2.05/1.56	WORST_CASE(?, O(n^2))
2.05/1.57	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.05/1.57	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.05/1.57	
2.05/1.57	
2.05/1.57	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2).
2.05/1.57	
2.05/1.57	(0) CpxIntTrs
2.05/1.57	(1) Koat Proof [FINISHED, 378 ms]
2.05/1.57	(2) BOUNDS(1, n^2)
2.05/1.57	
2.05/1.57	
2.05/1.57	----------------------------------------
2.05/1.57	
2.05/1.57	(0)
2.05/1.57	Obligation:
2.05/1.57	Complexity Int TRS consisting of the following rules:
2.05/1.57	eval_foo_start(v_.0, v_.01, v_i, v_j, v_k, v_n) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_i, v_j, v_k, v_n)) :|: TRUE
2.05/1.57	eval_foo_bb0_in(v_.0, v_.01, v_i, v_j, v_k, v_n) -> Com_1(eval_foo_bb1_in(0, v_.01, v_i, v_j, v_k, v_n)) :|: v_k >= 1
2.05/1.57	eval_foo_bb0_in(v_.0, v_.01, v_i, v_j, v_k, v_n) -> Com_1(eval_foo_bb5_in(v_.0, v_.01, v_i, v_j, v_k, v_n)) :|: v_k < 1
2.05/1.57	eval_foo_bb1_in(v_.0, v_.01, v_i, v_j, v_k, v_n) -> Com_1(eval_foo_bb2_in(v_.0, 0, v_i, v_j, v_k, v_n)) :|: v_.0 < v_n
2.05/1.57	eval_foo_bb1_in(v_.0, v_.01, v_i, v_j, v_k, v_n) -> Com_1(eval_foo_bb5_in(v_.0, v_.01, v_i, v_j, v_k, v_n)) :|: v_.0 >= v_n
2.05/1.57	eval_foo_bb2_in(v_.0, v_.01, v_i, v_j, v_k, v_n) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_i, v_j, v_k, v_n)) :|: v_.01 <= v_.0
2.05/1.57	eval_foo_bb2_in(v_.0, v_.01, v_i, v_j, v_k, v_n) -> Com_1(eval_foo_bb4_in(v_.0, v_.01, v_i, v_j, v_k, v_n)) :|: v_.01 > v_.0
2.05/1.57	eval_foo_bb3_in(v_.0, v_.01, v_i, v_j, v_k, v_n) -> Com_1(eval_foo_bb2_in(v_.0, v_.01 + v_k, v_i, v_j, v_k, v_n)) :|: TRUE
2.05/1.57	eval_foo_bb4_in(v_.0, v_.01, v_i, v_j, v_k, v_n) -> Com_1(eval_foo_bb1_in(v_.0 + 1, v_.01, v_i, v_j, v_k, v_n)) :|: TRUE
2.05/1.57	eval_foo_bb5_in(v_.0, v_.01, v_i, v_j, v_k, v_n) -> Com_1(eval_foo_stop(v_.0, v_.01, v_i, v_j, v_k, v_n)) :|: TRUE
2.05/1.57	
2.05/1.57	The start-symbols are:[eval_foo_start_6]
2.05/1.57	
2.05/1.57	
2.05/1.57	----------------------------------------
2.05/1.57	
2.05/1.57	(1) Koat Proof (FINISHED)
2.05/1.57	YES(?, 9*ar_2 + 4*ar_0*ar_2 + 4*ar_2^2 + 4*ar_0 + 12)
2.05/1.57	
2.05/1.57	
2.05/1.57	
2.05/1.57	Initial complexity problem:
2.05/1.57	
2.05/1.57	1:	T:
2.05/1.57	
2.05/1.57			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.05/1.57	
2.05/1.57			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, 0, ar_2, ar_3)) [ ar_0 >= 1 ]
2.05/1.57	
2.05/1.57			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.05/1.57	
2.05/1.57			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, 0)) [ ar_2 >= ar_1 + 1 ]
2.05/1.57	
2.05/1.57			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ]
2.05/1.57	
2.05/1.57			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 ]
2.05/1.57	
2.05/1.57			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 ]
2.05/1.57	
2.05/1.57			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 + ar_0))
2.05/1.57	
2.05/1.57			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1 + 1, ar_2, ar_3))
2.05/1.57	
2.05/1.57			(Comp: ?, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.05/1.57	
2.05/1.57			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.05/1.57	
2.05/1.57		start location:	koat_start
2.05/1.57	
2.05/1.57		leaf cost:	0
2.05/1.57	
2.05/1.57	
2.05/1.57	
2.05/1.57	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.05/1.57	
2.05/1.57	2:	T:
2.05/1.57	
2.05/1.57			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.05/1.57	
2.05/1.57			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, 0, ar_2, ar_3)) [ ar_0 >= 1 ]
2.05/1.57	
2.05/1.57			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.05/1.57	
2.05/1.57			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, 0)) [ ar_2 >= ar_1 + 1 ]
