/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 177 ms]
(2) LLVM problem
(3) LLVMToTerminationGraphProof [EQUIVALENT, 1702 ms]
(4) LLVM Symbolic Execution Graph
(5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms]
(6) AND
    (7) LLVM Symbolic Execution SCC
        (8) SCC2IRS [SOUND, 84 ms]
        (9) IntTRS
        (10) IRS2T2 [EQUIVALENT, 0 ms]
        (11) T2IntSys
        (12) T2 [EQUIVALENT, 893 ms]
        (13) YES
    (14) LLVM Symbolic Execution SCC
        (15) SCC2IRS [SOUND, 40 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: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc
	0:
		%1 = alloca i32, align 4
		%x1 = alloca *i32, align 8
		%x2 = alloca *i32, align 8
		store 0, %1
		%2 = alloca i8, numElementsLit: 4
		%3 = bitcast *i8 %2 to *i32
		store %3, %x1
		%4 = alloca i8, numElementsLit: 4
		%5 = bitcast *i8 %4 to *i32
		store %5, %x2
		br %6
	6:
		%7 = load %x1
		%8 = load %7
		%9 = icmp sle %8 10
		br %9, %10, %26
	10:
		%11 = load %x2
		store 1000, %11
		br %12
	12:
		%13 = load %x2
		%14 = load %13
		%15 = icmp sgt %14 1
		br %15, %16, %21
	16:
		%17 = load %x2
		%18 = load %17
		%19 = sub %18 1
		%20 = load %x2
		store %19, %20
		br %12
	21:
		%22 = load %x1
		%23 = load %22
		%24 = add %23 1
		%25 = load %x1
		store %24, %25
		br %6
	26:
		%27 = load %1
		ret %27


