6.62/3.57	WORST_CASE(?, O(n^2))
6.62/3.57	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
6.62/3.57	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.62/3.57	
6.62/3.57	
6.62/3.57	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2).
6.62/3.57	
6.62/3.57	(0) CpxIntTrs
6.62/3.57	(1) Koat Proof [FINISHED, 293 ms]
6.62/3.57	(2) BOUNDS(1, n^2)
6.62/3.57	
6.62/3.57	
6.62/3.57	----------------------------------------
6.62/3.57	
6.62/3.57	(0)
6.62/3.57	Obligation:
6.62/3.57	Complexity Int TRS consisting of the following rules:
6.62/3.57	eval_loops_start(v_n, v_x_0, v_y_0) -> Com_1(eval_loops_bb0_in(v_n, v_x_0, v_y_0)) :|: TRUE
6.62/3.57	eval_loops_bb0_in(v_n, v_x_0, v_y_0) -> Com_1(eval_loops_0(v_n, v_x_0, v_y_0)) :|: TRUE
6.62/3.57	eval_loops_0(v_n, v_x_0, v_y_0) -> Com_1(eval_loops_1(v_n, v_x_0, v_y_0)) :|: TRUE
6.62/3.57	eval_loops_1(v_n, v_x_0, v_y_0) -> Com_1(eval_loops_2(v_n, v_x_0, v_y_0)) :|: TRUE
6.62/3.57	eval_loops_2(v_n, v_x_0, v_y_0) -> Com_1(eval_loops_bb1_in(v_n, v_n, v_y_0)) :|: v_n >= 0
6.62/3.57	eval_loops_2(v_n, v_x_0, v_y_0) -> Com_1(eval_loops_bb6_in(v_n, v_x_0, v_y_0)) :|: v_n < 0
6.62/3.57	eval_loops_bb1_in(v_n, v_x_0, v_y_0) -> Com_1(eval_loops_bb2_in(v_n, v_x_0, v_y_0)) :|: v_x_0 >= 0
6.62/3.57	eval_loops_bb1_in(v_n, v_x_0, v_y_0) -> Com_1(eval_loops_bb6_in(v_n, v_x_0, v_y_0)) :|: v_x_0 < 0
6.62/3.57	eval_loops_bb2_in(v_n, v_x_0, v_y_0) -> Com_1(eval_loops_bb3_in(v_n, v_x_0, 1)) :|: 1 < v_x_0
6.62/3.57	eval_loops_bb2_in(v_n, v_x_0, v_y_0) -> Com_1(eval_loops_bb5_in(v_n, v_x_0, v_y_0)) :|: 1 >= v_x_0
6.62/3.57	eval_loops_bb3_in(v_n, v_x_0, v_y_0) -> Com_1(eval_loops_bb4_in(v_n, v_x_0, v_y_0)) :|: v_y_0 < v_x_0
6.62/3.57	eval_loops_bb3_in(v_n, v_x_0, v_y_0) -> Com_1(eval_loops_bb5_in(v_n, v_x_0, v_y_0)) :|: v_y_0 >= v_x_0
6.62/3.57	eval_loops_bb4_in(v_n, v_x_0, v_y_0) -> Com_1(eval_loops_bb3_in(v_n, v_x_0, 2 * v_y_0)) :|: TRUE
6.62/3.57	eval_loops_bb5_in(v_n, v_x_0, v_y_0) -> Com_1(eval_loops_bb1_in(v_n, v_x_0 - 1, v_y_0)) :|: TRUE
6.62/3.57	eval_loops_bb6_in(v_n, v_x_0, v_y_0) -> Com_1(eval_loops_stop(v_n, v_x_0, v_y_0)) :|: TRUE
6.62/3.57	
6.62/3.57	The start-symbols are:[eval_loops_start_3]
6.62/3.57	
6.62/3.57	
6.62/3.57	----------------------------------------
6.62/3.57	
6.62/3.57	(1) Koat Proof (FINISHED)
6.62/3.57	YES(?, 50*ar_0 + 8*ar_0^2 + 52)
6.62/3.57	
6.62/3.57	
6.62/3.57	
6.62/3.57	Initial complexity problem:
6.62/3.57	
6.62/3.57	1:	T:
6.62/3.57	
6.62/3.57			(Comp: ?, Cost: 1)    evalloopsstart(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb0in(ar_0, ar_1, ar_2))
6.62/3.58	
6.62/3.58			(Comp: ?, Cost: 1)    evalloopsbb0in(ar_0, ar_1, ar_2) -> Com_1(evalloops0(ar_0, ar_1, ar_2))
6.62/3.58	
6.62/3.58			(Comp: ?, Cost: 1)    evalloops0(ar_0, ar_1, ar_2) -> Com_1(evalloops1(ar_0, ar_1, ar_2))
6.62/3.58	
6.62/3.58			(Comp: ?, Cost: 1)    evalloops1(ar_0, ar_1, ar_2) -> Com_1(evalloops2(ar_0, ar_1, ar_2))
6.62/3.58	
6.62/3.58			(Comp: ?, Cost: 1)    evalloops2(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 0 ]
6.62/3.58	
6.62/3.58			(Comp: ?, Cost: 1)    evalloops2(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
6.62/3.58	
6.62/3.58			(Comp: ?, Cost: 1)    evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 0 ]
6.62/3.58	
6.62/3.58			(Comp: ?, Cost: 1)    evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 + 1 ]
6.62/3.58	
6.62/3.58			(Comp: ?, Cost: 1)    evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 1)) [ ar_1 >= 2 ]
6.62/3.58	
6.62/3.58			(Comp: ?, Cost: 1)    evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ 1 >= ar_1 ]
6.62/3.58	
6.62/3.58			(Comp: ?, Cost: 1)    evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb4in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]
6.62/3.58	
6.62/3.58			(Comp: ?, Cost: 1)    evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]
6.62/3.58	
6.62/3.58			(Comp: ?, Cost: 1)    evalloopsbb4in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 2*ar_2))
6.62/3.58	
6.62/3.58			(Comp: ?, Cost: 1)    evalloopsbb5in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb1in(ar_0, ar_1 - 1, ar_2))
6.62/3.58	
6.62/3.58			(Comp: ?, Cost: 1)    evalloopsbb6in(ar_0, ar_1, ar_2) -> Com_1(evalloopsstop(ar_0, ar_1, ar_2))
6.62/3.58	
6.62/3.58			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalloopsstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
6.62/3.58	
6.62/3.58		start location:	koat_start
6.62/3.58	
6.62/3.58		leaf cost:	0
6.62/3.58	
6.62/3.58	
6.62/3.58	
6.62/3.58	Repeatedly propagating knowledge in problem 1 produces the following problem:
6.62/3.58	
6.62/3.58	2:	T:
6.62/3.58	
6.62/3.58			(Comp: 1, Cost: 1)    evalloopsstart(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb0in(ar_0, ar_1, ar_2))
6.62/3.58	
6.62/3.58			(Comp: 1, Cost: 1)    evalloopsbb0in(ar_0, ar_1, ar_2) -> Com_1(evalloops0(ar_0, ar_1, ar_2))
6.62/3.58	
6.62/3.58			(Comp: 1, Cost: 1)    evalloops0(ar_0, ar_1, ar_2) -> Com_1(evalloops1(ar_0, ar_1, ar_2))
6.62/3.58	
6.62/3.58			(Comp: 1, Cost: 1)    evalloops1(ar_0, ar_1, ar_2) -> Com_1(evalloops2(ar_0, ar_1, ar_2))
6.62/3.58	
6.62/3.58			(Comp: 1, Cost: 1)    evalloops2(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 0 ]
6.62/3.58	
6.62/3.58			(Comp: 1, Cost: 1)    evalloops2(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
6.62/3.58	
