19.61/6.32	YES
19.61/6.33	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
19.61/6.33	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
19.61/6.33	
19.61/6.33	
19.61/6.33	Termination of the given C Problem could be proven:
19.61/6.33	
19.61/6.33	(0) C Problem
19.61/6.33	(1) CToLLVMProof [EQUIVALENT, 175 ms]
19.61/6.33	(2) LLVM problem
19.61/6.33	(3) LLVMToTerminationGraphProof [EQUIVALENT, 2409 ms]
19.61/6.33	(4) LLVM Symbolic Execution Graph
19.61/6.33	(5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms]
19.61/6.33	(6) LLVM Symbolic Execution SCC
19.61/6.33	(7) SCC2IRS [SOUND, 170 ms]
19.61/6.33	(8) IntTRS
19.61/6.33	(9) IntTRSCompressionProof [EQUIVALENT, 3 ms]
19.61/6.33	(10) IntTRS
19.61/6.33	(11) RankingReductionPairProof [EQUIVALENT, 19 ms]
19.61/6.33	(12) IntTRS
19.61/6.33	(13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
19.61/6.33	(14) IntTRS
19.61/6.33	(15) RankingReductionPairProof [EQUIVALENT, 4 ms]
19.61/6.33	(16) YES
19.61/6.33	
19.61/6.33	
19.61/6.33	----------------------------------------
19.61/6.33	
19.61/6.33	(0)
19.61/6.33	Obligation:
19.61/6.33	c file /export/starexec/sandbox/benchmark/theBenchmark.c
19.61/6.33	----------------------------------------
19.61/6.33	
19.61/6.33	(1) CToLLVMProof (EQUIVALENT)
19.61/6.33	Compiled c-file /export/starexec/sandbox/benchmark/theBenchmark.c to LLVM.
19.61/6.33	----------------------------------------
19.61/6.33	
19.61/6.33	(2)
19.61/6.33	Obligation:
19.61/6.33	LLVM Problem
19.61/6.33	
19.61/6.33	Aliases:
19.61/6.33	
19.61/6.33	Data layout:
19.61/6.33	
19.61/6.33	"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"
19.61/6.33	
19.61/6.33	Machine:
19.61/6.33	
19.61/6.33	"x86_64-pc-linux-gnu"
19.61/6.33	
19.61/6.33	Type definitions:
19.61/6.33	
19.61/6.33	Global variables:
19.61/6.33	
19.61/6.33	Function declarations and definitions:
19.61/6.33	
19.61/6.33	*BasicFunctionTypename: "__VERIFIER_nondet_int" returnParam: i32 parameters: () variableLength: true visibilityType: DEFAULT callingConvention: ccc
19.61/6.33	*BasicFunctionTypename: "f" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: (x i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc
19.61/6.33		0:
19.61/6.33			%1 = alloca i32, align 4
19.61/6.33			%2 = alloca i32, align 4
19.61/6.33			store %x, %2
19.61/6.33			%3 = load %2
19.61/6.33			%4 = icmp sle %3 0
19.61/6.33			br %4, %5, %6
19.61/6.33		5:
19.61/6.33			store 0, %1
19.61/6.33			br %13
19.61/6.33		6:
19.61/6.33			%7 = load %2
19.61/6.33			%8 = call i32 (...)* @g(i32 %7)
19.61/6.33			%9 = load %2
19.61/6.33			%10 = add %9 1
19.61/6.33			%11 = call i32 (...)* @g(i32 %10)
19.61/6.33			%12 = add %8 %11
19.61/6.33			store %12, %1
19.61/6.33			br %13
19.61/6.33		13:
19.61/6.33			%14 = load %1
19.61/6.33			ret %14
19.61/6.33	
19.61/6.33	*BasicFunctionTypename: "g" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: (x i32) variableLength: false visibilityType: DEFAULT callingConvention: ccc
19.61/6.33		0:
19.61/6.33			%1 = alloca i32, align 4
19.61/6.33			%2 = alloca i32, align 4
19.61/6.33			store %x, %2
19.61/6.33			%3 = load %2
19.61/6.33			%4 = icmp sle %3 0
19.61/6.33			br %4, %5, %6
19.61/6.33		5:
19.61/6.33			store 0, %1
19.61/6.33			br %14
19.61/6.33		6:
19.61/6.33			%7 = load %2
19.61/6.33			%8 = sub %7 2
19.61/6.33			%9 = call i32 @f(i32 %8)
19.61/6.33			%10 = load %2
19.61/6.33			%11 = sub %10 3
19.61/6.33			%12 = call i32 @f(i32 %11)
19.61/6.33			%13 = add %9 %12
19.61/6.33			store %13, %1
19.61/6.33			br %14
19.61/6.33		14:
19.61/6.33			%15 = load %1
19.61/6.33			ret %15
19.61/6.33	
19.61/6.33	*BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc
19.61/6.33		0:
19.61/6.33			%1 = alloca i32, align 4
19.61/6.33			%x = alloca i32, align 4
19.61/6.33			store 0, %1
19.61/6.33			%2 = call i32 (...)* @__VERIFIER_nondet_int()
19.61/6.33			store %2, %x
19.61/6.33			%3 = load %x
19.61/6.33			%4 = call i32 @g(i32 %3)
19.61/6.33			%5 = load %1
19.61/6.33			ret %5
19.61/6.33	
19.61/6.33	
19.61/6.33	Analyze Termination of all function calls matching the pattern:
19.61/6.33	main()
19.61/6.33	----------------------------------------
19.61/6.33	
19.61/6.33	(3) LLVMToTerminationGraphProof (EQUIVALENT)
19.61/6.33	Constructed symbolic execution graph for LLVM program and proved memory safety.
19.61/6.33	----------------------------------------
19.61/6.33	
19.61/6.33	(4)
19.61/6.33	Obligation:
19.61/6.33	SE Graph
19.61/6.33	----------------------------------------
19.61/6.33	
19.61/6.33	(5) SymbolicExecutionGraphToSCCProof (SOUND)
19.61/6.33	Splitted symbolic execution graph to 1 SCC.
19.61/6.33	----------------------------------------
19.61/6.33	
19.61/6.33	(6)
19.61/6.33	Obligation:
19.61/6.33	SCC
19.61/6.33	----------------------------------------
19.61/6.33	
19.61/6.33	(7) SCC2IRS (SOUND)
19.61/6.33	Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 
19.61/6.33	Generated rules. Obtained 74 rulesP rules:
19.61/6.33	f_293(v177, v178, v179, 3, 1, 4) -> f_294(v177, v178, v180, v179, v181, 3, 1, 4) :|: 1 <= v180 && v181 = 3 + v180 && 4 <= v181
19.61/6.33	f_294(v177, v178, v180, v179, v181, 3, 1, 4) -> f_295(v177, v178, v180, v179, v181, 3, 1, 4) :|: TRUE
19.61/6.33	f_295(v177, v178, v180, v179, v181, 3, 1, 4) -> f_296(v177, v178, v180, v179, v181, 3, 1, 4) :|: 0 = 0
19.61/6.33	f_296(v177, v178, v180, v179, v181, 3, 1, 4) -> f_298(v177, v178, v180, v179, v181, 3, 1, 4) :|: 0 < v177