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 39 rulesP rules:
f_257(v106, v107, v108, v109, v110, v111, 1, 0, 2, v122, v115, v116, v117, v118, v119, 3, 7, 10, 4, 8, 11) -> f_258(v106, v107, v108, v109, v110, v122, 1, 0, 2, v111, v115, v116, v117, v118, v119, 3, 7, 10, 4, 8, 11) :|: 0 = 0
f_258(v106, v107, v108, v109, v110, v122, 1, 0, 2, v111, v115, v116, v117, v118, v119, 3, 7, 10, 4, 8, 11) -> f_259(v106, v107, v108, v109, v110, v122, 1, 0, 2, v111, v115, v116, v117, v118, v119, 3, 7, 9, 4, 8, 10) :|: v122 <= 10 && v111 <= 9
f_259(v106, v107, v108, v109, v110, v122, 1, 0, 2, v111, v115, v116, v117, v118, v119, 3, 7, 9, 4, 8, 10) -> f_261(v106, v107, v108, v109, v110, v122, 1, 0, 2, v111, v115, v116, v117, v118, v119, 3, 7, 9, 4, 8, 10) :|: 0 = 0
f_261(v106, v107, v108, v109, v110, v122, 1, 0, 2, v111, v115, v116, v117, v118, v119, 3, 7, 9, 4, 8, 10) -> f_263(v106, v107, v108, v109, v110, v122, 1, 0, 2, v111, v115, v116, v117, v118, v119, 3, 7, 9, 4, 8, 10) :|: TRUE
f_263(v106, v107, v108, v109, v110, v122, 1, 0, 2, v111, v115, v116, v117, v118, v119, 3, 7, 9, 4, 8, 10) -> f_265(v106, v107, v108, v109, v110, v122, 1, 0, 2, v111, v115, v116, v117, v118, v119, 3, 7, 9, 4, 8, 10) :|: 0 = 0
f_265(v106, v107, v108, v109, v110, v122, 1, 0, 2, v111, v115, v116, v117, v118, v119, 3, 7, 9, 4, 8, 10) -> f_267(v106, v107, v108, v109, v110, v122, 1, 0, 2, v111, v115, v116, v117, v118, v119, 1000, 3, 7, 9, 4, 8, 10) :|: TRUE
f_267(v106, v107, v108, v109, v110, v122, 1, 0, 2, v111, v115, v116, v117, v118, v119, 1000, 3, 7, 9, 4, 8, 10) -> f_268(v106, v107, v108, v109, v110, v122, 1, 0, 2, v111, v115, v116, v117, v118, v119, 1000, 3, 7, 9, 4, 8, 10) :|: TRUE
f_268(v106, v107, v108, v109, v110, v122, 1, 0, 2, v111, v115, v116, v117, v118, v119, 1000, 3, 7, 9, 4, 8, 10) -> f_269(v106, v107, v108, v109, v110, v122, 1, 0, 2, v111, v115, v116, v117, v118, v119, 1000, 3, 7, 9, 4, 8, 10) :|: 0 = 0
f_269(v106, v107, v108, v109, v110, v122, 1, 0, 2, v111, v115, v116, v117, v118, v119, 1000, 3, 7, 9, 4, 8, 10) -> f_270(v106, v107, v108, v109, v110, v122, 1, 1000, 0, 2, v111, v115, v116, v117, v118, v119, 3, 7, 9, 4, 8, 10) :|: 0 = 0
f_270(v106, v107, v108, v109, v110, v122, 1, 1000, 0, 2, v111, v115, v116, v117, v118, v119, 3, 7, 9, 4, 8, 10) -> f_271(v106, v107, v108, v109, v110, v122, 1, 1000, 2, v111, v115, v116, v117, v118, v119, 0, 3, 7, 9, 4, 8, 10) :|: 0 = 0
f_271(v106, v107, v108, v109, v110, v122, 1, 1000, 2, v111, v115, v116, v117, v118, v119, 0, 3, 7, 9, 4, 8, 10) -> f_272(v106, v107, v108, v109, v110, v122, 1, 1000, 2, v111, v115, v116, v117, v118, v119, 0, 3, 7, 9, 4, 8, 10) :|: TRUE
f_272(v106, v107, v108, v109, v110, v122, 1, 1000, 2, v111, v115, v116, v117, v118, v119, 0, 3, 7, 9, 4, 8, 10) -> f_283(v106, v107, v108, v109, v110, v122, 1, 1000, 2, 1, v111, v115, v116, v117, v118, v119, 0, 3, 7, 10, 999, 1000, 2, 9, 4, 8) :|: TRUE
