/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination of the given C Problem could be proven:

(0) C Problem
(1) CToLLVMProof [EQUIVALENT, 174 ms]
(2) LLVM problem
(3) LLVMToTerminationGraphProof [EQUIVALENT, 3592 ms]
(4) LLVM Symbolic Execution Graph
(5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms]
(6) AND
    (7) LLVM Symbolic Execution SCC
        (8) SCC2IRS [SOUND, 88 ms]
        (9) IntTRS
        (10) IRS2T2 [EQUIVALENT, 0 ms]
        (11) T2IntSys
        (12) T2 [EQUIVALENT, 1194 ms]
        (13) YES
    (14) LLVM Symbolic Execution SCC
        (15) SCC2IRS [SOUND, 63 ms]
        (16) IntTRS
        (17) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (18) IntTRS
        (19) PolynomialOrderProcessor [EQUIVALENT, 13 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: "test_fun" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: (i i32, j i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc
	0:
		%1 = alloca i32, align 4
		%2 = alloca i32, align 4
		%c = alloca i32, align 4
		store %i, %1
		store %j, %2
		store 0, %c
		br %3
	3:
		%4 = load %1
		%5 = icmp sge %4 0
		br %5, %6, %20
	6:
		store 0, %2
		br %7
	7:
		%8 = load %2
		%9 = load %1
		%10 = sub %9 1
		%11 = icmp sle %8 %10
		br %11, %12, %17
	12:
		%13 = load %2
		%14 = add %13 1
		store %14, %2
		%15 = load %c
		%16 = add %15 1
		store %16, %c
		br %7
	17:
		%18 = load %1
		%19 = sub %18 1
		store %19, %1
		br %3
	20:
		%21 = load %c
		ret %21

*BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc
	0:
		%1 = alloca i32, align 4
		store 0, %1
		%2 = call i32 @__VERIFIER_nondet_int()
		%3 = call i32 @__VERIFIER_nondet_int()
		%4 = call i32 @test_fun(i32 %2, i32 %3)
		ret %4


