5.62/2.48	YES
5.75/2.50	proof of /export/starexec/sandbox/benchmark/theBenchmark.itrs
5.75/2.50	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.75/2.50	
5.75/2.50	
5.75/2.50	Termination of the given ITRS could be proven:
5.75/2.50	
5.75/2.50	(0) ITRS
5.75/2.50	(1) ITRStoIDPProof [EQUIVALENT, 0 ms]
5.75/2.50	(2) IDP
5.75/2.50	(3) UsableRulesProof [EQUIVALENT, 0 ms]
5.75/2.50	(4) IDP
5.75/2.50	(5) IDependencyGraphProof [EQUIVALENT, 0 ms]
5.75/2.50	(6) IDP
5.75/2.50	(7) IDPNonInfProof [SOUND, 517 ms]
5.75/2.50	(8) IDP
5.75/2.50	(9) IDependencyGraphProof [EQUIVALENT, 0 ms]
5.75/2.50	(10) TRUE
5.75/2.50	
5.75/2.50	
5.75/2.50	----------------------------------------
5.75/2.50	
5.75/2.50	(0)
5.75/2.50	Obligation:
5.75/2.50	ITRS problem:
5.75/2.50	
5.75/2.50	The following function symbols are pre-defined:
5.75/2.50	<<<
5.75/2.50	 & 	~ 	Bwand: (Integer, Integer) -> Integer
5.75/2.50	 >= 	~ 	Ge: (Integer, Integer) -> Boolean
5.75/2.50	 | 	~ 	Bwor: (Integer, Integer) -> Integer
5.75/2.50	 / 	~ 	Div: (Integer, Integer) -> Integer
5.75/2.50	 != 	~ 	Neq: (Integer, Integer) -> Boolean
5.75/2.50	 && 	~ 	Land: (Boolean, Boolean) -> Boolean
5.75/2.50	 ! 	~ 	Lnot: (Boolean) -> Boolean
5.75/2.50	 = 	~ 	Eq: (Integer, Integer) -> Boolean
5.75/2.50	 <= 	~ 	Le: (Integer, Integer) -> Boolean
5.75/2.50	 ^ 	~ 	Bwxor: (Integer, Integer) -> Integer
5.75/2.50	 % 	~ 	Mod: (Integer, Integer) -> Integer
5.75/2.50	 > 	~ 	Gt: (Integer, Integer) -> Boolean
5.75/2.50	 + 	~ 	Add: (Integer, Integer) -> Integer
5.75/2.50	 -1 	~ 	UnaryMinus: (Integer) -> Integer
5.75/2.50	 < 	~ 	Lt: (Integer, Integer) -> Boolean
5.75/2.50	 || 	~ 	Lor: (Boolean, Boolean) -> Boolean
5.75/2.50	 - 	~ 	Sub: (Integer, Integer) -> Integer
5.75/2.50	 ~ 	~ 	Bwnot: (Integer) -> Integer
5.75/2.50	 * 	~ 	Mul: (Integer, Integer) -> Integer
5.75/2.50	>>>
5.75/2.50	
5.75/2.50	The TRS R consists of the following rules:
5.75/2.50	eval_0(x, y, z) -> Cond_eval_0(y > 0, x, y, z)
5.75/2.50	Cond_eval_0(TRUE, x, y, z) -> eval_1(x, y, z)
5.75/2.50	eval_1(x, y, z) -> Cond_eval_1(y > x && z > y && y > 0, x, y, z)
5.75/2.50	Cond_eval_1(TRUE, x, y, z) -> eval_1(x + y, y, z)
5.75/2.50	eval_1(x, y, z) -> Cond_eval_11(y > x && z > y && y > 0, x, y, z)
5.75/2.50	Cond_eval_11(TRUE, x, y, z) -> eval_1(x, y, x - y)
5.75/2.50	The set Q consists of the following terms:
5.75/2.50	eval_0(x0, x1, x2)
5.75/2.50	Cond_eval_0(TRUE, x0, x1, x2)
5.75/2.50	eval_1(x0, x1, x2)
5.75/2.50	Cond_eval_1(TRUE, x0, x1, x2)
5.75/2.50	Cond_eval_11(TRUE, x0, x1, x2)
5.75/2.50	
5.75/2.50	----------------------------------------
5.75/2.50	
5.75/2.50	(1) ITRStoIDPProof (EQUIVALENT)
5.75/2.50	Added dependency pairs
5.75/2.50	----------------------------------------
5.75/2.50	
5.75/2.50	(2)
5.75/2.50	Obligation:
5.75/2.50	IDP problem:
5.75/2.50	The following function symbols are pre-defined:
5.75/2.50	<<<
5.75/2.50	 & 	~ 	Bwand: (Integer, Integer) -> Integer
5.75/2.50	 >= 	~ 	Ge: (Integer, Integer) -> Boolean
5.75/2.50	 | 	~ 	Bwor: (Integer, Integer) -> Integer
5.75/2.50	 / 	~ 	Div: (Integer, Integer) -> Integer
5.75/2.50	 != 	~ 	Neq: (Integer, Integer) -> Boolean
5.75/2.50	 && 	~ 	Land: (Boolean, Boolean) -> Boolean
5.75/2.50	 ! 	~ 	Lnot: (Boolean) -> Boolean
5.75/2.50	 = 	~ 	Eq: (Integer, Integer) -> Boolean
5.75/2.50	 <= 	~ 	Le: (Integer, Integer) -> Boolean
5.75/2.50	 ^ 	~ 	Bwxor: (Integer, Integer) -> Integer
5.75/2.50	 % 	~ 	Mod: (Integer, Integer) -> Integer
5.75/2.50	 > 	~ 	Gt: (Integer, Integer) -> Boolean
5.75/2.50	 + 	~ 	Add: (Integer, Integer) -> Integer
5.75/2.50	 -1 	~ 	UnaryMinus: (Integer) -> Integer
5.75/2.50	 < 	~ 	Lt: (Integer, Integer) -> Boolean
5.75/2.50	 || 	~ 	Lor: (Boolean, Boolean) -> Boolean
5.75/2.50	 - 	~ 	Sub: (Integer, Integer) -> Integer
5.75/2.50	 ~ 	~ 	Bwnot: (Integer) -> Integer
5.75/2.50	 * 	~ 	Mul: (Integer, Integer) -> Integer
5.75/2.50	>>>
5.75/2.50	
5.75/2.50	
5.75/2.50	The following domains are used:
5.75/2.50	   Integer, Boolean
5.75/2.50	
5.75/2.50	The ITRS R consists of the following rules:
5.75/2.50	eval_0(x, y, z) -> Cond_eval_0(y > 0, x, y, z)
5.75/2.50	Cond_eval_0(TRUE, x, y, z) -> eval_1(x, y, z)
5.75/2.50	eval_1(x, y, z) -> Cond_eval_1(y > x && z > y && y > 0, x, y, z)
5.75/2.50	Cond_eval_1(TRUE, x, y, z) -> eval_1(x + y, y, z)
5.75/2.50	eval_1(x, y, z) -> Cond_eval_11(y > x && z > y && y > 0, x, y, z)
5.75/2.50	Cond_eval_11(TRUE, x, y, z) -> eval_1(x, y, x - y)
5.75/2.50	
5.75/2.50	The integer pair graph contains the following rules and edges:
5.75/2.50	(0): EVAL_0(x[0], y[0], z[0]) -> COND_EVAL_0(y[0] > 0, x[0], y[0], z[0])
5.75/2.50	(1): COND_EVAL_0(TRUE, x[1], y[1], z[1]) -> EVAL_1(x[1], y[1], z[1])
5.75/2.50	(2): EVAL_1(x[2], y[2], z[2]) -> COND_EVAL_1(y[2] > x[2] && z[2] > y[2] && y[2] > 0, x[2], y[2], z[2])
5.75/2.50	(3): COND_EVAL_1(TRUE, x[3], y[3], z[3]) -> EVAL_1(x[3] + y[3], y[3], z[3])
5.75/2.50	(4): EVAL_1(x[4], y[4], z[4]) -> COND_EVAL_11(y[4] > x[4] && z[4] > y[4] && y[4] > 0, x[4], y[4], z[4])
5.75/2.50	(5): COND_EVAL_11(TRUE, x[5], y[5], z[5]) -> EVAL_1(x[5], y[5], x[5] - y[5])
5.75/2.50	
5.75/2.50	   (0) -> (1), if (y[0] > 0  & x[0] ->^* x[1] & y[0] ->^* y[1] & z[0] ->^* z[1])
5.75/2.50	   (1) -> (2), if (x[1] ->^* x[2] & y[1] ->^* y[2] & z[1] ->^* z[2])
5.75/2.50	   (1) -> (4), if (x[1] ->^* x[4] & y[1] ->^* y[4] & z[1] ->^* z[4])
5.75/2.50	   (2) -> (3), if (y[2] > x[2] && z[2] > y[2] && y[2] > 0  & x[2] ->^* x[3] & y[2] ->^* y[3] & z[2] ->^* z[3])