f_283(v184, v185, v186, v187, v188, v189, 1, v191, v192, v193, v194, v195, v196, v197, v198, v199, 0, 3, 7, 10, 999, 1000, 2, 9, 4, 8) -> f_294(v184, v185, v186, v187, v188, v189, 1, v191, v192, v193, v194, v195, v196, v197, v198, v199, 0, 3, 7, 10, 998, 1000, 2, 999, 9, 4, 8) :|: TRUE
f_294(v228, v229, v230, v231, v232, v233, 1, v235, v236, v237, v238, v239, v240, v241, v242, v243, 0, 3, 7, 10, 998, 1000, 2, 999, 9, 4, 8) -> f_305(v228, v229, v230, v231, v232, v233, 1, v235, v236, v237, v238, v239, v240, v241, v242, v243, 0, 3, 7, 10, 2, 1000, 999, 9, 4, 8) :|: TRUE
f_305(v272, v273, v274, v275, v276, v277, 1, v279, v280, v281, v282, v283, v284, v285, v286, v287, 0, 3, 7, 10, 2, 1000, 999, 9, 4, 8) -> f_319(v272, v273, v274, v275, v276, v277, 1, v279, v280, v281, v282, v283, v284, v285, v286, v287, 0, 3, 7, 10, 2, 1000, 999, 9, 4, 8) :|: TRUE
f_319(v316, v317, v318, v319, v320, v321, 1, v323, v324, v325, v326, v327, v328, v329, v330, v331, 0, 3, 7, 10, 2, 1000, 999, 9, 4, 8) -> f_333(v316, v317, v318, v319, v320, v321, 1, v323, v324, v325, v326, v327, v328, v329, v330, v331, 0, 3, 7, 10, 2, 1000, 999, 9, 4, 8) :|: TRUE
f_333(v360, v361, v362, v363, v364, v365, 1, v367, v368, v369, v370, v371, v372, v373, v374, v375, 0, 3, 7, 10, 2, 1000, 999, 9, 4, 8) -> f_334(v360, v361, v362, v363, v364, v365, 1, v367, v368, v369, v370, v371, v372, v373, v374, v375, 0, 3, 7, 10, 2, 1000, 999, 9, 4, 8) :|: 0 = 0
f_334(v360, v361, v362, v363, v364, v365, 1, v367, v368, v369, v370, v371, v372, v373, v374, v375, 0, 3, 7, 10, 2, 1000, 999, 9, 4, 8) -> f_335(v360, v361, v362, v363, v364, v365, 1, v367, v369, v370, v371, v372, v373, v374, v375, 0, 3, 7, 10, 2, 1000, 999, 9, 4, 8) :|: 0 = 0
f_335(v360, v361, v362, v363, v364, v365, 1, v367, v369, v370, v371, v372, v373, v374, v375, 0, 3, 7, 10, 2, 1000, 999, 9, 4, 8) -> f_336(v360, v361, v362, v363, v364, v365, 1, v367, v377, v370, v371, v372, v373, v374, v375, 0, 3, 7, 10, 2, 1000, 9, 4, 8, 999) :|: 1 + v377 = v367 && 1 <= v377 && v377 <= 999
f_336(v360, v361, v362, v363, v364, v365, 1, v367, v377, v370, v371, v372, v373, v374, v375, 0, 3, 7, 10, 2, 1000, 9, 4, 8, 999) -> f_337(v360, v361, v362, v363, v364, v365, 1, v367, v377, v370, v371, v372, v373, v374, v375, 0, 3, 7, 10, 2, 1000, 9, 4, 8, 999) :|: 0 = 0
f_337(v360, v361, v362, v363, v364, v365, 1, v367, v377, v370, v371, v372, v373, v374, v375, 0, 3, 7, 10, 2, 1000, 9, 4, 8, 999) -> f_338(v360, v361, v362, v363, v364, v365, 1, v367, v377, v370, v371, v372, v373, v374, v375, 0, 3, 7, 10, 2, 1000, 9, 4, 8, 999) :|: TRUE