19.61/6.33	f_298(v177, v178, v180, v179, v181, 3, 1, 4) -> f_300(v177, v178, v180, 0, v179, v181, 3, 1, 4) :|: 0 = 0
19.61/6.33	f_300(v177, v178, v180, 0, v179, v181, 3, 1, 4) -> f_302(v177, v178, v180, 0, v179, v181, 3, 1, 4) :|: TRUE
19.61/6.33	f_302(v177, v178, v180, 0, v179, v181, 3, 1, 4) -> f_304(v177, v178, v180, 0, v179, v181, 3, 1, 4) :|: 0 = 0
19.61/6.33	f_304(v177, v178, v180, 0, v179, v181, 3, 1, 4) -> f_306(v177, v178, v180, 0, v183, v179, v181, 3, 2, 1, 4) :|: 2 + v183 = v177 && 0 <= 1 + v183
19.61/6.33	f_306(v177, v178, v180, 0, v183, v179, v181, 3, 2, 1, 4) -> f_308(v183, v178, v179, v180, v181, v177, 0, 3, 2, 1, 4) :|: 0 = 0
19.61/6.33	f_308(v183, v178, v179, v180, v181, v177, 0, 3, 2, 1, 4) -> f_310(v183, v178, v179, v180, v181, v177, 3, 2, 1, 4, 0) :|: TRUE
19.61/6.33	f_308(v183, v178, v179, v180, v181, v177, 0, 3, 2, 1, 4) -> f_377(v183, 0, v178, v179, v180, v181, v177, 3, 2, 1, 4) :|: TRUE
19.61/6.33	f_308(v183, v178, v179, v180, v181, v177, 0, 3, 2, 1, 4) -> f_484(v183, 0, v178, v179, v180, v181, v177, 3, 2, 1, 4) :|: TRUE
19.61/6.33	f_308(v183, v178, v179, v180, v181, v177, 0, 3, 2, 1, 4) -> f_497(v183, 0, v178, v179, v180, v181, v177, 3, 2, 1, 4) :|: TRUE
19.61/6.33	f_308(v183, v178, v179, v180, v181, v177, 0, 3, 2, 1, 4) -> f_530(v183, 0, v178, v179, v180, v181, v177, 3, 2, 1, 4) :|: TRUE
19.61/6.33	f_308(v183, v178, v179, v180, v181, v177, 0, 3, 2, 1, 4) -> f_553(v183, 0, v178, v179, v180, v181, v177, 3, 2, 1, 4) :|: TRUE
19.61/6.33	f_310(v183, v178, v179, v180, v181, v177, 3, 2, 1, 4, 0) -> f_336(v183, v178, v179, v180, v181, v177, 3, 2, 0, 1, 4) :|: TRUE
19.61/6.33	f_336(v211, v212, v213, v214, v215, v216, 3, 2, 0, 1, 4) -> f_360(v211, 0, 2) :|: TRUE
19.61/6.33	f_360(v239, 0, 2) -> f_361(v239, v240, v241, 3, 0, 2, 1, 4) :|: 1 <= v240 && v241 = 3 + v240 && 4 <= v241
19.61/6.33	f_361(v239, v240, v241, 3, 0, 2, 1, 4) -> f_362(v239, v240, v242, v241, v243, 3, 0, 2, 1, 4) :|: 1 <= v242 && v243 = 3 + v242 && 4 <= v243
19.61/6.33	f_362(v239, v240, v242, v241, v243, 3, 0, 2, 1, 4) -> f_363(v239, v240, v242, v241, v243, 3, 0, 2, 1, 4) :|: TRUE
19.61/6.33	f_363(v239, v240, v242, v241, v243, 3, 0, 2, 1, 4) -> f_364(v239, v240, v242, v241, v243, 3, 0, 2, 1, 4) :|: 0 = 0
19.61/6.33	f_364(v239, v240, v242, v241, v243, 3, 0, 2, 1, 4) -> f_366(v239, v240, v242, v241, v243, 3, 1, 4) :|: 0 < v239
19.61/6.33	f_366(v239, v240, v242, v241, v243, 3, 1, 4) -> f_368(v239, v240, v242, 0, v241, v243, 3, 1, 4) :|: 0 = 0
19.61/6.33	f_368(v239, v240, v242, 0, v241, v243, 3, 1, 4) -> f_370(v239, v240, v242, 0, v241, v243, 3, 1, 4) :|: TRUE
19.61/6.33	f_370(v239, v240, v242, 0, v241, v243, 3, 1, 4) -> f_372(v239, v240, v242, 0, v241, v243, 3, 1, 4) :|: 0 = 0
19.61/6.33	f_372(v239, v240, v242, 0, v241, v243, 3, 1, 4) -> f_374(v239, v240, v241, v242, v243, 0, 3, 1, 4) :|: 0 = 0