5.75/2.50	   (3) -> (2), if (x[3] + y[3] ->^* x[2] & y[3] ->^* y[2] & z[3] ->^* z[2])
5.75/2.50	   (3) -> (4), if (x[3] + y[3] ->^* x[4] & y[3] ->^* y[4] & z[3] ->^* z[4])
5.75/2.50	   (4) -> (5), if (y[4] > x[4] && z[4] > y[4] && y[4] > 0  & x[4] ->^* x[5] & y[4] ->^* y[5] & z[4] ->^* z[5])
5.75/2.50	   (5) -> (2), if (x[5] ->^* x[2] & y[5] ->^* y[2] & x[5] - y[5] ->^* z[2])
5.75/2.50	   (5) -> (4), if (x[5] ->^* x[4] & y[5] ->^* y[4] & x[5] - y[5] ->^* z[4])
5.75/2.50	
5.75/2.50	The set Q consists of the following terms:
5.75/2.50	eval_0(x0, x1, x2)
5.75/2.50	Cond_eval_0(TRUE, x0, x1, x2)
5.75/2.50	eval_1(x0, x1, x2)
5.75/2.50	Cond_eval_1(TRUE, x0, x1, x2)
5.75/2.50	Cond_eval_11(TRUE, x0, x1, x2)
5.75/2.50	
5.75/2.50	----------------------------------------
5.75/2.50	
5.75/2.50	(3) UsableRulesProof (EQUIVALENT)
5.75/2.50	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.
5.75/2.50	----------------------------------------
5.75/2.50	
5.75/2.50	(4)
5.75/2.50	Obligation:
5.75/2.50	IDP problem:
5.75/2.50	The following function symbols are pre-defined:
5.75/2.50	<<<
5.75/2.50	 & 	~ 	Bwand: (Integer, Integer) -> Integer
5.75/2.50	 >= 	~ 	Ge: (Integer, Integer) -> Boolean
5.75/2.50	 | 	~ 	Bwor: (Integer, Integer) -> Integer
5.75/2.50	 / 	~ 	Div: (Integer, Integer) -> Integer
5.75/2.50	 != 	~ 	Neq: (Integer, Integer) -> Boolean
5.75/2.50	 && 	~ 	Land: (Boolean, Boolean) -> Boolean
5.75/2.50	 ! 	~ 	Lnot: (Boolean) -> Boolean
5.75/2.50	 = 	~ 	Eq: (Integer, Integer) -> Boolean
5.75/2.50	 <= 	~ 	Le: (Integer, Integer) -> Boolean
5.75/2.50	 ^ 	~ 	Bwxor: (Integer, Integer) -> Integer
5.75/2.50	 % 	~ 	Mod: (Integer, Integer) -> Integer
5.75/2.50	 > 	~ 	Gt: (Integer, Integer) -> Boolean
5.75/2.50	 + 	~ 	Add: (Integer, Integer) -> Integer
5.75/2.50	 -1 	~ 	UnaryMinus: (Integer) -> Integer
5.75/2.50	 < 	~ 	Lt: (Integer, Integer) -> Boolean
5.75/2.50	 || 	~ 	Lor: (Boolean, Boolean) -> Boolean
5.75/2.50	 - 	~ 	Sub: (Integer, Integer) -> Integer
5.75/2.50	 ~ 	~ 	Bwnot: (Integer) -> Integer
5.75/2.50	 * 	~ 	Mul: (Integer, Integer) -> Integer
5.75/2.50	>>>
5.75/2.50	
5.75/2.50	
5.75/2.50	The following domains are used:
5.75/2.50	   Integer, Boolean
5.75/2.50	
5.75/2.50	R is empty.
5.75/2.50	
5.75/2.50	The integer pair graph contains the following rules and edges:
5.75/2.50	(0): EVAL_0(x[0], y[0], z[0]) -> COND_EVAL_0(y[0] > 0, x[0], y[0], z[0])
5.75/2.50	(1): COND_EVAL_0(TRUE, x[1], y[1], z[1]) -> EVAL_1(x[1], y[1], z[1])
5.75/2.50	(2): EVAL_1(x[2], y[2], z[2]) -> COND_EVAL_1(y[2] > x[2] && z[2] > y[2] && y[2] > 0, x[2], y[2], z[2])
5.75/2.50	(3): COND_EVAL_1(TRUE, x[3], y[3], z[3]) -> EVAL_1(x[3] + y[3], y[3], z[3])
5.75/2.50	(4): EVAL_1(x[4], y[4], z[4]) -> COND_EVAL_11(y[4] > x[4] && z[4] > y[4] && y[4] > 0, x[4], y[4], z[4])
5.75/2.50	(5): COND_EVAL_11(TRUE, x[5], y[5], z[5]) -> EVAL_1(x[5], y[5], x[5] - y[5])
5.75/2.50	
5.75/2.50	   (0) -> (1), if (y[0] > 0  & x[0] ->^* x[1] & y[0] ->^* y[1] & z[0] ->^* z[1])
5.75/2.50	   (1) -> (2), if (x[1] ->^* x[2] & y[1] ->^* y[2] & z[1] ->^* z[2])
5.75/2.50	   (1) -> (4), if (x[1] ->^* x[4] & y[1] ->^* y[4] & z[1] ->^* z[4])
5.75/2.50	   (2) -> (3), if (y[2] > x[2] && z[2] > y[2] && y[2] > 0  & x[2] ->^* x[3] & y[2] ->^* y[3] & z[2] ->^* z[3])
5.75/2.50	   (3) -> (2), if (x[3] + y[3] ->^* x[2] & y[3] ->^* y[2] & z[3] ->^* z[2])
5.75/2.50	   (3) -> (4), if (x[3] + y[3] ->^* x[4] & y[3] ->^* y[4] & z[3] ->^* z[4])
5.75/2.50	   (4) -> (5), if (y[4] > x[4] && z[4] > y[4] && y[4] > 0  & x[4] ->^* x[5] & y[4] ->^* y[5] & z[4] ->^* z[5])
5.75/2.50	   (5) -> (2), if (x[5] ->^* x[2] & y[5] ->^* y[2] & x[5] - y[5] ->^* z[2])
5.75/2.50	   (5) -> (4), if (x[5] ->^* x[4] & y[5] ->^* y[4] & x[5] - y[5] ->^* z[4])
5.75/2.50	
5.75/2.50	The set Q consists of the following terms:
5.75/2.50	eval_0(x0, x1, x2)
5.75/2.50	Cond_eval_0(TRUE, x0, x1, x2)
5.75/2.50	eval_1(x0, x1, x2)
5.75/2.50	Cond_eval_1(TRUE, x0, x1, x2)
5.75/2.50	Cond_eval_11(TRUE, x0, x1, x2)
5.75/2.50	
5.75/2.50	----------------------------------------
5.75/2.50	
5.75/2.50	(5) IDependencyGraphProof (EQUIVALENT)
5.75/2.50	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
5.75/2.50	----------------------------------------
5.75/2.50	
5.75/2.50	(6)
5.75/2.50	Obligation:
5.75/2.50	IDP problem:
5.75/2.50	The following function symbols are pre-defined:
5.75/2.50	<<<
5.75/2.50	 & 	~ 	Bwand: (Integer, Integer) -> Integer
5.75/2.50	 >= 	~ 	Ge: (Integer, Integer) -> Boolean
5.75/2.50	 | 	~ 	Bwor: (Integer, Integer) -> Integer
5.75/2.50	 / 	~ 	Div: (Integer, Integer) -> Integer
5.75/2.50	 != 	~ 	Neq: (Integer, Integer) -> Boolean
5.75/2.50	 && 	~ 	Land: (Boolean, Boolean) -> Boolean
5.75/2.50	 ! 	~ 	Lnot: (Boolean) -> Boolean
5.75/2.50	 = 	~ 	Eq: (Integer, Integer) -> Boolean
5.75/2.50	 <= 	~ 	Le: (Integer, Integer) -> Boolean
5.75/2.50	 ^ 	~ 	Bwxor: (Integer, Integer) -> Integer
5.75/2.50	 % 	~ 	Mod: (Integer, Integer) -> Integer
5.75/2.50	 > 	~ 	Gt: (Integer, Integer) -> Boolean
5.75/2.50	 + 	~ 	Add: (Integer, Integer) -> Integer
5.75/2.50	 -1 	~ 	UnaryMinus: (Integer) -> Integer
5.75/2.50	 < 	~ 	Lt: (Integer, Integer) -> Boolean
5.75/2.50	 || 	~ 	Lor: (Boolean, Boolean) -> Boolean
5.75/2.50	 - 	~ 	Sub: (Integer, Integer) -> Integer
5.75/2.50	 ~ 	~ 	Bwnot: (Integer) -> Integer
5.75/2.50	 * 	~ 	Mul: (Integer, Integer) -> Integer
5.75/2.50	>>>
5.75/2.50	
5.75/2.50	
5.75/2.50	The following domains are used:
5.75/2.50	   Integer, Boolean
5.75/2.50	
5.75/2.50	R is empty.