f_338(v360, v361, v362, v363, v364, v365, 1, v367, v377, v370, v371, v372, v373, v374, v375, 0, 3, 7, 10, 2, 1000, 9, 4, 8, 999) -> f_339(v360, v361, v362, v363, v364, v365, 1, v367, v377, v370, v371, v372, v373, v374, v375, 0, 3, 7, 10, 2, 1000, 9, 4, 8, 999) :|: TRUE
f_339(v360, v361, v362, v363, v364, v365, 1, v367, v377, v370, v371, v372, v373, v374, v375, 0, 3, 7, 10, 2, 1000, 9, 4, 8, 999) -> f_340(v360, v361, v362, v363, v364, v365, 1, v367, v377, v370, v371, v372, v373, v374, v375, 0, 3, 7, 10, 2, 1000, 9, 4, 8, 999) :|: 0 = 0
f_340(v360, v361, v362, v363, v364, v365, 1, v367, v377, v370, v371, v372, v373, v374, v375, 0, 3, 7, 10, 2, 1000, 9, 4, 8, 999) -> f_341(v360, v361, v362, v363, v364, v365, 1, v377, v367, v370, v371, v372, v373, v374, v375, 0, 3, 7, 10, 2, 1000, 9, 4, 8, 999) :|: 0 = 0
f_341(v360, v361, v362, v363, v364, v365, 1, v377, v367, v370, v371, v372, v373, v374, v375, 0, 3, 7, 10, 2, 1000, 9, 4, 8, 999) -> f_342(v360, v361, v362, v363, v364, v365, 1, v377, v367, v370, v371, v372, v373, v374, v375, 0, 3, 7, 10, 1000, 9, 4, 8, 2, 999) :|: 1 < v377 && 3 <= v367
f_341(v360, v361, v362, v363, v364, v365, 1, v377, v367, v370, v371, v372, v373, v374, v375, 0, 3, 7, 10, 2, 1000, 9, 4, 8, 999) -> f_343(v360, v361, v362, v363, v364, v365, 1, 2, v370, v371, v372, v373, v374, v375, 0, 3, 7, 10, 9, 4, 8) :|: v377 <= 1 && v367 = 2 && v377 = 1 && 0 = 0
f_342(v360, v361, v362, v363, v364, v365, 1, v377, v367, v370, v371, v372, v373, v374, v375, 0, 3, 7, 10, 1000, 9, 4, 8, 2, 999) -> f_344(v360, v361, v362, v363, v364, v365, 1, v377, v367, v370, v371, v372, v373, v374, v375, 0, 3, 7, 10, 1000, 9, 4, 8, 2, 999) :|: 0 = 0
f_344(v360, v361, v362, v363, v364, v365, 1, v377, v367, v370, v371, v372, v373, v374, v375, 0, 3, 7, 10, 1000, 9, 4, 8, 2, 999) -> f_346(v360, v361, v362, v363, v364, v365, 1, v377, v367, v370, v371, v372, v373, v374, v375, 0, 3, 7, 10, 1000, 9, 4, 8, 2, 999) :|: TRUE
f_346(v360, v361, v362, v363, v364, v365, 1, v377, v367, v370, v371, v372, v373, v374, v375, 0, 3, 7, 10, 1000, 9, 4, 8, 2, 999) -> f_333(v360, v361, v362, v363, v364, v365, 1, v377, v367, v377, v370, v371, v372, v373, v374, v375, 0, 3, 7, 10, 2, 1000, 999, 9, 4, 8) :|: TRUE
f_343(v360, v361, v362, v363, v364, v365, 1, 2, v370, v371, v372, v373, v374, v375, 0, 3, 7, 10, 9, 4, 8) -> f_345(v360, v361, v362, v363, v364, v365, 1, 0, 2, v370, v371, v372, v373, v374, v375, 3, 7, 10, 9, 4, 8) :|: 0 = 0
f_345(v360, v361, v362, v363, v364, v365, 1, 0, 2, v370, v371, v372, v373, v374, v375, 3, 7, 10, 9, 4, 8) -> f_347(v360, v361, v362, v363, v364, v365, 1, 0, 2, v370, v371, v372, v373, v374, v375, 3, 7, 10, 9, 4, 8) :|: TRUE
f_347(v360, v361, v362, v363, v364, v365, 1, 0, 2, v370, v371, v372, v373, v374, v375, 3, 7, 10, 9, 4, 8) -> f_348(v360, v361, v362, v363, v364, v365, 1, 0, 2, v370, v371, v372, v373, v374, v375, 3, 7, 10, 9, 4, 8) :|: 0 = 0
