/export/starexec/sandbox/solver/bin/starexec_run_c /export/starexec/sandbox/benchmark/theBenchmark.c /export/starexec/sandbox/output/output_files


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


YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.c
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination of the given C Problem could be proven:

(0) C Problem
(1) CToLLVMProof [EQUIVALENT, 176 ms]
(2) LLVM problem
(3) LLVMToTerminationGraphProof [EQUIVALENT, 1591 ms]
(4) LLVM Symbolic Execution Graph
(5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms]
(6) AND
    (7) LLVM Symbolic Execution SCC
        (8) SCC2IRS [SOUND, 78 ms]
        (9) IntTRS
        (10) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (11) IntTRS
        (12) RankingReductionPairProof [EQUIVALENT, 2 ms]
        (13) YES
    (14) LLVM Symbolic Execution SCC
        (15) SCC2IRS [SOUND, 74 ms]
        (16) IntTRS
        (17) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (18) IntTRS
        (19) PolynomialOrderProcessor [EQUIVALENT, 11 ms]
        (20) YES


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

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

(1) CToLLVMProof (EQUIVALENT)
Compiled c-file /export/starexec/sandbox/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
		%y = alloca i32, align 4
		%z = alloca i32, align 4
		%x = alloca i32, align 4
		store 0, %1
		%2 = call i32 @__VERIFIER_nondet_int()
		store %2, %y
		%3 = call i32 @__VERIFIER_nondet_int()
		store %3, %z
		%4 = call i32 @__VERIFIER_nondet_int()
		%5 = icmp ne %4 0
		br %5, %6, %7
	6:
		store 1, %x
		br %8
	7:
		store -1, %x
		br %8
	8:
		%9 = load %x
		%10 = icmp sgt %9 0
		br %10, %11, %14
	11:
		%12 = load %x
		%13 = add %12 1
		store %13, %x
		br %17
	14:
		%15 = load %x
		%16 = add %15 -1
		store %16, %x
		br %17
	17:
		%18 = load %x
		%19 = icmp sgt %18 0
		br %19, %20, %23
	20:
		%21 = load %x
		%22 = add %21 1
		store %22, %x
		br %26
	23:
		%24 = load %x
		%25 = add %24 -1
		store %25, %x
		br %26
	26:
		%27 = load %x
		%28 = icmp sgt %27 0
		br %28, %29, %32
	29:
		%30 = load %x
		%31 = add %30 1
		store %31, %x
		br %35
	32:
		%33 = load %x
		%34 = add %33 -1
		store %34, %x
		br %35
	35:
		%36 = load %x
		%37 = icmp sgt %36 0
		br %37, %38, %41
	38:
		%39 = load %x
		%40 = add %39 1
		store %40, %x
		br %44
	41:
		%42 = load %x
		%43 = add %42 -1
		store %43, %x
		br %44
	44:
		%45 = load %x
		%46 = icmp sgt %45 0
		br %46, %47, %50
	47:
		%48 = load %x
		%49 = add %48 1
		store %49, %x
		br %53
	50:
		%51 = load %x
		%52 = add %51 -1
		store %52, %x
		br %53
	53:
		%54 = load %x
		%55 = icmp sgt %54 0
		br %55, %56, %59
	56:
		%57 = load %x
		%58 = add %57 1
		store %58, %x
		br %62
	59:
		%60 = load %x
		%61 = add %60 -1
		store %61, %x
		br %62
	62:
		%63 = load %x
		%64 = icmp sgt %63 0
		br %64, %65, %68
	65:
		%66 = load %x
		%67 = add %66 1
		store %67, %x
		br %71
	68:
		%69 = load %x
		%70 = add %69 -1
		store %70, %x
		br %71
	71:
		%72 = load %x
		%73 = icmp sgt %72 0
		br %73, %74, %77
	74:
		%75 = load %x
		%76 = add %75 1
		store %76, %x
		br %80
	77:
		%78 = load %x
		%79 = add %78 -1
		store %79, %x
		br %80
	80:
		br %81
	81:
		%82 = load %y
		%83 = icmp slt %82 100
		br %83, %84, %87
	84:
		%85 = load %z
		%86 = icmp slt %85 100
		br %87
	87:
		%88 = phi [0, %81], [%86, %84]
		br %88, %89, %96
	89:
		%90 = load %y
		%91 = load %x
		%92 = add %90 %91
		store %92, %y
		%93 = load %z
		%94 = load %x
		%95 = sub %93 %94
		store %95, %z
		br %81
	96:
		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 18 rulesP rules:
f_648(v939, v940, v941, v942, v943, v944, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, v958, 1, v957, v955, v959, v960, v961, v962, v963, 3, 9, 99, 90, 108, 4) -> f_651(v939, v940, v941, v942, v943, v944, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, v958, 1, v957, v955, v959, v960, v961, v962, v963, 3, 9, 99, 90, 108, 4) :|: 0 = 0
f_651(v939, v940, v941, v942, v943, v944, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, v958, 1, v957, v955, v959, v960, v961, v962, v963, 3, 9, 99, 90, 108, 4) -> f_654(v939, v940, v941, v942, v943, v944, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, v958, 1, v957, v955, v959, v960, v961, v962, v963, 3, 9, 99, 90, 108, 4) :|: TRUE
f_654(v939, v940, v941, v942, v943, v944, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, v958, 1, v957, v955, v959, v960, v961, v962, v963, 3, 9, 99, 90, 108, 4) -> f_657(v939, v940, v941, v942, v943, v944, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, v958, 1, v959, v955, v957, v960, v961, v962, v963, 3, 9, 99, 90, 108, 4) :|: 0 = 0
f_657(v939, v940, v941, v942, v943, v944, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, v958, 1, v959, v955, v957, v960, v961, v962, v963, 3, 9, 99, 90, 108, 4) -> f_660(v939, v940, v941, v942, v943, v944, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, v958, 1, v959, v955, v957, v960, v961, v962, v963, 3, 9, 99, 90, 4) :|: v959 < 100 && v957 <= 90
f_660(v939, v940, v941, v942, v943, v944, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, v958, 1, v959, v955, v957, v960, v961, v962, v963, 3, 9, 99, 90, 4) -> f_663(v939, v940, v941, v942, v943, v944, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, v958, 1, v959, v955, v957, v960, v961, v962, v963, 3, 9, 99, 90, 4) :|: 0 = 0