5.75/2.50	
5.75/2.50	The integer pair graph contains the following rules and edges:
5.75/2.50	(5): COND_EVAL_11(TRUE, x[5], y[5], z[5]) -> EVAL_1(x[5], y[5], x[5] - y[5])
5.75/2.50	(4): EVAL_1(x[4], y[4], z[4]) -> COND_EVAL_11(y[4] > x[4] && z[4] > y[4] && y[4] > 0, x[4], y[4], z[4])
5.75/2.50	(3): COND_EVAL_1(TRUE, x[3], y[3], z[3]) -> EVAL_1(x[3] + y[3], y[3], z[3])
5.75/2.50	(2): EVAL_1(x[2], y[2], z[2]) -> COND_EVAL_1(y[2] > x[2] && z[2] > y[2] && y[2] > 0, x[2], y[2], z[2])
5.75/2.50	
5.75/2.50	   (3) -> (2), if (x[3] + y[3] ->^* x[2] & y[3] ->^* y[2] & z[3] ->^* z[2])
5.75/2.50	   (5) -> (2), if (x[5] ->^* x[2] & y[5] ->^* y[2] & x[5] - y[5] ->^* z[2])
5.75/2.50	   (2) -> (3), if (y[2] > x[2] && z[2] > y[2] && y[2] > 0  & x[2] ->^* x[3] & y[2] ->^* y[3] & z[2] ->^* z[3])
5.75/2.50	   (3) -> (4), if (x[3] + y[3] ->^* x[4] & y[3] ->^* y[4] & z[3] ->^* z[4])
5.75/2.50	   (5) -> (4), if (x[5] ->^* x[4] & y[5] ->^* y[4] & x[5] - y[5] ->^* z[4])
5.75/2.50	   (4) -> (5), if (y[4] > x[4] && z[4] > y[4] && y[4] > 0  & x[4] ->^* x[5] & y[4] ->^* y[5] & z[4] ->^* z[5])
5.75/2.50	
5.75/2.50	The set Q consists of the following terms:
5.75/2.50	eval_0(x0, x1, x2)
5.75/2.50	Cond_eval_0(TRUE, x0, x1, x2)
5.75/2.50	eval_1(x0, x1, x2)
5.75/2.50	Cond_eval_1(TRUE, x0, x1, x2)
5.75/2.50	Cond_eval_11(TRUE, x0, x1, x2)
5.75/2.50	
5.75/2.50	----------------------------------------
5.75/2.50	
5.75/2.50	(7) IDPNonInfProof (SOUND)
5.75/2.50	Used the following options for this NonInfProof:
5.75/2.50	
5.75/2.50	IDPGPoloSolver:
5.75/2.50	Range: [(-1,2)]
5.75/2.50	IsNat: false
5.75/2.50	Interpretation Shape Heuristic: aprove.DPFramework.IDPProblem.Processors.nonInf.poly.IdpDefaultShapeHeuristic@7c041da7
5.75/2.50	Constraint Generator: NonInfConstraintGenerator:
5.75/2.50	PathGenerator: MetricPathGenerator:
5.75/2.50	Max Left Steps: 1
5.75/2.50	Max Right Steps: 1
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	The constraints were generated the following way:
5.75/2.50	
5.75/2.50	The DP Problem is simplified using the Induction Calculus [NONINF] with the following steps:
5.75/2.50	
5.75/2.50	Note that final constraints are written in bold face.
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	For Pair COND_EVAL_11(TRUE, x[5], y[5], z[5]) -> EVAL_1(x[5], y[5], -(x[5], y[5])) the following chains were created:
5.75/2.50	*We consider the chain EVAL_1(x[4], y[4], z[4]) -> COND_EVAL_11(&&(&&(>(y[4], x[4]), >(z[4], y[4])), >(y[4], 0)), x[4], y[4], z[4]), COND_EVAL_11(TRUE, x[5], y[5], z[5]) -> EVAL_1(x[5], y[5], -(x[5], y[5])), EVAL_1(x[2], y[2], z[2]) -> COND_EVAL_1(&&(&&(>(y[2], x[2]), >(z[2], y[2])), >(y[2], 0)), x[2], y[2], z[2]) which results in the following constraint:
5.75/2.50	
5.75/2.50	(1)    (&&(&&(>(y[4], x[4]), >(z[4], y[4])), >(y[4], 0))=TRUE & x[4]=x[5] & y[4]=y[5] & z[4]=z[5] & x[5]=x[2] & y[5]=y[2] & -(x[5], y[5])=z[2]  ==>  COND_EVAL_11(TRUE, x[5], y[5], z[5])_>=_NonInfC & COND_EVAL_11(TRUE, x[5], y[5], z[5])_>=_EVAL_1(x[5], y[5], -(x[5], y[5])) & (U^Increasing(EVAL_1(x[5], y[5], -(x[5], y[5]))), >=))
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	We simplified constraint (1) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
5.75/2.50	
5.75/2.50	(2)    (>(y[4], 0)=TRUE & >(y[4], x[4])=TRUE & >(z[4], y[4])=TRUE  ==>  COND_EVAL_11(TRUE, x[4], y[4], z[4])_>=_NonInfC & COND_EVAL_11(TRUE, x[4], y[4], z[4])_>=_EVAL_1(x[4], y[4], -(x[4], y[4])) & (U^Increasing(EVAL_1(x[5], y[5], -(x[5], y[5]))), >=))
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
5.75/2.50	
5.75/2.50	(3)    (y[4] + [-1] >= 0 & y[4] + [-1] + [-1]x[4] >= 0 & z[4] + [-1] + [-1]y[4] >= 0  ==>  (U^Increasing(EVAL_1(x[5], y[5], -(x[5], y[5]))), >=) & [(-1)bni_19 + (-1)Bound*bni_19] + [(-1)bni_19]x[4] >= 0 & [(-1)bso_20] + y[4] + [-1]x[4] >= 0)
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
5.75/2.50	
5.75/2.50	(4)    (y[4] + [-1] >= 0 & y[4] + [-1] + [-1]x[4] >= 0 & z[4] + [-1] + [-1]y[4] >= 0  ==>  (U^Increasing(EVAL_1(x[5], y[5], -(x[5], y[5]))), >=) & [(-1)bni_19 + (-1)Bound*bni_19] + [(-1)bni_19]x[4] >= 0 & [(-1)bso_20] + y[4] + [-1]x[4] >= 0)
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
5.75/2.50	
5.75/2.50	(5)    (y[4] + [-1] >= 0 & y[4] + [-1] + [-1]x[4] >= 0 & z[4] + [-1] + [-1]y[4] >= 0  ==>  (U^Increasing(EVAL_1(x[5], y[5], -(x[5], y[5]))), >=) & [(-1)bni_19 + (-1)Bound*bni_19] + [(-1)bni_19]x[4] >= 0 & [(-1)bso_20] + y[4] + [-1]x[4] >= 0)
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	We simplified constraint (5) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
5.75/2.50	
5.75/2.50	(6)    (y[4] + [-1] >= 0 & y[4] + [-1] + [-1]x[4] >= 0 & z[4] + [-1] + [-1]y[4] >= 0 & x[4] >= 0  ==>  (U^Increasing(EVAL_1(x[5], y[5], -(x[5], y[5]))), >=) & [(-1)bni_19 + (-1)Bound*bni_19] + [(-1)bni_19]x[4] >= 0 & [(-1)bso_20] + y[4] + [-1]x[4] >= 0)
5.75/2.50	
5.75/2.50	(7)    (y[4] + [-1] >= 0 & y[4] + [-1] + x[4] >= 0 & z[4] + [-1] + [-1]y[4] >= 0 & x[4] >= 0  ==>  (U^Increasing(EVAL_1(x[5], y[5], -(x[5], y[5]))), >=) & [(-1)bni_19 + (-1)Bound*bni_19] + [bni_19]x[4] >= 0 & [(-1)bso_20] + y[4] + x[4] >= 0)