f_348(v360, v361, v362, v363, v364, v365, 1, 0, 2, v370, v371, v372, v373, v374, v375, 3, 7, 10, 9, 4, 8) -> f_349(v360, v361, v362, v363, v364, v365, 1, 0, 2, v371, v372, v373, v374, v375, 3, 7, 10, 4, 8) :|: 0 = 0
f_349(v360, v361, v362, v363, v364, v365, 1, 0, 2, v371, v372, v373, v374, v375, 3, 7, 10, 4, 8) -> f_350(v360, v361, v362, v363, v364, v365, 1, 0, 2, v430, v371, v372, v373, v374, v375, 3, 7, 10, 4, 8, 11) :|: v430 = 1 + v365 && v430 <= 11
f_350(v360, v361, v362, v363, v364, v365, 1, 0, 2, v430, v371, v372, v373, v374, v375, 3, 7, 10, 4, 8, 11) -> f_351(v360, v361, v362, v363, v364, v365, 1, 0, 2, v430, v371, v372, v373, v374, v375, 3, 7, 10, 4, 8, 11) :|: 0 = 0
f_351(v360, v361, v362, v363, v364, v365, 1, 0, 2, v430, v371, v372, v373, v374, v375, 3, 7, 10, 4, 8, 11) -> f_352(v360, v361, v362, v363, v364, v365, 1, 0, 2, v430, v371, v372, v373, v374, v375, 3, 7, 10, 4, 8, 11) :|: TRUE
f_352(v360, v361, v362, v363, v364, v365, 1, 0, 2, v430, v371, v372, v373, v374, v375, 3, 7, 10, 4, 8, 11) -> f_353(v360, v361, v362, v363, v364, v365, 1, 0, 2, v430, v371, v372, v373, v374, v375, 3, 7, 10, 4, 8, 11) :|: TRUE
f_353(v360, v361, v362, v363, v364, v365, 1, 0, 2, v430, v371, v372, v373, v374, v375, 3, 7, 10, 4, 8, 11) -> f_256(v360, v361, v362, v363, v364, v365, 1, 0, 2, v430, v371, v372, v373, v374, v375, 3, 7, 10, 4, 8, 11) :|: TRUE
f_256(v106, v107, v108, v109, v110, v111, 1, 0, 2, v122, v115, v116, v117, v118, v119, 3, 7, 10, 4, 8, 11) -> f_257(v106, v107, v108, v109, v110, v111, 1, 0, 2, v122, v115, v116, v117, v118, v119, 3, 7, 10, 4, 8, 11) :|: 0 = 0
Combined rules. Obtained 2 rulesP rules:
f_341(v360:0, v361:0, v362:0, v363:0, v364:0, v365:0, 1, 1 + v377:1, v367:0, v370:0, v371:0, v372:0, v373:0, v374:0, v375:0, 0, 3, 7, 10, 2, 1000, 9, 4, 8, 999) -> f_341(v360:0, v361:0, v362:0, v363:0, v364:0, v365:0, 1, v377:1, 1 + v377:1, v370:0, v371:0, v372:0, v373:0, v374:0, v375:0, 0, 3, 7, 10, 2, 1000, 9, 4, 8, 999) :|: v377:1 > 0 && v377:1 < 1000 && v367:0 > 2
f_341(v360:0, v361:0, v362:0, v363:0, v364:0, v365:0, 1, 1, 2, v370:0, v371:0, v372:0, v373:0, v374:0, v375:0, 0, 3, 7, 10, 2, 1000, 9, 4, 8, 999) -> f_341(v360:0, v361:0, v362:0, v363:0, v364:0, 1 + v365:0, 1, 999, 1000, v365:0, v371:0, v372:0, v373:0, v374:0, v375:0, 0, 3, 7, 10, 2, 1000, 9, 4, 8, 999) :|: v365:0 < 10 && v365:0 < 11
Filtered unneeded arguments:
   f_341(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) -> f_341(x6, x8, x9)
Removed division, modulo operations, cleaned up constraints. Obtained 2 rules.P rules:
f_341(v365:0, sum~cons_1~v377:1, v367:0) -> f_341(v365:0, v377:1, 1 + v377:1) :|: v377:1 < 1000 && v367:0 > 2 && v377:1 > 0 && sum~cons_1~v377:1 = 1 + v377:1
f_341(v365:0, cons_1, cons_2) -> f_341(1 + v365:0, 999, 1000) :|: v365:0 < 10 && v365:0 < 11 && cons_1 = 1 && cons_2 = 2

