6.89/2.73	YES
6.89/2.76	proof of /export/starexec/sandbox/benchmark/theBenchmark.itrs
6.89/2.76	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.89/2.76	
6.89/2.76	
6.89/2.76	Termination of the given ITRS could be proven:
6.89/2.76	
6.89/2.76	(0) ITRS
6.89/2.76	(1) ITRStoIDPProof [EQUIVALENT, 0 ms]
6.89/2.76	(2) IDP
6.89/2.76	(3) UsableRulesProof [EQUIVALENT, 0 ms]
6.89/2.76	(4) IDP
6.89/2.76	(5) IDPNonInfProof [SOUND, 748 ms]
6.89/2.76	(6) IDP
6.89/2.76	(7) PisEmptyProof [EQUIVALENT, 0 ms]
6.89/2.76	(8) YES
6.89/2.76	
6.89/2.76	
6.89/2.76	----------------------------------------
6.89/2.76	
6.89/2.76	(0)
6.89/2.76	Obligation:
6.89/2.76	ITRS problem:
6.89/2.76	
6.89/2.76	The following function symbols are pre-defined:
6.89/2.76	<<<
6.89/2.76	 & 	~ 	Bwand: (Integer, Integer) -> Integer
6.89/2.76	 >= 	~ 	Ge: (Integer, Integer) -> Boolean
6.89/2.76	 | 	~ 	Bwor: (Integer, Integer) -> Integer
6.89/2.76	 / 	~ 	Div: (Integer, Integer) -> Integer
6.89/2.76	 != 	~ 	Neq: (Integer, Integer) -> Boolean
6.89/2.76	 && 	~ 	Land: (Boolean, Boolean) -> Boolean
6.89/2.76	 ! 	~ 	Lnot: (Boolean) -> Boolean
6.89/2.76	 = 	~ 	Eq: (Integer, Integer) -> Boolean
6.89/2.76	 <= 	~ 	Le: (Integer, Integer) -> Boolean
6.89/2.76	 ^ 	~ 	Bwxor: (Integer, Integer) -> Integer
6.89/2.76	 % 	~ 	Mod: (Integer, Integer) -> Integer
6.89/2.76	 > 	~ 	Gt: (Integer, Integer) -> Boolean
6.89/2.77	 + 	~ 	Add: (Integer, Integer) -> Integer
6.89/2.77	 -1 	~ 	UnaryMinus: (Integer) -> Integer
6.89/2.77	 < 	~ 	Lt: (Integer, Integer) -> Boolean
6.89/2.77	 || 	~ 	Lor: (Boolean, Boolean) -> Boolean
6.89/2.77	 - 	~ 	Sub: (Integer, Integer) -> Integer
6.89/2.77	 ~ 	~ 	Bwnot: (Integer) -> Integer
6.89/2.77	 * 	~ 	Mul: (Integer, Integer) -> Integer
6.89/2.77	>>>
6.89/2.77	
6.89/2.77	The TRS R consists of the following rules:
6.89/2.77	f(TRUE, x, y, z) -> f(x > y + z, x, y + 1, z)
6.89/2.77	f(TRUE, x, y, z) -> f(x > y + z, x, y, z + 1)
6.89/2.77	The set Q consists of the following terms:
6.89/2.77	f(TRUE, x0, x1, x2)
6.89/2.77	
6.89/2.77	----------------------------------------
6.89/2.77	
6.89/2.77	(1) ITRStoIDPProof (EQUIVALENT)
6.89/2.77	Added dependency pairs
6.89/2.77	----------------------------------------
6.89/2.77	
6.89/2.77	(2)
6.89/2.77	Obligation:
6.89/2.77	IDP problem:
6.89/2.77	The following function symbols are pre-defined:
6.89/2.77	<<<
6.89/2.77	 & 	~ 	Bwand: (Integer, Integer) -> Integer
6.89/2.77	 >= 	~ 	Ge: (Integer, Integer) -> Boolean
6.89/2.77	 | 	~ 	Bwor: (Integer, Integer) -> Integer
6.89/2.77	 / 	~ 	Div: (Integer, Integer) -> Integer
6.89/2.77	 != 	~ 	Neq: (Integer, Integer) -> Boolean
6.89/2.77	 && 	~ 	Land: (Boolean, Boolean) -> Boolean
6.89/2.77	 ! 	~ 	Lnot: (Boolean) -> Boolean
6.89/2.77	 = 	~ 	Eq: (Integer, Integer) -> Boolean
6.89/2.77	 <= 	~ 	Le: (Integer, Integer) -> Boolean
6.89/2.77	 ^ 	~ 	Bwxor: (Integer, Integer) -> Integer
6.89/2.77	 % 	~ 	Mod: (Integer, Integer) -> Integer
6.89/2.77	 > 	~ 	Gt: (Integer, Integer) -> Boolean
6.89/2.77	 + 	~ 	Add: (Integer, Integer) -> Integer
6.89/2.77	 -1 	~ 	UnaryMinus: (Integer) -> Integer
6.89/2.77	 < 	~ 	Lt: (Integer, Integer) -> Boolean
6.89/2.77	 || 	~ 	Lor: (Boolean, Boolean) -> Boolean
6.89/2.77	 - 	~ 	Sub: (Integer, Integer) -> Integer
6.89/2.77	 ~ 	~ 	Bwnot: (Integer) -> Integer
6.89/2.77	 * 	~ 	Mul: (Integer, Integer) -> Integer
6.89/2.77	>>>
6.89/2.77	
6.89/2.77	
6.89/2.77	The following domains are used:
6.89/2.77	   Integer
6.89/2.77	
6.89/2.77	The ITRS R consists of the following rules:
6.89/2.77	f(TRUE, x, y, z) -> f(x > y + z, x, y + 1, z)
6.89/2.77	f(TRUE, x, y, z) -> f(x > y + z, x, y, z + 1)
6.89/2.77	
6.89/2.77	The integer pair graph contains the following rules and edges:
6.89/2.77	(0): F(TRUE, x[0], y[0], z[0]) -> F(x[0] > y[0] + z[0], x[0], y[0] + 1, z[0])
6.89/2.77	(1): F(TRUE, x[1], y[1], z[1]) -> F(x[1] > y[1] + z[1], x[1], y[1], z[1] + 1)
6.89/2.77	
6.89/2.77	   (0) -> (0), if (x[0] > y[0] + z[0]  & x[0] ->^* x[0]' & y[0] + 1 ->^* y[0]' & z[0] ->^* z[0]')
6.89/2.77	   (0) -> (1), if (x[0] > y[0] + z[0]  & x[0] ->^* x[1] & y[0] + 1 ->^* y[1] & z[0] ->^* z[1])
6.89/2.77	   (1) -> (0), if (x[1] > y[1] + z[1]  & x[1] ->^* x[0] & y[1] ->^* y[0] & z[1] + 1 ->^* z[0])
6.89/2.77	   (1) -> (1), if (x[1] > y[1] + z[1]  & x[1] ->^* x[1]' & y[1] ->^* y[1]' & z[1] + 1 ->^* z[1]')
6.89/2.77	
6.89/2.77	The set Q consists of the following terms:
6.89/2.77	f(TRUE, x0, x1, x2)
6.89/2.77	
6.89/2.77	----------------------------------------
6.89/2.77	
6.89/2.77	(3) UsableRulesProof (EQUIVALENT)
6.89/2.77	As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R.