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 34 rulesP rules:
f_449(v562, v563, v564, v565, v566, v567, 1, 0, v569, v571, v572, v573, v574, v575, v576, v577, v578, v579, 3, 4) -> f_450(v562, v563, v564, v565, v566, v567, 1, 0, v571, v572, v573, v574, v569, v575, v576, v577, v578, v579, 3, 4) :|: 0 = 0
f_450(v562, v563, v564, v565, v566, v567, 1, 0, v571, v572, v573, v574, v569, v575, v576, v577, v578, v579, 3, 4) -> f_451(v562, v563, v564, v565, v566, v567, 1, 0, v590, v571, v572, v573, v574, v569, v575, v576, v577, v578, v579, 3, 4) :|: 1 + v590 = v567 && 0 <= 1 + v590
f_451(v562, v563, v564, v565, v566, v567, 1, 0, v590, v571, v572, v573, v574, v569, v575, v576, v577, v578, v579, 3, 4) -> f_452(v562, v563, v564, v565, v566, v567, 1, 0, v590, v571, v572, v573, v574, v569, v575, v576, v577, v578, v579, 3, 2, 4) :|: 0 <= v590 && 1 <= v567 && 2 <= v569 && 2 <= v562 && 2 <= v572 && 1 <= v571 && 2 <= v574 && 1 <= v573
f_452(v562, v563, v564, v565, v566, v567, 1, 0, v590, v571, v572, v573, v574, v569, v575, v576, v577, v578, v579, 3, 2, 4) -> f_454(v562, v563, v564, v565, v566, v567, 1, 0, v590, v571, v572, v573, v574, v569, v575, v576, v577, v578, v579, 3, 2, 4) :|: 0 = 0
f_454(v562, v563, v564, v565, v566, v567, 1, 0, v590, v571, v572, v573, v574, v569, v575, v576, v577, v578, v579, 3, 2, 4) -> f_456(v562, v563, v564, v565, v566, v567, 1, 0, v590, v571, v572, v573, v574, v569, v575, v576, v577, v578, v579, 3, 2, 4) :|: TRUE
f_456(v562, v563, v564, v565, v566, v567, 1, 0, v590, v571, v572, v573, v574, v569, v575, v576, v577, v578, v579, 3, 2, 4) -> f_457(v562, v563, v564, v565, v566, v567, 1, 0, v590, v571, v572, v573, v574, v569, v575, v576, v577, v578, v579, 0, 3, 2, 4) :|: TRUE
f_457(v604, v605, v606, v607, v608, v609, 1, v611, v612, v613, v614, v615, v616, v617, v618, v619, v620, v621, v622, 0, 3, 2, 4) -> f_459(v604, v605, v606, v607, v608, v609, 1, v611, v612, v614, v615, v616, v617, v618, v619, v620, v621, v622, 0, 3, 2, 4) :|: 0 = 0
f_459(v604, v605, v606, v607, v608, v609, 1, v611, v612, v614, v615, v616, v617, v618, v619, v620, v621, v622, 0, 3, 2, 4) -> f_461(v604, v605, v606, v607, v608, v609, 1, v611, v612, v629, v615, v616, v617, v618, v619, v620, v621, v622, 0, 3, 2, 4) :|: v629 = 1 + v611 && 1 <= v629
f_461(v604, v605, v606, v607, v608, v609, 1, v611, v612, v629, v615, v616, v617, v618, v619, v620, v621, v622, 0, 3, 2, 4) -> f_463(v604, v605, v606, v607, v608, v609, 1, v611, v612, v629, v615, v616, v617, v618, v619, v620, v621, v622, 0, 3, 2, 4) :|: TRUE
f_463(v604, v605, v606, v607, v608, v609, 1, v611, v612, v629, v615, v616, v617, v618, v619, v620, v621, v622, 0, 3, 2, 4) -> f_465(v604, v605, v606, v607, v608, v609, 1, v611, v612, v629, v616, v617, v618, v619, v620, v621, v622, 0, 3, 2, 4) :|: 0 = 0
f_465(v604, v605, v606, v607, v608, v609, 1, v611, v612, v629, v616, v617, v618, v619, v620, v621, v622, 0, 3, 2, 4) -> f_467(v604, v605, v606, v607, v608, v609, 1, v611, v612, v629, v616, v642, v617, v618, v619, v620, v621, v622, 0, 3, 2, 4) :|: v642 = 1 + v616 && 3 <= v642
f_467(v604, v605, v606, v607, v608, v609, 1, v611, v612, v629, v616, v642, v617, v618, v619, v620, v621, v622, 0, 3, 2, 4) -> f_469(v604, v605, v606, v607, v608, v609, 1, v611, v612, v629, v616, v642, v617, v618, v619, v620, v621, v622, 0, 3, 2, 4) :|: TRUE
f_469(v604, v605, v606, v607, v608, v609, 1, v611, v612, v629, v616, v642, v617, v618, v619, v620, v621, v622, 0, 3, 2, 4) -> f_471(v604, v605, v606, v607, v608, v609, 1, v611, v612, v629, v616, v642, v617, v618, v619, v620, v621, v622, 0, 3, 2, 4) :|: TRUE