2.05/1.57	
2.05/1.57			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ]
2.05/1.57	
2.05/1.57			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 ]
2.05/1.57	
2.05/1.57			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 ]
2.05/1.58	
2.05/1.58			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 + ar_0))
2.05/1.58	
2.05/1.58			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1 + 1, ar_2, ar_3))
2.05/1.58	
2.05/1.58			(Comp: ?, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.05/1.58	
2.05/1.58			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.05/1.58	
2.05/1.58		start location:	koat_start
2.05/1.58	
2.05/1.58		leaf cost:	0
2.05/1.58	
2.05/1.58	
2.05/1.58	
2.05/1.58	A polynomial rank function with
2.05/1.58	
2.05/1.58		Pol(evalfoostart) = 2
2.05/1.58	
2.05/1.58		Pol(evalfoobb0in) = 2
2.05/1.58	
2.05/1.58		Pol(evalfoobb1in) = 2
2.05/1.58	
2.05/1.58		Pol(evalfoobb5in) = 1
2.05/1.58	
2.05/1.58		Pol(evalfoobb2in) = 2
2.05/1.58	
2.05/1.58		Pol(evalfoobb3in) = 2
2.05/1.58	
2.05/1.58		Pol(evalfoobb4in) = 2
2.05/1.58	
2.05/1.58		Pol(evalfoostop) = 0
2.05/1.58	
2.05/1.58		Pol(koat_start) = 2
2.05/1.58	
2.05/1.58	orients all transitions weakly and the transitions
2.05/1.58	
2.05/1.58		evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.05/1.58	
2.05/1.58		evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ]
2.05/1.58	
2.05/1.58	strictly and produces the following problem:
2.05/1.58	
2.05/1.58	3:	T:
2.05/1.58	
2.05/1.58			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.05/1.58	
2.05/1.58			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, 0, ar_2, ar_3)) [ ar_0 >= 1 ]
2.05/1.58	
2.05/1.58			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.05/1.58	
2.05/1.58			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, 0)) [ ar_2 >= ar_1 + 1 ]
2.05/1.58	
2.05/1.58			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ]
2.05/1.58	
2.05/1.58			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 ]
2.05/1.58	
2.05/1.58			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 ]
2.05/1.58	
2.05/1.58			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 + ar_0))
2.05/1.58	
2.05/1.58			(Comp: ?, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1 + 1, ar_2, ar_3))
2.05/1.58	
2.05/1.58			(Comp: 2, Cost: 1)    evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.05/1.58	
2.05/1.58			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.05/1.58	
2.05/1.58		start location:	koat_start
2.05/1.58	
2.05/1.58		leaf cost:	0
2.05/1.58	
2.05/1.58	
2.05/1.58	
2.05/1.58	A polynomial rank function with
2.05/1.58	
2.05/1.58		Pol(evalfoobb4in) = -V_2 + V_3
2.05/1.58	
2.05/1.58		Pol(evalfoobb1in) = -V_2 + V_3 + 1
2.05/1.58	
2.05/1.58		Pol(evalfoobb3in) = -V_2 + V_3
2.05/1.58	
2.05/1.58		Pol(evalfoobb2in) = -V_2 + V_3
2.05/1.58	
2.05/1.58	and size complexities
2.05/1.58	
2.05/1.58		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
2.05/1.58	
2.05/1.58		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
2.05/1.58	
2.05/1.58		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
2.05/1.58	
2.05/1.58		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
2.05/1.58	
2.05/1.58		S("evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
2.05/1.58	
2.05/1.58		S("evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ?
2.05/1.58	
2.05/1.58		S("evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
2.05/1.58	
2.05/1.58		S("evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ?
2.05/1.58	
2.05/1.58		S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1 + 1, ar_2, ar_3))", 0-0) = ar_0
2.05/1.58	
2.05/1.58		S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1 + 1, ar_2, ar_3))", 0-1) = ?