6.89/2.77	----------------------------------------
6.89/2.77	
6.89/2.77	(4)
6.89/2.77	Obligation:
6.89/2.77	IDP problem:
6.89/2.77	The following function symbols are pre-defined:
6.89/2.77	<<<
6.89/2.77	 & 	~ 	Bwand: (Integer, Integer) -> Integer
6.89/2.77	 >= 	~ 	Ge: (Integer, Integer) -> Boolean
6.89/2.77	 | 	~ 	Bwor: (Integer, Integer) -> Integer
6.89/2.77	 / 	~ 	Div: (Integer, Integer) -> Integer
6.89/2.77	 != 	~ 	Neq: (Integer, Integer) -> Boolean
6.89/2.77	 && 	~ 	Land: (Boolean, Boolean) -> Boolean
6.89/2.77	 ! 	~ 	Lnot: (Boolean) -> Boolean
6.89/2.77	 = 	~ 	Eq: (Integer, Integer) -> Boolean
6.89/2.77	 <= 	~ 	Le: (Integer, Integer) -> Boolean
6.89/2.77	 ^ 	~ 	Bwxor: (Integer, Integer) -> Integer
6.89/2.77	 % 	~ 	Mod: (Integer, Integer) -> Integer
6.89/2.77	 > 	~ 	Gt: (Integer, Integer) -> Boolean
6.89/2.77	 + 	~ 	Add: (Integer, Integer) -> Integer
6.89/2.77	 -1 	~ 	UnaryMinus: (Integer) -> Integer
6.89/2.77	 < 	~ 	Lt: (Integer, Integer) -> Boolean
6.89/2.77	 || 	~ 	Lor: (Boolean, Boolean) -> Boolean
6.89/2.77	 - 	~ 	Sub: (Integer, Integer) -> Integer
6.89/2.77	 ~ 	~ 	Bwnot: (Integer) -> Integer
6.89/2.77	 * 	~ 	Mul: (Integer, Integer) -> Integer
6.89/2.77	>>>
6.89/2.77	
6.89/2.77	
6.89/2.77	The following domains are used:
6.89/2.77	   Integer
6.89/2.77	
6.89/2.77	R is empty.
6.89/2.77	
6.89/2.77	The integer pair graph contains the following rules and edges:
6.89/2.77	(0): F(TRUE, x[0], y[0], z[0]) -> F(x[0] > y[0] + z[0], x[0], y[0] + 1, z[0])
6.89/2.77	(1): F(TRUE, x[1], y[1], z[1]) -> F(x[1] > y[1] + z[1], x[1], y[1], z[1] + 1)
6.89/2.77	
6.89/2.77	   (0) -> (0), if (x[0] > y[0] + z[0]  & x[0] ->^* x[0]' & y[0] + 1 ->^* y[0]' & z[0] ->^* z[0]')
6.89/2.77	   (0) -> (1), if (x[0] > y[0] + z[0]  & x[0] ->^* x[1] & y[0] + 1 ->^* y[1] & z[0] ->^* z[1])
6.89/2.77	   (1) -> (0), if (x[1] > y[1] + z[1]  & x[1] ->^* x[0] & y[1] ->^* y[0] & z[1] + 1 ->^* z[0])
6.89/2.77	   (1) -> (1), if (x[1] > y[1] + z[1]  & x[1] ->^* x[1]' & y[1] ->^* y[1]' & z[1] + 1 ->^* z[1]')
6.89/2.77	
6.89/2.77	The set Q consists of the following terms:
6.89/2.77	f(TRUE, x0, x1, x2)
6.89/2.77	
6.89/2.77	----------------------------------------
6.89/2.77	
6.89/2.77	(5) IDPNonInfProof (SOUND)
6.89/2.77	Used the following options for this NonInfProof:
6.89/2.77	
6.89/2.77	IDPGPoloSolver:
6.89/2.77	Range: [(-1,2)]
6.89/2.77	IsNat: false
6.89/2.77	Interpretation Shape Heuristic: aprove.DPFramework.IDPProblem.Processors.nonInf.poly.IdpDefaultShapeHeuristic@52dbcf03
6.89/2.77	Constraint Generator: NonInfConstraintGenerator:
6.89/2.77	PathGenerator: MetricPathGenerator:
6.89/2.77	Max Left Steps: 1
6.89/2.77	Max Right Steps: 1
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	The constraints were generated the following way:
6.89/2.77	
6.89/2.77	The DP Problem is simplified using the Induction Calculus [NONINF] with the following steps:
6.89/2.77	
6.89/2.77	Note that final constraints are written in bold face.
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	For Pair F(TRUE, x, y, z) -> F(>(x, +(y, z)), x, +(y, 1), z) the following chains were created:
6.89/2.77	*We consider the chain F(TRUE, x[0], y[0], z[0]) -> F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0]), F(TRUE, x[0], y[0], z[0]) -> F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0]), F(TRUE, x[0], y[0], z[0]) -> F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0]) which results in the following constraint:
6.89/2.77	
6.89/2.77	(1)    (>(x[0], +(y[0], z[0]))=TRUE & x[0]=x[0]1 & +(y[0], 1)=y[0]1 & z[0]=z[0]1 & >(x[0]1, +(y[0]1, z[0]1))=TRUE & x[0]1=x[0]2 & +(y[0]1, 1)=y[0]2 & z[0]1=z[0]2  ==>  F(TRUE, x[0]1, y[0]1, z[0]1)_>=_NonInfC & F(TRUE, x[0]1, y[0]1, z[0]1)_>=_F(>(x[0]1, +(y[0]1, z[0]1)), x[0]1, +(y[0]1, 1), z[0]1) & (U^Increasing(F(>(x[0]1, +(y[0]1, z[0]1)), x[0]1, +(y[0]1, 1), z[0]1)), >=))
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (1) using rules (III), (IV) which results in the following new constraint:
6.89/2.77	
6.89/2.77	(2)    (>(x[0], +(y[0], z[0]))=TRUE & >(x[0], +(+(y[0], 1), z[0]))=TRUE  ==>  F(TRUE, x[0], +(y[0], 1), z[0])_>=_NonInfC & F(TRUE, x[0], +(y[0], 1), z[0])_>=_F(>(x[0], +(+(y[0], 1), z[0])), x[0], +(+(y[0], 1), 1), z[0]) & (U^Increasing(F(>(x[0]1, +(y[0]1, z[0]1)), x[0]1, +(y[0]1, 1), z[0]1)), >=))
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
6.89/2.77	
6.89/2.77	(3)    (x[0] + [-1] + [-1]y[0] + [-1]z[0] >= 0 & x[0] + [-2] + [-1]y[0] + [-1]z[0] >= 0  ==>  (U^Increasing(F(>(x[0]1, +(y[0]1, z[0]1)), x[0]1, +(y[0]1, 1), z[0]1)), >=) & [(-2)bni_9 + (-1)Bound*bni_9] + [(-1)bni_9]z[0] + [(-1)bni_9]y[0] + [bni_9]x[0] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
6.89/2.77	
6.89/2.77	(4)    (x[0] + [-1] + [-1]y[0] + [-1]z[0] >= 0 & x[0] + [-2] + [-1]y[0] + [-1]z[0] >= 0  ==>  (U^Increasing(F(>(x[0]1, +(y[0]1, z[0]1)), x[0]1, +(y[0]1, 1), z[0]1)), >=) & [(-2)bni_9 + (-1)Bound*bni_9] + [(-1)bni_9]z[0] + [(-1)bni_9]y[0] + [bni_9]x[0] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
6.89/2.77	
6.89/2.77	(5)    (x[0] + [-1] + [-1]y[0] + [-1]z[0] >= 0 & x[0] + [-2] + [-1]y[0] + [-1]z[0] >= 0  ==>  (U^Increasing(F(>(x[0]1, +(y[0]1, z[0]1)), x[0]1, +(y[0]1, 1), z[0]1)), >=) & [(-2)bni_9 + (-1)Bound*bni_9] + [(-1)bni_9]z[0] + [(-1)bni_9]y[0] + [bni_9]x[0] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (5) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
6.89/2.77	
6.89/2.77	(6)    (x[0] >= 0 & [-1] + x[0] >= 0  ==>  (U^Increasing(F(>(x[0]1, +(y[0]1, z[0]1)), x[0]1, +(y[0]1, 1), z[0]1)), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[0] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (6) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
6.89/2.77	
6.89/2.77	(7)    (x[0] >= 0 & [-1] + x[0] >= 0 & y[0] >= 0  ==>  (U^Increasing(F(>(x[0]1, +(y[0]1, z[0]1)), x[0]1, +(y[0]1, 1), z[0]1)), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[0] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	(8)    (x[0] >= 0 & [-1] + x[0] >= 0 & y[0] >= 0  ==>  (U^Increasing(F(>(x[0]1, +(y[0]1, z[0]1)), x[0]1, +(y[0]1, 1), z[0]1)), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[0] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (7) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
6.89/2.77	
6.89/2.77	(9)    (x[0] >= 0 & [-1] + x[0] >= 0 & y[0] >= 0 & z[0] >= 0  ==>  (U^Increasing(F(>(x[0]1, +(y[0]1, z[0]1)), x[0]1, +(y[0]1, 1), z[0]1)), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[0] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	(10)    (x[0] >= 0 & [-1] + x[0] >= 0 & y[0] >= 0 & z[0] >= 0  ==>  (U^Increasing(F(>(x[0]1, +(y[0]1, z[0]1)), x[0]1, +(y[0]1, 1), z[0]1)), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[0] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (8) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