f_471(v604, v605, v606, v607, v608, v609, 1, v611, v612, v629, v616, v642, v617, v618, v619, v620, v621, v622, 0, 3, 2, 4) -> f_473(v604, v605, v606, v607, v608, v609, 1, v629, v612, v611, v616, v642, v617, v618, v619, v620, v621, v622, 0, 3, 2, 4) :|: 0 = 0
f_473(v604, v605, v606, v607, v608, v609, 1, v629, v612, v611, v616, v642, v617, v618, v619, v620, v621, v622, 0, 3, 2, 4) -> f_475(v604, v605, v606, v607, v608, v609, 1, v629, v612, v611, v616, v642, v617, v618, v619, v620, v621, v622, 0, 3, 2, 4) :|: 0 = 0
f_475(v604, v605, v606, v607, v608, v609, 1, v629, v612, v611, v616, v642, v617, v618, v619, v620, v621, v622, 0, 3, 2, 4) -> f_477(v604, v605, v606, v607, v608, v609, 1, v629, v612, v611, v616, v642, v617, v618, v619, v620, v621, v622, 0, 3, 2, 4) :|: 1 + v612 = v609
f_477(v604, v605, v606, v607, v608, v609, 1, v629, v612, v611, v616, v642, v617, v618, v619, v620, v621, v622, 0, 3, 2, 4) -> f_478(v604, v605, v606, v607, v608, v609, 1, v629, v612, v611, v616, v642, v617, v618, v619, v620, v621, v622, 0, 3, 2, 4) :|: v629 <= v612 && 1 <= v612 && 2 <= v609 && 3 <= v617 && 3 <= v604 && 3 <= v616 && 4 <= v642
f_477(v604, v605, v606, v607, v608, v609, 1, v629, v612, v611, v616, v642, v617, v618, v619, v620, v621, v622, 0, 3, 2, 4) -> f_479(v604, v605, v606, v607, v608, v629, 1, v611, v616, v642, v617, v618, v619, v620, v621, v622, 0, 3, 2, 4) :|: v612 < v629 && v609 = v629 && v612 = v611
f_478(v604, v605, v606, v607, v608, v609, 1, v629, v612, v611, v616, v642, v617, v618, v619, v620, v621, v622, 0, 3, 2, 4) -> f_480(v604, v605, v606, v607, v608, v609, 1, v629, v612, v611, v616, v642, v617, v618, v619, v620, v621, v622, 0, 3, 2, 4) :|: 0 = 0
f_480(v604, v605, v606, v607, v608, v609, 1, v629, v612, v611, v616, v642, v617, v618, v619, v620, v621, v622, 0, 3, 2, 4) -> f_482(v604, v605, v606, v607, v608, v609, 1, v629, v612, v611, v616, v642, v617, v618, v619, v620, v621, v622, 0, 3, 2, 4) :|: TRUE
f_482(v604, v605, v606, v607, v608, v609, 1, v629, v612, v611, v616, v642, v617, v618, v619, v620, v621, v622, 0, 3, 2, 4) -> f_457(v604, v605, v606, v607, v608, v609, 1, v629, v612, v611, v629, v616, v642, v617, v618, v619, v620, v621, v622, 0, 3, 2, 4) :|: TRUE
f_479(v604, v605, v606, v607, v608, v629, 1, v611, v616, v642, v617, v618, v619, v620, v621, v622, 0, 3, 2, 4) -> f_481(v604, v605, v606, v607, v608, v629, 1, v611, 0, v616, v642, v617, v618, v619, v620, v621, v622, 3, 2, 4) :|: 0 = 0
f_481(v604, v605, v606, v607, v608, v629, 1, v611, 0, v616, v642, v617, v618, v619, v620, v621, v622, 3, 2, 4) -> f_483(v604, v605, v606, v607, v608, v629, 1, v611, 0, v616, v642, v617, v618, v619, v620, v621, v622, 3, 2, 4) :|: TRUE
f_483(v604, v605, v606, v607, v608, v629, 1, v611, 0, v616, v642, v617, v618, v619, v620, v621, v622, 3, 2, 4) -> f_484(v604, v605, v606, v607, v608, v629, 1, v611, 0, v616, v642, v618, v619, v620, v621, v622, 3, 2, 4) :|: 0 = 0
f_484(v604, v605, v606, v607, v608, v629, 1, v611, 0, v616, v642, v618, v619, v620, v621, v622, 3, 2, 4) -> f_485(v604, v605, v606, v607, v608, v629, 1, v611, 0, v616, v642, v618, v619, v620, v621, v622, 3, 2, 4) :|: 1 + v611 = v629
f_485(v604, v605, v606, v607, v608, v629, 1, v611, 0, v616, v642, v618, v619, v620, v621, v622, 3, 2, 4) -> f_486(v604, v605, v606, v607, v608, v629, 1, v611, 0, v616, v642, v618, v619, v620, v621, v622, 3, 2, 4) :|: TRUE
f_486(v604, v605, v606, v607, v608, v629, 1, v611, 0, v616, v642, v618, v619, v620, v621, v622, 3, 2, 4) -> f_487(v604, v605, v606, v607, v608, v629, 1, v611, 0, v616, v642, v618, v619, v620, v621, v622, 3, 2, 4) :|: TRUE