6.62/3.58			(Comp: ?, Cost: 1)    evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 0 ]
6.62/3.58	
6.62/3.58			(Comp: ?, Cost: 1)    evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 + 1 ]
6.62/3.58	
6.62/3.58			(Comp: ?, Cost: 1)    evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 1)) [ ar_1 >= 2 ]
6.62/3.58	
6.62/3.58			(Comp: ?, Cost: 1)    evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ 1 >= ar_1 ]
6.62/3.58	
6.62/3.58			(Comp: ?, Cost: 1)    evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb4in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]
6.62/3.58	
6.62/3.58			(Comp: ?, Cost: 1)    evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]
6.62/3.58	
6.62/3.58			(Comp: ?, Cost: 1)    evalloopsbb4in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 2*ar_2))
6.62/3.58	
6.62/3.58			(Comp: ?, Cost: 1)    evalloopsbb5in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb1in(ar_0, ar_1 - 1, ar_2))
6.62/3.58	
6.62/3.58			(Comp: ?, Cost: 1)    evalloopsbb6in(ar_0, ar_1, ar_2) -> Com_1(evalloopsstop(ar_0, ar_1, ar_2))
6.62/3.58	
6.62/3.58			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalloopsstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
6.62/3.58	
6.62/3.58		start location:	koat_start
6.62/3.58	
6.62/3.58		leaf cost:	0
6.62/3.58	
6.62/3.58	
6.62/3.58	
6.62/3.58	A polynomial rank function with
6.62/3.58	
6.62/3.58		Pol(evalloopsstart) = 2
6.62/3.58	
6.62/3.58		Pol(evalloopsbb0in) = 2
6.62/3.58	
6.62/3.58		Pol(evalloops0) = 2
6.62/3.58	
6.62/3.58		Pol(evalloops1) = 2
6.62/3.58	
6.62/3.58		Pol(evalloops2) = 2
6.62/3.58	
6.62/3.58		Pol(evalloopsbb1in) = 2
6.62/3.58	
6.62/3.58		Pol(evalloopsbb6in) = 1
6.62/3.58	
6.62/3.58		Pol(evalloopsbb2in) = 2
6.62/3.58	
6.62/3.58		Pol(evalloopsbb3in) = 2
6.62/3.58	
6.62/3.58		Pol(evalloopsbb5in) = 2
6.62/3.58	
6.62/3.58		Pol(evalloopsbb4in) = 2
6.62/3.58	
6.62/3.58		Pol(evalloopsstop) = 0
6.62/3.58	
6.62/3.58		Pol(koat_start) = 2
6.62/3.58	
6.62/3.58	orients all transitions weakly and the transitions
6.62/3.58	
6.62/3.58		evalloopsbb6in(ar_0, ar_1, ar_2) -> Com_1(evalloopsstop(ar_0, ar_1, ar_2))
6.62/3.58	
6.62/3.58		evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 + 1 ]
6.62/3.58	
6.62/3.58	strictly and produces the following problem:
6.62/3.58	
6.62/3.58	3:	T:
6.62/3.58	
6.62/3.58			(Comp: 1, Cost: 1)    evalloopsstart(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb0in(ar_0, ar_1, ar_2))
6.62/3.58	
6.62/3.58			(Comp: 1, Cost: 1)    evalloopsbb0in(ar_0, ar_1, ar_2) -> Com_1(evalloops0(ar_0, ar_1, ar_2))
6.62/3.58	
6.62/3.58			(Comp: 1, Cost: 1)    evalloops0(ar_0, ar_1, ar_2) -> Com_1(evalloops1(ar_0, ar_1, ar_2))
6.62/3.58	
6.62/3.58			(Comp: 1, Cost: 1)    evalloops1(ar_0, ar_1, ar_2) -> Com_1(evalloops2(ar_0, ar_1, ar_2))
6.62/3.58	
6.62/3.58			(Comp: 1, Cost: 1)    evalloops2(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 0 ]
6.62/3.58	
6.62/3.58			(Comp: 1, Cost: 1)    evalloops2(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
6.62/3.58	
6.62/3.58			(Comp: ?, Cost: 1)    evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 0 ]
6.62/3.58	
6.62/3.58			(Comp: 2, Cost: 1)    evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 + 1 ]
6.62/3.58	
6.62/3.58			(Comp: ?, Cost: 1)    evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 1)) [ ar_1 >= 2 ]
6.62/3.58	
6.62/3.58			(Comp: ?, Cost: 1)    evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ 1 >= ar_1 ]
6.62/3.58	
6.62/3.58			(Comp: ?, Cost: 1)    evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb4in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]
6.62/3.58	
6.62/3.58			(Comp: ?, Cost: 1)    evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]
6.62/3.58	
6.62/3.58			(Comp: ?, Cost: 1)    evalloopsbb4in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 2*ar_2))
6.62/3.58	
6.62/3.58			(Comp: ?, Cost: 1)    evalloopsbb5in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb1in(ar_0, ar_1 - 1, ar_2))
6.62/3.58	
6.62/3.58			(Comp: 2, Cost: 1)    evalloopsbb6in(ar_0, ar_1, ar_2) -> Com_1(evalloopsstop(ar_0, ar_1, ar_2))
6.62/3.58	
6.62/3.58			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalloopsstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
6.62/3.58	
6.62/3.58		start location:	koat_start
6.62/3.58	
6.62/3.58		leaf cost:	0
6.62/3.58	
6.62/3.58	
6.62/3.58	
6.62/3.58	A polynomial rank function with
6.62/3.58	
6.62/3.58		Pol(evalloopsbb5in) = 2*V_2
6.62/3.58	
6.62/3.58		Pol(evalloopsbb1in) = 2*V_2 + 2
6.62/3.58	
6.62/3.58		Pol(evalloopsbb4in) = 2*V_2
6.62/3.58	
6.62/3.58		Pol(evalloopsbb3in) = 2*V_2
6.62/3.58	
6.62/3.58		Pol(evalloopsbb2in) = 2*V_2 + 1
6.62/3.58	
6.62/3.58	and size complexities
6.62/3.58	
6.62/3.58		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalloopsstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
6.62/3.58	
6.62/3.58		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalloopsstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
6.62/3.58	
6.62/3.58		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalloopsstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
6.62/3.58	
6.62/3.58		S("evalloopsbb6in(ar_0, ar_1, ar_2) -> Com_1(evalloopsstop(ar_0, ar_1, ar_2))", 0-0) = ar_0
6.62/3.58	
6.62/3.58		S("evalloopsbb6in(ar_0, ar_1, ar_2) -> Com_1(evalloopsstop(ar_0, ar_1, ar_2))", 0-1) = ?