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	*We consider the chain EVAL_1(x[4], y[4], z[4]) -> COND_EVAL_11(&&(&&(>(y[4], x[4]), >(z[4], y[4])), >(y[4], 0)), x[4], y[4], z[4]), COND_EVAL_11(TRUE, x[5], y[5], z[5]) -> EVAL_1(x[5], y[5], -(x[5], y[5])), EVAL_1(x[4], y[4], z[4]) -> COND_EVAL_11(&&(&&(>(y[4], x[4]), >(z[4], y[4])), >(y[4], 0)), x[4], y[4], z[4]) which results in the following constraint:
5.75/2.50	
5.75/2.50	(1)    (&&(&&(>(y[4], x[4]), >(z[4], y[4])), >(y[4], 0))=TRUE & x[4]=x[5] & y[4]=y[5] & z[4]=z[5] & x[5]=x[4]1 & y[5]=y[4]1 & -(x[5], y[5])=z[4]1  ==>  COND_EVAL_11(TRUE, x[5], y[5], z[5])_>=_NonInfC & COND_EVAL_11(TRUE, x[5], y[5], z[5])_>=_EVAL_1(x[5], y[5], -(x[5], y[5])) & (U^Increasing(EVAL_1(x[5], y[5], -(x[5], y[5]))), >=))
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	We simplified constraint (1) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
5.75/2.50	
5.75/2.50	(2)    (>(y[4], 0)=TRUE & >(y[4], x[4])=TRUE & >(z[4], y[4])=TRUE  ==>  COND_EVAL_11(TRUE, x[4], y[4], z[4])_>=_NonInfC & COND_EVAL_11(TRUE, x[4], y[4], z[4])_>=_EVAL_1(x[4], y[4], -(x[4], y[4])) & (U^Increasing(EVAL_1(x[5], y[5], -(x[5], y[5]))), >=))
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
5.75/2.50	
5.75/2.50	(3)    (y[4] + [-1] >= 0 & y[4] + [-1] + [-1]x[4] >= 0 & z[4] + [-1] + [-1]y[4] >= 0  ==>  (U^Increasing(EVAL_1(x[5], y[5], -(x[5], y[5]))), >=) & [(-1)bni_19 + (-1)Bound*bni_19] + [(-1)bni_19]x[4] >= 0 & [(-1)bso_20] + y[4] + [-1]x[4] >= 0)
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
5.75/2.50	
5.75/2.50	(4)    (y[4] + [-1] >= 0 & y[4] + [-1] + [-1]x[4] >= 0 & z[4] + [-1] + [-1]y[4] >= 0  ==>  (U^Increasing(EVAL_1(x[5], y[5], -(x[5], y[5]))), >=) & [(-1)bni_19 + (-1)Bound*bni_19] + [(-1)bni_19]x[4] >= 0 & [(-1)bso_20] + y[4] + [-1]x[4] >= 0)
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
5.75/2.50	
5.75/2.50	(5)    (y[4] + [-1] >= 0 & y[4] + [-1] + [-1]x[4] >= 0 & z[4] + [-1] + [-1]y[4] >= 0  ==>  (U^Increasing(EVAL_1(x[5], y[5], -(x[5], y[5]))), >=) & [(-1)bni_19 + (-1)Bound*bni_19] + [(-1)bni_19]x[4] >= 0 & [(-1)bso_20] + y[4] + [-1]x[4] >= 0)
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	We simplified constraint (5) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
5.75/2.50	
5.75/2.50	(6)    (y[4] + [-1] >= 0 & y[4] + [-1] + [-1]x[4] >= 0 & z[4] + [-1] + [-1]y[4] >= 0 & x[4] >= 0  ==>  (U^Increasing(EVAL_1(x[5], y[5], -(x[5], y[5]))), >=) & [(-1)bni_19 + (-1)Bound*bni_19] + [(-1)bni_19]x[4] >= 0 & [(-1)bso_20] + y[4] + [-1]x[4] >= 0)
5.75/2.50	
5.75/2.50	(7)    (y[4] + [-1] >= 0 & y[4] + [-1] + x[4] >= 0 & z[4] + [-1] + [-1]y[4] >= 0 & x[4] >= 0  ==>  (U^Increasing(EVAL_1(x[5], y[5], -(x[5], y[5]))), >=) & [(-1)bni_19 + (-1)Bound*bni_19] + [bni_19]x[4] >= 0 & [(-1)bso_20] + y[4] + x[4] >= 0)
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	For Pair EVAL_1(x[4], y[4], z[4]) -> COND_EVAL_11(&&(&&(>(y[4], x[4]), >(z[4], y[4])), >(y[4], 0)), x[4], y[4], z[4]) the following chains were created:
5.75/2.50	*We consider the chain EVAL_1(x[4], y[4], z[4]) -> COND_EVAL_11(&&(&&(>(y[4], x[4]), >(z[4], y[4])), >(y[4], 0)), x[4], y[4], z[4]), COND_EVAL_11(TRUE, x[5], y[5], z[5]) -> EVAL_1(x[5], y[5], -(x[5], y[5])) which results in the following constraint:
5.75/2.50	
5.75/2.50	(1)    (&&(&&(>(y[4], x[4]), >(z[4], y[4])), >(y[4], 0))=TRUE & x[4]=x[5] & y[4]=y[5] & z[4]=z[5]  ==>  EVAL_1(x[4], y[4], z[4])_>=_NonInfC & EVAL_1(x[4], y[4], z[4])_>=_COND_EVAL_11(&&(&&(>(y[4], x[4]), >(z[4], y[4])), >(y[4], 0)), x[4], y[4], z[4]) & (U^Increasing(COND_EVAL_11(&&(&&(>(y[4], x[4]), >(z[4], y[4])), >(y[4], 0)), x[4], y[4], z[4])), >=))
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	We simplified constraint (1) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:
5.75/2.50	
5.75/2.50	(2)    (>(y[4], 0)=TRUE & >(y[4], x[4])=TRUE & >(z[4], y[4])=TRUE  ==>  EVAL_1(x[4], y[4], z[4])_>=_NonInfC & EVAL_1(x[4], y[4], z[4])_>=_COND_EVAL_11(&&(&&(>(y[4], x[4]), >(z[4], y[4])), >(y[4], 0)), x[4], y[4], z[4]) & (U^Increasing(COND_EVAL_11(&&(&&(>(y[4], x[4]), >(z[4], y[4])), >(y[4], 0)), x[4], y[4], z[4])), >=))
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
5.75/2.50	
5.75/2.50	(3)    (y[4] + [-1] >= 0 & y[4] + [-1] + [-1]x[4] >= 0 & z[4] + [-1] + [-1]y[4] >= 0  ==>  (U^Increasing(COND_EVAL_11(&&(&&(>(y[4], x[4]), >(z[4], y[4])), >(y[4], 0)), x[4], y[4], z[4])), >=) & [(-1)bni_21 + (-1)Bound*bni_21] + [bni_21]z[4] + [(-1)bni_21]x[4] >= 0 & [(-1)bso_22] + z[4] >= 0)
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
5.75/2.50	
5.75/2.50	(4)    (y[4] + [-1] >= 0 & y[4] + [-1] + [-1]x[4] >= 0 & z[4] + [-1] + [-1]y[4] >= 0  ==>  (U^Increasing(COND_EVAL_11(&&(&&(>(y[4], x[4]), >(z[4], y[4])), >(y[4], 0)), x[4], y[4], z[4])), >=) & [(-1)bni_21 + (-1)Bound*bni_21] + [bni_21]z[4] + [(-1)bni_21]x[4] >= 0 & [(-1)bso_22] + z[4] >= 0)
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
5.75/2.50	
5.75/2.50	(5)    (y[4] + [-1] >= 0 & y[4] + [-1] + [-1]x[4] >= 0 & z[4] + [-1] + [-1]y[4] >= 0  ==>  (U^Increasing(COND_EVAL_11(&&(&&(>(y[4], x[4]), >(z[4], y[4])), >(y[4], 0)), x[4], y[4], z[4])), >=) & [(-1)bni_21 + (-1)Bound*bni_21] + [bni_21]z[4] + [(-1)bni_21]x[4] >= 0 & [(-1)bso_22] + z[4] >= 0)