f_487(v604, v605, v606, v607, v608, v629, 1, v611, 0, v616, v642, v618, v619, v620, v621, v622, 3, 2, 4) -> f_488(v604, v605, v606, v607, v608, v611, 1, v629, 0, v616, v642, v618, v619, v620, v621, v622, 3, 2, 4) :|: 0 = 0
f_488(v604, v605, v606, v607, v608, v611, 1, v629, 0, v616, v642, v618, v619, v620, v621, v622, 3, 2, 4) -> f_489(v604, v605, v606, v607, v608, v611, 1, v629, 0, v616, v642, v618, v619, v620, v621, v622, 3, 2, 4) :|: 0 = 0
f_489(v604, v605, v606, v607, v608, v611, 1, v629, 0, v616, v642, v618, v619, v620, v621, v622, 3, 2, 4) -> f_490(v604, v605, v606, v607, v608, v611, 1, v629, 0, v616, v642, v618, v619, v620, v621, v622, 3, 2, 4) :|: TRUE
f_490(v604, v605, v606, v607, v608, v611, 1, v629, 0, v616, v642, v618, v619, v620, v621, v622, 3, 2, 4) -> f_491(v604, v605, v606, v607, v608, v611, 1, v629, 0, v616, v642, v618, v619, v620, v621, v622, 3, 2, 4) :|: TRUE
f_491(v604, v605, v606, v607, v608, v611, 1, v629, 0, v616, v642, v618, v619, v620, v621, v622, 3, 2, 4) -> f_492(v604, v605, v606, v607, v608, v611, 1, v629, 0, v616, v642, v618, v619, v620, v621, v622, 3, 2, 4) :|: TRUE
f_492(v604, v605, v606, v607, v608, v611, 1, v629, 0, v616, v642, v618, v619, v620, v621, v622, 3, 2, 4) -> f_448(v604, v605, v606, v607, v608, v611, 1, v629, 0, v611, v629, v616, v642, v618, v619, v620, v621, v622, 3, 4) :|: TRUE
f_448(v562, v563, v564, v565, v566, v567, 1, v569, 0, v571, v572, v573, v574, v575, v576, v577, v578, v579, 3, 4) -> f_449(v562, v563, v564, v565, v566, v567, 1, 0, v569, v571, v572, v573, v574, v575, v576, v577, v578, v579, 3, 4) :|: 0 = 0
Combined rules. Obtained 2 rulesP rules:
f_477(v604:0, v605:0, v606:0, v607:0, v608:0, 1 + (1 + v590:0), 1, 1 + (1 + v590:0), 1 + v590:0, 1 + v590:0, v616:0, v642:0, v617:0, v618:0, v619:0, v620:0, v621:0, v622:0, 0, 3, 2, 4) -> f_477(v604:0, v605:0, v606:0, v607:0, v608:0, 1 + v590:0, 1, 1, v590:0, 0, v642:0, 1 + v642:0, 1 + (1 + v590:0), v618:0, v619:0, v620:0, v621:0, v622:0, 0, 3, 2, 4) :|: v590:0 > -1 && v604:0 > 1 && v642:0 > 1 && v616:0 > 0 && 1 + v590:0 < 1 + (1 + v590:0)
f_477(v604:0, v605:0, v606:0, v607:0, v608:0, 1 + v612:0, 1, v629:0, v612:0, v611:0, v616:0, v642:0, v617:0, v618:0, v619:0, v620:0, v621:0, v622:0, 0, 3, 2, 4) -> f_477(v604:0, v605:0, v606:0, v607:0, v608:0, 1 + v612:0, 1, 1 + v629:0, v612:0, v629:0, v642:0, 1 + v642:0, v617:0, v618:0, v619:0, v620:0, v621:0, v622:0, 0, 3, 2, 4) :|: v642:0 > 3 && v629:0 > -1 && v612:0 > 0 && v629:0 <= v612:0 && v617:0 > 2 && v616:0 > 2 && v604:0 > 2
Filtered unneeded arguments:
   f_477(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) -> f_477(x1, x6, x8, x9, x10, x11, x12, x13)
Removed division, modulo operations, cleaned up constraints. Obtained 2 rules.P rules:
f_477(v604:0, sum~cons_1~sum~cons_1~v590:0, sum~cons_1~sum~cons_1~v590:01, sum~cons_1~v590:0, sum~cons_1~v590:01, v616:0, v642:0, v617:0) -> f_477(v604:0, 1 + v590:0, 1, v590:0, 0, v642:0, 1 + v642:0, 1 + (1 + v590:0)) :|: v604:0 > 1 && v590:0 > -1 && v642:0 > 1 && 1 + v590:0 < 1 + (1 + v590:0) && v616:0 > 0 && sum~cons_1~sum~cons_1~v590:0 = 1 + (1 + v590:0) && sum~cons_1~sum~cons_1~v590:01 = 1 + (1 + v590:0) && sum~cons_1~v590:0 = 1 + v590:0 && sum~cons_1~v590:01 = 1 + v590:0
f_477(v604:0, sum~cons_1~v612:0, v629:0, v612:0, v611:0, v616:0, v642:0, v617:0) -> f_477(v604:0, 1 + v612:0, 1 + v629:0, v612:0, v629:0, v642:0, 1 + v642:0, v617:0) :|: v629:0 > -1 && v642:0 > 3 && v612:0 > 0 && v629:0 <= v612:0 && v617:0 > 2 && v604:0 > 2 && v616:0 > 2 && sum~cons_1~v612:0 = 1 + v612:0