6.62/3.58	
6.62/3.58		S("evalloopsbb6in(ar_0, ar_1, ar_2) -> Com_1(evalloopsstop(ar_0, ar_1, ar_2))", 0-2) = ?
6.62/3.58	
6.62/3.58		S("evalloopsbb5in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb1in(ar_0, ar_1 - 1, ar_2))", 0-0) = ar_0
6.62/3.58	
6.62/3.58		S("evalloopsbb5in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb1in(ar_0, ar_1 - 1, ar_2))", 0-1) = ?
6.62/3.58	
6.62/3.58		S("evalloopsbb5in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb1in(ar_0, ar_1 - 1, ar_2))", 0-2) = ?
6.62/3.58	
6.62/3.58		S("evalloopsbb4in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 2*ar_2))", 0-0) = ar_0
6.62/3.58	
6.62/3.58		S("evalloopsbb4in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 2*ar_2))", 0-1) = ?
6.62/3.58	
6.62/3.58		S("evalloopsbb4in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 2*ar_2))", 0-2) = ?
6.62/3.58	
6.62/3.58		S("evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]", 0-0) = ar_0
6.62/3.58	
6.62/3.58		S("evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]", 0-1) = ?
6.62/3.58	
6.62/3.58		S("evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]", 0-2) = ?
6.62/3.58	
6.62/3.58		S("evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb4in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]", 0-0) = ar_0
6.62/3.58	
6.62/3.58		S("evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb4in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]", 0-1) = ?
6.62/3.58	
6.62/3.58		S("evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb4in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]", 0-2) = ?
6.62/3.58	
6.62/3.58		S("evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ 1 >= ar_1 ]", 0-0) = ar_0
6.62/3.58	
6.62/3.58		S("evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ 1 >= ar_1 ]", 0-1) = ?
6.62/3.58	
6.62/3.58		S("evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ 1 >= ar_1 ]", 0-2) = ?
6.62/3.58	
6.62/3.58		S("evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 1)) [ ar_1 >= 2 ]", 0-0) = ar_0
6.62/3.58	
6.62/3.58		S("evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 1)) [ ar_1 >= 2 ]", 0-1) = ?
6.62/3.58	
6.62/3.58		S("evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 1)) [ ar_1 >= 2 ]", 0-2) = 1
6.62/3.58	
6.62/3.58		S("evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 + 1 ]", 0-0) = ar_0
6.62/3.58	
6.62/3.58		S("evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 + 1 ]", 0-1) = ?
6.62/3.58	
6.62/3.58		S("evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 + 1 ]", 0-2) = ?
6.62/3.58	
6.62/3.58		S("evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 0 ]", 0-0) = ar_0
6.62/3.58	
6.62/3.58		S("evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 0 ]", 0-1) = ?
6.62/3.58	
6.62/3.58		S("evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 0 ]", 0-2) = ?
6.62/3.58	
6.62/3.58		S("evalloops2(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]", 0-0) = ar_0
6.62/3.58	
6.62/3.58		S("evalloops2(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]", 0-1) = ar_1
6.62/3.58	
6.62/3.58		S("evalloops2(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]", 0-2) = ar_2
6.62/3.58	
6.62/3.58		S("evalloops2(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 0 ]", 0-0) = ar_0
6.62/3.58	
6.62/3.58		S("evalloops2(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 0 ]", 0-1) = ar_0
6.62/3.58	
6.62/3.58		S("evalloops2(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 0 ]", 0-2) = ar_2
6.62/3.58	
6.62/3.58		S("evalloops1(ar_0, ar_1, ar_2) -> Com_1(evalloops2(ar_0, ar_1, ar_2))", 0-0) = ar_0
6.62/3.58	
6.62/3.58		S("evalloops1(ar_0, ar_1, ar_2) -> Com_1(evalloops2(ar_0, ar_1, ar_2))", 0-1) = ar_1
6.62/3.58	
6.62/3.58		S("evalloops1(ar_0, ar_1, ar_2) -> Com_1(evalloops2(ar_0, ar_1, ar_2))", 0-2) = ar_2
6.62/3.58	
6.62/3.58		S("evalloops0(ar_0, ar_1, ar_2) -> Com_1(evalloops1(ar_0, ar_1, ar_2))", 0-0) = ar_0
6.62/3.58	
6.62/3.58		S("evalloops0(ar_0, ar_1, ar_2) -> Com_1(evalloops1(ar_0, ar_1, ar_2))", 0-1) = ar_1
6.62/3.58	
6.62/3.58		S("evalloops0(ar_0, ar_1, ar_2) -> Com_1(evalloops1(ar_0, ar_1, ar_2))", 0-2) = ar_2
6.62/3.58	
6.62/3.58		S("evalloopsbb0in(ar_0, ar_1, ar_2) -> Com_1(evalloops0(ar_0, ar_1, ar_2))", 0-0) = ar_0
6.62/3.58	
6.62/3.58		S("evalloopsbb0in(ar_0, ar_1, ar_2) -> Com_1(evalloops0(ar_0, ar_1, ar_2))", 0-1) = ar_1
6.62/3.58	
6.62/3.58		S("evalloopsbb0in(ar_0, ar_1, ar_2) -> Com_1(evalloops0(ar_0, ar_1, ar_2))", 0-2) = ar_2
6.62/3.58	
6.62/3.58		S("evalloopsstart(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb0in(ar_0, ar_1, ar_2))", 0-0) = ar_0
6.62/3.58	
6.62/3.58		S("evalloopsstart(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb0in(ar_0, ar_1, ar_2))", 0-1) = ar_1
6.62/3.58	
6.62/3.58		S("evalloopsstart(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb0in(ar_0, ar_1, ar_2))", 0-2) = ar_2
6.62/3.58	
6.62/3.58	orients the transitions
6.62/3.58	
6.62/3.58		evalloopsbb5in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb1in(ar_0, ar_1 - 1, ar_2))
6.62/3.58	
6.62/3.58		evalloopsbb4in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 2*ar_2))
6.62/3.58	
6.62/3.58		evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]
6.62/3.58	
6.62/3.58		evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb4in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]
6.62/3.58	
6.62/3.58		evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ 1 >= ar_1 ]
6.62/3.58	
6.62/3.58		evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 1)) [ ar_1 >= 2 ]
6.62/3.58	
6.62/3.58		evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 0 ]
6.62/3.58	
6.62/3.58	weakly and the transitions
6.62/3.58	
6.62/3.58		evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 1)) [ ar_1 >= 2 ]
