, v989, v990, 1, 0, v993, v994, v995, v996, v997, 3, 4) :|: TRUE 26.81/8.26 f_328(v984, v985, v986, v987, v988, v989, v990, 1, 0, v993, v994, v995, v996, v997, 3, 4) -> f_329(v984, v985, v986, v987, v988, v989, v993, 1, 0, v990, v994, v995, v996, v997, 3, 4) :|: 0 = 0 26.81/8.26 f_329(v984, v985, v986, v987, v988, v989, v993, 1, 0, v990, v994, v995, v996, v997, 3, 4) -> f_330(v984, v985, v986, v987, v988, v989, v993, 1, 0, v990, v994, v995, v996, v997, 3, 2, 4) :|: 0 < v993 && 2 <= v990 && 2 <= v989 26.81/8.26 f_330(v984, v985, v986, v987, v988, v989, v993, 1, 0, v990, v994, v995, v996, v997, 3, 2, 4) -> f_332(v984, v985, v986, v987, v988, v989, v993, 1, 0, v990, v994, v995, v996, v997, 3, 2, 4) :|: 0 = 0 26.81/8.26 f_332(v984, v985, v986, v987, v988, v989, v993, 1, 0, v990, v994, v995, v996, v997, 3, 2, 4) -> f_334(v984, v985, v986, v987, v988, v989, v993, 1, 0, v990, v994, v995, v996, v997, 3, 2, 4) :|: TRUE 26.81/8.26 f_334(v984, v985, v986, v987, v988, v989, v993, 1, 0, v990, v994, v995, v996, v997, 3, 2, 4) -> f_336(v984, v985, v986, v987, v988, v989, v993, 1, 0, v990, v994, v995, v996, v997, 3, 2, 4) :|: 0 = 0 26.81/8.26 f_336(v984, v985, v986, v987, v988, v989, v993, 1, 0, v990, v994, v995, v996, v997, 3, 2, 4) -> f_337(v984, v985, v986, v987, v988, v989, v993, 1, 0, v990, v994, v995, v996, v997, 3, 2, 4) :|: 0 = 0 26.81/8.26 f_337(v984, v985, v986, v987, v988, v989, v993, 1, 0, v990, v994, v995, v996, v997, 3, 2, 4) -> f_338(v984, v985, v986, v987, v988, v989, v993, 1, 0, v990, v994, v995, v996, v997, 3, 2, 4) :|: TRUE 26.81/8.26 f_338(v984, v985, v986, v987, v988, v989, v993, 1, 0, v990, v994, v995, v996, v997, 3, 2, 4) -> f_315(v984, v985, v986, v987, v988, v989, v993, 1, v989, v990, 1, 0, v994, v995, v996, v997, 0, 3, 2, 4) :|: TRUE 26.81/8.26 Combined rules. Obtained 2 rulesP rules: 26.81/8.26 f_305(v793:0, v794:0, v795:0, v796:0, v797:0, 1 + v915:0, 1 + v962:0, 1, 1, v802:0, 0, v804:0, v805:0, v806:0, v807:0, 0, 3, 2, 4) -> f_305(v793:0, v794:0, v795:0, v796:0, v797:0, 1 + v915:0, v962:0, 1, 1 + v915:0, 1 + v962:0, v915:0, v804:0, v805:0, v806:0, v807:0, 0, 3, 2, 4) :|: v915:0 > 0 && v962:0 > 0 26.81/8.26 f_305(v793:0, v794:0, v795:0, v796:0, v797:0, v798:0, v799:0, 1, v801:0, v802:0, 1 + v915:0, v804:0, v805:0, v806:0, v807:0, 0, 3, 2, 4) -> f_305(v793:0, v794:0, v795:0, v796:0, v797:0, v798:0, v799:0, 1, 1 + v915:0, v802:0, v915:0, v804:0, v805:0, v806:0, v807:0, 0, 3, 2, 4) :|: v801:0 > 1 && v915:0 > -1 26.81/8.26 Filtered unneeded arguments: 26.81/8.26 f_305(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) -> f_305(x6, x7, x9, x11) 26.81/8.26 Removed division, modulo operations, cleaned up constraints. Obtained 2 rules.P rules: 26.81/8.26 f_305(sum~cons_1~v915:0, sum~cons_1~v962:0, cons_1, cons_0) -> f_305(1 + v915:0, v962:0, 1 + v915:0, v915:0) :|: v915:0 > 0 && v962:0 > 0 && sum~cons_1~v915:0 = 1 + v915:0 && sum~cons_1~v962:0 = 1 + v962:0 && cons_1 = 1 && cons_0 = 0 26.81/8.26 f_305(v798:0, v799:0, v801:0, sum~cons_1~v915:0) -> f_305(v798:0, v799:0, 1 + v915:0, v915:0) :|: v801:0 > 1 && v915:0 > -1 && sum~cons_1~v915:0 = 1 + v915:0 26.81/8.26 26.81/8.26 ---------------------------------------- 26.81/8.26 26.81/8.26 (9) 26.81/8.26 Obligation: 26.81/8.26 Rules: 26.81/8.26 f_305(sum~cons_1~v915:0, sum~cons_1~v962:0, cons_1, cons_0) -> f_305(1 + v915:0, v962:0, 1 + v915:0, v915:0) :|: v915:0 > 0 && v962:0 > 0 && sum~cons_1~v915:0 = 1 + v915:0 && sum~cons_1~v962:0 = 1 + v962:0 && cons_1 = 1 && cons_0 = 0 26.81/8.26 f_305(x, x1, x2, x3) -> f_305(x, x1, 1 + x4, x4) :|: x2 > 1 && x4 > -1 && x3 = 1 + x4 26.81/8.26 26.81/8.26 ---------------------------------------- 26.81/8.26 26.81/8.26 (10) IRS2T2 (EQUIVALENT) 26.81/8.26 Transformed input IRS into an integer transition system.Used the following mapping from defined symbols to location IDs: 26.81/8.26 26.81/8.26 (f_305_4,1) 26.81/8.26 26.81/8.26 ---------------------------------------- 26.81/8.26 26.81/8.26 (11) 26.81/8.26 Obligation: 26.81/8.26 START: 0; 26.81/8.26 26.81/8.26 FROM: 0; 26.81/8.26 TO: 1; 26.81/8.26 26.81/8.26 FROM: 1; 26.81/8.26 oldX0 := x0; 26.81/8.26 oldX1 := x1; 26.81/8.26 oldX2 := x2; 26.81/8.26 oldX3 := x3; 26.81/8.26 oldX4 := oldX0 - 1; 26.81/8.26 oldX5 := oldX1 - 1; 26.81/8.26 assume(oldX4 > 0 && oldX5 > 0 && oldX0 = 1 + oldX4 && oldX1 = 1 + oldX5 && oldX2 = 1 && oldX3 = 0); 26.81/8.26 x0 := 1 + oldX4; 26.81/8.26 x1 := oldX1 - 1; 26.81/8.26 x2 := 1 + oldX4; 26.81/8.26 x3 := oldX0 - 1; 26.81/8.26 TO: 1; 26.81/8.26 26.81/8.26 FROM: 1; 26.81/8.26 oldX0 := x0; 26.81/8.26 oldX1 := x1; 26.81/8.26 oldX2 := x2; 26.81/8.26 oldX3 := x3; 26.81/8.26 oldX4 := oldX3 - 1; 26.81/8.26 assume(oldX2 > 1 && oldX4 > -1 && oldX3 = 1 + oldX4); 26.81/8.26 x0 := oldX0; 26.81/8.26 x1 := oldX1; 26.81/8.26 x2 := 1 + oldX4; 26.81/8.26 x3 := oldX3 - 1; 26.81/8.26 TO: 1; 26.81/8.26 26.81/8.26 26.81/8.26 ---------------------------------------- 26.81/8.26 26.81/8.26 (12) T2 (EQUIVALENT) 26.81/8.26 Initially, performed program simplifications using lexicographic rank functions: 26.81/8.26 * Removed transitions 1, 4, 5 using the following rank functions: 26.81/8.26 - Rank function 1: 26.81/8.26 RF for loc. 5: 2*x1 26.81/8.26 RF for loc. 6: 2*x1 26.81/8.26 Bound for (chained) transitions 4: 4 26.81/8.26 - Rank function 2: 26.81/8.26 RF for loc. 5: 1+2*x3 26.81/8.26 RF for loc. 6: 2*x3 26.81/8.26 Bound for (chained) transitions 5: 2 26.81/8.26 - Rank function 3: 26.81/8.26 RF for loc. 5: 0 26.81/8.26 RF for loc. 6: -1 26.81/8.26 Bound for (chained) transitions 1: 0 26.81/8.26 26.81/8.26 ---------------------------------------- 26.81/8.26 26.81/8.26 (13) 26.81/8.26 YES 26.81/8.26 26.81/8.26 ---------------------------------------- 26.81/8.26 26.81/8.26 (14) 26.81/8.26 Obligation: 26.81/8.26 SCC 26.81/8.26 ---------------------------------------- 26.81/8.26 26.81/8.26 (15) SCC2IRS (SOUND) 26.81/8.26 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 26.81/8.26 Generated rules. Obtained 13 rulesP rules: 26.81/8.26 f_198(v158, v159, v160, v161, v162, v163, 1, v165, v166, v167, v168, v169, v170, 0, 3, 4) -> f_200(v158, v159, v160, v161, v162, v163, 1, v165, v166, v167, v168, v169, v170, 0, 3, 4) :|: 0 = 0 26.81/8.26 f_200(v158, v159, v160, v161, v162, v163, 1, v165, v166, v167, v168, v169, v170, 0, 3, 4) -> f_202(v158, v159, v160, v161, v162, v163, 1, v165, v166, v167, v168, v169, v170, 0, 3, 4) :|: TRUE 26.81/8.26 f_202(v158, v159, v160, v161, v162, v163, 1, v165, v166, v167, v168, v169, v170, 0, 3, 4) -> f_204(v158, v159, v160, v161, v162, v163, 1, v166, v165, v167, v168, v169, v170, 0, 3, 4) :|: 0 = 0 26.81/8.26 f_204(v158, v159, v160, v161, v162, v163, 1, v166, v165, v167, v168, v169, v170, 0, 3, 4) -> f_206(v158, v159, v160, v161, v162, v163, 1, v166, v165, v167, v168, v169, v170, 0, 3, 2, 4) :|: 0 < v166 && 2 <= v165 && 2 <= v162 26.81/8.26 f_206(v158, v159, v160, v161, v162, v163, 1, v166, v165, v167, v168, v169, v170, 0, 3, 2, 4) -> f_209(v158, v159, v160, v161, v162, v163, 1, v166, v165, v167, v168, v169, v170, 0, 3, 2, 4) :|: 0 = 0 26.81/8.26 f_209(v158, v159, v160, v161, v162, v163, 1, v166, v165, v167, v168, v169, v170, 0, 3, 2, 4) -> f_213(v158, v159, v160, v161, v162, v163, 1, v166, v165, v167, v168, v169, v170, 0, 3, 2, 4) :|: TRUE 26.81/8.26 f_213(v158, v159, v160, v161, v162, v163, 1, v166, v165, v167, v168, v169, v170, 0, 3, 2, 4) -> f_217(v158, v159, v160, v161, v162, v163, 1, v166, v167, v168, v169, v170, 0, 3, 2, 4) :|: 0 = 0 26.81/8.26 f_217(v158, v159, v160, v161, v162, v163, 1, v166, v167, v168, v169, v170, 0, 3, 2, 4) -> f_221(v158, v159, v160, v161, v162, v163, 1, v166, v252, v167, v168, v169, v170, 0, 3, 2, 4) :|: 1 + v252 = v166 && 0 <= v252 26.81/8.26 f_221(v158, v159, v160, v161, v162, v163, 1, v166, v252, v167, v168, v169, v170, 0, 3, 2, 4) -> f_225(v158, v159, v160, v161, v162, v163, 1, v166, v252, v167, v168, v169, v170, 0, 3, 2, 4) :|: TRUE 26.81/8.26 f_225(v158, v159, v160, v161, v162, v163, 1, v166, v252, v167, v168, v169, v170, 0, 3, 2, 4) -> f_229(v158, v159, v160, v161, v162, v163, 1, v166, v252, v167, v168, v169, v170, 0, 3, 2, 4) :|: TRUE 26.81/8.26 f_229(v158, v159, v160, v161, v162, v163, 1, v166, v252, v167, v168, v169, v170, 0, 3, 2, 4) -> f_233(v158, v159, v160, v161, v162, v163, 