f_663(v939, v940, v941, v942, v943, v944, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, v958, 1, v959, v955, v957, v960, v961, v962, v963, 3, 9, 99, 90, 4) -> f_666(v939, v940, v941, v942, v943, v944, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, v958, 1, v959, v955, v957, v960, v961, v962, v963, 3, 9, 99, 90, 4) :|: 0 = 0
f_666(v939, v940, v941, v942, v943, v944, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, v958, 1, v959, v955, v957, v960, v961, v962, v963, 3, 9, 99, 90, 4) -> f_669(v939, v940, v941, v942, v943, v944, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, v958, 1, v959, v955, v957, v960, v961, v962, v963, 3, 9, 99, 90, 4) :|: TRUE
f_669(v939, v940, v941, v942, v943, v944, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, v958, 1, v959, v955, v957, v960, v961, v962, v963, 3, 9, 99, 90, 4) -> f_672(v939, v940, v941, v942, v943, v944, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, v958, 1, v959, v957, v960, v961, v962, v963, 3, 9, 99, 90, 4) :|: 0 = 0
f_672(v939, v940, v941, v942, v943, v944, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, v958, 1, v959, v957, v960, v961, v962, v963, 3, 9, 99, 90, 4) -> f_674(v939, v940, v941, v942, v943, v944, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, v958, 1, v959, v957, v960, v961, v962, v963, 3, 9, 99, 90, 4) :|: 0 = 0
f_674(v939, v940, v941, v942, v943, v944, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, v958, 1, v959, v957, v960, v961, v962, v963, 3, 9, 99, 90, 4) -> f_676(v939, v940, v941, v942, v943, v944, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, v958, 1, v959, v1269, v957, v960, v961, v962, v963, 3, 9, 99, 90, 4, 81) :|: 9 + v1269 = v958 && v1269 <= 81
f_676(v939, v940, v941, v942, v943, v944, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, v958, 1, v959, v1269, v957, v960, v961, v962, v963, 3, 9, 99, 90, 4, 81) -> f_678(v939, v940, v941, v942, v943, v944, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, v958, 1, v959, v1269, v957, v960, v961, v962, v963, 3, 9, 99, 90, 4, 81) :|: TRUE
f_678(v939, v940, v941, v942, v943, v944, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, v958, 1, v959, v1269, v957, v960, v961, v962, v963, 3, 9, 99, 90, 4, 81) -> f_680(v939, v940, v941, v942, v943, v944, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, v958, 1, v959, v1269, v960, v961, v962, v963, 3, 9, 99, 90, 4, 81) :|: 0 = 0
f_680(v939, v940, v941, v942, v943, v944, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, v958, 1, v959, v1269, v960, v961, v962, v963, 3, 9, 99, 90, 4, 81) -> f_682(v939, v940, v941, v942, v943, v944, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, v958, 1, v959, v1269, v960, v961, v962, v963, 3, 9, 99, 90, 4, 81) :|: 0 = 0
f_682(v939, v940, v941, v942, v943, v944, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, v958, 1, v959, v1269, v960, v961, v962, v963, 3, 9, 99, 90, 4, 81) -> f_684(v939, v940, v941, v942, v943, v944, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, v958, 1, v959, v1269, v1273, v960, v961, v962, v963, 3, 9, 99, 90, 4, 81, 108) :|: v1273 = 9 + v959 && v1273 <= 108
f_684(v939, v940, v941, v942, v943, v944, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, v958, 1, v959, v1269, v1273, v960, v961, v962, v963, 3, 9, 99, 90, 4, 81, 108) -> f_686(v939, v940, v941, v942, v943, v944, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, v958, 1, v959, v1269, v1273, v960, v961, v962, v963, 3, 9, 99, 90, 4, 81, 108) :|: TRUE
f_686(v939, v940, v941, v942, v943, v944, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, v958, 1, v959, v1269, v1273, v960, v961, v962, v963, 3, 9, 99, 90, 4, 81, 108) -> f_688(v939, v940, v941, v942, v943, v944, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, v958, 1, v959, v1269, v1273, v960, v961, v962, v963, 3, 9, 99, 90, 4, 81, 108) :|: TRUE
f_688(v939, v940, v941, v942, v943, v944, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, v958, 1, v959, v1269, v1273, v960, v961, v962, v963, 3, 9, 99, 90, 4, 81, 108) -> f_646(v939, v940, v941, v942, v943, v944, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, v958, 1, v959, v1269, v1273, v960, v961, v962, v963, 3, 9, 99, 90, 108, 4) :|: TRUE
f_646(v939, v940, v941, v942, v943, v944, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, v955, 1, v957, v958, v959, v960, v961, v962, v963, 3, 9, 99, 90, 108, 4) -> f_648(v939, v940, v941, v942, v943, v944, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, v958, 1, v957, v955, v959, v960, v961, v962, v963, 3, 9, 99, 90, 108, 4) :|: 0 = 0
Combined rules. Obtained 1 rulesP rules:
f_648(v939:0, v940:0, v941:0, v942:0, v943:0, v944:0, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, 9 + v1269:0, 1, v957:0, v955:0, v959:0, v960:0, v961:0, v962:0, v963:0, 3, 9, 99, 90, 108, 4) -> f_648(v939:0, v940:0, v941:0, v942:0, v943:0, v944:0, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, v1269:0, 1, v959:0, 9 + v1269:0, 9 + v959:0, v960:0, v961:0, v962:0, v963:0, 3, 9, 99, 90, 108, 4) :|: v957:0 < 91 && v959:0 < 100 && v1269:0 < 82
Filtered unneeded arguments:
   f_648(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30, x31) -> f_648(x17, x19, x21)
Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules:
f_648(sum~cons_9~v1269:0, v957:0, v959:0) -> f_648(v1269:0, v959:0, 9 + v959:0) :|: v959:0 < 100 && v1269:0 < 82 && v957:0 < 91 && sum~cons_9~v1269:0 = 9 + v1269:0