6.62/3.58	
6.62/3.58		evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 0 ]
6.62/3.58	
6.62/3.58	strictly and produces the following problem:
6.62/3.58	
6.62/3.58	4:	T:
6.62/3.58	
6.62/3.58			(Comp: 1, Cost: 1)             evalloopsstart(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb0in(ar_0, ar_1, ar_2))
6.62/3.58	
6.62/3.58			(Comp: 1, Cost: 1)             evalloopsbb0in(ar_0, ar_1, ar_2) -> Com_1(evalloops0(ar_0, ar_1, ar_2))
6.62/3.58	
6.62/3.58			(Comp: 1, Cost: 1)             evalloops0(ar_0, ar_1, ar_2) -> Com_1(evalloops1(ar_0, ar_1, ar_2))
6.62/3.58	
6.62/3.58			(Comp: 1, Cost: 1)             evalloops1(ar_0, ar_1, ar_2) -> Com_1(evalloops2(ar_0, ar_1, ar_2))
6.62/3.58	
6.62/3.58			(Comp: 1, Cost: 1)             evalloops2(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 0 ]
6.62/3.58	
6.62/3.58			(Comp: 1, Cost: 1)             evalloops2(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
6.62/3.58	
6.62/3.58			(Comp: 2*ar_0 + 2, Cost: 1)    evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 0 ]
6.62/3.58	
6.62/3.58			(Comp: 2, Cost: 1)             evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 + 1 ]
6.62/3.58	
6.62/3.58			(Comp: 2*ar_0 + 2, Cost: 1)    evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 1)) [ ar_1 >= 2 ]
6.62/3.58	
6.62/3.58			(Comp: ?, Cost: 1)             evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ 1 >= ar_1 ]
6.62/3.58	
6.62/3.58			(Comp: ?, Cost: 1)             evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb4in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]
6.62/3.58	
6.62/3.58			(Comp: ?, Cost: 1)             evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]
6.62/3.58	
6.62/3.58			(Comp: ?, Cost: 1)             evalloopsbb4in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 2*ar_2))
6.62/3.58	
6.62/3.58			(Comp: ?, Cost: 1)             evalloopsbb5in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb1in(ar_0, ar_1 - 1, ar_2))
6.62/3.58	
6.62/3.58			(Comp: 2, Cost: 1)             evalloopsbb6in(ar_0, ar_1, ar_2) -> Com_1(evalloopsstop(ar_0, ar_1, ar_2))
6.62/3.58	
6.62/3.58			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2) -> Com_1(evalloopsstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
6.62/3.58	
6.62/3.58		start location:	koat_start
6.62/3.58	
6.62/3.58		leaf cost:	0
6.62/3.58	
6.62/3.58	
6.62/3.58	
6.62/3.58	Repeatedly propagating knowledge in problem 4 produces the following problem:
6.62/3.58	
6.62/3.58	5:	T:
6.62/3.58	
6.62/3.58			(Comp: 1, Cost: 1)             evalloopsstart(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb0in(ar_0, ar_1, ar_2))
6.62/3.58	
6.62/3.58			(Comp: 1, Cost: 1)             evalloopsbb0in(ar_0, ar_1, ar_2) -> Com_1(evalloops0(ar_0, ar_1, ar_2))
6.62/3.58	
6.62/3.58			(Comp: 1, Cost: 1)             evalloops0(ar_0, ar_1, ar_2) -> Com_1(evalloops1(ar_0, ar_1, ar_2))
6.62/3.58	
6.62/3.58			(Comp: 1, Cost: 1)             evalloops1(ar_0, ar_1, ar_2) -> Com_1(evalloops2(ar_0, ar_1, ar_2))
6.62/3.58	
6.62/3.58			(Comp: 1, Cost: 1)             evalloops2(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 0 ]
6.62/3.58	
6.62/3.58			(Comp: 1, Cost: 1)             evalloops2(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
6.62/3.58	
6.62/3.58			(Comp: 2*ar_0 + 2, Cost: 1)    evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 0 ]
6.62/3.58	
6.62/3.58			(Comp: 2, Cost: 1)             evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 + 1 ]
6.62/3.58	
6.62/3.58			(Comp: 2*ar_0 + 2, Cost: 1)    evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 1)) [ ar_1 >= 2 ]
6.62/3.58	
6.62/3.58			(Comp: 2*ar_0 + 2, Cost: 1)    evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ 1 >= ar_1 ]
6.62/3.58	
6.62/3.58			(Comp: ?, Cost: 1)             evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb4in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]
6.62/3.58	
6.62/3.58			(Comp: ?, Cost: 1)             evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]
6.62/3.58	
6.62/3.58			(Comp: ?, Cost: 1)             evalloopsbb4in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 2*ar_2))
6.62/3.58	
6.62/3.58			(Comp: ?, Cost: 1)             evalloopsbb5in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb1in(ar_0, ar_1 - 1, ar_2))
6.62/3.58	
6.62/3.58			(Comp: 2, Cost: 1)             evalloopsbb6in(ar_0, ar_1, ar_2) -> Com_1(evalloopsstop(ar_0, ar_1, ar_2))
6.62/3.58	
6.62/3.58			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2) -> Com_1(evalloopsstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
6.62/3.58	
6.62/3.58		start location:	koat_start
6.62/3.58	
6.62/3.58		leaf cost:	0
6.62/3.58	
6.62/3.58	
6.62/3.58	
6.62/3.58	A polynomial rank function with
6.62/3.58	
6.62/3.58		Pol(evalloopsbb5in) = 1
6.62/3.58	
6.62/3.58		Pol(evalloopsbb1in) = 0
6.62/3.58	
6.62/3.58		Pol(evalloopsbb4in) = 2
6.62/3.58	
6.62/3.58		Pol(evalloopsbb3in) = 2
6.62/3.58	
6.62/3.58	and size complexities
6.62/3.58	
6.62/3.58		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalloopsstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
6.62/3.58	
6.62/3.58		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalloopsstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
6.62/3.58	
6.62/3.58		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalloopsstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
6.62/3.58	
6.62/3.58		S("evalloopsbb6in(ar_0, ar_1, ar_2) -> Com_1(evalloopsstop(ar_0, ar_1, ar_2))", 0-0) = ar_0
6.62/3.58	
6.62/3.58		S("evalloopsbb6in(ar_0, ar_1, ar_2) -> Com_1(evalloopsstop(ar_0, ar_1, ar_2))", 0-1) = ?
6.62/3.58	
6.62/3.58		S("evalloopsbb6in(ar_0, ar_1, ar_2) -> Com_1(evalloopsstop(ar_0, ar_1, ar_2))", 0-2) = ?