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	We simplified constraint (5) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
5.75/2.50	
5.75/2.50	(6)    (y[4] + [-1] >= 0 & y[4] + [-1] + [-1]x[4] >= 0 & z[4] + [-1] + [-1]y[4] >= 0 & x[4] >= 0  ==>  (U^Increasing(COND_EVAL_11(&&(&&(>(y[4], x[4]), >(z[4], y[4])), >(y[4], 0)), x[4], y[4], z[4])), >=) & [(-1)bni_21 + (-1)Bound*bni_21] + [bni_21]z[4] + [(-1)bni_21]x[4] >= 0 & [(-1)bso_22] + z[4] >= 0)
5.75/2.50	
5.75/2.50	(7)    (y[4] + [-1] >= 0 & y[4] + [-1] + x[4] >= 0 & z[4] + [-1] + [-1]y[4] >= 0 & x[4] >= 0  ==>  (U^Increasing(COND_EVAL_11(&&(&&(>(y[4], x[4]), >(z[4], y[4])), >(y[4], 0)), x[4], y[4], z[4])), >=) & [(-1)bni_21 + (-1)Bound*bni_21] + [bni_21]z[4] + [bni_21]x[4] >= 0 & [(-1)bso_22] + z[4] >= 0)
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	For Pair COND_EVAL_1(TRUE, x[3], y[3], z[3]) -> EVAL_1(+(x[3], y[3]), y[3], z[3]) the following chains were created:
5.75/2.50	*We consider the chain EVAL_1(x[2], y[2], z[2]) -> COND_EVAL_1(&&(&&(>(y[2], x[2]), >(z[2], y[2])), >(y[2], 0)), x[2], y[2], z[2]), COND_EVAL_1(TRUE, x[3], y[3], z[3]) -> EVAL_1(+(x[3], y[3]), y[3], z[3]), EVAL_1(x[2], y[2], z[2]) -> COND_EVAL_1(&&(&&(>(y[2], x[2]), >(z[2], y[2])), >(y[2], 0)), x[2], y[2], z[2]) which results in the following constraint:
5.75/2.50	
5.75/2.50	(1)    (&&(&&(>(y[2], x[2]), >(z[2], y[2])), >(y[2], 0))=TRUE & x[2]=x[3] & y[2]=y[3] & z[2]=z[3] & +(x[3], y[3])=x[2]1 & y[3]=y[2]1 & z[3]=z[2]1  ==>  COND_EVAL_1(TRUE, x[3], y[3], z[3])_>=_NonInfC & COND_EVAL_1(TRUE, x[3], y[3], z[3])_>=_EVAL_1(+(x[3], y[3]), y[3], z[3]) & (U^Increasing(EVAL_1(+(x[3], y[3]), y[3], z[3])), >=))
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	We simplified constraint (1) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
5.75/2.50	
5.75/2.50	(2)    (>(y[2], 0)=TRUE & >(y[2], x[2])=TRUE & >(z[2], y[2])=TRUE  ==>  COND_EVAL_1(TRUE, x[2], y[2], z[2])_>=_NonInfC & COND_EVAL_1(TRUE, x[2], y[2], z[2])_>=_EVAL_1(+(x[2], y[2]), y[2], z[2]) & (U^Increasing(EVAL_1(+(x[3], y[3]), y[3], z[3])), >=))
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
5.75/2.50	
5.75/2.50	(3)    (y[2] + [-1] >= 0 & y[2] + [-1] + [-1]x[2] >= 0 & z[2] + [-1] + [-1]y[2] >= 0  ==>  (U^Increasing(EVAL_1(+(x[3], y[3]), y[3], z[3])), >=) & [(-1)bni_23 + (-1)Bound*bni_23] + [bni_23]z[2] + [(-1)bni_23]y[2] + [(-1)bni_23]x[2] >= 0 & [(-1)bso_24] >= 0)
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
5.75/2.50	
5.75/2.50	(4)    (y[2] + [-1] >= 0 & y[2] + [-1] + [-1]x[2] >= 0 & z[2] + [-1] + [-1]y[2] >= 0  ==>  (U^Increasing(EVAL_1(+(x[3], y[3]), y[3], z[3])), >=) & [(-1)bni_23 + (-1)Bound*bni_23] + [bni_23]z[2] + [(-1)bni_23]y[2] + [(-1)bni_23]x[2] >= 0 & [(-1)bso_24] >= 0)
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
5.75/2.50	
5.75/2.50	(5)    (y[2] + [-1] >= 0 & y[2] + [-1] + [-1]x[2] >= 0 & z[2] + [-1] + [-1]y[2] >= 0  ==>  (U^Increasing(EVAL_1(+(x[3], y[3]), y[3], z[3])), >=) & [(-1)bni_23 + (-1)Bound*bni_23] + [bni_23]z[2] + [(-1)bni_23]y[2] + [(-1)bni_23]x[2] >= 0 & [(-1)bso_24] >= 0)
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	We simplified constraint (5) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
5.75/2.50	
5.75/2.50	(6)    (y[2] + [-1] >= 0 & y[2] + [-1] + x[2] >= 0 & z[2] + [-1] + [-1]y[2] >= 0 & x[2] >= 0  ==>  (U^Increasing(EVAL_1(+(x[3], y[3]), y[3], z[3])), >=) & [(-1)bni_23 + (-1)Bound*bni_23] + [bni_23]z[2] + [(-1)bni_23]y[2] + [bni_23]x[2] >= 0 & [(-1)bso_24] >= 0)
5.75/2.50	
5.75/2.50	(7)    (y[2] + [-1] >= 0 & y[2] + [-1] + [-1]x[2] >= 0 & z[2] + [-1] + [-1]y[2] >= 0 & x[2] >= 0  ==>  (U^Increasing(EVAL_1(+(x[3], y[3]), y[3], z[3])), >=) & [(-1)bni_23 + (-1)Bound*bni_23] + [bni_23]z[2] + [(-1)bni_23]y[2] + [(-1)bni_23]x[2] >= 0 & [(-1)bso_24] >= 0)
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	*We consider the chain EVAL_1(x[2], y[2], z[2]) -> COND_EVAL_1(&&(&&(>(y[2], x[2]), >(z[2], y[2])), >(y[2], 0)), x[2], y[2], z[2]), COND_EVAL_1(TRUE, x[3], y[3], z[3]) -> EVAL_1(+(x[3], y[3]), y[3], z[3]), EVAL_1(x[4], y[4], z[4]) -> COND_EVAL_11(&&(&&(>(y[4], x[4]), >(z[4], y[4])), >(y[4], 0)), x[4], y[4], z[4]) which results in the following constraint:
5.75/2.50	
5.75/2.50	(1)    (&&(&&(>(y[2], x[2]), >(z[2], y[2])), >(y[2], 0))=TRUE & x[2]=x[3] & y[2]=y[3] & z[2]=z[3] & +(x[3], y[3])=x[4] & y[3]=y[4] & z[3]=z[4]  ==>  COND_EVAL_1(TRUE, x[3], y[3], z[3])_>=_NonInfC & COND_EVAL_1(TRUE, x[3], y[3], z[3])_>=_EVAL_1(+(x[3], y[3]), y[3], z[3]) & (U^Increasing(EVAL_1(+(x[3], y[3]), y[3], z[3])), >=))
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	We simplified constraint (1) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
5.75/2.50	
5.75/2.50	(2)    (>(y[2], 0)=TRUE & >(y[2], x[2])=TRUE & >(z[2], y[2])=TRUE  ==>  COND_EVAL_1(TRUE, x[2], y[2], z[2])_>=_NonInfC & COND_EVAL_1(TRUE, x[2], y[2], z[2])_>=_EVAL_1(+(x[2], y[2]), y[2], z[2]) & (U^Increasing(EVAL_1(+(x[3], y[3]), y[3], z[3])), >=))