2.05/1.58	
2.05/1.58		S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1 + 1, ar_2, ar_3))", 0-2) = ar_2
2.05/1.58	
2.05/1.58		S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1 + 1, ar_2, ar_3))", 0-3) = ?
2.05/1.58	
2.05/1.58		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 + ar_0))", 0-0) = ar_0
2.05/1.58	
2.05/1.58		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 + ar_0))", 0-1) = ?
2.05/1.58	
2.05/1.58		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 + ar_0))", 0-2) = ar_2
2.05/1.58	
2.05/1.58		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 + ar_0))", 0-3) = ?
2.05/1.58	
2.05/1.58		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 ]", 0-0) = ar_0
2.05/1.58	
2.05/1.58		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 ]", 0-1) = ?
2.05/1.58	
2.05/1.58		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 ]", 0-2) = ar_2
2.05/1.58	
2.05/1.58		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 ]", 0-3) = ?
2.05/1.58	
2.05/1.58		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 ]", 0-0) = ar_0
2.05/1.58	
2.05/1.58		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 ]", 0-1) = ?
2.05/1.58	
2.05/1.58		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 ]", 0-2) = ar_2
2.05/1.58	
2.05/1.58		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 ]", 0-3) = ?
2.05/1.58	
2.05/1.58		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ]", 0-0) = ar_0
2.05/1.58	
2.05/1.58		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ]", 0-1) = ?
2.05/1.58	
2.05/1.58		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ]", 0-2) = ar_2
2.05/1.58	
2.05/1.58		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ]", 0-3) = ?
2.05/1.58	
2.05/1.58		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, 0)) [ ar_2 >= ar_1 + 1 ]", 0-0) = ar_0
2.05/1.58	
2.05/1.58		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, 0)) [ ar_2 >= ar_1 + 1 ]", 0-1) = ?
2.05/1.58	
2.05/1.58		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, 0)) [ ar_2 >= ar_1 + 1 ]", 0-2) = ar_2
2.05/1.58	
2.05/1.58		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, 0)) [ ar_2 >= ar_1 + 1 ]", 0-3) = 0
2.05/1.58	
2.05/1.58		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-0) = ar_0
2.05/1.58	
2.05/1.58		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-1) = ar_1
2.05/1.58	
2.05/1.58		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-2) = ar_2
2.05/1.58	
2.05/1.58		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-3) = ar_3
2.05/1.58	
2.05/1.58		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, 0, ar_2, ar_3)) [ ar_0 >= 1 ]", 0-0) = ar_0
2.05/1.58	
2.05/1.58		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, 0, ar_2, ar_3)) [ ar_0 >= 1 ]", 0-1) = 0
2.05/1.58	
2.05/1.58		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, 0, ar_2, ar_3)) [ ar_0 >= 1 ]", 0-2) = ar_2
2.05/1.58	
2.05/1.58		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, 0, ar_2, ar_3)) [ ar_0 >= 1 ]", 0-3) = ar_3
2.05/1.58	
2.05/1.58		S("evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
2.05/1.58	
2.05/1.58		S("evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.05/1.58	
2.05/1.58		S("evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
2.05/1.58	
2.05/1.58		S("evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
2.05/1.58	
2.05/1.58	orients the transitions
2.05/1.58	
2.05/1.58		evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1 + 1, ar_2, ar_3))
2.05/1.58	
2.05/1.58		evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 + ar_0))
2.05/1.58	
2.05/1.58		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 ]
2.05/1.58	
2.05/1.58		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 ]
2.05/1.58	
2.05/1.58		evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, 0)) [ ar_2 >= ar_1 + 1 ]
2.05/1.58	
2.05/1.58	weakly and the transition
2.05/1.58	
2.05/1.58		evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, 0)) [ ar_2 >= ar_1 + 1 ]
2.05/1.58	
2.05/1.58	strictly and produces the following problem:
2.05/1.58	
2.05/1.58	4:	T:
2.05/1.58	
2.05/1.58			(Comp: 1, Cost: 1)           evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.05/1.58	
2.05/1.58			(Comp: 1, Cost: 1)           evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, 0, ar_2, ar_3)) [ ar_0 >= 1 ]