6.62/3.58	
6.62/3.58		S("evalloopsbb5in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb1in(ar_0, ar_1 - 1, ar_2))", 0-0) = ar_0
6.62/3.58	
6.62/3.58		S("evalloopsbb5in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb1in(ar_0, ar_1 - 1, ar_2))", 0-1) = ?
6.62/3.58	
6.62/3.58		S("evalloopsbb5in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb1in(ar_0, ar_1 - 1, ar_2))", 0-2) = ?
6.62/3.58	
6.62/3.58		S("evalloopsbb4in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 2*ar_2))", 0-0) = ar_0
6.62/3.58	
6.62/3.58		S("evalloopsbb4in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 2*ar_2))", 0-1) = ?
6.62/3.58	
6.62/3.58		S("evalloopsbb4in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 2*ar_2))", 0-2) = ?
6.62/3.58	
6.62/3.58		S("evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]", 0-0) = ar_0
6.62/3.58	
6.62/3.58		S("evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]", 0-1) = ?
6.62/3.58	
6.62/3.58		S("evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]", 0-2) = ?
6.62/3.58	
6.62/3.58		S("evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb4in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]", 0-0) = ar_0
6.62/3.58	
6.62/3.58		S("evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb4in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]", 0-1) = ?
6.62/3.58	
6.62/3.58		S("evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb4in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]", 0-2) = ?
6.62/3.58	
6.62/3.58		S("evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ 1 >= ar_1 ]", 0-0) = ar_0
6.62/3.58	
6.62/3.58		S("evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ 1 >= ar_1 ]", 0-1) = ?
6.62/3.58	
6.62/3.58		S("evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ 1 >= ar_1 ]", 0-2) = ?
6.62/3.58	
6.62/3.58		S("evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 1)) [ ar_1 >= 2 ]", 0-0) = ar_0
6.62/3.58	
6.62/3.58		S("evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 1)) [ ar_1 >= 2 ]", 0-1) = ?
6.62/3.58	
6.62/3.58		S("evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 1)) [ ar_1 >= 2 ]", 0-2) = 1
6.62/3.58	
6.62/3.58		S("evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 + 1 ]", 0-0) = ar_0
6.62/3.58	
6.62/3.58		S("evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 + 1 ]", 0-1) = ?
6.62/3.58	
6.62/3.58		S("evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 + 1 ]", 0-2) = ?
6.62/3.58	
6.62/3.58		S("evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 0 ]", 0-0) = ar_0
6.62/3.58	
6.62/3.58		S("evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 0 ]", 0-1) = ?
6.62/3.58	
6.62/3.58		S("evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 0 ]", 0-2) = ?
6.62/3.58	
6.62/3.58		S("evalloops2(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]", 0-0) = ar_0
6.62/3.58	
6.62/3.58		S("evalloops2(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]", 0-1) = ar_1
6.62/3.58	
6.62/3.58		S("evalloops2(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]", 0-2) = ar_2
6.62/3.58	
6.62/3.58		S("evalloops2(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 0 ]", 0-0) = ar_0
6.62/3.58	
6.62/3.58		S("evalloops2(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 0 ]", 0-1) = ar_0
6.62/3.58	
6.62/3.58		S("evalloops2(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 0 ]", 0-2) = ar_2
6.62/3.58	
6.62/3.58		S("evalloops1(ar_0, ar_1, ar_2) -> Com_1(evalloops2(ar_0, ar_1, ar_2))", 0-0) = ar_0
6.62/3.58	
6.62/3.58		S("evalloops1(ar_0, ar_1, ar_2) -> Com_1(evalloops2(ar_0, ar_1, ar_2))", 0-1) = ar_1
6.62/3.58	
6.62/3.58		S("evalloops1(ar_0, ar_1, ar_2) -> Com_1(evalloops2(ar_0, ar_1, ar_2))", 0-2) = ar_2
6.62/3.58	
6.62/3.58		S("evalloops0(ar_0, ar_1, ar_2) -> Com_1(evalloops1(ar_0, ar_1, ar_2))", 0-0) = ar_0
6.62/3.58	
6.62/3.58		S("evalloops0(ar_0, ar_1, ar_2) -> Com_1(evalloops1(ar_0, ar_1, ar_2))", 0-1) = ar_1
6.62/3.58	
6.62/3.58		S("evalloops0(ar_0, ar_1, ar_2) -> Com_1(evalloops1(ar_0, ar_1, ar_2))", 0-2) = ar_2
6.62/3.58	
6.62/3.58		S("evalloopsbb0in(ar_0, ar_1, ar_2) -> Com_1(evalloops0(ar_0, ar_1, ar_2))", 0-0) = ar_0
6.62/3.58	
6.62/3.58		S("evalloopsbb0in(ar_0, ar_1, ar_2) -> Com_1(evalloops0(ar_0, ar_1, ar_2))", 0-1) = ar_1
6.62/3.58	
6.62/3.58		S("evalloopsbb0in(ar_0, ar_1, ar_2) -> Com_1(evalloops0(ar_0, ar_1, ar_2))", 0-2) = ar_2
6.62/3.58	
6.62/3.58		S("evalloopsstart(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb0in(ar_0, ar_1, ar_2))", 0-0) = ar_0
6.62/3.58	
6.62/3.58		S("evalloopsstart(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb0in(ar_0, ar_1, ar_2))", 0-1) = ar_1
6.62/3.58	
6.62/3.58		S("evalloopsstart(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb0in(ar_0, ar_1, ar_2))", 0-2) = ar_2
6.62/3.58	
6.62/3.58	orients the transitions
6.62/3.58	
6.62/3.58		evalloopsbb5in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb1in(ar_0, ar_1 - 1, ar_2))
6.62/3.58	
6.62/3.58		evalloopsbb4in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 2*ar_2))
6.62/3.58	
6.62/3.58		evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]
6.62/3.58	
6.62/3.58		evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb4in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]
6.62/3.58	
6.62/3.58	weakly and the transitions
6.62/3.58	
6.62/3.58		evalloopsbb5in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb1in(ar_0, ar_1 - 1, ar_2))
6.62/3.58	
6.62/3.58		evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]
6.62/3.58	
6.62/3.58	strictly and produces the following problem:
6.62/3.58	
6.62/3.58	6:	T:
6.62/3.58	
6.62/3.58			(Comp: 1, Cost: 1)             evalloopsstart(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb0in(ar_0, ar_1, ar_2))
6.62/3.58	
6.62/3.58			(Comp: 1, Cost: 1)             evalloopsbb0in(ar_0, ar_1, ar_2) -> Com_1(evalloops0(ar_0, ar_1, ar_2))
6.62/3.58	