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
5.75/2.50	
5.75/2.50	(3)    (y[2] + [-1] >= 0 & y[2] + [-1] + [-1]x[2] >= 0 & z[2] + [-1] + [-1]y[2] >= 0  ==>  (U^Increasing(EVAL_1(+(x[3], y[3]), y[3], z[3])), >=) & [(-1)bni_23 + (-1)Bound*bni_23] + [bni_23]z[2] + [(-1)bni_23]y[2] + [(-1)bni_23]x[2] >= 0 & [(-1)bso_24] >= 0)
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
5.75/2.50	
5.75/2.50	(4)    (y[2] + [-1] >= 0 & y[2] + [-1] + [-1]x[2] >= 0 & z[2] + [-1] + [-1]y[2] >= 0  ==>  (U^Increasing(EVAL_1(+(x[3], y[3]), y[3], z[3])), >=) & [(-1)bni_23 + (-1)Bound*bni_23] + [bni_23]z[2] + [(-1)bni_23]y[2] + [(-1)bni_23]x[2] >= 0 & [(-1)bso_24] >= 0)
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
5.75/2.50	
5.75/2.50	(5)    (y[2] + [-1] >= 0 & y[2] + [-1] + [-1]x[2] >= 0 & z[2] + [-1] + [-1]y[2] >= 0  ==>  (U^Increasing(EVAL_1(+(x[3], y[3]), y[3], z[3])), >=) & [(-1)bni_23 + (-1)Bound*bni_23] + [bni_23]z[2] + [(-1)bni_23]y[2] + [(-1)bni_23]x[2] >= 0 & [(-1)bso_24] >= 0)
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	We simplified constraint (5) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
5.75/2.50	
5.75/2.50	(6)    (y[2] + [-1] >= 0 & y[2] + [-1] + [-1]x[2] >= 0 & z[2] + [-1] + [-1]y[2] >= 0 & x[2] >= 0  ==>  (U^Increasing(EVAL_1(+(x[3], y[3]), y[3], z[3])), >=) & [(-1)bni_23 + (-1)Bound*bni_23] + [bni_23]z[2] + [(-1)bni_23]y[2] + [(-1)bni_23]x[2] >= 0 & [(-1)bso_24] >= 0)
5.75/2.50	
5.75/2.50	(7)    (y[2] + [-1] >= 0 & y[2] + [-1] + x[2] >= 0 & z[2] + [-1] + [-1]y[2] >= 0 & x[2] >= 0  ==>  (U^Increasing(EVAL_1(+(x[3], y[3]), y[3], z[3])), >=) & [(-1)bni_23 + (-1)Bound*bni_23] + [bni_23]z[2] + [(-1)bni_23]y[2] + [bni_23]x[2] >= 0 & [(-1)bso_24] >= 0)
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	For Pair EVAL_1(x[2], y[2], z[2]) -> COND_EVAL_1(&&(&&(>(y[2], x[2]), >(z[2], y[2])), >(y[2], 0)), x[2], y[2], z[2]) the following chains were created:
5.75/2.50	*We consider the chain EVAL_1(x[2], y[2], z[2]) -> COND_EVAL_1(&&(&&(>(y[2], x[2]), >(z[2], y[2])), >(y[2], 0)), x[2], y[2], z[2]), COND_EVAL_1(TRUE, x[3], y[3], z[3]) -> EVAL_1(+(x[3], y[3]), y[3], z[3]) which results in the following constraint:
5.75/2.50	
5.75/2.50	(1)    (&&(&&(>(y[2], x[2]), >(z[2], y[2])), >(y[2], 0))=TRUE & x[2]=x[3] & y[2]=y[3] & z[2]=z[3]  ==>  EVAL_1(x[2], y[2], z[2])_>=_NonInfC & EVAL_1(x[2], y[2], z[2])_>=_COND_EVAL_1(&&(&&(>(y[2], x[2]), >(z[2], y[2])), >(y[2], 0)), x[2], y[2], z[2]) & (U^Increasing(COND_EVAL_1(&&(&&(>(y[2], x[2]), >(z[2], y[2])), >(y[2], 0)), x[2], y[2], z[2])), >=))
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	We simplified constraint (1) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:
5.75/2.50	
5.75/2.50	(2)    (>(y[2], 0)=TRUE & >(y[2], x[2])=TRUE & >(z[2], y[2])=TRUE  ==>  EVAL_1(x[2], y[2], z[2])_>=_NonInfC & EVAL_1(x[2], y[2], z[2])_>=_COND_EVAL_1(&&(&&(>(y[2], x[2]), >(z[2], y[2])), >(y[2], 0)), x[2], y[2], z[2]) & (U^Increasing(COND_EVAL_1(&&(&&(>(y[2], x[2]), >(z[2], y[2])), >(y[2], 0)), x[2], y[2], z[2])), >=))
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
5.75/2.50	
5.75/2.50	(3)    (y[2] + [-1] >= 0 & y[2] + [-1] + [-1]x[2] >= 0 & z[2] + [-1] + [-1]y[2] >= 0  ==>  (U^Increasing(COND_EVAL_1(&&(&&(>(y[2], x[2]), >(z[2], y[2])), >(y[2], 0)), x[2], y[2], z[2])), >=) & [(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]z[2] + [(-1)bni_25]x[2] >= 0 & [(-1)bso_26] + y[2] >= 0)
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
5.75/2.50	
5.75/2.50	(4)    (y[2] + [-1] >= 0 & y[2] + [-1] + [-1]x[2] >= 0 & z[2] + [-1] + [-1]y[2] >= 0  ==>  (U^Increasing(COND_EVAL_1(&&(&&(>(y[2], x[2]), >(z[2], y[2])), >(y[2], 0)), x[2], y[2], z[2])), >=) & [(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]z[2] + [(-1)bni_25]x[2] >= 0 & [(-1)bso_26] + y[2] >= 0)
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
5.75/2.50	
5.75/2.50	(5)    (y[2] + [-1] >= 0 & y[2] + [-1] + [-1]x[2] >= 0 & z[2] + [-1] + [-1]y[2] >= 0  ==>  (U^Increasing(COND_EVAL_1(&&(&&(>(y[2], x[2]), >(z[2], y[2])), >(y[2], 0)), x[2], y[2], z[2])), >=) & [(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]z[2] + [(-1)bni_25]x[2] >= 0 & [(-1)bso_26] + y[2] >= 0)
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	We simplified constraint (5) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
5.75/2.50	
5.75/2.50	(6)    (y[2] + [-1] >= 0 & y[2] + [-1] + [-1]x[2] >= 0 & z[2] + [-1] + [-1]y[2] >= 0 & x[2] >= 0  ==>  (U^Increasing(COND_EVAL_1(&&(&&(>(y[2], x[2]), >(z[2], y[2])), >(y[2], 0)), x[2], y[2], z[2])), >=) & [(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]z[2] + [(-1)bni_25]x[2] >= 0 & [(-1)bso_26] + y[2] >= 0)
5.75/2.50	
5.75/2.50	(7)    (y[2] + [-1] >= 0 & y[2] + [-1] + x[2] >= 0 & z[2] + [-1] + [-1]y[2] >= 0 & x[2] >= 0  ==>  (U^Increasing(COND_EVAL_1(&&(&&(>(y[2], x[2]), >(z[2], y[2])), >(y[2], 0)), x[2], y[2], z[2])), >=) & [(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]z[2] + [bni_25]x[2] >= 0 & [(-1)bso_26] + y[2] >= 0)
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	To summarize, we get the following constraints P__>=_ for the following pairs.