6.89/2.77	
6.89/2.77	(11)    (x[0] >= 0 & [-1] + x[0] >= 0 & y[0] >= 0 & z[0] >= 0  ==>  (U^Increasing(F(>(x[0]1, +(y[0]1, z[0]1)), x[0]1, +(y[0]1, 1), z[0]1)), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[0] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	(12)    (x[0] >= 0 & [-1] + x[0] >= 0 & y[0] >= 0 & z[0] >= 0  ==>  (U^Increasing(F(>(x[0]1, +(y[0]1, z[0]1)), x[0]1, +(y[0]1, 1), z[0]1)), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[0] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	*We consider the chain F(TRUE, x[1], y[1], z[1]) -> F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1)), F(TRUE, x[0], y[0], z[0]) -> F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0]), F(TRUE, x[0], y[0], z[0]) -> F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0]) which results in the following constraint:
6.89/2.77	
6.89/2.77	(1)    (>(x[1], +(y[1], z[1]))=TRUE & x[1]=x[0] & y[1]=y[0] & +(z[1], 1)=z[0] & >(x[0], +(y[0], z[0]))=TRUE & x[0]=x[0]1 & +(y[0], 1)=y[0]1 & z[0]=z[0]1  ==>  F(TRUE, x[0], y[0], z[0])_>=_NonInfC & F(TRUE, x[0], y[0], z[0])_>=_F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0]) & (U^Increasing(F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0])), >=))
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (1) using rules (III), (IV) which results in the following new constraint:
6.89/2.77	
6.89/2.77	(2)    (>(x[1], +(y[1], z[1]))=TRUE & >(x[1], +(y[1], +(z[1], 1)))=TRUE  ==>  F(TRUE, x[1], y[1], +(z[1], 1))_>=_NonInfC & F(TRUE, x[1], y[1], +(z[1], 1))_>=_F(>(x[1], +(y[1], +(z[1], 1))), x[1], +(y[1], 1), +(z[1], 1)) & (U^Increasing(F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0])), >=))
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
6.89/2.77	
6.89/2.77	(3)    (x[1] + [-1] + [-1]y[1] + [-1]z[1] >= 0 & x[1] + [-2] + [-1]y[1] + [-1]z[1] >= 0  ==>  (U^Increasing(F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0])), >=) & [(-2)bni_9 + (-1)Bound*bni_9] + [(-1)bni_9]z[1] + [(-1)bni_9]y[1] + [bni_9]x[1] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
6.89/2.77	
6.89/2.77	(4)    (x[1] + [-1] + [-1]y[1] + [-1]z[1] >= 0 & x[1] + [-2] + [-1]y[1] + [-1]z[1] >= 0  ==>  (U^Increasing(F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0])), >=) & [(-2)bni_9 + (-1)Bound*bni_9] + [(-1)bni_9]z[1] + [(-1)bni_9]y[1] + [bni_9]x[1] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
6.89/2.77	
6.89/2.77	(5)    (x[1] + [-1] + [-1]y[1] + [-1]z[1] >= 0 & x[1] + [-2] + [-1]y[1] + [-1]z[1] >= 0  ==>  (U^Increasing(F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0])), >=) & [(-2)bni_9 + (-1)Bound*bni_9] + [(-1)bni_9]z[1] + [(-1)bni_9]y[1] + [bni_9]x[1] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (5) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
6.89/2.77	
6.89/2.77	(6)    (x[1] >= 0 & [-1] + x[1] >= 0  ==>  (U^Increasing(F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0])), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[1] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (6) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
6.89/2.77	
6.89/2.77	(7)    (x[1] >= 0 & [-1] + x[1] >= 0 & y[1] >= 0  ==>  (U^Increasing(F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0])), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[1] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	(8)    (x[1] >= 0 & [-1] + x[1] >= 0 & y[1] >= 0  ==>  (U^Increasing(F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0])), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[1] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (7) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
6.89/2.77	
6.89/2.77	(9)    (x[1] >= 0 & [-1] + x[1] >= 0 & y[1] >= 0 & z[1] >= 0  ==>  (U^Increasing(F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0])), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[1] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	(10)    (x[1] >= 0 & [-1] + x[1] >= 0 & y[1] >= 0 & z[1] >= 0  ==>  (U^Increasing(F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0])), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[1] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (8) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
6.89/2.77	
6.89/2.77	(11)    (x[1] >= 0 & [-1] + x[1] >= 0 & y[1] >= 0 & z[1] >= 0  ==>  (U^Increasing(F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0])), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[1] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	(12)    (x[1] >= 0 & [-1] + x[1] >= 0 & y[1] >= 0 & z[1] >= 0  ==>  (U^Increasing(F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0])), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[1] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	*We consider the chain F(TRUE, x[0], y[0], z[0]) -> F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0]), F(TRUE, x[0], y[0], z[0]) -> F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0]), F(TRUE, x[1], y[1], z[1]) -> F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1)) which results in the following constraint:
6.89/2.77	
6.89/2.77	(1)    (>(x[0], +(y[0], z[0]))=TRUE & x[0]=x[0]1 & +(y[0], 1)=y[0]1 & z[0]=z[0]1 & >(x[0]1, +(y[0]1, z[0]1))=TRUE & x[0]1=x[1] & +(y[0]1, 1)=y[1] & z[0]1=z[1]  ==>  F(TRUE, x[0]1, y[0]1, z[0]1)_>=_NonInfC & F(TRUE, x[0]1, y[0]1, z[0]1)_>=_F(>(x[0]1, +(y[0]1, z[0]1)), x[0]1, +(y[0]1, 1), z[0]1) & (U^Increasing(F(>(x[0]1, +(y[0]1, z[0]1)), x[0]1, +(y[0]1, 1), z[0]1)), >=))
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (1) using rules (III), (IV) which results in the following new constraint:
6.89/2.77	
6.89/2.77	(2)    (>(x[0], +(y[0], z[0]))=TRUE & >(x[0], +(+(y[0], 1), z[0]))=TRUE  ==>  F(TRUE, x[0], +(y[0], 1), z[0])_>=_NonInfC & F(TRUE, x[0], +(y[0], 1), z[0])_>=_F(>(x[0], +(+(y[0], 1), z[0])), x[0], +(+(y[0], 1), 1), z[0]) & (U^Increasing(F(>(x[0]1, +(y[0]1, z[0]1)), x[0]1, +(y[0]1, 1), z[0]1)), >=))
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
6.89/2.77	
6.89/2.77	(3)    (x[0] + [-1] + [-1]y[0] + [-1]z[0] >= 0 & x[0] + [-2] + [-1]y[0] + [-1]z[0] >= 0  ==>  (U^Increasing(F(>(x[0]1, +(y[0]1, z[0]1)), x[0]1, +(y[0]1, 1), z[0]1)), >=) & [(-2)bni_9 + (-1)Bound*bni_9] + [(-1)bni_9]z[0] + [(-1)bni_9]y[0] + [bni_9]x[0] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
6.89/2.77	
6.89/2.77	(4)    (x[0] + [-1] + [-1]y[0] + [-1]z[0] >= 0 & x[0] + [-2] + [-1]y[0] + [-1]z[0] >= 0  ==>  (U^Increasing(F(>(x[0]1, +(y[0]1, z[0]1)), x[0]1, +(y[0]1, 1), z[0]1)), >=) & [(-2)bni_9 + (-1)Bound*bni_9] + [(-1)bni_9]z[0] + [(-1)bni_9]y[0] + [bni_9]x[0] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
