/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 4311 ms]
(4) LLVM Symbolic Execution Graph
(5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms]
(6) AND
    (7) LLVM Symbolic Execution SCC
        (8) SCC2IRS [SOUND, 64 ms]
        (9) IntTRS
        (10) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (11) IntTRS
        (12) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (13) YES
    (14) LLVM Symbolic Execution SCC
        (15) SCC2IRS [SOUND, 95 ms]
        (16) IntTRS
        (17) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (18) IntTRS
        (19) RankingReductionPairProof [EQUIVALENT, 13 ms]
        (20) YES
    (21) LLVM Symbolic Execution SCC
        (22) SCC2IRS [SOUND, 101 ms]
        (23) IntTRS
        (24) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (25) IntTRS
        (26) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (27) 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: (x i32, y i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc
	0:
		%1 = alloca i32, align 4
		%2 = alloca i32, align 4
		%c = alloca i32, align 4
		store %x, %1
		store %y, %2
		store 0, %c
		br %3
	3:
		%4 = load %1
		%5 = load %2
		%6 = add %4 %5
		%7 = icmp sgt %6 0
		br %7, %8, %25
	8:
		%9 = load %1
		%10 = icmp sgt %9 0
		br %10, %11, %14
	11:
		%12 = load %1
		%13 = sub %12 1
		store %13, %1
		br %22
	14:
		%15 = load %2
		%16 = icmp sgt %15 0
		br %16, %17, %20
	17:
		%18 = load %2
		%19 = sub %18 1
		store %19, %2
		br %21
	20:
		br %21
	21:
		br %22
	22:
		%23 = load %c
		%24 = add %23 1
		store %24, %c
		br %3
	25:
		%26 = load %c
		ret %26