2.05/1.58	
2.05/1.58			(Comp: 1, Cost: 1)           evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.05/1.58	
2.05/1.58			(Comp: ar_2 + 1, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, 0)) [ ar_2 >= ar_1 + 1 ]
2.05/1.58	
2.05/1.58			(Comp: 2, Cost: 1)           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ]
2.05/1.58	
2.05/1.58			(Comp: ?, Cost: 1)           evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 ]
2.05/1.58	
2.05/1.58			(Comp: ?, Cost: 1)           evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 ]
2.05/1.58	
2.05/1.58			(Comp: ?, Cost: 1)           evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 + ar_0))
2.05/1.58	
2.05/1.58			(Comp: ?, Cost: 1)           evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1 + 1, ar_2, ar_3))
2.05/1.58	
2.05/1.58			(Comp: 2, Cost: 1)           evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.05/1.58	
2.05/1.58			(Comp: 1, Cost: 0)           koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.05/1.58	
2.05/1.58		start location:	koat_start
2.05/1.58	
2.05/1.58		leaf cost:	0
2.05/1.58	
2.05/1.58	
2.05/1.58	
2.05/1.58	A polynomial rank function with
2.05/1.58	
2.05/1.58		Pol(evalfoobb4in) = 1
2.05/1.58	
2.05/1.58		Pol(evalfoobb1in) = 0
2.05/1.58	
2.05/1.58		Pol(evalfoobb3in) = 2
2.05/1.58	
2.05/1.58		Pol(evalfoobb2in) = 2
2.05/1.58	
2.05/1.58	and size complexities
2.05/1.58	
2.05/1.58		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
2.05/1.58	
2.05/1.58		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
2.05/1.58	
2.05/1.58		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
2.05/1.58	
2.05/1.58		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
2.05/1.58	
2.05/1.58		S("evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
2.05/1.58	
2.05/1.58		S("evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ?
2.05/1.58	
2.05/1.58		S("evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
2.05/1.58	
2.05/1.58		S("evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ?
2.05/1.58	
2.05/1.58		S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1 + 1, ar_2, ar_3))", 0-0) = ar_0
2.05/1.58	
2.05/1.58		S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1 + 1, ar_2, ar_3))", 0-1) = ?
2.05/1.58	
2.05/1.58		S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1 + 1, ar_2, ar_3))", 0-2) = ar_2
2.05/1.58	
2.05/1.58		S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1 + 1, ar_2, ar_3))", 0-3) = ?
2.05/1.58	
2.05/1.58		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 + ar_0))", 0-0) = ar_0
2.05/1.58	
2.05/1.58		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 + ar_0))", 0-1) = ?
2.05/1.58	
2.05/1.58		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 + ar_0))", 0-2) = ar_2
2.05/1.58	
2.05/1.58		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 + ar_0))", 0-3) = ?
2.05/1.58	
2.05/1.58		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 ]", 0-0) = ar_0
2.05/1.58	
2.05/1.58		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 ]", 0-1) = ?
2.05/1.58	
2.05/1.58		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 ]", 0-2) = ar_2
2.05/1.58	
2.05/1.58		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 ]", 0-3) = ?
2.05/1.58	
2.05/1.58		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 ]", 0-0) = ar_0
2.05/1.58	
2.05/1.58		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 ]", 0-1) = ?
2.05/1.58	
2.05/1.58		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 ]", 0-2) = ar_2
2.05/1.58	
2.05/1.58		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 ]", 0-3) = ?
2.05/1.58	
2.05/1.58		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ]", 0-0) = ar_0
2.05/1.58	
2.05/1.58		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ]", 0-1) = ?
2.05/1.58	
2.05/1.58		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ]", 0-2) = ar_2
2.05/1.58	
2.05/1.58		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ]", 0-3) = ?
2.05/1.58	
2.05/1.58		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, 0)) [ ar_2 >= ar_1 + 1 ]", 0-0) = ar_0
2.05/1.58	
2.05/1.58		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, 0)) [ ar_2 >= ar_1 + 1 ]", 0-1) = ?