19.61/6.33	f_374(v239, v240, v241, v242, v243, 0, 3, 1, 4) -> f_376(v239, v240, v241, v242, v243, 3, 1, 4) :|: TRUE
19.61/6.33	f_374(v239, v240, v241, v242, v243, 0, 3, 1, 4) -> f_435(v239, 0, v240, v241, v242, v243, 3, 1, 4) :|: TRUE
19.61/6.33	f_374(v239, v240, v241, v242, v243, 0, 3, 1, 4) -> f_470(v239, 0, v240, v241, v242, v243, 3, 1, 4) :|: TRUE
19.61/6.33	f_374(v239, v240, v241, v242, v243, 0, 3, 1, 4) -> f_512(v239, 0, v240, v241, v242, v243, 3, 1, 4) :|: TRUE
19.61/6.33	f_374(v239, v240, v241, v242, v243, 0, 3, 1, 4) -> f_548(v239, 0, v240, v241, v242, v243, 3, 1, 4) :|: TRUE
19.61/6.33	f_374(v239, v240, v241, v242, v243, 0, 3, 1, 4) -> f_567(v239, 0, v240, v241, v242, v243, 3, 1, 4) :|: TRUE
19.61/6.33	f_376(v239, v240, v241, v242, v243, 3, 1, 4) -> f_291(v239) :|: TRUE
19.61/6.33	f_291(v177) -> f_293(v177, v178, v179, 3, 1, 4) :|: 1 <= v178 && v179 = 3 + v178 && 4 <= v179
19.61/6.33	f_435(v239, 0, v240, v241, v242, v243, 3, 1, 4) -> f_437(v239, v240, v242, 0, v241, v243, 3, 1, 4) :|: 0 = 0
19.61/6.33	f_437(v239, v240, v242, 0, v241, v243, 3, 1, 4) -> f_439(v239, v240, v242, 0, v241, v243, 3, 1, 4) :|: 0 = 0
19.61/6.33	f_439(v239, v240, v242, 0, v241, v243, 3, 1, 4) -> f_440(v239, v240, v242, 0, v348, v241, v243, 3, 1, 4, 2) :|: v348 = 1 + v239 && 2 <= v348
19.61/6.33	f_440(v239, v240, v242, 0, v348, v241, v243, 3, 1, 4, 2) -> f_441(v348, v240, v241, v242, v243, v239, 0, 3, 1, 4, 2) :|: 0 = 0
19.61/6.33	f_441(v348, v240, v241, v242, v243, v239, 0, 3, 1, 4, 2) -> f_442(v348, v240, v241, v242, v243, v239, 3, 1, 4, 2) :|: TRUE
19.61/6.33	f_442(v348, v240, v241, v242, v243, v239, 3, 1, 4, 2) -> f_291(v348) :|: TRUE
19.61/6.33	f_470(v239, 0, v240, v241, v242, v243, 3, 1, 4) -> f_473(v239, v240, v242, 0, v241, v243, 3, 1, 4) :|: 0 = 0
19.61/6.33	f_473(v239, v240, v242, 0, v241, v243, 3, 1, 4) -> f_476(v239, v240, v242, 0, v241, v243, 3, 1, 4) :|: 0 = 0
19.61/6.33	f_476(v239, v240, v242, 0, v241, v243, 3, 1, 4) -> f_478(v239, v240, v242, 0, v424, v241, v243, 3, 1, 4, 2) :|: v424 = 1 + v239 && 2 <= v424
19.61/6.33	f_478(v239, v240, v242, 0, v424, v241, v243, 3, 1, 4, 2) -> f_480(v424, v240, v241, v242, v243, v239, 0, 3, 1, 4, 2) :|: 0 = 0
19.61/6.33	f_480(v424, v240, v241, v242, v243, v239, 0, 3, 1, 4, 2) -> f_482(v424, v240, v241, v242, v243, v239, 3, 1, 4, 2) :|: TRUE
19.61/6.33	f_482(v424, v240, v241, v242, v243, v239, 3, 1, 4, 2) -> f_291(v424) :|: TRUE
19.61/6.33	f_512(v239, 0, v240, v241, v242, v243, 3, 1, 4) -> f_516(v239, v240, v242, 0, v241, v243, 3, 1, 4) :|: 0 = 0
19.61/6.33	f_516(v239, v240, v242, 0, v241, v243, 3, 1, 4) -> f_520(v239, v240, v242, 0, v241, v243, 3, 1, 4) :|: 0 = 0