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

(9)
Obligation:
Rules:
f_477(v604:0, sum~cons_1~sum~cons_1~v590:0, sum~cons_1~sum~cons_1~v590:01, sum~cons_1~v590:0, sum~cons_1~v590:01, v616:0, v642:0, v617:0) -> f_477(v604:0, 1 + v590:0, 1, v590:0, 0, v642:0, 1 + v642:0, 1 + (1 + v590:0)) :|: v604:0 > 1 && v590:0 > -1 && v642:0 > 1 && 1 + v590:0 < 1 + (1 + v590:0) && v616:0 > 0 && sum~cons_1~sum~cons_1~v590:0 = 1 + (1 + v590:0) && sum~cons_1~sum~cons_1~v590:01 = 1 + (1 + v590:0) && sum~cons_1~v590:0 = 1 + v590:0 && sum~cons_1~v590:01 = 1 + v590:0
f_477(x, x1, x2, x3, x4, x5, x6, x7) -> f_477(x, 1 + x3, 1 + x2, x3, x2, x6, 1 + x6, x7) :|: x2 > -1 && x6 > 3 && x3 > 0 && x2 <= x3 && x7 > 2 && x > 2 && x5 > 2 && x1 = 1 + x3

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

(10) IRS2T2 (EQUIVALENT)
Transformed input IRS into an integer transition system.Used the following mapping from defined symbols to location IDs:

   (f_477_8,1)

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

(11)
Obligation:
START: 0;

FROM: 0;
TO: 1;

FROM: 1;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := x5;
oldX6 := x6;
oldX7 := x7;
oldX8 := oldX1 - 2;
assume(oldX0 > 1 && oldX8 > -1 && oldX6 > 1 && 1 + oldX8 < 1 + (1 + oldX8) && oldX5 > 0 && oldX1 = 1 + (1 + oldX8) && oldX2 = 1 + (1 + oldX8) && oldX3 = 1 + oldX8 && oldX4 = 1 + oldX8);
x0 := oldX0;
x1 := 1 + oldX8;
x2 := 1;
x3 := oldX1 - 2;
x4 := 0;
x5 := oldX6;
x6 := 1 + oldX6;
x7 := 1 + (1 + oldX8);
TO: 1;