*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 3 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 22 rulesP rules:
f_593(v631, v632, v633, v634, v635, 0, v637, 1, v639, v640, v641, v642, v643, v644, v645, v646, 3, 4) -> f_594(v631, v632, v633, v634, v635, 0, v637, 1, v640, v641, v642, v643, v644, v645, v646, 3, 4) :|: 0 = 0
f_594(v631, v632, v633, v634, v635, 0, v637, 1, v640, v641, v642, v643, v644, v645, v646, 3, 4) -> f_595(v631, v632, v633, v634, v635, 0, v637, 1, v640, v647, v641, v642, v643, v644, v645, v646, 3, 4, 2) :|: v647 = 1 + v640 && 2 <= v647
f_595(v631, v632, v633, v634, v635, 0, v637, 1, v640, v647, v641, v642, v643, v644, v645, v646, 3, 4, 2) -> f_596(v631, v632, v633, v634, v635, 0, v637, 1, v640, v647, v641, v642, v643, v644, v645, v646, 3, 4, 2) :|: TRUE
f_596(v631, v632, v633, v634, v635, 0, v637, 1, v640, v647, v641, v642, v643, v644, v645, v646, 3, 4, 2) -> f_597(v631, v632, v633, v634, v635, 0, v637, 1, v640, v647, v641, v642, v643, v644, v645, v646, 3, 4, 2) :|: TRUE
f_597(v631, v632, v633, v634, v635, 0, v637, 1, v640, v647, v641, v642, v643, v644, v645, v646, 3, 4, 2) -> f_598(v631, v632, v633, v634, v635, 0, v637, 1, v640, v647, v641, v642, v643, v644, v645, v646, 3, 4, 2) :|: 0 = 0
f_598(v631, v632, v633, v634, v635, 0, v637, 1, v640, v647, v641, v642, v643, v644, v645, v646, 3, 4, 2) -> f_599(v631, v632, v633, v634, v635, 0, v641, v637, 1, v640, v647, v642, v643, v644, v645, v646, 3, 4, 2) :|: 0 = 0
f_599(v631, v632, v633, v634, v635, 0, v641, v637, 1, v640, v647, v642, v643, v644, v645, v646, 3, 4, 2) -> f_600(v631, v632, v633, v634, v635, 0, v641, 1, v640, v647, v637, v642, v643, v644, v645, v646, 3, 4, 2) :|: 0 = 0
f_600(v631, v632, v633, v634, v635, 0, v641, 1, v640, v647, v637, v642, v643, v644, v645, v646, 3, 4, 2) -> f_601(v631, v632, v633, v634, v635, 0, v641, 1, v640, v647, v637, v642, v643, v644, v645, v646, 3, 2, 4) :|: 0 < v641 && 2 <= v637 && 2 <= v632
f_601(v631, v632, v633, v634, v635, 0, v641, 1, v640, v647, v637, v642, v643, v644, v645, v646, 3, 2, 4) -> f_603(v631, v632, v633, v634, v635, 0, v641, 1, v640, v647, v637, v642, v643, v644, v645, v646, 3, 2, 4) :|: 0 = 0
f_603(v631, v632, v633, v634, v635, 0, v641, 1, v640, v647, v637, v642, v643, v644, v645, v646, 3, 2, 4) -> f_605(v631, v632, v633, v634, v635, 0, v641, 1, v640, v647, v637, v642, v643, v644, v645, v646, 3, 2, 4) :|: TRUE
f_605(v631, v632, v633, v634, v635, 0, v641, 1, v640, v647, v637, v642, v643, v644, v645, v646, 3, 2, 4) -> f_607(v631, v632, v633, v634, v635, 0, v641, 1, v640, v647, v637, v642, v643, v644, v645, v646, 3, 2, 4) :|: 0 = 0
f_607(v631, v632, v633, v634, v635, 0, v641, 1, v640, v647, v637, v642, v643, v644, v645, v646, 3, 2, 4) -> f_609(v631, v632, v633, v634, v635, 0, v641, 1, v640, v647, v637, v642, v643, v644, v645, v646, 3, 2, 4) :|: 0 = 0
f_609(v631, v632, v633, v634, v635, 0, v641, 1, v640, v647, v637, v642, v643, v644, v645, v646, 3, 2, 4) -> f_611(v631, v632, v633, v634, v635, 0, v641, 1, v640, v647, v637, v642, v643, v644, v645, v646, 3, 2, 4) :|: TRUE
f_611(v631, v632, v633, v634, v635, 0, v641, 1, v640, v647, v637, v642, v643, v644, v645, v646, 3, 2, 4) -> f_612(v631, v632, v633, v634, v635, 0, v641, 1, v640, v647, v637, v642, v643, v644, v645, v646, 3, 2, 4) :|: 0 = 0
f_612(v631, v632, v633, v634, v635, 0, v641, 1, v640, v647, v637, v642, v643, v644, v645, v646, 3, 2, 4) -> f_613(v631, v632, v633, v634, v635, 0, v641, 1, v640, v647, v637, v642, v643, v644, v645, v646, 3, 2, 4) :|: 0 = 0
f_613(v631, v632, v633, v634, v635, 0, v641, 1, v640, v647, v637, v642, v643, v644, v645, v646, 3, 2, 4) -> f_614(v631, v632, v633, v634, v635, 0, v641, 1, v640, v647, v637, v642, v643, v644, v645, v646, 3, 2, 4) :|: TRUE
f_614(v631, v632, v633, v634, v635, 0, v641, 1, v640, v647, v637, v642, v643, v644, v645, v646, 3, 2, 4) -> f_615(v631, v632, v633, v634, v635, 0, v641, 1, v640, v647, v642, v643, v644, v645, v646, 3, 2, 4) :|: 0 = 0
f_615(v631, v632, v633, v634, v635, 0, v641, 1, v640, v647, v642, v643, v644, v645, v646, 3, 2, 4) -> f_616(v631, v632, v633, v634, v635, 0, v641, 1, v640, v647, v676, v642, v643, v644, v645, v646, 3, 2, 4) :|: 1 + v676 = v641 && 0 <= v676
f_616(v631, v632, v633, v634, v635, 0, v641, 1, v640, v647, v676, v642, v643, v644, v645, v646, 3, 2, 4) -> f_617(v631, v632, v633, v634, v635, 0, v641, 1, v640, v647, v676, v642, v643, v644, v645, v646, 3, 2, 4) :|: TRUE
f_617(v631, v632, v633, v634, v635, 0, v641, 1, v640, v647, v676, v642, v643, v644, v645, v646, 3, 2, 4) -> f_618(v631, v632, v633, v634, v635, 0, v641, 1, v640, v647, v676, v642, v643, v644, v645, v646, 3, 2, 4) :|: TRUE
f_618(v631, v632, v633, v634, v635, 0, v641, 1, v640, v647, v676, v642, v643, v644, v645, v646, 3, 2, 4) -> f_592(v631, v632, v633, v634, v635, 0, v641, 1, v640, v647, v676, v642, v643, v644, v645, v646, 3, 4) :|: TRUE
f_592(v631, v632, v633, v634, v635, 0, v637, 1, v639, v640, v641, v642, v643, v644, v645, v646, 3, 4) -> f_593(v631, v632, v633, v634, v635, 0, v637, 1, v639, v640, v641, v642, v643, v644, v645, v646, 3, 4) :|: TRUE
Combined rules. Obtained 1 rulesP rules:
f_593(v631:0, v632:0, v633:0, v634:0, v635:0, 0, v637:0, 1, v639:0, v640:0, 1 + v676:0, v642:0, v643:0, v644:0, v645:0, v646:0, 3, 4) -> f_593(v631:0, v632:0, v633:0, v634:0, v635:0, 0, 1 + v676:0, 1, v640:0, 1 + v640:0, v676:0, v642:0, v643:0, v644:0, v645:0, v646:0, 3, 4) :|: v640:0 > 0 && v637:0 > 1 && v676:0 > -1 && v632:0 > 1
Filtered unneeded arguments:
   f_593(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18) -> f_593(x2, x7, x10, x11)
Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules:
f_593(v632:0, v637:0, v640:0, sum~cons_1~v676:0) -> f_593(v632:0, 1 + v676:0, 1 + v640:0, v676:0) :|: v637:0 > 1 && v640:0 > 0 && v632:0 > 1 && v676:0 > -1 && sum~cons_1~v676:0 = 1 + v676:0