2.05/1.58	
2.05/1.58		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, 0)) [ ar_2 >= ar_1 + 1 ]", 0-2) = ar_2
2.05/1.58	
2.05/1.58		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, 0)) [ ar_2 >= ar_1 + 1 ]", 0-3) = 0
2.05/1.58	
2.05/1.58		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-0) = ar_0
2.05/1.58	
2.05/1.58		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-1) = ar_1
2.05/1.58	
2.05/1.58		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-2) = ar_2
2.05/1.58	
2.05/1.58		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-3) = ar_3
2.05/1.58	
2.05/1.58		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, 0, ar_2, ar_3)) [ ar_0 >= 1 ]", 0-0) = ar_0
2.05/1.58	
2.05/1.58		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, 0, ar_2, ar_3)) [ ar_0 >= 1 ]", 0-1) = 0
2.05/1.58	
2.05/1.58		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, 0, ar_2, ar_3)) [ ar_0 >= 1 ]", 0-2) = ar_2
2.05/1.58	
2.05/1.58		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, 0, ar_2, ar_3)) [ ar_0 >= 1 ]", 0-3) = ar_3
2.05/1.58	
2.05/1.58		S("evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
2.05/1.58	
2.05/1.58		S("evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.05/1.58	
2.05/1.58		S("evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
2.05/1.58	
2.05/1.58		S("evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
2.05/1.58	
2.05/1.58	orients the transitions
2.05/1.58	
2.05/1.58		evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1 + 1, ar_2, ar_3))
2.05/1.58	
2.05/1.58		evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 + ar_0))
2.05/1.58	
2.05/1.58		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 ]
2.05/1.58	
2.05/1.58		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 ]
2.05/1.58	
2.05/1.58	weakly and the transitions
2.05/1.58	
2.05/1.58		evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1 + 1, ar_2, ar_3))
2.05/1.58	
2.05/1.58		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 ]
2.05/1.58	
2.05/1.58	strictly and produces the following problem:
2.05/1.58	
2.05/1.58	5:	T:
2.05/1.58	
2.05/1.58			(Comp: 1, Cost: 1)             evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.05/1.58	
2.05/1.58			(Comp: 1, Cost: 1)             evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, 0, ar_2, ar_3)) [ ar_0 >= 1 ]
2.05/1.58	
2.05/1.58			(Comp: 1, Cost: 1)             evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.05/1.58	
2.05/1.58			(Comp: ar_2 + 1, Cost: 1)      evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, 0)) [ ar_2 >= ar_1 + 1 ]
2.05/1.58	
2.05/1.58			(Comp: 2, Cost: 1)             evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ]
2.05/1.58	
2.05/1.58			(Comp: ?, Cost: 1)             evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 ]
2.05/1.58	
2.05/1.58			(Comp: 2*ar_2 + 2, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_1 + 1 ]
2.05/1.58	
2.05/1.58			(Comp: ?, Cost: 1)             evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 + ar_0))
2.05/1.58	
2.05/1.58			(Comp: 2*ar_2 + 2, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1 + 1, ar_2, ar_3))
2.05/1.58	
2.05/1.58			(Comp: 2, Cost: 1)             evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.05/1.58	
2.05/1.58			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.05/1.58	
2.05/1.58		start location:	koat_start
2.05/1.58	
2.05/1.58		leaf cost:	0
2.05/1.58	
2.05/1.58	
2.05/1.58	
2.05/1.58	Applied AI with 'oct' on problem 5 to obtain the following invariants:
2.05/1.58	
2.05/1.58	  For symbol evalfoobb1in: X_2 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ X_1 - 1 >= 0
2.05/1.58	
2.05/1.58	  For symbol evalfoobb2in: X_4 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 >= 0 /\ X_1 + X_4 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ -X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 2 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ X_1 - 1 >= 0
2.05/1.58	
2.05/1.58	  For symbol evalfoobb3in: X_3 - X_4 - 1 >= 0 /\ X_2 - X_4 >= 0 /\ X_4 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 >= 0 /\ X_1 + X_4 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ -X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 2 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ X_1 - 1 >= 0
2.05/1.58	
2.05/1.58	  For symbol evalfoobb4in: X_4 - 1 >= 0 /\ X_3 + X_4 - 2 >= 0 /\ X_2 + X_4 - 1 >= 0 /\ -X_2 + X_4 - 1 >= 0 /\ X_1 + X_4 - 2 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ -X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 2 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ X_1 - 1 >= 0
2.05/1.58	
2.05/1.58	
2.05/1.58	
2.05/1.58	
2.05/1.58	
2.05/1.58	This yielded the following problem:
2.05/1.58	
2.05/1.58	6:	T:
2.05/1.58	
2.05/1.58			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.05/1.58	