6.62/3.58			(Comp: 1, Cost: 1)             evalloops0(ar_0, ar_1, ar_2) -> Com_1(evalloops1(ar_0, ar_1, ar_2))
6.62/3.58	
6.62/3.58			(Comp: 1, Cost: 1)             evalloops1(ar_0, ar_1, ar_2) -> Com_1(evalloops2(ar_0, ar_1, ar_2))
6.62/3.58	
6.62/3.58			(Comp: 1, Cost: 1)             evalloops2(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 0 ]
6.62/3.58	
6.62/3.58			(Comp: 1, Cost: 1)             evalloops2(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
6.62/3.58	
6.62/3.58			(Comp: 2*ar_0 + 2, Cost: 1)    evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 0 ]
6.62/3.58	
6.62/3.58			(Comp: 2, Cost: 1)             evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 + 1 ]
6.62/3.58	
6.62/3.58			(Comp: 2*ar_0 + 2, Cost: 1)    evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 1)) [ ar_1 >= 2 ]
6.73/3.58	
6.73/3.58			(Comp: 2*ar_0 + 2, Cost: 1)    evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ 1 >= ar_1 ]
6.73/3.58	
6.73/3.58			(Comp: ?, Cost: 1)             evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb4in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 + 1 ]
6.73/3.58	
6.73/3.58			(Comp: 6*ar_0 + 6, Cost: 1)    evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]
6.73/3.58	
6.73/3.58			(Comp: ?, Cost: 1)             evalloopsbb4in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 2*ar_2))
6.73/3.58	
6.73/3.58			(Comp: 6*ar_0 + 6, Cost: 1)    evalloopsbb5in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb1in(ar_0, ar_1 - 1, ar_2))
6.73/3.58	
6.73/3.58			(Comp: 2, Cost: 1)             evalloopsbb6in(ar_0, ar_1, ar_2) -> Com_1(evalloopsstop(ar_0, ar_1, ar_2))
6.73/3.58	
6.73/3.58			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2) -> Com_1(evalloopsstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
6.73/3.58	
6.73/3.58		start location:	koat_start
6.73/3.58	
6.73/3.58		leaf cost:	0
6.73/3.58	
6.73/3.58	
6.73/3.58	
6.73/3.58	Applied AI with 'oct' on problem 6 to obtain the following invariants:
6.73/3.58	
6.73/3.58	  For symbol evalloopsbb1in: X_1 - X_2 >= 0 /\ X_1 >= 0
6.73/3.58	
6.73/3.58	  For symbol evalloopsbb2in: X_1 - X_2 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ X_1 >= 0
6.73/3.58	
6.73/3.58	  For symbol evalloopsbb3in: X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ X_1 + X_3 - 3 >= 0 /\ X_1 - X_2 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 4 >= 0 /\ X_1 - 2 >= 0
6.73/3.58	
6.73/3.58	  For symbol evalloopsbb4in: X_2 - X_3 - 1 >= 0 /\ X_1 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ X_1 + X_3 - 3 >= 0 /\ X_1 - X_2 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 4 >= 0 /\ X_1 - 2 >= 0
6.73/3.58	
6.73/3.58	  For symbol evalloopsbb5in: X_1 - X_2 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ X_1 >= 0
6.73/3.58	
6.73/3.58	
6.73/3.58	
6.73/3.58	
6.73/3.58	
6.73/3.58	This yielded the following problem:
6.73/3.58	
6.73/3.58	7:	T:
6.73/3.58	
6.73/3.58			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2) -> Com_1(evalloopsstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
6.73/3.58	
6.73/3.58			(Comp: 2, Cost: 1)             evalloopsbb6in(ar_0, ar_1, ar_2) -> Com_1(evalloopsstop(ar_0, ar_1, ar_2))
6.73/3.58	
6.73/3.58			(Comp: 6*ar_0 + 6, Cost: 1)    evalloopsbb5in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb1in(ar_0, ar_1 - 1, ar_2)) [ ar_0 - ar_1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
6.73/3.58	
6.73/3.58			(Comp: ?, Cost: 1)             evalloopsbb4in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 2*ar_2)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ ar_0 - 2 >= 0 ]
6.73/3.58	
6.73/3.58			(Comp: 6*ar_0 + 6, Cost: 1)    evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ ar_0 - 2 >= 0 /\ ar_2 >= ar_1 ]
6.73/3.58	
6.73/3.58			(Comp: ?, Cost: 1)             evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb4in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ ar_0 - 2 >= 0 /\ ar_1 >= ar_2 + 1 ]
6.73/3.58	
6.73/3.58			(Comp: 2*ar_0 + 2, Cost: 1)    evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ ar_0 - ar_1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ 1 >= ar_1 ]
6.73/3.58	
6.73/3.58			(Comp: 2*ar_0 + 2, Cost: 1)    evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 1)) [ ar_0 - ar_1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_1 >= 2 ]
6.73/3.58	
6.73/3.58			(Comp: 2, Cost: 1)             evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb6in(ar_0, ar_1, ar_2)) [ ar_0 - ar_1 >= 0 /\ ar_0 >= 0 /\ 0 >= ar_1 + 1 ]
6.73/3.58	
6.73/3.58			(Comp: 2*ar_0 + 2, Cost: 1)    evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb2in(ar_0, ar_1, ar_2)) [ ar_0 - ar_1 >= 0 /\ ar_0 >= 0 /\ ar_1 >= 0 ]
6.73/3.58	
6.73/3.58			(Comp: 1, Cost: 1)             evalloops2(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
6.73/3.58	
6.73/3.58			(Comp: 1, Cost: 1)             evalloops2(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 0 ]
6.73/3.58	
6.73/3.58			(Comp: 1, Cost: 1)             evalloops1(ar_0, ar_1, ar_2) -> Com_1(evalloops2(ar_0, ar_1, ar_2))
6.73/3.58	
6.73/3.58			(Comp: 1, Cost: 1)             evalloops0(ar_0, ar_1, ar_2) -> Com_1(evalloops1(ar_0, ar_1, ar_2))
6.73/3.58	
6.73/3.58			(Comp: 1, Cost: 1)             evalloopsbb0in(ar_0, ar_1, ar_2) -> Com_1(evalloops0(ar_0, ar_1, ar_2))
6.73/3.58	
6.73/3.58			(Comp: 1, Cost: 1)             evalloopsstart(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb0in(ar_0, ar_1, ar_2))
6.73/3.58	
6.73/3.58		start location:	koat_start
6.73/3.58	
6.73/3.58		leaf cost:	0
6.73/3.58	
6.73/3.58	
6.73/3.58	
6.73/3.58	A polynomial rank function with
6.73/3.58	
6.73/3.58		Pol(evalloopsbb4in) = 2*V_2 - 2*V_3 - 1
6.73/3.58	
6.73/3.58		Pol(evalloopsbb3in) = 2*V_2 - 2*V_3
6.73/3.58	
6.73/3.58	and size complexities
6.73/3.58	
6.73/3.58		S("evalloopsstart(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb0in(ar_0, ar_1, ar_2))", 0-0) = ar_0