6.89/2.77	
6.89/2.77	(5)    (x[0] + [-1] + [-1]y[0] + [-1]z[0] >= 0 & x[0] + [-2] + [-1]y[0] + [-1]z[0] >= 0  ==>  (U^Increasing(F(>(x[0]1, +(y[0]1, z[0]1)), x[0]1, +(y[0]1, 1), z[0]1)), >=) & [(-2)bni_9 + (-1)Bound*bni_9] + [(-1)bni_9]z[0] + [(-1)bni_9]y[0] + [bni_9]x[0] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (5) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
6.89/2.77	
6.89/2.77	(6)    (x[0] >= 0 & [-1] + x[0] >= 0  ==>  (U^Increasing(F(>(x[0]1, +(y[0]1, z[0]1)), x[0]1, +(y[0]1, 1), z[0]1)), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[0] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (6) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
6.89/2.77	
6.89/2.77	(7)    (x[0] >= 0 & [-1] + x[0] >= 0 & y[0] >= 0  ==>  (U^Increasing(F(>(x[0]1, +(y[0]1, z[0]1)), x[0]1, +(y[0]1, 1), z[0]1)), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[0] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	(8)    (x[0] >= 0 & [-1] + x[0] >= 0 & y[0] >= 0  ==>  (U^Increasing(F(>(x[0]1, +(y[0]1, z[0]1)), x[0]1, +(y[0]1, 1), z[0]1)), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[0] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (7) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
6.89/2.77	
6.89/2.77	(9)    (x[0] >= 0 & [-1] + x[0] >= 0 & y[0] >= 0 & z[0] >= 0  ==>  (U^Increasing(F(>(x[0]1, +(y[0]1, z[0]1)), x[0]1, +(y[0]1, 1), z[0]1)), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[0] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	(10)    (x[0] >= 0 & [-1] + x[0] >= 0 & y[0] >= 0 & z[0] >= 0  ==>  (U^Increasing(F(>(x[0]1, +(y[0]1, z[0]1)), x[0]1, +(y[0]1, 1), z[0]1)), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[0] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (8) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
6.89/2.77	
6.89/2.77	(11)    (x[0] >= 0 & [-1] + x[0] >= 0 & y[0] >= 0 & z[0] >= 0  ==>  (U^Increasing(F(>(x[0]1, +(y[0]1, z[0]1)), x[0]1, +(y[0]1, 1), z[0]1)), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[0] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	(12)    (x[0] >= 0 & [-1] + x[0] >= 0 & y[0] >= 0 & z[0] >= 0  ==>  (U^Increasing(F(>(x[0]1, +(y[0]1, z[0]1)), x[0]1, +(y[0]1, 1), z[0]1)), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[0] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	*We consider the chain F(TRUE, x[1], y[1], z[1]) -> F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1)), F(TRUE, x[0], y[0], z[0]) -> F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0]), F(TRUE, x[1], y[1], z[1]) -> F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1)) which results in the following constraint:
6.89/2.77	
6.89/2.77	(1)    (>(x[1], +(y[1], z[1]))=TRUE & x[1]=x[0] & y[1]=y[0] & +(z[1], 1)=z[0] & >(x[0], +(y[0], z[0]))=TRUE & x[0]=x[1]1 & +(y[0], 1)=y[1]1 & z[0]=z[1]1  ==>  F(TRUE, x[0], y[0], z[0])_>=_NonInfC & F(TRUE, x[0], y[0], z[0])_>=_F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0]) & (U^Increasing(F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0])), >=))
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (1) using rules (III), (IV) which results in the following new constraint:
6.89/2.77	
6.89/2.77	(2)    (>(x[1], +(y[1], z[1]))=TRUE & >(x[1], +(y[1], +(z[1], 1)))=TRUE  ==>  F(TRUE, x[1], y[1], +(z[1], 1))_>=_NonInfC & F(TRUE, x[1], y[1], +(z[1], 1))_>=_F(>(x[1], +(y[1], +(z[1], 1))), x[1], +(y[1], 1), +(z[1], 1)) & (U^Increasing(F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0])), >=))
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
6.89/2.77	
6.89/2.77	(3)    (x[1] + [-1] + [-1]y[1] + [-1]z[1] >= 0 & x[1] + [-2] + [-1]y[1] + [-1]z[1] >= 0  ==>  (U^Increasing(F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0])), >=) & [(-2)bni_9 + (-1)Bound*bni_9] + [(-1)bni_9]z[1] + [(-1)bni_9]y[1] + [bni_9]x[1] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
6.89/2.77	
6.89/2.77	(4)    (x[1] + [-1] + [-1]y[1] + [-1]z[1] >= 0 & x[1] + [-2] + [-1]y[1] + [-1]z[1] >= 0  ==>  (U^Increasing(F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0])), >=) & [(-2)bni_9 + (-1)Bound*bni_9] + [(-1)bni_9]z[1] + [(-1)bni_9]y[1] + [bni_9]x[1] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
6.89/2.77	
6.89/2.77	(5)    (x[1] + [-1] + [-1]y[1] + [-1]z[1] >= 0 & x[1] + [-2] + [-1]y[1] + [-1]z[1] >= 0  ==>  (U^Increasing(F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0])), >=) & [(-2)bni_9 + (-1)Bound*bni_9] + [(-1)bni_9]z[1] + [(-1)bni_9]y[1] + [bni_9]x[1] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (5) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
6.89/2.77	
6.89/2.77	(6)    (x[1] >= 0 & [-1] + x[1] >= 0  ==>  (U^Increasing(F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0])), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[1] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (6) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
6.89/2.77	
6.89/2.77	(7)    (x[1] >= 0 & [-1] + x[1] >= 0 & y[1] >= 0  ==>  (U^Increasing(F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0])), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[1] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	(8)    (x[1] >= 0 & [-1] + x[1] >= 0 & y[1] >= 0  ==>  (U^Increasing(F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0])), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[1] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (7) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
6.89/2.77	
6.89/2.77	(9)    (x[1] >= 0 & [-1] + x[1] >= 0 & y[1] >= 0 & z[1] >= 0  ==>  (U^Increasing(F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0])), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[1] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	(10)    (x[1] >= 0 & [-1] + x[1] >= 0 & y[1] >= 0 & z[1] >= 0  ==>  (U^Increasing(F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0])), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[1] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (8) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
6.89/2.77	
6.89/2.77	(11)    (x[1] >= 0 & [-1] + x[1] >= 0 & y[1] >= 0 & z[1] >= 0  ==>  (U^Increasing(F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0])), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[1] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	(12)    (x[1] >= 0 & [-1] + x[1] >= 0 & y[1] >= 0 & z[1] >= 0  ==>  (U^Increasing(F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0])), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[1] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	For Pair F(TRUE, x, y, z) -> F(>(x, +(y, z)), x, y, +(z, 1)) the following chains were created:
6.89/2.77	*We consider the chain F(TRUE, x[0], y[0], z[0]) -> F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0]), F(TRUE, x[1], y[1], z[1]) -> F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1)), F(TRUE, x[0], y[0], z[0]) -> F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0]) which results in the following constraint:
6.89/2.77	
6.89/2.77	(1)    (>(x[0], +(y[0], z[0]))=TRUE & x[0]=x[1] & +(y[0], 1)=y[1] & z[0]=z[1] & >(x[1], +(y[1], z[1]))=TRUE & x[1]=x[0]1 & y[1]=y[0]1 & +(z[1], 1)=z[0]1  ==>  F(TRUE, x[1], y[1], z[1])_>=_NonInfC & F(TRUE, x[1], y[1], z[1])_>=_F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1)) & (U^Increasing(F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1))), >=))
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (1) using rules (III), (IV) which results in the following new constraint:
6.89/2.77	
6.89/2.77	(2)    (>(x[0], +(y[0], z[0]))=TRUE & >(x[0], +(+(y[0], 1), z[0]))=TRUE  ==>  F(TRUE, x[0], +(y[0], 1), z[0])_>=_NonInfC & F(TRUE, x[0], +(y[0], 1), z[0])_>=_F(>(x[0], +(+(y[0], 1), z[0])), x[0], +(y[0], 1), +(z[0], 1)) & (U^Increasing(F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1))), >=))
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
6.89/2.77	
6.89/2.77	(3)    (x[0] + [-1] + [-1]y[0] + [-1]z[0] >= 0 & x[0] + [-2] + [-1]y[0] + [-1]z[0] >= 0  ==>  (U^Increasing(F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1))), >=) & [(-2)bni_11 + (-1)Bound*bni_11] + [(-1)bni_11]z[0] + [(-1)bni_11]y[0] + [bni_11]x[0] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
6.89/2.77	
6.89/2.77	(4)    (x[0] + [-1] + [-1]y[0] + [-1]z[0] >= 0 & x[0] + [-2] + [-1]y[0] + [-1]z[0] >= 0  ==>  (U^Increasing(F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1))), >=) & [(-2)bni_11 + (-1)Bound*bni_11] + [(-1)bni_11]z[0] + [(-1)bni_11]y[0] + [bni_11]x[0] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
6.89/2.77	
6.89/2.77	(5)    (x[0] + [-1] + [-1]y[0] + [-1]z[0] >= 0 & x[0] + [-2] + [-1]y[0] + [-1]z[0] >= 0  ==>  (U^Increasing(F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1))), >=) & [(-2)bni_11 + (-1)Bound*bni_11] + [(-1)bni_11]z[0] + [(-1)bni_11]y[0] + [bni_11]x[0] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (5) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
6.89/2.77	
6.89/2.77	(6)    (x[0] >= 0 & [-1] + x[0] >= 0  ==>  (U^Increasing(F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[0] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (6) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
6.89/2.77	
6.89/2.77	(7)    (x[0] >= 0 & [-1] + x[0] >= 0 & y[0] >= 0  ==>  (U^Increasing(F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[0] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	(8)    (x[0] >= 0 & [-1] + x[0] >= 0 & y[0] >= 0  ==>  (U^Increasing(F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[0] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (7) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
6.89/2.77	
6.89/2.77	(9)    (x[0] >= 0 & [-1] + x[0] >= 0 & y[0] >= 0 & z[0] >= 0  ==>  (U^Increasing(F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[0] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	(10)    (x[0] >= 0 & [-1] + x[0] >= 0 & y[0] >= 0 & z[0] >= 0  ==>  (U^Increasing(F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[0] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (8) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
6.89/2.77	
6.89/2.77	(11)    (x[0] >= 0 & [-1] + x[0] >= 0 & y[0] >= 0 & z[0] >= 0  ==>  (U^Increasing(F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[0] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	(12)    (x[0] >= 0 & [-1] + x[0] >= 0 & y[0] >= 0 & z[0] >= 0  ==>  (U^Increasing(F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[0] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	*We consider the chain F(TRUE, x[1], y[1], z[1]) -> F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1)), F(TRUE, x[1], y[1], z[1]) -> F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1)), F(TRUE, x[0], y[0], z[0]) -> F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0]) which results in the following constraint:
6.89/2.77	
6.89/2.77	(1)    (>(x[1], +(y[1], z[1]))=TRUE & x[1]=x[1]1 & y[1]=y[1]1 & +(z[1], 1)=z[1]1 & >(x[1]1, +(y[1]1, z[1]1))=TRUE & x[1]1=x[0] & y[1]1=y[0] & +(z[1]1, 1)=z[0]  ==>  F(TRUE, x[1]1, y[1]1, z[1]1)_>=_NonInfC & F(TRUE, x[1]1, y[1]1, z[1]1)_>=_F(>(x[1]1, +(y[1]1, z[1]1)), x[1]1, y[1]1, +(z[1]1, 1)) & (U^Increasing(F(>(x[1]1, +(y[1]1, z[1]1)), x[1]1, y[1]1, +(z[1]1, 1))), >=))
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (1) using rules (III), (IV) which results in the following new constraint:
6.89/2.77	
6.89/2.77	(2)    (>(x[1], +(y[1], z[1]))=TRUE & >(x[1], +(y[1], +(z[1], 1)))=TRUE  ==>  F(TRUE, x[1], y[1], +(z[1], 1))_>=_NonInfC & F(TRUE, x[1], y[1], +(z[1], 1))_>=_F(>(x[1], +(y[1], +(z[1], 1))), x[1], y[1], +(+(z[1], 1), 1)) & (U^Increasing(F(>(x[1]1, +(y[1]1, z[1]1)), x[1]1, y[1]1, +(z[1]1, 1))), >=))
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
6.89/2.77	
6.89/2.77	(3)    (x[1] + [-1] + [-1]y[1] + [-1]z[1] >= 0 & x[1] + [-2] + [-1]y[1] + [-1]z[1] >= 0  ==>  (U^Increasing(F(>(x[1]1, +(y[1]1, z[1]1)), x[1]1, y[1]1, +(z[1]1, 1))), >=) & [(-2)bni_11 + (-1)Bound*bni_11] + [(-1)bni_11]z[1] + [(-1)bni_11]y[1] + [bni_11]x[1] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
6.89/2.77	
6.89/2.77	(4)    (x[1] + [-1] + [-1]y[1] + [-1]z[1] >= 0 & x[1] + [-2] + [-1]y[1] + [-1]z[1] >= 0  ==>  (U^Increasing(F(>(x[1]1, +(y[1]1, z[1]1)), x[1]1, y[1]1, +(z[1]1, 1))), >=) & [(-2)bni_11 + (-1)Bound*bni_11] + [(-1)bni_11]z[1] + [(-1)bni_11]y[1] + [bni_11]x[1] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
6.89/2.77	
6.89/2.77	(5)    (x[1] + [-1] + [-1]y[1] + [-1]z[1] >= 0 & x[1] + [-2] + [-1]y[1] + [-1]z[1] >= 0  ==>  (U^Increasing(F(>(x[1]1, +(y[1]1, z[1]1)), x[1]1, y[1]1, +(z[1]1, 1))), >=) & [(-2)bni_11 + (-1)Bound*bni_11] + [(-1)bni_11]z[1] + [(-1)bni_11]y[1] + [bni_11]x[1] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (5) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
6.89/2.77	
6.89/2.77	(6)    (x[1] >= 0 & [-1] + x[1] >= 0  ==>  (U^Increasing(F(>(x[1]1, +(y[1]1, z[1]1)), x[1]1, y[1]1, +(z[1]1, 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[1] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (6) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
6.89/2.77	
6.89/2.77	(7)    (x[1] >= 0 & [-1] + x[1] >= 0 & y[1] >= 0  ==>  (U^Increasing(F(>(x[1]1, +(y[1]1, z[1]1)), x[1]1, y[1]1, +(z[1]1, 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[1] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	(8)    (x[1] >= 0 & [-1] + x[1] >= 0 & y[1] >= 0  ==>  (U^Increasing(F(>(x[1]1, +(y[1]1, z[1]1)), x[1]1, y[1]1, +(z[1]1, 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[1] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (7) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