FROM: 1;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := x5;
oldX6 := x6;
oldX7 := x7;
assume(oldX2 > -1 && oldX6 > 3 && oldX3 > 0 && oldX2 <= oldX3 && oldX7 > 2 && oldX0 > 2 && oldX5 > 2 && oldX1 = 1 + oldX3);
x0 := oldX0;
x1 := 1 + oldX3;
x2 := 1 + oldX2;
x3 := oldX3;
x4 := oldX2;
x5 := oldX6;
x6 := 1 + oldX6;
x7 := oldX7;
TO: 1;


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(12) T2 (EQUIVALENT)
Initially, performed program simplifications using lexicographic rank functions:
 * Removed transitions 1, 4, 5 using the following rank functions:
    - Rank function 1:
      RF for loc. 5: x1
      RF for loc. 6: x1
      Bound for (chained) transitions 4: 2
    - Rank function 2:
      RF for loc. 5: 1-2*x2+2*x3
      RF for loc. 6: -2*x2+2*x3
      Bound for (chained) transitions 5: 0
    - Rank function 3:
      RF for loc. 5: 0
      RF for loc. 6: -1
      Bound for (chained) transitions 1: 0

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(13)
YES

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(14)
Obligation:
SCC
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(15) SCC2IRS (SOUND)
Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 
Generated rules. Obtained 14 rulesP rules:
f_276(v90, v91, v92, v93, v94, 1, v98, v97, v96, v99, v100, v101, v102, v103, 0, 3, 4) -> f_277(v90, v91, v92, v93, v94, 1, v98, v97, v96, v99, v100, v101, v102, v103, 0, 3, 4) :|: 0 = 0
f_277(v90, v91, v92, v93, v94, 1, v98, v97, v96, v99, v100, v101, v102, v103, 0, 3, 4) -> f_278(v90, v91, v92, v93, v94, 1, v98, v97, v96, v99, v100, v101, v102, v103, 0, 3, 4) :|: 1 + v97 = v90
f_278(v90, v91, v92, v93, v94, 1, v98, v97, v96, v99, v100, v101, v102, v103, 0, 3, 4) -> f_279(v90, v91, v92, v93, v94, 1, v98, v97, v96, v99, v100, v101, v102, v103, 0, 3, 2, 4) :|: v98 <= v97 && 1 <= v97 && 2 <= v90
f_279(v90, v91, v92, v93, v94, 1, v98, v97, v96, v99, v100, v101, v102, v103, 0, 3, 2, 4) -> f_281(v90, v91, v92, v93, v94, 1, v98, v97, v96, v99, v100, v101, v102, v103, 0, 3, 2, 4) :|: 0 = 0
f_281(v90, v91, v92, v93, v94, 1, v98, v97, v96, v99, v100, v101, v102, v103, 0, 3, 2, 4) -> f_283(v90, v91, v92, v93, v94, 1, v98, v97, v96, v99, v100, v101, v102, v103, 0, 3, 2, 4) :|: TRUE
f_283(v90, v91, v92, v93, v94, 1, v98, v97, v96, v99, v100, v101, v102, v103, 0, 3, 2, 4) -> f_285(v90, v91, v92, v93, v94, 1, v98, v97, v96, v99, v100, v101, v102, v103, 0, 3, 2, 4) :|: 0 = 0
f_285(v90, v91, v92, v93, v94, 1, v98, v97, v96, v99, v100, v101, v102, v103, 0, 3, 2, 4) -> f_287(v90, v91, v92, v93, v94, 1, v98, v97, v105, v96, v99, v100, v101, v102, v103, 0, 3, 2, 4) :|: v105 = 1 + v98 && 2 <= v105
f_287(v90, v91, v92, v93, v94, 1, v98, v97, v105, v96, v99, v100, v101, v102, v103, 0, 3, 2, 4) -> f_289(v90, v91, v92, v93, v94, 1, v98, v97, v105, v96, v99, v100, v101, v102, v103, 0, 3, 2, 4) :|: TRUE
f_289(v90, v91, v92, v93, v94, 1, v98, v97, v105, v96, v99, v100, v101, v102, v103, 0, 3, 2, 4) -> f_291(v90, v91, v92, v93, v94, 1, v98, v97, v105, v99, v100, v101, v102, v103, 0, 3, 2, 4) :|: 0 = 0
f_291(v90, v91, v92, v93, v94, 1, v98, v97, v105, v99, v100, v101, v102, v103, 0, 3, 2, 4) -> f_293(v90, v91, v92, v93, v94, 1, v98, v97, v105, v99, v100, v101, v102, v103, 0, 3, 2, 4) :|: v105 = 1 + v98
f_293(v90, v91, v92, v93, v94, 1, v98, v97, v105, v99, v100, v101, v102, v103, 0, 3, 2, 4) -> f_295(v90, v91, v92, v93, v94, 1, v98, v97, v105, v99, v100, v101, v102, v103, 0, 3, 2, 4) :|: TRUE
f_295(v90, v91, v92, v93, v94, 1, v98, v97, v105, v99, v100, v101, v102, v103, 0, 3, 2, 4) -> f_297(v90, v91, v92, v93, v94, 1, v98, v97, v105, v99, v100, v101, v102, v103, 0, 3, 2, 4) :|: TRUE
f_297(v90, v91, v92, v93, v94, 1, v98, v97, v105, v99, v100, v101, v102, v103, 0, 3, 2, 4) -> f_275(v90, v91, v92, v93, v94, 1, v98, v97, v105, v99, v100, v101, v102, v103, 0, 3, 4) :|: TRUE
f_275(v90, v91, v92, v93, v94, 1, v96, v97, v98, v99, v100, v101, v102, v103, 0, 3, 4) -> f_276(v90, v91, v92, v93, v94, 1, v98, v97, v96, v99, v100, v101, v102, v103, 0, 3, 4) :|: 0 = 0
Combined rules. Obtained 1 rulesP rules:
f_276(1 + v97:0, v91:0, v92:0, v93:0, v94:0, 1, v98:0, v97:0, v96:0, v99:0, v100:0, v101:0, v102:0, v103:0, 0, 3, 4) -> f_276(1 + v97:0, v91:0, v92:0, v93:0, v94:0, 1, 1 + v98:0, v97:0, v98:0, v99:0, v100:0, v101:0, v102:0, v103:0, 0, 3, 4) :|: v97:0 > 0 && v98:0 <= v97:0 && v98:0 > 0
Filtered unneeded arguments:
   f_276(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17) -> f_276(x1, x7, x8)
Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules:
f_276(sum~cons_1~v97:0, v98:0, v97:0) -> f_276(1 + v97:0, 1 + v98:0, v97:0) :|: v98:0 <= v97:0 && v98:0 > 0 && v97:0 > 0 && sum~cons_1~v97:0 = 1 + v97:0