19.61/6.33	f_520(v239, v240, v242, 0, v241, v243, 3, 1, 4) -> f_523(v239, v240, v242, 0, v520, v241, v243, 3, 1, 4, 2) :|: v520 = 1 + v239 && 2 <= v520
19.61/6.33	f_523(v239, v240, v242, 0, v520, v241, v243, 3, 1, 4, 2) -> f_526(v520, v240, v241, v242, v243, v239, 0, 3, 1, 4, 2) :|: 0 = 0
19.61/6.33	f_526(v520, v240, v241, v242, v243, v239, 0, 3, 1, 4, 2) -> f_529(v520, v240, v241, v242, v243, v239, 3, 1, 4, 2) :|: TRUE
19.61/6.33	f_529(v520, v240, v241, v242, v243, v239, 3, 1, 4, 2) -> f_291(v520) :|: TRUE
19.61/6.33	f_548(v239, 0, v240, v241, v242, v243, 3, 1, 4) -> f_512(v239, 0, v240, v241, v242, v243, 3, 1, 4) :|: TRUE
19.61/6.33	f_567(v239, 0, v240, v241, v242, v243, 3, 1, 4) -> f_548(v239, 0, v240, v241, v242, v243, 3, 1, 4) :|: TRUE
19.61/6.33	f_377(v183, 0, v178, v179, v180, v181, v177, 3, 2, 1, 4) -> f_378(v177, v178, v180, 0, v183, v179, v181, 3, 2, 1, 4) :|: 0 = 0
19.61/6.33	f_378(v177, v178, v180, 0, v183, v179, v181, 3, 2, 1, 4) -> f_380(v177, v178, v180, 0, v183, v179, v181, 3, 2, 1, 4) :|: 0 = 0
19.61/6.33	f_380(v177, v178, v180, 0, v183, v179, v181, 3, 2, 1, 4) -> f_381(v177, v178, v180, 0, v183, v256, v179, v181, 3, 2, 1, 4) :|: 3 + v256 = v177 && 0 <= 2 + v256 && 1 + v256 <= 0
19.61/6.33	f_381(v177, v178, v180, 0, v183, v256, v179, v181, 3, 2, 1, 4) -> f_382(v256, v178, v179, v180, v181, v177, 0, v183, 3, 2, 1, 4) :|: 0 = 0
19.61/6.33	f_382(v256, v178, v179, v180, v181, v177, 0, v183, 3, 2, 1, 4) -> f_383(v256, v178, v179, v180, v181, v177, 3, 1, 2, 4, 0) :|: TRUE
19.61/6.33	f_383(v256, v178, v179, v180, v181, v177, 3, 1, 2, 4, 0) -> f_360(v256, 0, 2) :|: TRUE
19.61/6.33	f_484(v183, 0, v178, v179, v180, v181, v177, 3, 2, 1, 4) -> f_488(v177, v178, v180, 0, v183, v179, v181, 3, 2, 1, 4) :|: 0 = 0
19.61/6.33	f_488(v177, v178, v180, 0, v183, v179, v181, 3, 2, 1, 4) -> f_490(v177, v178, v180, 0, v183, v179, v181, 3, 2, 1, 4) :|: 0 = 0
19.61/6.33	f_490(v177, v178, v180, 0, v183, v179, v181, 3, 2, 1, 4) -> f_492(v177, v178, v180, 0, v183, v450, v179, v181, 3, 2, 1, 4) :|: 3 + v450 = v177 && 0 <= v450
19.61/6.33	f_492(v177, v178, v180, 0, v183, v450, v179, v181, 3, 2, 1, 4) -> f_494(v450, v178, v179, v180, v181, v177, 0, v183, 3, 2, 1, 4) :|: 0 = 0
19.61/6.33	f_494(v450, v178, v179, v180, v181, v177, 0, v183, 3, 2, 1, 4) -> f_496(v450, v178, v179, v180, v181, v177, 3, 1, 4, 0) :|: TRUE
19.61/6.33	f_496(v450, v178, v179, v180, v181, v177, 3, 1, 4, 0) -> f_360(v450, 0, 2) :|: TRUE
19.61/6.33	f_497(v183, 0, v178, v179, v180, v181, v177, 3, 2, 1, 4) -> f_484(v183, 0, v178, v179, v180, v181, v177, 3, 2, 1, 4) :|: TRUE
19.61/6.33	f_530(v183, 0, v178, v179, v180, v181, v177, 3, 2, 1, 4) -> f_533(v177, v178, v180, 0, v183, v179, v181, 3, 2, 1, 4) :|: 0 = 0