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

(9)
Obligation:
Rules:
f_593(v632:0, v637:0, v640:0, sum~cons_1~v676:0) -> f_593(v632:0, 1 + v676:0, 1 + v640:0, v676:0) :|: v637:0 > 1 && v640:0 > 0 && v632:0 > 1 && v676:0 > -1 && sum~cons_1~v676:0 = 1 + v676:0

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

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

(11)
Obligation:
Rules:
f_593(v632:0:0, v637:0:0, v640:0:0, sum~cons_1~v676:0:0) -> f_593(v632:0:0, 1 + v676:0:0, 1 + v640:0:0, v676:0:0) :|: v632:0:0 > 1 && v676:0:0 > -1 && v640:0:0 > 0 && v637:0:0 > 1 && sum~cons_1~v676:0:0 = 1 + v676:0:0

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

(12) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f_593(x, x1, x2, x3)] = x3

The following rules are decreasing:
f_593(v632:0:0, v637:0:0, v640:0:0, sum~cons_1~v676:0:0) -> f_593(v632:0:0, 1 + v676:0:0, 1 + v640:0:0, v676:0:0) :|: v632:0:0 > 1 && v676:0:0 > -1 && v640:0:0 > 0 && v637:0:0 > 1 && sum~cons_1~v676:0:0 = 1 + v676:0:0
The following rules are bounded:
f_593(v632:0:0, v637:0:0, v640:0:0, sum~cons_1~v676:0:0) -> f_593(v632:0:0, 1 + v676:0:0, 1 + v640:0:0, v676:0:0) :|: v632:0:0 > 1 && v676:0:0 > -1 && v640:0:0 > 0 && v637:0:0 > 1 && sum~cons_1~v676:0:0 = 1 + v676:0:0