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(16)
Obligation:
Rules:
f_276(sum~cons_1~v97:0, v98:0, v97:0) -> f_276(1 + v97:0, 1 + v98:0, v97:0) :|: v98:0 <= v97:0 && v98:0 > 0 && v97:0 > 0 && sum~cons_1~v97:0 = 1 + v97:0

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(17) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(18)
Obligation:
Rules:
f_276(sum~cons_1~v97:0:0, v98:0:0, v97:0:0) -> f_276(1 + v97:0:0, 1 + v98:0:0, v97:0:0) :|: v98:0:0 <= v97:0:0 && v98:0:0 > 0 && v97:0:0 > 0 && sum~cons_1~v97:0:0 = 1 + v97:0:0

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(19) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f_276(x, x1, x2)] = -x1 + x2

The following rules are decreasing:
f_276(sum~cons_1~v97:0:0, v98:0:0, v97:0:0) -> f_276(1 + v97:0:0, 1 + v98:0:0, v97:0:0) :|: v98:0:0 <= v97:0:0 && v98:0:0 > 0 && v97:0:0 > 0 && sum~cons_1~v97:0:0 = 1 + v97:0:0
The following rules are bounded:
f_276(sum~cons_1~v97:0:0, v98:0:0, v97:0:0) -> f_276(1 + v97:0:0, 1 + v98:0:0, v97:0:0) :|: v98:0:0 <= v97:0:0 && v98:0:0 > 0 && v97:0:0 > 0 && sum~cons_1~v97:0:0 = 1 + v97:0:0

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(20)
YES