5.75/2.50	
5.75/2.50	*COND_EVAL_11(TRUE, x[5], y[5], z[5]) -> EVAL_1(x[5], y[5], -(x[5], y[5]))
5.75/2.50	
5.75/2.50	*(y[4] + [-1] >= 0 & y[4] + [-1] + [-1]x[4] >= 0 & z[4] + [-1] + [-1]y[4] >= 0 & x[4] >= 0  ==>  (U^Increasing(EVAL_1(x[5], y[5], -(x[5], y[5]))), >=) & [(-1)bni_19 + (-1)Bound*bni_19] + [(-1)bni_19]x[4] >= 0 & [(-1)bso_20] + y[4] + [-1]x[4] >= 0)
5.75/2.50	
5.75/2.50	
5.75/2.50	*(y[4] + [-1] >= 0 & y[4] + [-1] + x[4] >= 0 & z[4] + [-1] + [-1]y[4] >= 0 & x[4] >= 0  ==>  (U^Increasing(EVAL_1(x[5], y[5], -(x[5], y[5]))), >=) & [(-1)bni_19 + (-1)Bound*bni_19] + [bni_19]x[4] >= 0 & [(-1)bso_20] + y[4] + x[4] >= 0)
5.75/2.50	
5.75/2.50	
5.75/2.50	*(y[4] + [-1] >= 0 & y[4] + [-1] + [-1]x[4] >= 0 & z[4] + [-1] + [-1]y[4] >= 0 & x[4] >= 0  ==>  (U^Increasing(EVAL_1(x[5], y[5], -(x[5], y[5]))), >=) & [(-1)bni_19 + (-1)Bound*bni_19] + [(-1)bni_19]x[4] >= 0 & [(-1)bso_20] + y[4] + [-1]x[4] >= 0)
5.75/2.50	
5.75/2.50	
5.75/2.50	*(y[4] + [-1] >= 0 & y[4] + [-1] + x[4] >= 0 & z[4] + [-1] + [-1]y[4] >= 0 & x[4] >= 0  ==>  (U^Increasing(EVAL_1(x[5], y[5], -(x[5], y[5]))), >=) & [(-1)bni_19 + (-1)Bound*bni_19] + [bni_19]x[4] >= 0 & [(-1)bso_20] + y[4] + x[4] >= 0)
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	*EVAL_1(x[4], y[4], z[4]) -> COND_EVAL_11(&&(&&(>(y[4], x[4]), >(z[4], y[4])), >(y[4], 0)), x[4], y[4], z[4])
5.75/2.50	
5.75/2.50	*(y[4] + [-1] >= 0 & y[4] + [-1] + [-1]x[4] >= 0 & z[4] + [-1] + [-1]y[4] >= 0 & x[4] >= 0  ==>  (U^Increasing(COND_EVAL_11(&&(&&(>(y[4], x[4]), >(z[4], y[4])), >(y[4], 0)), x[4], y[4], z[4])), >=) & [(-1)bni_21 + (-1)Bound*bni_21] + [bni_21]z[4] + [(-1)bni_21]x[4] >= 0 & [(-1)bso_22] + z[4] >= 0)
5.75/2.50	
5.75/2.50	
5.75/2.50	*(y[4] + [-1] >= 0 & y[4] + [-1] + x[4] >= 0 & z[4] + [-1] + [-1]y[4] >= 0 & x[4] >= 0  ==>  (U^Increasing(COND_EVAL_11(&&(&&(>(y[4], x[4]), >(z[4], y[4])), >(y[4], 0)), x[4], y[4], z[4])), >=) & [(-1)bni_21 + (-1)Bound*bni_21] + [bni_21]z[4] + [bni_21]x[4] >= 0 & [(-1)bso_22] + z[4] >= 0)
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	*COND_EVAL_1(TRUE, x[3], y[3], z[3]) -> EVAL_1(+(x[3], y[3]), y[3], z[3])
5.75/2.50	
5.75/2.50	*(y[2] + [-1] >= 0 & y[2] + [-1] + x[2] >= 0 & z[2] + [-1] + [-1]y[2] >= 0 & x[2] >= 0  ==>  (U^Increasing(EVAL_1(+(x[3], y[3]), y[3], z[3])), >=) & [(-1)bni_23 + (-1)Bound*bni_23] + [bni_23]z[2] + [(-1)bni_23]y[2] + [bni_23]x[2] >= 0 & [(-1)bso_24] >= 0)
5.75/2.50	
5.75/2.50	
5.75/2.50	*(y[2] + [-1] >= 0 & y[2] + [-1] + [-1]x[2] >= 0 & z[2] + [-1] + [-1]y[2] >= 0 & x[2] >= 0  ==>  (U^Increasing(EVAL_1(+(x[3], y[3]), y[3], z[3])), >=) & [(-1)bni_23 + (-1)Bound*bni_23] + [bni_23]z[2] + [(-1)bni_23]y[2] + [(-1)bni_23]x[2] >= 0 & [(-1)bso_24] >= 0)
5.75/2.50	
5.75/2.50	
5.75/2.50	*(y[2] + [-1] >= 0 & y[2] + [-1] + [-1]x[2] >= 0 & z[2] + [-1] + [-1]y[2] >= 0 & x[2] >= 0  ==>  (U^Increasing(EVAL_1(+(x[3], y[3]), y[3], z[3])), >=) & [(-1)bni_23 + (-1)Bound*bni_23] + [bni_23]z[2] + [(-1)bni_23]y[2] + [(-1)bni_23]x[2] >= 0 & [(-1)bso_24] >= 0)
5.75/2.50	
5.75/2.50	
5.75/2.50	*(y[2] + [-1] >= 0 & y[2] + [-1] + x[2] >= 0 & z[2] + [-1] + [-1]y[2] >= 0 & x[2] >= 0  ==>  (U^Increasing(EVAL_1(+(x[3], y[3]), y[3], z[3])), >=) & [(-1)bni_23 + (-1)Bound*bni_23] + [bni_23]z[2] + [(-1)bni_23]y[2] + [bni_23]x[2] >= 0 & [(-1)bso_24] >= 0)
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	*EVAL_1(x[2], y[2], z[2]) -> COND_EVAL_1(&&(&&(>(y[2], x[2]), >(z[2], y[2])), >(y[2], 0)), x[2], y[2], z[2])
5.75/2.50	
5.75/2.50	*(y[2] + [-1] >= 0 & y[2] + [-1] + [-1]x[2] >= 0 & z[2] + [-1] + [-1]y[2] >= 0 & x[2] >= 0  ==>  (U^Increasing(COND_EVAL_1(&&(&&(>(y[2], x[2]), >(z[2], y[2])), >(y[2], 0)), x[2], y[2], z[2])), >=) & [(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]z[2] + [(-1)bni_25]x[2] >= 0 & [(-1)bso_26] + y[2] >= 0)
5.75/2.50	
5.75/2.50	
5.75/2.50	*(y[2] + [-1] >= 0 & y[2] + [-1] + x[2] >= 0 & z[2] + [-1] + [-1]y[2] >= 0 & x[2] >= 0  ==>  (U^Increasing(COND_EVAL_1(&&(&&(>(y[2], x[2]), >(z[2], y[2])), >(y[2], 0)), x[2], y[2], z[2])), >=) & [(-1)bni_25 + (-1)Bound*bni_25] + [bni_25]z[2] + [bni_25]x[2] >= 0 & [(-1)bso_26] + y[2] >= 0)
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	
5.75/2.50	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. 