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

(13)
YES

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

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

(15) SCC2IRS (SOUND)
Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 
Generated rules. Obtained 22 rulesP rules:
f_516(v400, v401, v402, v403, v404, v405, v406, 1, 0, v409, v410, v411, v412, v413, v414, v415, v416, 3, 4) -> f_518(v400, v401, v402, v403, v404, v409, v406, 1, 0, v405, v410, v411, v412, v413, v414, v415, v416, 3, 4) :|: 0 = 0
f_518(v400, v401, v402, v403, v404, v409, v406, 1, 0, v405, v410, v411, v412, v413, v414, v415, v416, 3, 4) -> f_520(v400, v401, v402, v403, v404, v409, v449, 1, 0, v405, v410, v411, v412, v413, v414, v415, v416, 3, 4) :|: v449 = v400 + v409
f_520(v400, v401, v402, v403, v404, v409, v449, 1, 0, v405, v410, v411, v412, v413, v414, v415, v416, 3, 4) -> f_522(v400, v401, v402, v403, v404, v409, v449, 1, 0, v405, v410, v411, v412, v413, v414, v415, v416, 3, 2, 4) :|: 0 < v449 && 1 <= v409 && 2 <= v405 && 2 <= v401
f_522(v400, v401, v402, v403, v404, v409, v449, 1, 0, v405, v410, v411, v412, v413, v414, v415, v416, 3, 2, 4) -> f_525(v400, v401, v402, v403, v404, v409, v449, 1, 0, v405, v410, v411, v412, v413, v414, v415, v416, 3, 2, 4) :|: 0 = 0
f_525(v400, v401, v402, v403, v404, v409, v449, 1, 0, v405, v410, v411, v412, v413, v414, v415, v416, 3, 2, 4) -> f_528(v400, v401, v402, v403, v404, v409, v449, 1, 0, v405, v410, v411, v412, v413, v414, v415, v416, 3, 2, 4) :|: TRUE
f_528(v400, v401, v402, v403, v404, v409, v449, 1, 0, v405, v410, v411, v412, v413, v414, v415, v416, 3, 2, 4) -> f_532(v400, v401, v402, v403, v404, v409, v449, 1, 0, v405, v410, v411, v412, v413, v414, v415, v416, 3, 2, 4) :|: 0 = 0
f_532(v400, v401, v402, v403, v404, v409, v449, 1, 0, v405, v410, v411, v412, v413, v414, v415, v416, 3, 2, 4) -> f_536(v400, v401, v402, v403, v404, v409, v449, 1, 0, v405, v410, v411, v412, v413, v414, v415, v416, 3, 2, 4) :|: 0 = 0
f_536(v400, v401, v402, v403, v404, v409, v449, 1, 0, v405, v410, v411, v412, v413, v414, v415, v416, 3, 2, 4) -> f_540(v400, v401, v402, v403, v404, v409, v449, 1, 0, v405, v410, v411, v412, v413, v414, v415, v416, 3, 2, 4) :|: TRUE
f_540(v400, v401, v402, v403, v404, v409, v449, 1, 0, v405, v410, v411, v412, v413, v414, v415, v416, 3, 2, 4) -> f_543(v400, v401, v402, v403, v404, v409, v449, 1, 0, v405, v410, v411, v412, v413, v414, v415, v416, 3, 2, 4) :|: 0 = 0
f_543(v400, v401, v402, v403, v404, v409, v449, 1, 0, v405, v410, v411, v412, v413, v414, v415, v416, 3, 2, 4) -> f_546(v400, v401, v402, v403, v404, v409, v449, 1, 0, v405, v410, v411, v412, v413, v414, v415, v416, 3, 2, 4) :|: 0 = 0
f_546(v400, v401, v402, v403, v404, v409, v449, 1, 0, v405, v410, v411, v412, v413, v414, v415, v416, 3, 2, 4) -> f_548(v400, v401, v402, v403, v404, v409, v449, 1, 0, v405, v410, v411, v412, v413, v414, v415, v416, 3, 2, 4) :|: TRUE
f_548(v400, v401, v402, v403, v404, v409, v449, 1, 0, v405, v410, v411, v412, v413, v414, v415, v416, 3, 2, 4) -> f_550(v400, v401, v402, v403, v404, v409, v449, 1, 0, v410, v411, v412, v413, v414, v415, v416, 3, 2, 4) :|: 0 = 0