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

(9)
Obligation:
Rules:
f_648(sum~cons_9~v1269:0, v957:0, v959:0) -> f_648(v1269:0, v959:0, 9 + v959:0) :|: v959:0 < 100 && v1269:0 < 82 && v957:0 < 91 && sum~cons_9~v1269:0 = 9 + v1269:0

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

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

(11)
Obligation:
Rules:
f_648(sum~cons_9~v1269:0:0, v957:0:0, v959:0:0) -> f_648(v1269:0:0, v959:0:0, 9 + v959:0:0) :|: v959:0:0 < 100 && v1269:0:0 < 82 && v957:0:0 < 91 && sum~cons_9~v1269:0:0 = 9 + v1269:0:0

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

(12) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f_648 ] = -1/9*f_648_3

The following rules are decreasing:
f_648(sum~cons_9~v1269:0:0, v957:0:0, v959:0:0) -> f_648(v1269:0:0, v959:0:0, 9 + v959:0:0) :|: v959:0:0 < 100 && v1269:0:0 < 82 && v957:0:0 < 91 && sum~cons_9~v1269:0:0 = 9 + v1269:0:0

The following rules are bounded:
f_648(sum~cons_9~v1269:0:0, v957:0:0, v959:0:0) -> f_648(v1269:0:0, v959:0:0, 9 + v959:0:0) :|: v959:0:0 < 100 && v1269:0:0 < 82 && v957:0:0 < 91 && sum~cons_9~v1269:0:0 = 9 + v1269:0:0