6.89/2.77	
6.89/2.77	(9)    (x[1] >= 0 & [-1] + x[1] >= 0 & y[1] >= 0 & z[1] >= 0  ==>  (U^Increasing(F(>(x[1]1, +(y[1]1, z[1]1)), x[1]1, y[1]1, +(z[1]1, 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[1] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	(10)    (x[1] >= 0 & [-1] + x[1] >= 0 & y[1] >= 0 & z[1] >= 0  ==>  (U^Increasing(F(>(x[1]1, +(y[1]1, z[1]1)), x[1]1, y[1]1, +(z[1]1, 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[1] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (8) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
6.89/2.77	
6.89/2.77	(11)    (x[1] >= 0 & [-1] + x[1] >= 0 & y[1] >= 0 & z[1] >= 0  ==>  (U^Increasing(F(>(x[1]1, +(y[1]1, z[1]1)), x[1]1, y[1]1, +(z[1]1, 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[1] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	(12)    (x[1] >= 0 & [-1] + x[1] >= 0 & y[1] >= 0 & z[1] >= 0  ==>  (U^Increasing(F(>(x[1]1, +(y[1]1, z[1]1)), x[1]1, y[1]1, +(z[1]1, 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[1] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	*We consider the chain F(TRUE, x[0], y[0], z[0]) -> F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0]), F(TRUE, x[1], y[1], z[1]) -> F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1)), F(TRUE, x[1], y[1], z[1]) -> F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1)) which results in the following constraint:
6.89/2.77	
6.89/2.77	(1)    (>(x[0], +(y[0], z[0]))=TRUE & x[0]=x[1] & +(y[0], 1)=y[1] & z[0]=z[1] & >(x[1], +(y[1], z[1]))=TRUE & x[1]=x[1]1 & y[1]=y[1]1 & +(z[1], 1)=z[1]1  ==>  F(TRUE, x[1], y[1], z[1])_>=_NonInfC & F(TRUE, x[1], y[1], z[1])_>=_F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1)) & (U^Increasing(F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1))), >=))
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (1) using rules (III), (IV) which results in the following new constraint:
6.89/2.77	
6.89/2.77	(2)    (>(x[0], +(y[0], z[0]))=TRUE & >(x[0], +(+(y[0], 1), z[0]))=TRUE  ==>  F(TRUE, x[0], +(y[0], 1), z[0])_>=_NonInfC & F(TRUE, x[0], +(y[0], 1), z[0])_>=_F(>(x[0], +(+(y[0], 1), z[0])), x[0], +(y[0], 1), +(z[0], 1)) & (U^Increasing(F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1))), >=))
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
6.89/2.77	
6.89/2.77	(3)    (x[0] + [-1] + [-1]y[0] + [-1]z[0] >= 0 & x[0] + [-2] + [-1]y[0] + [-1]z[0] >= 0  ==>  (U^Increasing(F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1))), >=) & [(-2)bni_11 + (-1)Bound*bni_11] + [(-1)bni_11]z[0] + [(-1)bni_11]y[0] + [bni_11]x[0] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
6.89/2.77	
6.89/2.77	(4)    (x[0] + [-1] + [-1]y[0] + [-1]z[0] >= 0 & x[0] + [-2] + [-1]y[0] + [-1]z[0] >= 0  ==>  (U^Increasing(F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1))), >=) & [(-2)bni_11 + (-1)Bound*bni_11] + [(-1)bni_11]z[0] + [(-1)bni_11]y[0] + [bni_11]x[0] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
6.89/2.77	
6.89/2.77	(5)    (x[0] + [-1] + [-1]y[0] + [-1]z[0] >= 0 & x[0] + [-2] + [-1]y[0] + [-1]z[0] >= 0  ==>  (U^Increasing(F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1))), >=) & [(-2)bni_11 + (-1)Bound*bni_11] + [(-1)bni_11]z[0] + [(-1)bni_11]y[0] + [bni_11]x[0] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (5) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
6.89/2.77	
6.89/2.77	(6)    (x[0] >= 0 & [-1] + x[0] >= 0  ==>  (U^Increasing(F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[0] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (6) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
6.89/2.77	
6.89/2.77	(7)    (x[0] >= 0 & [-1] + x[0] >= 0 & y[0] >= 0  ==>  (U^Increasing(F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[0] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	(8)    (x[0] >= 0 & [-1] + x[0] >= 0 & y[0] >= 0  ==>  (U^Increasing(F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[0] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (7) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
6.89/2.77	
6.89/2.77	(9)    (x[0] >= 0 & [-1] + x[0] >= 0 & y[0] >= 0 & z[0] >= 0  ==>  (U^Increasing(F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[0] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	(10)    (x[0] >= 0 & [-1] + x[0] >= 0 & y[0] >= 0 & z[0] >= 0  ==>  (U^Increasing(F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[0] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (8) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
6.89/2.77	
6.89/2.77	(11)    (x[0] >= 0 & [-1] + x[0] >= 0 & y[0] >= 0 & z[0] >= 0  ==>  (U^Increasing(F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[0] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	(12)    (x[0] >= 0 & [-1] + x[0] >= 0 & y[0] >= 0 & z[0] >= 0  ==>  (U^Increasing(F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[0] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	*We consider the chain F(TRUE, x[1], y[1], z[1]) -> F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1)), F(TRUE, x[1], y[1], z[1]) -> F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1)), F(TRUE, x[1], y[1], z[1]) -> F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1)) which results in the following constraint:
6.89/2.77	
6.89/2.77	(1)    (>(x[1], +(y[1], z[1]))=TRUE & x[1]=x[1]1 & y[1]=y[1]1 & +(z[1], 1)=z[1]1 & >(x[1]1, +(y[1]1, z[1]1))=TRUE & x[1]1=x[1]2 & y[1]1=y[1]2 & +(z[1]1, 1)=z[1]2  ==>  F(TRUE, x[1]1, y[1]1, z[1]1)_>=_NonInfC & F(TRUE, x[1]1, y[1]1, z[1]1)_>=_F(>(x[1]1, +(y[1]1, z[1]1)), x[1]1, y[1]1, +(z[1]1, 1)) & (U^Increasing(F(>(x[1]1, +(y[1]1, z[1]1)), x[1]1, y[1]1, +(z[1]1, 1))), >=))
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (1) using rules (III), (IV) which results in the following new constraint:
6.89/2.77	
6.89/2.77	(2)    (>(x[1], +(y[1], z[1]))=TRUE & >(x[1], +(y[1], +(z[1], 1)))=TRUE  ==>  F(TRUE, x[1], y[1], +(z[1], 1))_>=_NonInfC & F(TRUE, x[1], y[1], +(z[1], 1))_>=_F(>(x[1], +(y[1], +(z[1], 1))), x[1], y[1], +(+(z[1], 1), 1)) & (U^Increasing(F(>(x[1]1, +(y[1]1, z[1]1)), x[1]1, y[1]1, +(z[1]1, 1))), >=))
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
6.89/2.77	
6.89/2.77	(3)    (x[1] + [-1] + [-1]y[1] + [-1]z[1] >= 0 & x[1] + [-2] + [-1]y[1] + [-1]z[1] >= 0  ==>  (U^Increasing(F(>(x[1]1, +(y[1]1, z[1]1)), x[1]1, y[1]1, +(z[1]1, 1))), >=) & [(-2)bni_11 + (-1)Bound*bni_11] + [(-1)bni_11]z[1] + [(-1)bni_11]y[1] + [bni_11]x[1] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