6.73/3.58	
6.73/3.58		S("evalloopsstart(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb0in(ar_0, ar_1, ar_2))", 0-1) = ar_1
6.73/3.58	
6.73/3.58		S("evalloopsstart(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb0in(ar_0, ar_1, ar_2))", 0-2) = ar_2
6.73/3.58	
6.73/3.58		S("evalloopsbb0in(ar_0, ar_1, ar_2) -> Com_1(evalloops0(ar_0, ar_1, ar_2))", 0-0) = ar_0
6.73/3.58	
6.73/3.58		S("evalloopsbb0in(ar_0, ar_1, ar_2) -> Com_1(evalloops0(ar_0, ar_1, ar_2))", 0-1) = ar_1
6.73/3.58	
6.73/3.58		S("evalloopsbb0in(ar_0, ar_1, ar_2) -> Com_1(evalloops0(ar_0, ar_1, ar_2))", 0-2) = ar_2
6.73/3.58	
6.73/3.58		S("evalloops0(ar_0, ar_1, ar_2) -> Com_1(evalloops1(ar_0, ar_1, ar_2))", 0-0) = ar_0
6.73/3.58	
6.73/3.58		S("evalloops0(ar_0, ar_1, ar_2) -> Com_1(evalloops1(ar_0, ar_1, ar_2))", 0-1) = ar_1
6.73/3.58	
6.73/3.58		S("evalloops0(ar_0, ar_1, ar_2) -> Com_1(evalloops1(ar_0, ar_1, ar_2))", 0-2) = ar_2
6.73/3.58	
6.73/3.58		S("evalloops1(ar_0, ar_1, ar_2) -> Com_1(evalloops2(ar_0, ar_1, ar_2))", 0-0) = ar_0
6.73/3.58	
6.73/3.58		S("evalloops1(ar_0, ar_1, ar_2) -> Com_1(evalloops2(ar_0, ar_1, ar_2))", 0-1) = ar_1
6.73/3.58	
6.73/3.58		S("evalloops1(ar_0, ar_1, ar_2) -> Com_1(evalloops2(ar_0, ar_1, ar_2))", 0-2) = ar_2
6.73/3.58	
6.73/3.58		S("evalloops2(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 0 ]", 0-0) = ar_0
6.73/3.58	
6.73/3.58		S("evalloops2(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 0 ]", 0-1) = ar_0
6.73/3.58	
6.73/3.58		S("evalloops2(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 0 ]", 0-2) = ar_2
6.73/3.58	
6.73/3.58		S("evalloops2(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]", 0-0) = ar_0
6.73/3.58	
6.73/3.58		S("evalloops2(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]", 0-1) = ar_1
6.73/3.58	
6.73/3.58		S("evalloops2(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]", 0-2) = ar_2
6.73/3.58	
6.73/3.58		S("evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb2in(ar_0, ar_1, ar_2)) [ ar_0 - ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_1 >= 0 ]", 0-0) = ar_0
6.73/3.58	
6.73/3.58		S("evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb2in(ar_0, ar_1, ar_2)) [ ar_0 - ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_1 >= 0 ]", 0-1) = ar_0 + 2
6.73/3.58	
6.73/3.58		S("evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb2in(ar_0, ar_1, ar_2)) [ ar_0 - ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_1 >= 0 ]", 0-2) = 2*ar_0 + 2*ar_2 + 16
6.73/3.58	
6.73/3.58		S("evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb6in(ar_0, ar_1, ar_2)) [ ar_0 - ar_1 >= 0 /\\ ar_0 >= 0 /\\ 0 >= ar_1 + 1 ]", 0-0) = ar_0
6.73/3.58	
6.73/3.58		S("evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb6in(ar_0, ar_1, ar_2)) [ ar_0 - ar_1 >= 0 /\\ ar_0 >= 0 /\\ 0 >= ar_1 + 1 ]", 0-1) = ar_0 + 2
6.73/3.58	
6.73/3.58		S("evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb6in(ar_0, ar_1, ar_2)) [ ar_0 - ar_1 >= 0 /\\ ar_0 >= 0 /\\ 0 >= ar_1 + 1 ]", 0-2) = 2*ar_0 + 2*ar_2 + 32
6.73/3.58	
6.73/3.58		S("evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 1)) [ ar_0 - ar_1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_1 >= 2 ]", 0-0) = ar_0
6.73/3.58	
6.73/3.58		S("evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 1)) [ ar_0 - ar_1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_1 >= 2 ]", 0-1) = ar_0 + 2
6.73/3.58	
6.73/3.58		S("evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 1)) [ ar_0 - ar_1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_1 >= 2 ]", 0-2) = 1
6.73/3.58	
6.73/3.58		S("evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ ar_0 - ar_1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ 1 >= ar_1 ]", 0-0) = ar_0
6.73/3.58	
6.73/3.58		S("evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ ar_0 - ar_1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ 1 >= ar_1 ]", 0-1) = 1
6.73/3.58	
6.73/3.58		S("evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ ar_0 - ar_1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ 1 >= ar_1 ]", 0-2) = 2*ar_0 + 2*ar_2 + 16
6.73/3.58	
6.73/3.58		S("evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb4in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 4 >= 0 /\\ ar_0 - 2 >= 0 /\\ ar_1 >= ar_2 + 1 ]", 0-0) = ar_0
6.73/3.58	
6.73/3.58		S("evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb4in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 4 >= 0 /\\ ar_0 - 2 >= 0 /\\ ar_1 >= ar_2 + 1 ]", 0-1) = ar_0 + 2
6.73/3.58	
6.73/3.58		S("evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb4in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 4 >= 0 /\\ ar_0 - 2 >= 0 /\\ ar_1 >= ar_2 + 1 ]", 0-2) = 2*ar_0 + 10
6.73/3.58	
6.73/3.58		S("evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 4 >= 0 /\\ ar_0 - 2 >= 0 /\\ ar_2 >= ar_1 ]", 0-0) = ar_0
6.73/3.58	
6.73/3.58		S("evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 4 >= 0 /\\ ar_0 - 2 >= 0 /\\ ar_2 >= ar_1 ]", 0-1) = ar_0 + 2
6.73/3.58	
6.73/3.58		S("evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 4 >= 0 /\\ ar_0 - 2 >= 0 /\\ ar_2 >= ar_1 ]", 0-2) = 2*ar_0 + 8
6.73/3.58	
6.73/3.58		S("evalloopsbb4in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 2*ar_2)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_0 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 4 >= 0 /\\ ar_0 - 2 >= 0 ]", 0-0) = ar_0
6.73/3.58	
6.73/3.58		S("evalloopsbb4in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 2*ar_2)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_0 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 4 >= 0 /\\ ar_0 - 2 >= 0 ]", 0-1) = ar_0 + 2
6.73/3.58	
6.73/3.58		S("evalloopsbb4in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 2*ar_2)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_0 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 3 >= 0 /\\ ar_0 - ar_1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 4 >= 0 /\\ ar_0 - 2 >= 0 ]", 0-2) = 2*ar_0 + 4