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

(13)
YES

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

(14)
Obligation:
SCC
----------------------------------------

(15) SCC2IRS (SOUND)
Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 
Generated rules. Obtained 18 rulesP rules:
f_647(v891, v892, v893, v894, v895, v896, v897, 1, 2, 3, 4, 5, 6, 7, 8, 9, v909, v908, v907, v910, v911, v912, v913, v914, 0, 99, 108, 90) -> f_649(v891, v892, v893, v894, v895, v896, v897, 1, 2, 3, 4, 5, 6, 7, 8, 9, v909, v908, v907, v910, v911, v912, v913, v914, 0, 99, 90) :|: v909 < 100 && v907 <= 90
f_649(v891, v892, v893, v894, v895, v896, v897, 1, 2, 3, 4, 5, 6, 7, 8, 9, v909, v908, v907, v910, v911, v912, v913, v914, 0, 99, 90) -> f_652(v891, v892, v893, v894, v895, v896, v897, 1, 2, 3, 4, 5, 6, 7, 8, 9, v909, v908, v907, v910, v911, v912, v913, v914, 0, 99, 90) :|: 0 = 0
f_652(v891, v892, v893, v894, v895, v896, v897, 1, 2, 3, 4, 5, 6, 7, 8, 9, v909, v908, v907, v910, v911, v912, v913, v914, 0, 99, 90) -> f_655(v891, v892, v893, v894, v895, v896, v897, 1, 2, 3, 4, 5, 6, 7, 8, 9, v909, v908, v907, v910, v911, v912, v913, v914, 0, 99, 90) :|: TRUE
f_655(v891, v892, v893, v894, v895, v896, v897, 1, 2, 3, 4, 5, 6, 7, 8, 9, v909, v908, v907, v910, v911, v912, v913, v914, 0, 99, 90) -> f_658(v891, v892, v893, v894, v895, v896, v897, 1, 2, 3, 4, 5, 6, 7, 8, 9, v909, v910, v907, v908, v911, v912, v913, v914, 0, 99, 90) :|: 0 = 0
f_658(v891, v892, v893, v894, v895, v896, v897, 1, 2, 3, 4, 5, 6, 7, 8, 9, v909, v910, v907, v908, v911, v912, v913, v914, 0, 99, 90) -> f_662(v891, v892, v893, v894, v895, v896, v897, 1, 2, 3, 4, 5, 6, 7, 8, 9, v909, v910, v907, v908, v911, v912, v913, v914, 0, 99, 90) :|: 0 = 0
f_662(v891, v892, v893, v894, v895, v896, v897, 1, 2, 3, 4, 5, 6, 7, 8, 9, v909, v910, v907, v908, v911, v912, v913, v914, 0, 99, 90) -> f_665(v891, v892, v893, v894, v895, v896, v897, 1, 2, 3, 4, 5, 6, 7, 8, 9, v909, v910, v907, v908, v911, v912, v913, v914, 0, 99, 90) :|: 0 = 0
f_665(v891, v892, v893, v894, v895, v896, v897, 1, 2, 3, 4, 5, 6, 7, 8, 9, v909, v910, v907, v908, v911, v912, v913, v914, 0, 99, 90) -> f_668(v891, v892, v893, v894, v895, v896, v897, 1, 2, 3, 4, 5, 6, 7, 8, 9, v909, v910, v907, v908, v911, v912, v913, v914, 0, 99, 90) :|: TRUE
f_668(v891, v892, v893, v894, v895, v896, v897, 1, 2, 3, 4, 5, 6, 7, 8, 9, v909, v910, v907, v908, v911, v912, v913, v914, 0, 99, 90) -> f_671(v891, v892, v893, v894, v895, v896, v897, 1, 2, 3, 4, 5, 6, 7, 8, 9, v909, v910, v908, v911, v912, v913, v914, 0, 99, 90) :|: 0 = 0
f_671(v891, v892, v893, v894, v895, v896, v897, 1, 2, 3, 4, 5, 6, 7, 8, 9, v909, v910, v908, v911, v912, v913, v914, 0, 99, 90) -> f_673(v891, v892, v893, v894, v895, v896, v897, 1, 2, 3, 4, 5, 6, 7, 8, 9, v909, v910, v908, v911, v912, v913, v914, 0, 99, 90) :|: 0 = 0
f_673(v891, v892, v893, v894, v895, v896, v897, 1, 2, 3, 4, 5, 6, 7, 8, 9, v909, v910, v908, v911, v912, v913, v914, 0, 99, 90) -> f_675(v891, v892, v893, v894, v895, v896, v897, 1, 2, 3, 4, 5, 6, 7, 8, 9, v909, v910, v1268, v908, v911, v912, v913, v914, 0, 99, 90, 108) :|: v1268 = 9 + v909 && v1268 <= 108