19.61/6.33	f_533(v177, v178, v180, 0, v183, v179, v181, 3, 2, 1, 4) -> f_537(v177, v178, v180, 0, v183, v179, v181, 3, 2, 1, 4) :|: 0 = 0
19.61/6.33	f_537(v177, v178, v180, 0, v183, v179, v181, 3, 2, 1, 4) -> f_540(v177, v178, v180, 0, v183, v566, v179, v181, 3, 2, 1, 4) :|: 3 + v566 = v177 && 0 <= v566
19.61/6.33	f_540(v177, v178, v180, 0, v183, v566, v179, v181, 3, 2, 1, 4) -> f_543(v566, v178, v179, v180, v181, v177, 0, v183, 3, 2, 1, 4) :|: 0 = 0
19.61/6.33	f_543(v566, v178, v179, v180, v181, v177, 0, v183, 3, 2, 1, 4) -> f_546(v566, v178, v179, v180, v181, v177, 3, 1, 4, 0) :|: TRUE
19.61/6.33	f_546(v566, v178, v179, v180, v181, v177, 3, 1, 4, 0) -> f_360(v566, 0, 2) :|: TRUE
19.61/6.33	f_553(v183, 0, v178, v179, v180, v181, v177, 3, 2, 1, 4) -> f_530(v183, 0, v178, v179, v180, v181, v177, 3, 2, 1, 4) :|: TRUE
19.61/6.33	Combined rules. Obtained 4 rulesP rules:
19.61/6.33	f_374(v239:0, v240:0, v241:0, v242:0, v243:0, 0, 3, 1, 4) -> f_293(1 + v239:0, v178:0, 3 + v178:0, 3, 1, 4) :|: v239:0 > 0 && v178:0 > 0
19.61/6.33	f_293(3 + v450:0, v178:0, v179:0, 3, 1, 4) -> f_374(v450:0, v240:0, 3 + v240:0, v242:0, 3 + v242:0, 0, 3, 1, 4) :|: v450:0 > 0 && v180:0 > 0 && v240:0 > 0 && v242:0 > 0 && 3 + v450:0 = 2 + v183:0 && v183:0 > -2
19.61/6.33	f_374(v239:0, v240:0, v241:0, v242:0, v243:0, 0, 3, 1, 4) -> f_293(v239:0, v178:0, 3 + v178:0, 3, 1, 4) :|: v178:0 > 0
19.61/6.33	f_293(2 + v183:0, v178:0, v179:0, 3, 1, 4) -> f_374(v183:0, v240:0, 3 + v240:0, v242:0, 3 + v242:0, 0, 3, 1, 4) :|: v183:0 > 0 && v180:0 > 0 && v240:0 > 0 && v242:0 > 0
19.61/6.33	Filtered unneeded arguments:
19.61/6.33	   f_374(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f_374(x1)
19.61/6.33	   f_293(x1, x2, x3, x4, x5, x6) -> f_293(x1)
19.61/6.33	Removed division, modulo operations, cleaned up constraints. Obtained 4 rules.P rules:
19.61/6.33	f_374(v239:0) -> f_293(1 + v239:0) :|: v239:0 > 0
19.61/6.33	f_293(sum~cons_3~v450:0) -> f_374(v450:0) :|: v450:0 > 0 && sum~cons_3~v450:0 = 3 + v450:0
19.61/6.33	f_374(v239:0) -> f_293(v239:0) :|: TRUE
19.61/6.33	f_293(sum~cons_2~v183:0) -> f_374(v183:0) :|: v183:0 > 0 && sum~cons_2~v183:0 = 2 + v183:0
19.61/6.33	
19.61/6.33	----------------------------------------
19.61/6.33	
19.61/6.33	(8)
19.61/6.33	Obligation:
19.61/6.33	Rules:
19.61/6.33	f_374(v239:0) -> f_293(1 + v239:0) :|: v239:0 > 0
19.61/6.33	f_293(sum~cons_3~v450:0) -> f_374(v450:0) :|: v450:0 > 0 && sum~cons_3~v450:0 = 3 + v450:0
19.61/6.33	f_374(x) -> f_293(x) :|: TRUE
19.61/6.33	f_293(sum~cons_2~v183:0) -> f_374(v183:0) :|: v183:0 > 0 && sum~cons_2~v183:0 = 2 + v183:0
19.61/6.33	
19.61/6.33	----------------------------------------
19.61/6.33	
19.61/6.33	(9) IntTRSCompressionProof (EQUIVALENT)
19.61/6.33	Compressed rules.