f_550(v400, v401, v402, v403, v404, v409, v449, 1, 0, v410, v411, v412, v413, v414, v415, v416, 3, 2, 4) -> f_552(v400, v401, v402, v403, v404, v409, v449, 1, 0, v497, v410, v411, v412, v413, v414, v415, v416, 3, 2, 4) :|: 1 + v497 = v409 && 0 <= v497
f_552(v400, v401, v402, v403, v404, v409, v449, 1, 0, v497, v410, v411, v412, v413, v414, v415, v416, 3, 2, 4) -> f_554(v400, v401, v402, v403, v404, v409, v449, 1, 0, v497, v410, v411, v412, v413, v414, v415, v416, 3, 2, 4) :|: TRUE
f_554(v400, v401, v402, v403, v404, v409, v449, 1, 0, v497, v410, v411, v412, v413, v414, v415, v416, 3, 2, 4) -> f_556(v400, v401, v402, v403, v404, v409, v449, 1, 0, v497, v410, v411, v412, v413, v414, v415, v416, 3, 2, 4) :|: TRUE
f_556(v400, v401, v402, v403, v404, v409, v449, 1, 0, v497, v410, v411, v412, v413, v414, v415, v416, 3, 2, 4) -> f_558(v400, v401, v402, v403, v404, v409, v449, 1, 0, v497, v410, v411, v412, v413, v414, v415, v416, 3, 2, 4) :|: TRUE
f_558(v400, v401, v402, v403, v404, v409, v449, 1, 0, v497, v410, v411, v412, v413, v414, v415, v416, 3, 2, 4) -> f_560(v400, v401, v402, v403, v404, v409, v449, 1, 0, v497, v411, v412, v413, v414, v415, v416, 3, 2, 4) :|: 0 = 0
f_560(v400, v401, v402, v403, v404, v409, v449, 1, 0, v497, v411, v412, v413, v414, v415, v416, 3, 2, 4) -> f_563(v400, v401, v402, v403, v404, v409, v449, 1, 0, v497, v411, v559, v412, v413, v414, v415, v416, 3, 2, 4) :|: v559 = 1 + v411 && 2 <= v559
f_563(v400, v401, v402, v403, v404, v409, v449, 1, 0, v497, v411, v559, v412, v413, v414, v415, v416, 3, 2, 4) -> f_565(v400, v401, v402, v403, v404, v409, v449, 1, 0, v497, v411, v559, v412, v413, v414, v415, v416, 3, 2, 4) :|: TRUE
f_565(v400, v401, v402, v403, v404, v409, v449, 1, 0, v497, v411, v559, v412, v413, v414, v415, v416, 3, 2, 4) -> f_567(v400, v401, v402, v403, v404, v409, v449, 1, 0, v497, v411, v559, v412, v413, v414, v415, v416, 3, 2, 4) :|: TRUE
f_567(v400, v401, v402, v403, v404, v409, v449, 1, 0, v497, v411, v559, v412, v413, v414, v415, v416, 3, 2, 4) -> f_514(v400, v401, v402, v403, v404, v409, v449, 1, 0, v497, v411, v559, v412, v413, v414, v415, v416, 3, 4) :|: TRUE
f_514(v400, v401, v402, v403, v404, v405, v406, 1, 0, v409, v410, v411, v412, v413, v414, v415, v416, 3, 4) -> f_516(v400, v401, v402, v403, v404, v405, v406, 1, 0, v409, v410, v411, v412, v413, v414, v415, v416, 3, 4) :|: 0 = 0
Combined rules. Obtained 1 rulesP rules:
f_516(v400:0, v401:0, v402:0, v403:0, v404:0, v405:0, v406:0, 1, 0, 1 + v497:0, v410:0, v411:0, v412:0, v413:0, v414:0, v415:0, v416:0, 3, 4) -> f_516(v400:0, v401:0, v402:0, v403:0, v404:0, 1 + v497:0, v400:0 + (1 + v497:0), 1, 0, v497:0, v411:0, 1 + v411:0, v412:0, v413:0, v414:0, v415:0, v416:0, 3, 4) :|: v497:0 > -1 && v400:0 + (1 + v497:0) > 0 && v405:0 > 1 && v401:0 > 1 && v411:0 > 0
Filtered unneeded arguments:
   f_516(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) -> f_516(x1, x2, x6, x10, x12)
Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules:
f_516(v400:0, v401:0, v405:0, sum~cons_1~v497:0, v411:0) -> f_516(v400:0, v401:0, 1 + v497:0, v497:0, 1 + v411:0) :|: v400:0 + (1 + v497:0) > 0 && v497:0 > -1 && v405:0 > 1 && v411:0 > 0 && v401:0 > 1 && sum~cons_1~v497:0 = 1 + v497:0