f_675(v891, v892, v893, v894, v895, v896, v897, 1, 2, 3, 4, 5, 6, 7, 8, 9, v909, v910, v1268, v908, v911, v912, v913, v914, 0, 99, 90, 108) -> f_677(v891, v892, v893, v894, v895, v896, v897, 1, 2, 3, 4, 5, 6, 7, 8, 9, v909, v910, v1268, v908, v911, v912, v913, v914, 0, 99, 90, 108) :|: TRUE
f_677(v891, v892, v893, v894, v895, v896, v897, 1, 2, 3, 4, 5, 6, 7, 8, 9, v909, v910, v1268, v908, v911, v912, v913, v914, 0, 99, 90, 108) -> f_679(v891, v892, v893, v894, v895, v896, v897, 1, 2, 3, 4, 5, 6, 7, 8, 9, v909, v910, v1268, v911, v912, v913, v914, 0, 99, 90, 108) :|: 0 = 0
f_679(v891, v892, v893, v894, v895, v896, v897, 1, 2, 3, 4, 5, 6, 7, 8, 9, v909, v910, v1268, v911, v912, v913, v914, 0, 99, 90, 108) -> f_681(v891, v892, v893, v894, v895, v896, v897, 1, 2, 3, 4, 5, 6, 7, 8, 9, v909, v910, v1268, v911, v912, v913, v914, 0, 99, 90, 108) :|: 0 = 0
f_681(v891, v892, v893, v894, v895, v896, v897, 1, 2, 3, 4, 5, 6, 7, 8, 9, v909, v910, v1268, v911, v912, v913, v914, 0, 99, 90, 108) -> f_683(v891, v892, v893, v894, v895, v896, v897, 1, 2, 3, 4, 5, 6, 7, 8, 9, v909, v910, v1268, v1272, v911, v912, v913, v914, 0, 99, 90, 108, 81) :|: 9 + v1272 = v910 && v1272 <= 81
f_683(v891, v892, v893, v894, v895, v896, v897, 1, 2, 3, 4, 5, 6, 7, 8, 9, v909, v910, v1268, v1272, v911, v912, v913, v914, 0, 99, 90, 108, 81) -> f_685(v891, v892, v893, v894, v895, v896, v897, 1, 2, 3, 4, 5, 6, 7, 8, 9, v909, v910, v1268, v1272, v911, v912, v913, v914, 0, 99, 90, 108, 81) :|: TRUE
f_685(v891, v892, v893, v894, v895, v896, v897, 1, 2, 3, 4, 5, 6, 7, 8, 9, v909, v910, v1268, v1272, v911, v912, v913, v914, 0, 99, 90, 108, 81) -> f_687(v891, v892, v893, v894, v895, v896, v897, 1, 2, 3, 4, 5, 6, 7, 8, 9, v909, v910, v1268, v1272, v911, v912, v913, v914, 0, 99, 90, 108, 81) :|: TRUE
f_687(v891, v892, v893, v894, v895, v896, v897, 1, 2, 3, 4, 5, 6, 7, 8, 9, v909, v910, v1268, v1272, v911, v912, v913, v914, 0, 99, 90, 108, 81) -> f_644(v891, v892, v893, v894, v895, v896, v897, 1, 2, 3, 4, 5, 6, 7, 8, 9, v909, v910, v1268, v1272, v911, v912, v913, v914, 0, 99, 108, 90) :|: TRUE
f_644(v891, v892, v893, v894, v895, v896, v897, 1, 2, 3, 4, 5, 6, 7, 8, 9, v907, v908, v909, v910, v911, v912, v913, v914, 0, 99, 108, 90) -> f_647(v891, v892, v893, v894, v895, v896, v897, 1, 2, 3, 4, 5, 6, 7, 8, 9, v909, v908, v907, v910, v911, v912, v913, v914, 0, 99, 108, 90) :|: 0 = 0
Combined rules. Obtained 1 rulesP rules:
f_647(v891:0, v892:0, v893:0, v894:0, v895:0, v896:0, v897:0, 1, 2, 3, 4, 5, 6, 7, 8, 9, v909:0, v908:0, v907:0, 9 + v1272:0, v911:0, v912:0, v913:0, v914:0, 0, 99, 108, 90) -> f_647(v891:0, v892:0, v893:0, v894:0, v895:0, v896:0, v897:0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 9 + v909:0, 9 + v1272:0, v909:0, v1272:0, v911:0, v912:0, v913:0, v914:0, 0, 99, 108, 90) :|: v907:0 < 91 && v909:0 < 100 && v1272:0 < 82
Filtered unneeded arguments:
   f_647(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28) -> f_647(x17, x19, x20)
Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules:
f_647(v909:0, v907:0, sum~cons_9~v1272:0) -> f_647(9 + v909:0, v909:0, v1272:0) :|: v909:0 < 100 && v1272:0 < 82 && v907:0 < 91 && sum~cons_9~v1272:0 = 9 + v1272:0