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

(9)
Obligation:
Rules:
f_341(v365:0, sum~cons_1~v377:1, v367:0) -> f_341(v365:0, v377:1, 1 + v377:1) :|: v377:1 < 1000 && v367:0 > 2 && v377:1 > 0 && sum~cons_1~v377:1 = 1 + v377:1
f_341(x, x1, x2) -> f_341(1 + x, 999, 1000) :|: x < 10 && x < 11 && x1 = 1 && x2 = 2

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

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

   (f_341_3,1)

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

(11)
Obligation:
START: 0;

FROM: 0;
TO: 1;

FROM: 1;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := oldX1 - 1;
assume(oldX3 < 1000 && oldX2 > 2 && oldX3 > 0 && oldX1 = 1 + oldX3);
x0 := oldX0;
x1 := oldX1 - 1;
x2 := 1 + oldX3;
TO: 1;

FROM: 1;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX0 < 10 && oldX0 < 11 && oldX1 = 1 && oldX2 = 2);
x0 := 1 + oldX0;
x1 := 999;
x2 := 1000;
TO: 1;


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

(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: 1-1998*x0+2*x1
      RF for loc. 6: -1998*x0+2*x1
      Bound for (chained) transitions 5: -17980
    - Rank function 2:
      RF for loc. 5: 1+2*x1
      RF for loc. 6: 2*x1
      Bound for (chained) transitions 4: 4
    - Rank function 3:
      RF for loc. 5: 0
      RF for loc. 6: -1
      Bound for (chained) transitions 1: 0

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

(13)
YES

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

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

(15) SCC2IRS (SOUND)
Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 
Generated rules. Obtained 12 rulesP rules:
f_237(v106, v107, v108, v109, v110, v111, 1, v113, v114, v115, v116, v117, v118, v119, 0, 3, 7, 10, 2, 1000, 999, 4, 8) -> f_238(v106, v107, v108, v109, v110, v111, 1, v114, v113, v115, v116, v117, v118, v119, 0, 3, 7, 10, 2, 1000, 999, 4, 8) :|: 0 = 0
f_238(v106, v107, v108, v109, v110, v111, 1, v114, v113, v115, v116, v117, v118, v119, 0, 3, 7, 10, 2, 1000, 999, 4, 8) -> f_239(v106, v107, v108, v109, v110, v111, 1, v114, v113, v115, v116, v117, v118, v119, 0, 3, 7, 10, 1000, 2, 999, 4, 8) :|: 1 < v114 && 3 <= v113
f_239(v106, v107, v108, v109, v110, v111, 1, v114, v113, v115, v116, v117, v118, v119, 0, 3, 7, 10, 1000, 2, 999, 4, 8) -> f_241(v106, v107, v108, v109, v110, v111, 1, v114, v113, v115, v116, v117, v118, v119, 0, 3, 7, 10, 1000, 2, 999, 4, 8) :|: 0 = 0
f_241(v106, v107, v108, v109, v110, v111, 1, v114, v113, v115, v116, v117, v118, v119, 0, 3, 7, 10, 1000, 2, 999, 4, 8) -> f_243(v106, v107, v108, v109, v110, v111, 1, v114, v113, v115, v116, v117, v118, v119, 0, 3, 7, 10, 1000, 2, 999, 4, 8) :|: TRUE
f_243(v106, v107, v108, v109, v110, v111, 1, v114, v113, v115, v116, v117, v118, v119, 0, 3, 7, 10, 1000, 2, 999, 4, 8) -> f_245(v106, v107, v108, v109, v110, v111, 1, v114, v113, v115, v116, v117, v118, v119, 0, 3, 7, 10, 1000, 2, 999, 4, 8) :|: 0 = 0
f_245(v106, v107, v108, v109, v110, v111, 1, v114, v113, v115, v116, v117, v118, v119, 0, 3, 7, 10, 1000, 2, 999, 4, 8) -> f_247(v106, v107, v108, v109, v110, v111, 1, v114, v115, v116, v117, v118, v119, 0, 3, 7, 10, 2, 999, 4, 8) :|: 0 = 0
f_247(v106, v107, v108, v109, v110, v111, 1, v114, v115, v116, v117, v118, v119, 0, 3, 7, 10, 2, 999, 4, 8) -> f_249(v106, v107, v108, v109, v110, v111, 1, v114, v121, v115, v116, v117, v118, v119, 0, 3, 7, 10, 2, 999, 4, 8, 998) :|: 1 + v121 = v114 && 1 <= v121 && v121 <= 998
f_249(v106, v107, v108, v109, v110, v111, 1, v114, v121, v115, v116, v117, v118, v119, 0, 3, 7, 10, 2, 999, 4, 8, 998) -> f_251(v106, v107, v108, v109, v110, v111, 1, v114, v121, v115, v116, v117, v118, v119, 0, 3, 7, 10, 2, 999, 4, 8, 998) :|: 0 = 0
f_251(v106, v107, v108, v109, v110, v111, 1, v114, v121, v115, v116, v117, v118, v119, 0, 3, 7, 10, 2, 999, 4, 8, 998) -> f_253(v106, v107, v108, v109, v110, v111, 1, v114, v121, v115, v116, v117, v118, v119, 0, 3, 7, 10, 2, 999, 4, 8, 998) :|: TRUE
f_253(v106, v107, v108, v109, v110, v111, 1, v114, v121, v115, v116, v117, v118, v119, 0, 3, 7, 10, 2, 999, 4, 8, 998) -> f_255(v106, v107, v108, v109, v110, v111, 1, v114, v121, v115, v116, v117, v118, v119, 0, 3, 7, 10, 2, 999, 4, 8, 998) :|: TRUE
f_255(v106, v107, v108, v109, v110, v111, 1, v114, v121, v115, v116, v117, v118, v119, 0, 3, 7, 10, 2, 999, 4, 8, 998) -> f_236(v106, v107, v108, v109, v110, v111, 1, v114, v121, v115, v116, v117, v118, v119, 0, 3, 7, 10, 2, 1000, 999, 4, 8) :|: TRUE
f_236(v106, v107, v108, v109, v110, v111, 1, v113, v114, v115, v116, v117, v118, v119, 0, 3, 7, 10, 2, 1000, 999, 4, 8) -> f_237(v106, v107, v108, v109, v110, v111, 1, v113, v114, v115, v116, v117, v118, v119, 0, 3, 7, 10, 2, 1000, 999, 4, 8) :|: 0 = 0
Combined rules. Obtained 1 rulesP rules:
f_237(v106:0, v107:0, v108:0, v109:0, v110:0, v111:0, 1, v113:0, 1 + v121:0, v115:0, v116:0, v117:0, v118:0, v119:0, 0, 3, 7, 10, 2, 1000, 999, 4, 8) -> f_237(v106:0, v107:0, v108:0, v109:0, v110:0, v111:0, 1, 1 + v121:0, v121:0, v115:0, v116:0, v117:0, v118:0, v119:0, 0, 3, 7, 10, 2, 1000, 999, 4, 8) :|: v113:0 > 2 && v121:0 > 0 && v121:0 < 999
Filtered unneeded arguments:
   f_237(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23) -> f_237(x8, x9)
Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules:
f_237(v113:0, sum~cons_1~v121:0) -> f_237(1 + v121:0, v121:0) :|: v121:0 > 0 && v121:0 < 999 && v113:0 > 2 && sum~cons_1~v121:0 = 1 + v121:0