5.75/2.50	
5.75/2.50	Using the following integer polynomial ordering the  resulting constraints can be solved 
5.75/2.50	
5.75/2.50	Polynomial interpretation over integers[POLO]:
5.75/2.50	
5.75/2.50	   POL(TRUE) = 0
5.75/2.50	   POL(FALSE) = [1]
5.75/2.50	   POL(COND_EVAL_11(x_1, x_2, x_3, x_4)) = [-1] + [-1]x_2
5.75/2.50	   POL(EVAL_1(x_1, x_2, x_3)) = [-1] + x_3 + [-1]x_1
5.75/2.50	   POL(-(x_1, x_2)) = x_1 + [-1]x_2
5.75/2.50	   POL(&&(x_1, x_2)) = [-1]
5.75/2.50	   POL(>(x_1, x_2)) = [-1]
5.75/2.50	   POL(0) = 0
5.75/2.50	   POL(COND_EVAL_1(x_1, x_2, x_3, x_4)) = [-1] + x_4 + [-1]x_3 + [-1]x_2
5.75/2.50	   POL(+(x_1, x_2)) = x_1 + x_2
5.75/2.50	
5.75/2.50	
5.75/2.50	The following pairs are in P_>:
5.75/2.50	
5.75/2.50	
5.75/2.50	   COND_EVAL_11(TRUE, x[5], y[5], z[5]) -> EVAL_1(x[5], y[5], -(x[5], y[5]))
5.75/2.50	   EVAL_1(x[4], y[4], z[4]) -> COND_EVAL_11(&&(&&(>(y[4], x[4]), >(z[4], y[4])), >(y[4], 0)), x[4], y[4], z[4])
5.75/2.50	   EVAL_1(x[2], y[2], z[2]) -> COND_EVAL_1(&&(&&(>(y[2], x[2]), >(z[2], y[2])), >(y[2], 0)), x[2], y[2], z[2])
5.75/2.50	
5.75/2.50	
5.75/2.50	The following pairs are in P_bound:
5.75/2.50	
5.75/2.50	
5.75/2.50	   EVAL_1(x[4], y[4], z[4]) -> COND_EVAL_11(&&(&&(>(y[4], x[4]), >(z[4], y[4])), >(y[4], 0)), x[4], y[4], z[4])
5.75/2.50	   EVAL_1(x[2], y[2], z[2]) -> COND_EVAL_1(&&(&&(>(y[2], x[2]), >(z[2], y[2])), >(y[2], 0)), x[2], y[2], z[2])
5.75/2.50	
5.75/2.50	
5.75/2.50	The following pairs are in P_>=:
5.75/2.50	
5.75/2.50	
5.75/2.50	   COND_EVAL_1(TRUE, x[3], y[3], z[3]) -> EVAL_1(+(x[3], y[3]), y[3], z[3])
5.75/2.50	
5.75/2.50	
5.75/2.50	At least the following rules have been oriented under context sensitive arithmetic replacement:
5.75/2.50	
5.75/2.50	   TRUE^1 -> &&(TRUE, TRUE)^1
5.75/2.50	   FALSE^1 -> &&(TRUE, FALSE)^1
5.75/2.50	   FALSE^1 -> &&(FALSE, TRUE)^1
5.75/2.50	   FALSE^1 -> &&(FALSE, FALSE)^1
5.75/2.50	
5.75/2.50	----------------------------------------
5.75/2.50	
5.75/2.50	(8)
5.75/2.50	Obligation:
5.75/2.50	IDP problem:
5.75/2.50	The following function symbols are pre-defined:
5.75/2.50	<<<
5.75/2.50	 & 	~ 	Bwand: (Integer, Integer) -> Integer
5.75/2.50	 >= 	~ 	Ge: (Integer, Integer) -> Boolean
5.75/2.50	 | 	~ 	Bwor: (Integer, Integer) -> Integer
5.75/2.50	 / 	~ 	Div: (Integer, Integer) -> Integer
5.75/2.50	 != 	~ 	Neq: (Integer, Integer) -> Boolean
5.75/2.50	 && 	~ 	Land: (Boolean, Boolean) -> Boolean
5.75/2.50	 ! 	~ 	Lnot: (Boolean) -> Boolean
5.75/2.50	 = 	~ 	Eq: (Integer, Integer) -> Boolean
5.75/2.50	 <= 	~ 	Le: (Integer, Integer) -> Boolean
5.75/2.50	 ^ 	~ 	Bwxor: (Integer, Integer) -> Integer
5.75/2.50	 % 	~ 	Mod: (Integer, Integer) -> Integer
5.75/2.50	 > 	~ 	Gt: (Integer, Integer) -> Boolean
5.75/2.50	 + 	~ 	Add: (Integer, Integer) -> Integer
5.75/2.50	 -1 	~ 	UnaryMinus: (Integer) -> Integer
5.75/2.50	 < 	~ 	Lt: (Integer, Integer) -> Boolean
5.75/2.50	 || 	~ 	Lor: (Boolean, Boolean) -> Boolean
5.75/2.50	 - 	~ 	Sub: (Integer, Integer) -> Integer
5.75/2.50	 ~ 	~ 	Bwnot: (Integer) -> Integer
5.75/2.50	 * 	~ 	Mul: (Integer, Integer) -> Integer
5.75/2.50	>>>
5.75/2.50	
5.75/2.50	
5.75/2.50	The following domains are used:
5.75/2.50	   Integer
5.75/2.50	
5.75/2.50	R is empty.
5.75/2.50	
5.75/2.50	The integer pair graph contains the following rules and edges:
5.75/2.50	(5): COND_EVAL_11(TRUE, x[5], y[5], z[5]) -> EVAL_1(x[5], y[5], x[5] - y[5])
5.75/2.50	(3): COND_EVAL_1(TRUE, x[3], y[3], z[3]) -> EVAL_1(x[3] + y[3], y[3], z[3])
5.75/2.50	
5.75/2.50	
5.75/2.50	The set Q consists of the following terms:
5.75/2.50	eval_0(x0, x1, x2)
5.75/2.50	Cond_eval_0(TRUE, x0, x1, x2)
5.75/2.50	eval_1(x0, x1, x2)
5.75/2.50	Cond_eval_1(TRUE, x0, x1, x2)
5.75/2.50	Cond_eval_11(TRUE, x0, x1, x2)
5.75/2.50	
5.75/2.50	----------------------------------------
5.75/2.50	
5.75/2.50	(9) IDependencyGraphProof (EQUIVALENT)
5.75/2.50	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 2 less nodes.
5.75/2.50	----------------------------------------
5.75/2.50	
5.75/2.50	(10)
5.75/2.50	TRUE
5.75/2.53	EOF