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(16)
Obligation:
Rules:
f_516(v400:0, v401:0, v405:0, sum~cons_1~v497:0, v411:0) -> f_516(v400:0, v401:0, 1 + v497:0, v497:0, 1 + v411:0) :|: v400:0 + (1 + v497:0) > 0 && v497:0 > -1 && v405:0 > 1 && v411:0 > 0 && v401:0 > 1 && sum~cons_1~v497:0 = 1 + v497:0

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

(18)
Obligation:
Rules:
f_516(v400:0:0, v401:0:0, v405:0:0, sum~cons_1~v497:0:0, v411:0:0) -> f_516(v400:0:0, v401:0:0, 1 + v497:0:0, v497:0:0, 1 + v411:0:0) :|: v411:0:0 > 0 && v401:0:0 > 1 && v405:0:0 > 1 && v497:0:0 > -1 && v400:0:0 + (1 + v497:0:0) > 0 && sum~cons_1~v497:0:0 = 1 + v497:0:0

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(19) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f_516 ] = f_516_4

The following rules are decreasing:
f_516(v400:0:0, v401:0:0, v405:0:0, sum~cons_1~v497:0:0, v411:0:0) -> f_516(v400:0:0, v401:0:0, 1 + v497:0:0, v497:0:0, 1 + v411:0:0) :|: v411:0:0 > 0 && v401:0:0 > 1 && v405:0:0 > 1 && v497:0:0 > -1 && v400:0:0 + (1 + v497:0:0) > 0 && sum~cons_1~v497:0:0 = 1 + v497:0:0

The following rules are bounded:
f_516(v400:0:0, v401:0:0, v405:0:0, sum~cons_1~v497:0:0, v411:0:0) -> f_516(v400:0:0, v401:0:0, 1 + v497:0:0, v497:0:0, 1 + v411:0:0) :|: v411:0:0 > 0 && v401:0:0 > 1 && v405:0:0 > 1 && v497:0:0 > -1 && v400:0:0 + (1 + v497:0:0) > 0 && sum~cons_1~v497:0:0 = 1 + v497:0:0


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(20)
YES

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(21)
Obligation:
SCC
----------------------------------------