1, v166, v252, v167, v168, v169, v170, 0, 3, 2, 4) :|: TRUE 26.81/8.26 f_233(v158, v159, v160, v161, v162, v163, 1, v166, v252, v167, v168, v169, v170, 0, 3, 2, 4) -> f_195(v158, v159, v160, v161, v162, v163, 1, v166, v252, v167, v168, v169, v170, 0, 3, 4) :|: TRUE 26.81/8.26 f_195(v158, v159, v160, v161, v162, v163, 1, v165, v166, v167, v168, v169, v170, 0, 3, 4) -> f_198(v158, v159, v160, v161, v162, v163, 1, v165, v166, v167, v168, v169, v170, 0, 3, 4) :|: 0 = 0 26.81/8.26 Combined rules. Obtained 1 rulesP rules: 26.81/8.26 f_198(v158:0, v159:0, v160:0, v161:0, v162:0, v163:0, 1, v165:0, 1 + v252:0, v167:0, v168:0, v169:0, v170:0, 0, 3, 4) -> f_198(v158:0, v159:0, v160:0, v161:0, v162:0, v163:0, 1, 1 + v252:0, v252:0, v167:0, v168:0, v169:0, v170:0, 0, 3, 4) :|: v165:0 > 1 && v252:0 > -1 && v162:0 > 1 26.81/8.26 Filtered unneeded arguments: 26.81/8.26 f_198(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16) -> f_198(x5, x8, x9) 26.81/8.26 Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: 26.81/8.26 f_198(v162:0, v165:0, sum~cons_1~v252:0) -> f_198(v162:0, 1 + v252:0, v252:0) :|: v252:0 > -1 && v162:0 > 1 && v165:0 > 1 && sum~cons_1~v252:0 = 1 + v252:0 26.81/8.26 26.81/8.26 ---------------------------------------- 26.81/8.26 26.81/8.26 (16) 26.81/8.26 Obligation: 26.81/8.26 Rules: 26.81/8.26 f_198(v162:0, v165:0, sum~cons_1~v252:0) -> f_198(v162:0, 1 + v252:0, v252:0) :|: v252:0 > -1 && v162:0 > 1 && v165:0 > 1 && sum~cons_1~v252:0 = 1 + v252:0 26.81/8.26 26.81/8.26 ---------------------------------------- 26.81/8.26 26.81/8.26 (17) IntTRSCompressionProof (EQUIVALENT) 26.81/8.26 Compressed rules. 26.81/8.26 ---------------------------------------- 26.81/8.26 26.81/8.26 (18) 26.81/8.26 Obligation: 26.81/8.26 Rules: 26.81/8.26 f_198(v162:0:0, v165:0:0, sum~cons_1~v252:0:0) -> f_198(v162:0:0, 1 + v252:0:0, v252:0:0) :|: v252:0:0 > -1 && v162:0:0 > 1 && v165:0:0 > 1 && sum~cons_1~v252:0:0 = 1 + v252:0:0 26.81/8.26 26.81/8.26 ---------------------------------------- 26.81/8.26 26.81/8.26 (19) PolynomialOrderProcessor (EQUIVALENT) 26.81/8.26 Found the following polynomial interpretation: 26.81/8.26 [f_198(x, x1, x2)] = x2 26.81/8.26 26.81/8.26 The following rules are decreasing: 26.81/8.26 f_198(v162:0:0, v165:0:0, sum~cons_1~v252:0:0) -> f_198(v162:0:0, 1 + v252:0:0, v252:0:0) :|: v252:0:0 > -1 && v162:0:0 > 1 && v165:0:0 > 1 && sum~cons_1~v252:0:0 = 1 + v252:0:0 26.81/8.26 The following rules are bounded: 26.81/8.26 f_198(v162:0:0, v165:0:0, sum~cons_1~v252:0:0) -> f_198(v162:0:0, 1 + v252:0:0, v252:0:0) :|: v252:0:0 > -1 && v162:0:0 > 1 && v165:0:0 > 1 && sum~cons_1~v252:0:0 = 1 + v252:0:0 26.81/8.26 26.81/8.26 ---------------------------------------- 26.81/8.26 26.81/8.26 (20) 26.81/8.26 YES 26.88/10.88 EOF