19.61/6.33	----------------------------------------
19.61/6.33	
19.61/6.33	(10)
19.61/6.33	Obligation:
19.61/6.33	Rules:
19.61/6.33	f_293(sum~cons_2~v183:0:0) -> f_374(v183:0:0) :|: v183:0:0 > 0 && sum~cons_2~v183:0:0 = 2 + v183:0:0
19.61/6.33	f_374(x:0) -> f_293(x:0) :|: TRUE
19.61/6.33	f_374(v239:0:0) -> f_293(1 + v239:0:0) :|: v239:0:0 > 0
19.61/6.33	f_293(sum~cons_3~v450:0:0) -> f_374(v450:0:0) :|: v450:0:0 > 0 && sum~cons_3~v450:0:0 = 3 + v450:0:0
19.61/6.33	
19.61/6.33	----------------------------------------
19.61/6.33	
19.61/6.33	(11) RankingReductionPairProof (EQUIVALENT)
19.61/6.33	Interpretation:
19.61/6.33	[ f_293 ] = 2*f_293_1 + -3
19.61/6.33	[ f_374 ] = 2*f_374_1
19.61/6.33	
19.61/6.33	The following rules are decreasing:
19.61/6.33	f_293(sum~cons_2~v183:0:0) -> f_374(v183:0:0) :|: v183:0:0 > 0 && sum~cons_2~v183:0:0 = 2 + v183:0:0
19.61/6.33	f_374(x:0) -> f_293(x:0) :|: TRUE
19.61/6.33	f_374(v239:0:0) -> f_293(1 + v239:0:0) :|: v239:0:0 > 0
19.61/6.33	f_293(sum~cons_3~v450:0:0) -> f_374(v450:0:0) :|: v450:0:0 > 0 && sum~cons_3~v450:0:0 = 3 + v450:0:0
19.61/6.33	
19.61/6.33	The following rules are bounded:
19.61/6.33	f_293(sum~cons_2~v183:0:0) -> f_374(v183:0:0) :|: v183:0:0 > 0 && sum~cons_2~v183:0:0 = 2 + v183:0:0
19.61/6.33	f_374(v239:0:0) -> f_293(1 + v239:0:0) :|: v239:0:0 > 0
19.61/6.33	
19.61/6.33	
19.61/6.33	----------------------------------------
19.61/6.33	
19.61/6.33	(12)
19.61/6.33	Obligation:
19.61/6.33	Rules:
19.61/6.33	f_374(x:0) -> f_293(x:0) :|: TRUE
19.61/6.33	f_293(sum~cons_3~v450:0:0) -> f_374(v450:0:0) :|: v450:0:0 > 0 && sum~cons_3~v450:0:0 = 3 + v450:0:0
19.61/6.33	
19.61/6.33	----------------------------------------
19.61/6.33	
19.61/6.33	(13) IntTRSCompressionProof (EQUIVALENT)
19.61/6.33	Compressed rules.
19.61/6.33	----------------------------------------
19.61/6.33	
19.61/6.33	(14)
19.61/6.33	Obligation:
19.61/6.33	Rules:
19.61/6.33	f_374(sum~cons_3~v450:0:0:0) -> f_374(v450:0:0:0) :|: v450:0:0:0 > 0 && sum~cons_3~v450:0:0:0 = 3 + v450:0:0:0
19.61/6.33	
19.61/6.33	----------------------------------------
19.61/6.33	
19.61/6.33	(15) RankingReductionPairProof (EQUIVALENT)
19.61/6.33	Interpretation:
19.61/6.33	[ f_374 ] = 1/3*f_374_1
19.61/6.33	
19.61/6.33	The following rules are decreasing:
19.61/6.33	f_374(sum~cons_3~v450:0:0:0) -> f_374(v450:0:0:0) :|: v450:0:0:0 > 0 && sum~cons_3~v450:0:0:0 = 3 + v450:0:0:0
19.61/6.33	
19.61/6.33	The following rules are bounded:
19.61/6.33	f_374(sum~cons_3~v450:0:0:0) -> f_374(v450:0:0:0) :|: v450:0:0:0 > 0 && sum~cons_3~v450:0:0:0 = 3 + v450:0:0:0
19.61/6.33	
19.61/6.33	
19.61/6.33	----------------------------------------
19.61/6.33	
19.61/6.33	(16)
19.61/6.33	YES
19.61/6.38	EOF