(22) SCC2IRS (SOUND)
Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 
Generated rules. Obtained 19 rulesP rules:
f_455(v299, v300, v301, v302, v303, v307, v305, 1, v304, v308, v309, v310, v311, v312, v313, v314, 0, 3, 4) -> f_457(v299, v300, v301, v302, v303, v307, v305, 1, v304, v308, v309, v310, v311, v312, v313, v314, 0, 3, 4) :|: 0 = 0
f_457(v299, v300, v301, v302, v303, v307, v305, 1, v304, v308, v309, v310, v311, v312, v313, v314, 0, 3, 4) -> f_460(v299, v300, v301, v302, v303, v307, v326, 1, v304, v308, v309, v310, v311, v312, v313, v314, 0, 3, 4) :|: v326 = v307 + v300
f_460(v299, v300, v301, v302, v303, v307, v326, 1, v304, v308, v309, v310, v311, v312, v313, v314, 0, 3, 4) -> f_463(v299, v300, v301, v302, v303, v307, v326, 1, v304, v308, v309, v310, v311, v312, v313, v314, 0, 3, 4) :|: 0 < v326
f_463(v299, v300, v301, v302, v303, v307, v326, 1, v304, v308, v309, v310, v311, v312, v313, v314, 0, 3, 4) -> f_467(v299, v300, v301, v302, v303, v307, v326, 1, v304, v308, v309, v310, v311, v312, v313, v314, 0, 3, 4) :|: 0 = 0
f_467(v299, v300, v301, v302, v303, v307, v326, 1, v304, v308, v309, v310, v311, v312, v313, v314, 0, 3, 4) -> f_471(v299, v300, v301, v302, v303, v307, v326, 1, v304, v308, v309, v310, v311, v312, v313, v314, 0, 3, 4) :|: TRUE
f_471(v299, v300, v301, v302, v303, v307, v326, 1, v304, v308, v309, v310, v311, v312, v313, v314, 0, 3, 4) -> f_475(v299, v300, v301, v302, v303, v307, v326, 1, v304, v308, v309, v310, v311, v312, v313, v314, 0, 3, 4) :|: 0 = 0
f_475(v299, v300, v301, v302, v303, v307, v326, 1, v304, v308, v309, v310, v311, v312, v313, v314, 0, 3, 4) -> f_478(v299, v300, v301, v302, v303, v307, v326, 1, v304, v308, v309, v310, v311, v312, v313, v314, 0, 3, 2, 4) :|: 0 < v307 && 2 <= v304 && 2 <= v299
f_478(v299, v300, v301, v302, v303, v307, v326, 1, v304, v308, v309, v310, v311, v312, v313, v314, 0, 3, 2, 4) -> f_482(v299, v300, v301, v302, v303, v307, v326, 1, v304, v308, v309, v310, v311, v312, v313, v314, 0, 3, 2, 4) :|: 0 = 0
f_482(v299, v300, v301, v302, v303, v307, v326, 1, v304, v308, v309, v310, v311, v312, v313, v314, 0, 3, 2, 4) -> f_485(v299, v300, v301, v302, v303, v307, v326, 1, v304, v308, v309, v310, v311, v312, v313, v314, 0, 3, 2, 4) :|: TRUE
f_485(v299, v300, v301, v302, v303, v307, v326, 1, v304, v308, v309, v310, v311, v312, v313, v314, 0, 3, 2, 4) -> f_488(v299, v300, v301, v302, v303, v307, v326, 1, v308, v309, v310, v311, v312, v313, v314, 0, 3, 2, 4) :|: 0 = 0
f_488(v299, v300, v301, v302, v303, v307, v326, 1, v308, v309, v310, v311, v312, v313, v314, 0, 3, 2, 4) -> f_491(v299, v300, v301, v302, v303, v307, v326, 1, v327, v308, v309, v310, v311, v312, v313, v314, 0, 3, 2, 4) :|: 1 + v327 = v307 && 0 <= v327
f_491(v299, v300, v301, v302, v303, v307, v326, 1, v327, v308, v309, v310, v311, v312, v313, v314, 0, 3, 2, 4) -> f_494(v299, v300, v301, v302, v303, v307, v326, 1, v327, v308, v309, v310, v311, v312, v313, v314, 0, 3, 2, 4) :|: TRUE
f_494(v299, v300, v301, v302, v303, v307, v326, 1, v327, v308, v309, v310, v311, v312, v313, v314, 0, 3, 2, 4) -> f_497(v299, v300, v301, v302, v303, v307, v326, 1, v327, v308, v309, v310, v311, v312, v313, v314, 0, 3, 2, 4) :|: TRUE
f_497(v299, v300, v301, v302, v303, v307, v326, 1, v327, v308, v309, v310, v311, v312, v313, v314, 0, 3, 2, 4) -> f_500(v299, v300, v301, v302, v303, v307, v326, 1, v327, v309, v310, v311, v312, v313, v314, 0, 3, 2, 4) :|: 0 = 0
f_500(v299, v300, v301, v302, v303, v307, v326, 1, v327, v309, v310, v311, v312, v313, v314, 0, 3, 2, 4) -> f_503(v299, v300, v301, v302, v303, v307, v326, 1, v327, v309, v338, v310, v311, v312, v313, v314, 0, 3, 2, 4) :|: v338 = 1 + v309 && 2 <= v338
f_503(v299, v300, v301, v302, v303, v307, v326, 1, v327, v309, v338, v310, v311, v312, v313, v314, 0, 3, 2, 4) -> f_506(v299, v300, v301, v302, v303, v307, v326, 1, v327, v309, v338, v310, v311, v312, v313, v314, 0, 3, 2, 4) :|: TRUE
f_506(v299, v300, v301, v302, v303, v307, v326, 1, v327, v309, v338, v310, v311, v312, v313, v314, 0, 3, 2, 4) -> f_509(v299, v300, v301, v302, v303, v307, v326, 1, v327, v309, v338, v310, v311, v312, v313, v314, 0, 3, 2, 4) :|: TRUE
f_509(v299, v300, v301, v302, v303, v307, v326, 1, v327, v309, v338, v310, v311, v312, v313, v314, 0, 3, 2, 4) -> f_453(v299, v300, v301, v302, v303, v307, v326, 1, v327, v309, v338, v310, v311, v312, v313, v314, 0, 3, 4) :|: TRUE
f_453(v299, v300, v301, v302, v303, v304, v305, 1, v307, v308, v309, v310, v311, v312, v313, v314, 0, 3, 4) -> f_455(v299, v300, v301, v302, v303, v307, v305, 1, v304, v308, v309, v310, v311, v312, v313, v314, 0, 3, 4) :|: 0 = 0
Combined rules. Obtained 1 rulesP rules:
f_455(v299:0, v300:0, v301:0, v302:0, v303:0, 1 + v327:0, v305:0, 1, v304:0, v308:0, v309:0, v310:0, v311:0, v312:0, v313:0, v314:0, 0, 3, 4) -> f_455(v299:0, v300:0, v301:0, v302:0, v303:0, v327:0, 1 + v327:0 + v300:0, 1, 1 + v327:0, v309:0, 1 + v309:0, v310:0, v311:0, v312:0, v313:0, v314:0, 0, 3, 4) :|: 1 + v327:0 + v300:0 > 0 && v304:0 > 1 && v327:0 > -1 && v299:0 > 1 && v309:0 > 0
Filtered unneeded arguments:
   f_455(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) -> f_455(x1, x2, x6, x9, x11)
Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules:
f_455(v299:0, v300:0, sum~cons_1~v327:0, v304:0, v309:0) -> f_455(v299:0, v300:0, v327:0, 1 + v327:0, 1 + v309:0) :|: v304:0 > 1 && 1 + v327:0 + v300:0 > 0 && v327:0 > -1 && v309:0 > 0 && v299:0 > 1 && sum~cons_1~v327:0 = 1 + v327:0