6.89/2.77	
6.89/2.77	(4)    (x[1] + [-1] + [-1]y[1] + [-1]z[1] >= 0 & x[1] + [-2] + [-1]y[1] + [-1]z[1] >= 0  ==>  (U^Increasing(F(>(x[1]1, +(y[1]1, z[1]1)), x[1]1, y[1]1, +(z[1]1, 1))), >=) & [(-2)bni_11 + (-1)Bound*bni_11] + [(-1)bni_11]z[1] + [(-1)bni_11]y[1] + [bni_11]x[1] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
6.89/2.77	
6.89/2.77	(5)    (x[1] + [-1] + [-1]y[1] + [-1]z[1] >= 0 & x[1] + [-2] + [-1]y[1] + [-1]z[1] >= 0  ==>  (U^Increasing(F(>(x[1]1, +(y[1]1, z[1]1)), x[1]1, y[1]1, +(z[1]1, 1))), >=) & [(-2)bni_11 + (-1)Bound*bni_11] + [(-1)bni_11]z[1] + [(-1)bni_11]y[1] + [bni_11]x[1] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (5) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
6.89/2.77	
6.89/2.77	(6)    (x[1] >= 0 & [-1] + x[1] >= 0  ==>  (U^Increasing(F(>(x[1]1, +(y[1]1, z[1]1)), x[1]1, y[1]1, +(z[1]1, 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[1] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (6) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
6.89/2.77	
6.89/2.77	(7)    (x[1] >= 0 & [-1] + x[1] >= 0 & y[1] >= 0  ==>  (U^Increasing(F(>(x[1]1, +(y[1]1, z[1]1)), x[1]1, y[1]1, +(z[1]1, 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[1] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	(8)    (x[1] >= 0 & [-1] + x[1] >= 0 & y[1] >= 0  ==>  (U^Increasing(F(>(x[1]1, +(y[1]1, z[1]1)), x[1]1, y[1]1, +(z[1]1, 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[1] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (7) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
6.89/2.77	
6.89/2.77	(9)    (x[1] >= 0 & [-1] + x[1] >= 0 & y[1] >= 0 & z[1] >= 0  ==>  (U^Increasing(F(>(x[1]1, +(y[1]1, z[1]1)), x[1]1, y[1]1, +(z[1]1, 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[1] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	(10)    (x[1] >= 0 & [-1] + x[1] >= 0 & y[1] >= 0 & z[1] >= 0  ==>  (U^Increasing(F(>(x[1]1, +(y[1]1, z[1]1)), x[1]1, y[1]1, +(z[1]1, 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[1] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	We simplified constraint (8) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
6.89/2.77	
6.89/2.77	(11)    (x[1] >= 0 & [-1] + x[1] >= 0 & y[1] >= 0 & z[1] >= 0  ==>  (U^Increasing(F(>(x[1]1, +(y[1]1, z[1]1)), x[1]1, y[1]1, +(z[1]1, 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[1] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	(12)    (x[1] >= 0 & [-1] + x[1] >= 0 & y[1] >= 0 & z[1] >= 0  ==>  (U^Increasing(F(>(x[1]1, +(y[1]1, z[1]1)), x[1]1, y[1]1, +(z[1]1, 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[1] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	To summarize, we get the following constraints P__>=_ for the following pairs.
6.89/2.77	
6.89/2.77	*F(TRUE, x, y, z) -> F(>(x, +(y, z)), x, +(y, 1), z)
6.89/2.77	
6.89/2.77	*(x[0] >= 0 & [-1] + x[0] >= 0 & y[0] >= 0 & z[0] >= 0  ==>  (U^Increasing(F(>(x[0]1, +(y[0]1, z[0]1)), x[0]1, +(y[0]1, 1), z[0]1)), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[0] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	*(x[0] >= 0 & [-1] + x[0] >= 0 & y[0] >= 0 & z[0] >= 0  ==>  (U^Increasing(F(>(x[0]1, +(y[0]1, z[0]1)), x[0]1, +(y[0]1, 1), z[0]1)), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[0] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	*(x[0] >= 0 & [-1] + x[0] >= 0 & y[0] >= 0 & z[0] >= 0  ==>  (U^Increasing(F(>(x[0]1, +(y[0]1, z[0]1)), x[0]1, +(y[0]1, 1), z[0]1)), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[0] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	*(x[0] >= 0 & [-1] + x[0] >= 0 & y[0] >= 0 & z[0] >= 0  ==>  (U^Increasing(F(>(x[0]1, +(y[0]1, z[0]1)), x[0]1, +(y[0]1, 1), z[0]1)), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[0] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	*(x[1] >= 0 & [-1] + x[1] >= 0 & y[1] >= 0 & z[1] >= 0  ==>  (U^Increasing(F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0])), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[1] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	*(x[1] >= 0 & [-1] + x[1] >= 0 & y[1] >= 0 & z[1] >= 0  ==>  (U^Increasing(F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0])), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[1] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	*(x[1] >= 0 & [-1] + x[1] >= 0 & y[1] >= 0 & z[1] >= 0  ==>  (U^Increasing(F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0])), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[1] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	*(x[1] >= 0 & [-1] + x[1] >= 0 & y[1] >= 0 & z[1] >= 0  ==>  (U^Increasing(F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0])), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[1] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	*(x[0] >= 0 & [-1] + x[0] >= 0 & y[0] >= 0 & z[0] >= 0  ==>  (U^Increasing(F(>(x[0]1, +(y[0]1, z[0]1)), x[0]1, +(y[0]1, 1), z[0]1)), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[0] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	*(x[0] >= 0 & [-1] + x[0] >= 0 & y[0] >= 0 & z[0] >= 0  ==>  (U^Increasing(F(>(x[0]1, +(y[0]1, z[0]1)), x[0]1, +(y[0]1, 1), z[0]1)), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[0] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	*(x[0] >= 0 & [-1] + x[0] >= 0 & y[0] >= 0 & z[0] >= 0  ==>  (U^Increasing(F(>(x[0]1, +(y[0]1, z[0]1)), x[0]1, +(y[0]1, 1), z[0]1)), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[0] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	*(x[0] >= 0 & [-1] + x[0] >= 0 & y[0] >= 0 & z[0] >= 0  ==>  (U^Increasing(F(>(x[0]1, +(y[0]1, z[0]1)), x[0]1, +(y[0]1, 1), z[0]1)), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[0] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	*(x[1] >= 0 & [-1] + x[1] >= 0 & y[1] >= 0 & z[1] >= 0  ==>  (U^Increasing(F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0])), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[1] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	*(x[1] >= 0 & [-1] + x[1] >= 0 & y[1] >= 0 & z[1] >= 0  ==>  (U^Increasing(F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0])), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[1] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	*(x[1] >= 0 & [-1] + x[1] >= 0 & y[1] >= 0 & z[1] >= 0  ==>  (U^Increasing(F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0])), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[1] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	*(x[1] >= 0 & [-1] + x[1] >= 0 & y[1] >= 0 & z[1] >= 0  ==>  (U^Increasing(F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0])), >=) & [(-1)bni_9 + (-1)Bound*bni_9] + [bni_9]x[1] >= 0 & [1 + (-1)bso_10] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	*F(TRUE, x, y, z) -> F(>(x, +(y, z)), x, y, +(z, 1))
