YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 175 ms]
(2) LLVM problem
(3) LLVMToTerminationGraphProof [EQUIVALENT, 1586 ms]
(4) LLVM Symbolic Execution Graph
(5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms]
(6) AND
    (7) LLVM Symbolic Execution SCC
        (8) SCC2IRS [SOUND, 69 ms]
        (9) IntTRS
        (10) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (11) IntTRS
        (12) PolynomialOrderProcessor [EQUIVALENT, 19 ms]
        (13) AND
            (14) IntTRS
                (15) TerminationGraphProcessor [EQUIVALENT, 4 ms]
                (16) YES
            (17) IntTRS
                (18) IntTRSCompressionProof [EQUIVALENT, 0 ms]
                (19) IntTRS
                (20) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
                (21) IntTRS
                (22) RankingReductionPairProof [EQUIVALENT, 5 ms]
                (23) YES
    (24) LLVM Symbolic Execution SCC
        (25) SCC2IRS [SOUND, 37 ms]
        (26) IntTRS
        (27) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (28) IntTRS
        (29) PolynomialOrderProcessor [EQUIVALENT, 11 ms]
        (30) YES


----------------------------------------

(0)
Obligation:
c file /export/starexec/sandbox2/benchmark/theBenchmark.c
----------------------------------------

(1) CToLLVMProof (EQUIVALENT)
Compiled c-file /export/starexec/sandbox2/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
		%j = alloca i32, align 4
		%N = alloca i32, align 4
		%i = alloca i32, align 4
		store 0, %1
		%2 = call i32 @__VERIFIER_nondet_int()
		store %2, %j
		%3 = call i32 @__VERIFIER_nondet_int()
		store %3, %N
		%4 = load %N
		store %4, %i
		br %5
	5:
		%6 = load %i
		%7 = icmp sgt %6 0
		br %7, %8, %19
	8:
		%9 = load %j
		%10 = icmp sgt %9 0
		br %10, %11, %14
	11:
		%12 = load %j
		%13 = add %12 -1
		store %13, %j
		br %18
	14:
		%15 = load %N
		store %15, %j
		%16 = load %i
		%17 = add %16 -1
		store %17, %i
		br %18
	18:
		br %5
	19:
		ret 0


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 2 SCCs.
----------------------------------------

(6)
Complex Obligation (AND)

----------------------------------------

(7)
Obligation:
SCC
----------------------------------------

(8) SCC2IRS (SOUND)
Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 
Generated rules. Obtained 33 rulesP rules:
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Combined rules. Obtained 2 rulesP rules:
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
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
Filtered unneeded arguments:
   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)
Removed division, modulo operations, cleaned up constraints. Obtained 2 rules.P rules:
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
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

----------------------------------------

(9)
Obligation:
Rules:
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
f_305(x, x1, x2, x3) -> f_305(x, x1, 1 + x4, x4) :|: x2 > 1 && x4 > -1 && x3 = 1 + x4

----------------------------------------

(10) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
----------------------------------------

(11)
Obligation:
Rules:
f_305(sum~cons_1~v915:0:0, sum~cons_1~v962:0:0, cons_1, cons_0) -> f_305(1 + v915:0:0, v962:0:0, 1 + v915:0:0, v915:0:0) :|: v915:0:0 > 0 && v962:0:0 > 0 && sum~cons_1~v915:0:0 = 1 + v915:0:0 && sum~cons_1~v962:0:0 = 1 + v962:0:0 && cons_1 = 1 && cons_0 = 0
f_305(x:0, x1:0, x2:0, sum~cons_1~x4:0) -> f_305(x:0, x1:0, 1 + x4:0, x4:0) :|: x2:0 > 1 && x4:0 > -1 && sum~cons_1~x4:0 = 1 + x4:0

----------------------------------------

(12) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f_305(x, x1, x2, x3)] = -2 - x + x*x1 + x^2 - 4*x1 + x1^2 + x3