2.05/1.58			(Comp: 2, Cost: 1)             evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.05/1.58	
2.05/1.58			(Comp: 2*ar_2 + 2, Cost: 1)    evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ -ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ -ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ]
2.43/1.58	
2.43/1.58			(Comp: ?, Cost: 1)             evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 + ar_0)) [ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ -ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ]
2.43/1.58	
2.43/1.58			(Comp: 2*ar_2 + 2, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ -ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= ar_1 + 1 ]
2.43/1.58	
2.43/1.58			(Comp: ?, Cost: 1)             evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ -ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_3 ]
2.43/1.58	
2.43/1.58			(Comp: 2, Cost: 1)             evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_2 ]
2.43/1.58	
2.43/1.58			(Comp: ar_2 + 1, Cost: 1)      evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, 0)) [ ar_1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 + 1 ]
2.43/1.58	
2.43/1.58			(Comp: 1, Cost: 1)             evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.43/1.58	
2.43/1.58			(Comp: 1, Cost: 1)             evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, 0, ar_2, ar_3)) [ ar_0 >= 1 ]
2.43/1.58	
2.43/1.58			(Comp: 1, Cost: 1)             evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.43/1.58	
2.43/1.58		start location:	koat_start
2.43/1.58	
2.43/1.58		leaf cost:	0
2.43/1.58	
2.43/1.58	
2.43/1.58	
2.43/1.58	A polynomial rank function with
2.43/1.58	
2.43/1.58		Pol(evalfoobb3in) = 2*V_2 - 2*V_4 + 1
2.43/1.58	
2.43/1.58		Pol(evalfoobb2in) = 2*V_1 + 2*V_2 - 2*V_4
2.43/1.58	
2.43/1.58	and size complexities
2.43/1.58	
2.43/1.58		S("evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
2.43/1.58	
2.43/1.58		S("evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.43/1.58	
2.43/1.58		S("evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
2.43/1.58	
2.43/1.58		S("evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
2.43/1.58	
2.43/1.58		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, 0, ar_2, ar_3)) [ ar_0 >= 1 ]", 0-0) = ar_0
2.43/1.58	
2.43/1.58		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, 0, ar_2, ar_3)) [ ar_0 >= 1 ]", 0-1) = 0
2.43/1.58	
2.43/1.58		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, 0, ar_2, ar_3)) [ ar_0 >= 1 ]", 0-2) = ar_2
2.43/1.58	
2.43/1.58		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, 0, ar_2, ar_3)) [ ar_0 >= 1 ]", 0-3) = ar_3
2.43/1.58	
2.43/1.58		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-0) = ar_0
2.43/1.58	
2.43/1.58		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-1) = ar_1
2.43/1.58	
2.43/1.58		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-2) = ar_2
2.43/1.58	
2.43/1.58		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-3) = ar_3
2.43/1.58	
2.43/1.58		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, 0)) [ ar_1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= ar_1 + 1 ]", 0-0) = ar_0
2.43/1.58	
2.43/1.58		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, 0)) [ ar_1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= ar_1 + 1 ]", 0-1) = ar_2
2.43/1.58	
2.43/1.58		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, 0)) [ ar_1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= ar_1 + 1 ]", 0-2) = ar_2
2.43/1.58	
2.43/1.58		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, 0)) [ ar_1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= ar_1 + 1 ]", 0-3) = 0
2.43/1.58	
2.43/1.58		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_2 ]", 0-0) = ar_0
2.43/1.58	
2.43/1.58		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_2 ]", 0-1) = ar_2
2.43/1.58	
2.43/1.58		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_2 ]", 0-2) = ar_2
2.43/1.58	
2.43/1.58		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_2 ]", 0-3) = ?
2.43/1.58	
2.43/1.58		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_3 ]", 0-0) = ar_0
2.43/1.58	
2.43/1.58		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_3 ]", 0-1) = ar_2
2.43/1.58	
2.43/1.58		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_3 ]", 0-2) = ar_2
2.43/1.58	
2.43/1.58		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_3 ]", 0-3) = ?
2.43/1.58	
2.43/1.58		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= ar_1 + 1 ]", 0-0) = ar_0
2.43/1.58	
2.43/1.58		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= ar_1 + 1 ]", 0-1) = ar_2
2.43/1.58	
2.43/1.58		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= ar_1 + 1 ]", 0-2) = ar_2
2.43/1.58	
2.43/1.58		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= ar_1 + 1 ]", 0-3) = ?