6.89/2.77	
6.89/2.77	*(x[0] >= 0 & [-1] + x[0] >= 0 & y[0] >= 0 & z[0] >= 0  ==>  (U^Increasing(F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[0] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	*(x[0] >= 0 & [-1] + x[0] >= 0 & y[0] >= 0 & z[0] >= 0  ==>  (U^Increasing(F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[0] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	*(x[0] >= 0 & [-1] + x[0] >= 0 & y[0] >= 0 & z[0] >= 0  ==>  (U^Increasing(F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[0] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	*(x[0] >= 0 & [-1] + x[0] >= 0 & y[0] >= 0 & z[0] >= 0  ==>  (U^Increasing(F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[0] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	*(x[1] >= 0 & [-1] + x[1] >= 0 & y[1] >= 0 & z[1] >= 0  ==>  (U^Increasing(F(>(x[1]1, +(y[1]1, z[1]1)), x[1]1, y[1]1, +(z[1]1, 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[1] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	*(x[1] >= 0 & [-1] + x[1] >= 0 & y[1] >= 0 & z[1] >= 0  ==>  (U^Increasing(F(>(x[1]1, +(y[1]1, z[1]1)), x[1]1, y[1]1, +(z[1]1, 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[1] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	*(x[1] >= 0 & [-1] + x[1] >= 0 & y[1] >= 0 & z[1] >= 0  ==>  (U^Increasing(F(>(x[1]1, +(y[1]1, z[1]1)), x[1]1, y[1]1, +(z[1]1, 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[1] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	*(x[1] >= 0 & [-1] + x[1] >= 0 & y[1] >= 0 & z[1] >= 0  ==>  (U^Increasing(F(>(x[1]1, +(y[1]1, z[1]1)), x[1]1, y[1]1, +(z[1]1, 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[1] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	*(x[0] >= 0 & [-1] + x[0] >= 0 & y[0] >= 0 & z[0] >= 0  ==>  (U^Increasing(F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[0] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	*(x[0] >= 0 & [-1] + x[0] >= 0 & y[0] >= 0 & z[0] >= 0  ==>  (U^Increasing(F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[0] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	*(x[0] >= 0 & [-1] + x[0] >= 0 & y[0] >= 0 & z[0] >= 0  ==>  (U^Increasing(F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[0] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	*(x[0] >= 0 & [-1] + x[0] >= 0 & y[0] >= 0 & z[0] >= 0  ==>  (U^Increasing(F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[0] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	*(x[1] >= 0 & [-1] + x[1] >= 0 & y[1] >= 0 & z[1] >= 0  ==>  (U^Increasing(F(>(x[1]1, +(y[1]1, z[1]1)), x[1]1, y[1]1, +(z[1]1, 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[1] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	*(x[1] >= 0 & [-1] + x[1] >= 0 & y[1] >= 0 & z[1] >= 0  ==>  (U^Increasing(F(>(x[1]1, +(y[1]1, z[1]1)), x[1]1, y[1]1, +(z[1]1, 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[1] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	*(x[1] >= 0 & [-1] + x[1] >= 0 & y[1] >= 0 & z[1] >= 0  ==>  (U^Increasing(F(>(x[1]1, +(y[1]1, z[1]1)), x[1]1, y[1]1, +(z[1]1, 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[1] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	*(x[1] >= 0 & [-1] + x[1] >= 0 & y[1] >= 0 & z[1] >= 0  ==>  (U^Increasing(F(>(x[1]1, +(y[1]1, z[1]1)), x[1]1, y[1]1, +(z[1]1, 1))), >=) & [(-1)bni_11 + (-1)Bound*bni_11] + [bni_11]x[1] >= 0 & [1 + (-1)bso_12] >= 0)
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	
6.89/2.77	The constraints for P_> respective P_bound are constructed from P__>=_ where we just replace every occurence of "t _>=_ s" in P__>=_ by  "t > s" respective "t _>=_ c". Here c stands for the fresh constant used for P_bound. 
6.89/2.77	
6.89/2.77	Using the following integer polynomial ordering the  resulting constraints can be solved 
6.89/2.77	
6.89/2.77	Polynomial interpretation over integers[POLO]:
6.89/2.77	
6.89/2.77	   POL(TRUE) = 0
6.89/2.77	   POL(FALSE) = 0
6.89/2.77	   POL(F(x_1, x_2, x_3, x_4)) = [-1] + [-1]x_4 + [-1]x_3 + x_2
6.89/2.77	   POL(>(x_1, x_2)) = 0
6.89/2.77	   POL(+(x_1, x_2)) = x_1 + x_2
6.89/2.77	   POL(1) = [1]
6.89/2.77	
6.89/2.77	
6.89/2.77	The following pairs are in P_>:
6.89/2.77	
6.89/2.77	
6.89/2.77	   F(TRUE, x[0], y[0], z[0]) -> F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0])
6.89/2.77	   F(TRUE, x[1], y[1], z[1]) -> F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1))
6.89/2.77	
6.89/2.77	
6.89/2.77	The following pairs are in P_bound:
6.89/2.77	
6.89/2.77	
6.89/2.77	   F(TRUE, x[0], y[0], z[0]) -> F(>(x[0], +(y[0], z[0])), x[0], +(y[0], 1), z[0])
6.89/2.77	   F(TRUE, x[1], y[1], z[1]) -> F(>(x[1], +(y[1], z[1])), x[1], y[1], +(z[1], 1))
6.89/2.77	
6.89/2.77	
6.89/2.77	The following pairs are in P_>=:
6.89/2.77	
6.89/2.77	none
6.89/2.77	
6.89/2.77	
6.89/2.77	There are no usable rules.
6.89/2.77	----------------------------------------
6.89/2.77	
6.89/2.77	(6)
6.89/2.77	Obligation:
6.89/2.77	IDP problem:
6.89/2.77	The following function symbols are pre-defined:
6.89/2.77	<<<
6.89/2.77	 & 	~ 	Bwand: (Integer, Integer) -> Integer
6.89/2.77	 >= 	~ 	Ge: (Integer, Integer) -> Boolean
6.89/2.77	 | 	~ 	Bwor: (Integer, Integer) -> Integer
6.89/2.77	 / 	~ 	Div: (Integer, Integer) -> Integer
6.89/2.77	 != 	~ 	Neq: (Integer, Integer) -> Boolean
6.89/2.77	 && 	~ 	Land: (Boolean, Boolean) -> Boolean
6.89/2.77	 ! 	~ 	Lnot: (Boolean) -> Boolean
6.89/2.77	 = 	~ 	Eq: (Integer, Integer) -> Boolean
6.89/2.77	 <= 	~ 	Le: (Integer, Integer) -> Boolean
6.89/2.77	 ^ 	~ 	Bwxor: (Integer, Integer) -> Integer
6.89/2.77	 % 	~ 	Mod: (Integer, Integer) -> Integer
6.89/2.77	 > 	~ 	Gt: (Integer, Integer) -> Boolean
6.89/2.77	 + 	~ 	Add: (Integer, Integer) -> Integer
6.89/2.77	 -1 	~ 	UnaryMinus: (Integer) -> Integer
6.89/2.77	 < 	~ 	Lt: (Integer, Integer) -> Boolean
6.89/2.77	 || 	~ 	Lor: (Boolean, Boolean) -> Boolean
6.89/2.77	 - 	~ 	Sub: (Integer, Integer) -> Integer
6.89/2.77	 ~ 	~ 	Bwnot: (Integer) -> Integer
6.89/2.77	 * 	~ 	Mul: (Integer, Integer) -> Integer
6.89/2.77	>>>
6.89/2.77	
6.89/2.77	
6.89/2.77	The following domains are used:
6.89/2.77	none
6.89/2.77	
6.89/2.77	R is empty.
6.89/2.77	
6.89/2.77	The integer pair graph is empty.
6.89/2.77	
6.89/2.77	The set Q consists of the following terms:
6.89/2.77	f(TRUE, x0, x1, x2)
6.89/2.77	
6.89/2.77	----------------------------------------
6.89/2.77	
6.89/2.77	(7) PisEmptyProof (EQUIVALENT)
6.89/2.77	The TRS P is empty. Hence, there is no (P,Q,R) chain.
6.89/2.77	----------------------------------------
6.89/2.77	
6.89/2.77	(8)
6.89/2.77	YES
6.89/2.80	EOF