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(23)
Obligation:
Rules:
f_455(v299:0, v300:0, sum~cons_1~v327:0, v304:0, v309:0) -> f_455(v299:0, v300:0, v327:0, 1 + v327:0, 1 + v309:0) :|: v304:0 > 1 && 1 + v327:0 + v300:0 > 0 && v327:0 > -1 && v309:0 > 0 && v299:0 > 1 && sum~cons_1~v327:0 = 1 + v327:0

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

(25)
Obligation:
Rules:
f_455(v299:0:0, v300:0:0, sum~cons_1~v327:0:0, v304:0:0, v309:0:0) -> f_455(v299:0:0, v300:0:0, v327:0:0, 1 + v327:0:0, 1 + v309:0:0) :|: v309:0:0 > 0 && v299:0:0 > 1 && v327:0:0 > -1 && 1 + v327:0:0 + v300:0:0 > 0 && v304:0:0 > 1 && sum~cons_1~v327:0:0 = 1 + v327:0:0

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(26) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f_455 ] = f_455_3

The following rules are decreasing:
f_455(v299:0:0, v300:0:0, sum~cons_1~v327:0:0, v304:0:0, v309:0:0) -> f_455(v299:0:0, v300:0:0, v327:0:0, 1 + v327:0:0, 1 + v309:0:0) :|: v309:0:0 > 0 && v299:0:0 > 1 && v327:0:0 > -1 && 1 + v327:0:0 + v300:0:0 > 0 && v304:0:0 > 1 && sum~cons_1~v327:0:0 = 1 + v327:0:0

The following rules are bounded:
f_455(v299:0:0, v300:0:0, sum~cons_1~v327:0:0, v304:0:0, v309:0:0) -> f_455(v299:0:0, v300:0:0, v327:0:0, 1 + v327:0:0, 1 + v309:0:0) :|: v309:0:0 > 0 && v299:0:0 > 1 && v327:0:0 > -1 && 1 + v327:0:0 + v300:0:0 > 0 && v304:0:0 > 1 && sum~cons_1~v327:0:0 = 1 + v327:0:0


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(27)
YES