2.43/1.58	
2.43/1.58		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 + ar_0)) [ ar_2 - ar_3 - 1 >= 0 /\\ ar_1 - ar_3 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-0) = ar_0
2.43/1.58	
2.43/1.58		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 + ar_0)) [ ar_2 - ar_3 - 1 >= 0 /\\ ar_1 - ar_3 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-1) = ar_2
2.43/1.58	
2.43/1.58		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 + ar_0)) [ ar_2 - ar_3 - 1 >= 0 /\\ ar_1 - ar_3 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-2) = ar_2
2.43/1.58	
2.43/1.58		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 + ar_0)) [ ar_2 - ar_3 - 1 >= 0 /\\ ar_1 - ar_3 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-3) = ?
2.43/1.58	
2.43/1.58		S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 2 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ -ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-0) = ar_0
2.43/1.58	
2.43/1.58		S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 2 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ -ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-1) = ar_2
2.43/1.58	
2.43/1.58		S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 2 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ -ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-2) = ar_2
2.43/1.58	
2.43/1.58		S("evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 2 >= 0 /\\ ar_1 + ar_3 - 1 >= 0 /\\ -ar_1 + ar_3 - 1 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ -ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-3) = ?
2.43/1.58	
2.43/1.58		S("evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
2.43/1.58	
2.43/1.58		S("evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 + ar_2
2.43/1.58	
2.43/1.58		S("evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
2.43/1.58	
2.43/1.58		S("evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ?
2.43/1.58	
2.43/1.58		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
2.43/1.58	
2.43/1.58		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
2.43/1.58	
2.43/1.58		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
2.43/1.58	
2.43/1.58		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
2.43/1.58	
2.43/1.58	orients the transitions
2.43/1.58	
2.43/1.58		evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 + ar_0)) [ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ -ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ]
2.43/1.58	
2.43/1.58		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ -ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_3 ]
2.43/1.58	
2.43/1.58	weakly and the transitions
2.43/1.58	
2.43/1.58		evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 + ar_0)) [ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ -ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ]
2.43/1.58	
2.43/1.58		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ -ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_3 ]
2.43/1.58	
2.43/1.58	strictly and produces the following problem:
2.43/1.58	
2.43/1.58	7:	T:
2.43/1.58	
2.43/1.58			(Comp: 1, Cost: 0)                                           koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.43/1.58	
2.43/1.58			(Comp: 2, Cost: 1)                                           evalfoobb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.43/1.58	
2.43/1.58			(Comp: 2*ar_2 + 2, Cost: 1)                                  evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ -ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ -ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ]
2.43/1.58	
2.43/1.58			(Comp: 2*ar_0*ar_2 + 2*ar_2^2 + 2*ar_0 + 2*ar_2, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3 + ar_0)) [ ar_2 - ar_3 - 1 >= 0 /\ ar_1 - ar_3 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ -ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ]
2.43/1.58	
2.43/1.58			(Comp: 2*ar_2 + 2, Cost: 1)                                  evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ -ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= ar_1 + 1 ]
2.43/1.58	
2.43/1.58			(Comp: 2*ar_0*ar_2 + 2*ar_2^2 + 2*ar_0 + 2*ar_2, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ -ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_3 ]
2.43/1.58	
2.43/1.58			(Comp: 2, Cost: 1)                                           evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_2 ]
2.43/1.58	
2.43/1.58			(Comp: ar_2 + 1, Cost: 1)                                    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, 0)) [ ar_1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 + 1 ]
2.43/1.58	
2.43/1.58			(Comp: 1, Cost: 1)                                           evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.43/1.58	
2.43/1.58			(Comp: 1, Cost: 1)                                           evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, 0, ar_2, ar_3)) [ ar_0 >= 1 ]
2.43/1.58	
2.43/1.58			(Comp: 1, Cost: 1)                                           evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.43/1.58	
2.43/1.58		start location:	koat_start
2.43/1.58	
2.43/1.58		leaf cost:	0
2.43/1.58	
2.43/1.58	
2.43/1.58	
2.43/1.58	Complexity upper bound 9*ar_2 + 4*ar_0*ar_2 + 4*ar_2^2 + 4*ar_0 + 12
2.43/1.58	
2.43/1.58	
2.43/1.58	
2.43/1.58	Time: 0.322 sec (SMT: 0.263 sec)
2.43/1.58	
2.43/1.58	
2.43/1.58	----------------------------------------
2.43/1.58	
2.43/1.58	(2)
2.43/1.58	BOUNDS(1, n^2)
2.43/1.60	EOF