6.73/3.58	
6.73/3.58		S("evalloopsbb5in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb1in(ar_0, ar_1 - 1, ar_2)) [ ar_0 - ar_1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 ]", 0-0) = ar_0
6.73/3.58	
6.73/3.58		S("evalloopsbb5in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb1in(ar_0, ar_1 - 1, ar_2)) [ ar_0 - ar_1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 ]", 0-1) = ar_0 + 2
6.73/3.58	
6.73/3.58		S("evalloopsbb5in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb1in(ar_0, ar_1 - 1, ar_2)) [ ar_0 - ar_1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 ]", 0-2) = 2*ar_0 + 2*ar_2 + 16
6.73/3.58	
6.73/3.58		S("evalloopsbb6in(ar_0, ar_1, ar_2) -> Com_1(evalloopsstop(ar_0, ar_1, ar_2))", 0-0) = ar_0
6.73/3.58	
6.73/3.58		S("evalloopsbb6in(ar_0, ar_1, ar_2) -> Com_1(evalloopsstop(ar_0, ar_1, ar_2))", 0-1) = ar_0 + ar_1 + 2
6.73/3.58	
6.73/3.58		S("evalloopsbb6in(ar_0, ar_1, ar_2) -> Com_1(evalloopsstop(ar_0, ar_1, ar_2))", 0-2) = 2*ar_0 + 2*ar_2 + 64
6.73/3.58	
6.73/3.58		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalloopsstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
6.73/3.58	
6.73/3.58		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalloopsstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
6.73/3.58	
6.73/3.58		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalloopsstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
6.73/3.58	
6.73/3.58	orients the transitions
6.73/3.58	
6.73/3.58		evalloopsbb4in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 2*ar_2)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ ar_0 - 2 >= 0 ]
6.73/3.58	
6.73/3.58		evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb4in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ ar_0 - 2 >= 0 /\ ar_1 >= ar_2 + 1 ]
6.73/3.58	
6.73/3.58	weakly and the transitions
6.73/3.58	
6.73/3.58		evalloopsbb4in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 2*ar_2)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ ar_0 - 2 >= 0 ]
6.73/3.58	
6.73/3.58		evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb4in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ ar_0 - 2 >= 0 /\ ar_1 >= ar_2 + 1 ]
6.73/3.58	
6.73/3.58	strictly and produces the following problem:
6.73/3.58	
6.73/3.58	8:	T:
6.73/3.58	
6.73/3.58			(Comp: 1, Cost: 0)                          koat_start(ar_0, ar_1, ar_2) -> Com_1(evalloopsstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
6.73/3.58	
6.73/3.58			(Comp: 2, Cost: 1)                          evalloopsbb6in(ar_0, ar_1, ar_2) -> Com_1(evalloopsstop(ar_0, ar_1, ar_2))
6.73/3.58	
6.73/3.58			(Comp: 6*ar_0 + 6, Cost: 1)                 evalloopsbb5in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb1in(ar_0, ar_1 - 1, ar_2)) [ ar_0 - ar_1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
6.73/3.58	
6.73/3.58			(Comp: 4*ar_0^2 + 16*ar_0 + 12, Cost: 1)    evalloopsbb4in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 2*ar_2)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ ar_0 - 2 >= 0 ]
6.73/3.58	
6.73/3.58			(Comp: 6*ar_0 + 6, Cost: 1)                 evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ ar_0 - 2 >= 0 /\ ar_2 >= ar_1 ]
6.73/3.58	
6.73/3.58			(Comp: 4*ar_0^2 + 16*ar_0 + 12, Cost: 1)    evalloopsbb3in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb4in(ar_0, ar_1, ar_2)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 3 >= 0 /\ ar_0 - ar_1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 4 >= 0 /\ ar_0 - 2 >= 0 /\ ar_1 >= ar_2 + 1 ]
6.73/3.58	
6.73/3.58			(Comp: 2*ar_0 + 2, Cost: 1)                 evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb5in(ar_0, ar_1, ar_2)) [ ar_0 - ar_1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ 1 >= ar_1 ]
6.73/3.58	
6.73/3.58			(Comp: 2*ar_0 + 2, Cost: 1)                 evalloopsbb2in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb3in(ar_0, ar_1, 1)) [ ar_0 - ar_1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_1 >= 2 ]
6.73/3.58	
6.73/3.58			(Comp: 2, Cost: 1)                          evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb6in(ar_0, ar_1, ar_2)) [ ar_0 - ar_1 >= 0 /\ ar_0 >= 0 /\ 0 >= ar_1 + 1 ]
6.73/3.58	
6.73/3.58			(Comp: 2*ar_0 + 2, Cost: 1)                 evalloopsbb1in(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb2in(ar_0, ar_1, ar_2)) [ ar_0 - ar_1 >= 0 /\ ar_0 >= 0 /\ ar_1 >= 0 ]
6.73/3.58	
6.73/3.58			(Comp: 1, Cost: 1)                          evalloops2(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb6in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
6.73/3.58	
6.73/3.58			(Comp: 1, Cost: 1)                          evalloops2(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb1in(ar_0, ar_0, ar_2)) [ ar_0 >= 0 ]
6.73/3.58	
6.73/3.58			(Comp: 1, Cost: 1)                          evalloops1(ar_0, ar_1, ar_2) -> Com_1(evalloops2(ar_0, ar_1, ar_2))
6.73/3.58	
6.73/3.58			(Comp: 1, Cost: 1)                          evalloops0(ar_0, ar_1, ar_2) -> Com_1(evalloops1(ar_0, ar_1, ar_2))
6.73/3.58	
6.73/3.58			(Comp: 1, Cost: 1)                          evalloopsbb0in(ar_0, ar_1, ar_2) -> Com_1(evalloops0(ar_0, ar_1, ar_2))
6.73/3.58	
6.73/3.58			(Comp: 1, Cost: 1)                          evalloopsstart(ar_0, ar_1, ar_2) -> Com_1(evalloopsbb0in(ar_0, ar_1, ar_2))
6.73/3.58	
6.73/3.58		start location:	koat_start
6.73/3.58	
6.73/3.58		leaf cost:	0
6.73/3.58	
6.73/3.58	
6.73/3.58	
6.73/3.58	Complexity upper bound 50*ar_0 + 8*ar_0^2 + 52
6.73/3.58	
6.73/3.58	
6.73/3.58	
6.73/3.58	Time: 0.343 sec (SMT: 0.290 sec)
6.73/3.58	
6.73/3.58	
6.73/3.58	----------------------------------------
6.73/3.58	
6.73/3.58	(2)
6.73/3.58	BOUNDS(1, n^2)
6.74/3.61	EOF