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(16)
Obligation:
Rules:
f_647(v909:0, v907:0, sum~cons_9~v1272:0) -> f_647(9 + v909:0, v909:0, v1272:0) :|: v909:0 < 100 && v1272:0 < 82 && v907:0 < 91 && sum~cons_9~v1272:0 = 9 + v1272:0

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(17) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(18)
Obligation:
Rules:
f_647(v909:0:0, v907:0:0, sum~cons_9~v1272:0:0) -> f_647(9 + v909:0:0, v909:0:0, v1272:0:0) :|: v909:0:0 < 100 && v1272:0:0 < 82 && v907:0:0 < 91 && sum~cons_9~v1272:0:0 = 9 + v1272:0:0

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(19) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f_647(x, x1, x2)] = 288 - 2*x - x2

The following rules are decreasing:
f_647(v909:0:0, v907:0:0, sum~cons_9~v1272:0:0) -> f_647(9 + v909:0:0, v909:0:0, v1272:0:0) :|: v909:0:0 < 100 && v1272:0:0 < 82 && v907:0:0 < 91 && sum~cons_9~v1272:0:0 = 9 + v1272:0:0
The following rules are bounded:
f_647(v909:0:0, v907:0:0, sum~cons_9~v1272:0:0) -> f_647(9 + v909:0:0, v909:0:0, v1272:0:0) :|: v909:0:0 < 100 && v1272:0:0 < 82 && v907:0:0 < 91 && sum~cons_9~v1272:0:0 = 9 + v1272:0:0

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(20)
YES