The following rules are decreasing:
f_305(x:0, x1:0, x2:0, sum~cons_1~x4:0) -> f_305(x:0, x1:0, 1 + x4:0, x4:0) :|: x2:0 > 1 && x4:0 > -1 && sum~cons_1~x4:0 = 1 + x4:0
The following rules are bounded:
f_305(sum~cons_1~v915:0:0, sum~cons_1~v962:0:0, cons_1, cons_0) -> f_305(1 + v915:0:0, v962:0:0, 1 + v915:0:0, v915:0:0) :|: v915:0:0 > 0 && v962:0:0 > 0 && sum~cons_1~v915:0:0 = 1 + v915:0:0 && sum~cons_1~v962:0:0 = 1 + v962:0:0 && cons_1 = 1 && cons_0 = 0

----------------------------------------

(13)
Complex Obligation (AND)

----------------------------------------

(14)
Obligation:
Rules:
f_305(sum~cons_1~v915:0:0, sum~cons_1~v962:0:0, cons_1, cons_0) -> f_305(1 + v915:0:0, v962:0:0, 1 + v915:0:0, v915:0:0) :|: v915:0:0 > 0 && v962:0:0 > 0 && sum~cons_1~v915:0:0 = 1 + v915:0:0 && sum~cons_1~v962:0:0 = 1 + v962:0:0 && cons_1 = 1 && cons_0 = 0

----------------------------------------

(15) TerminationGraphProcessor (EQUIVALENT)
Constructed the termination graph and obtained no non-trivial SCC(s).

----------------------------------------

(16)
YES

----------------------------------------

(17)
Obligation:
Rules:
f_305(x:0, x1:0, x2:0, sum~cons_1~x4:0) -> f_305(x:0, x1:0, 1 + x4:0, x4:0) :|: x2:0 > 1 && x4:0 > -1 && sum~cons_1~x4:0 = 1 + x4:0

----------------------------------------

(18) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
----------------------------------------

(19)
Obligation:
Rules:
f_305(x:0:0, x1:0:0, x2:0:0, sum~cons_1~x4:0:0) -> f_305(x:0:0, x1:0:0, 1 + x4:0:0, x4:0:0) :|: x2:0:0 > 1 && x4:0:0 > -1 && sum~cons_1~x4:0:0 = 1 + x4:0:0

----------------------------------------

(20) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:

   f_305(x1, x2, x3, x4) -> f_305(x3, x4)

----------------------------------------

(21)
Obligation:
Rules:
f_305(x2:0:0, sum~cons_1~x4:0:0) -> f_305(1 + x4:0:0, x4:0:0) :|: x2:0:0 > 1 && x4:0:0 > -1 && sum~cons_1~x4:0:0 = 1 + x4:0:0

----------------------------------------

(22) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f_305 ] = f_305_2

The following rules are decreasing:
f_305(x2:0:0, sum~cons_1~x4:0:0) -> f_305(1 + x4:0:0, x4:0:0) :|: x2:0:0 > 1 && x4:0:0 > -1 && sum~cons_1~x4:0:0 = 1 + x4:0:0

The following rules are bounded:
f_305(x2:0:0, sum~cons_1~x4:0:0) -> f_305(1 + x4:0:0, x4:0:0) :|: x2:0:0 > 1 && x4:0:0 > -1 && sum~cons_1~x4:0:0 = 1 + x4:0:0


----------------------------------------

(23)
YES

----------------------------------------

(24)
Obligation:
SCC
----------------------------------------

(25) SCC2IRS (SOUND)
Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 
Generated rules. Obtained 13 rulesP rules:
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
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
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
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
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
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
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
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
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
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
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
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
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
Combined rules. Obtained 1 rulesP rules:
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
Filtered unneeded arguments:
   f_198(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16) -> f_198(x5, x8, x9)
Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules:
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

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(26)
Obligation:
Rules:
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

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(27) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(28)
Obligation:
Rules:
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

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(29) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f_198(x, x1, x2)] = x2

The following rules are decreasing:
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
The following rules are bounded:
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

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(30)
YES