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(16)
Obligation:
Rules:
f_237(v113:0, sum~cons_1~v121:0) -> f_237(1 + v121:0, v121:0) :|: v121:0 > 0 && v121:0 < 999 && v113:0 > 2 && sum~cons_1~v121:0 = 1 + v121:0

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(17) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(18)
Obligation:
Rules:
f_237(v113:0:0, sum~cons_1~v121:0:0) -> f_237(1 + v121:0:0, v121:0:0) :|: v121:0:0 > 0 && v121:0:0 < 999 && v113:0:0 > 2 && sum~cons_1~v121:0:0 = 1 + v121:0:0

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(19) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f_237(x, x1)] = x1

The following rules are decreasing:
f_237(v113:0:0, sum~cons_1~v121:0:0) -> f_237(1 + v121:0:0, v121:0:0) :|: v121:0:0 > 0 && v121:0:0 < 999 && v113:0:0 > 2 && sum~cons_1~v121:0:0 = 1 + v121:0:0
The following rules are bounded:
f_237(v113:0:0, sum~cons_1~v121:0:0) -> f_237(1 + v121:0:0, v121:0:0) :|: v121:0:0 > 0 && v121:0:0 < 999 && v113:0:0 > 2 && sum~cons_1~v121:0:0 = 1 + v121:0:0

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(20)
YES