2.17/1.33	WORST_CASE(?, O(n^2))
2.23/1.34	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.23/1.34	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.23/1.34	
2.23/1.34	
2.23/1.34	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2).
2.23/1.34	
2.23/1.34	(0) CpxIntTrs
2.23/1.34	(1) Koat Proof [FINISHED, 79 ms]
2.23/1.34	(2) BOUNDS(1, n^2)
2.23/1.34	
2.23/1.34	
2.23/1.34	----------------------------------------
2.23/1.34	
2.23/1.34	(0)
2.23/1.34	Obligation:
2.23/1.34	Complexity Int TRS consisting of the following rules:
2.23/1.34	eval_foo_start(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_x, v_y)) :|: TRUE
2.23/1.34	eval_foo_bb0_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_x, v_y, v_x, v_y)) :|: TRUE
2.23/1.34	eval_foo_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 < v_.01
2.23/1.34	eval_foo_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 > v_.01
2.23/1.34	eval_foo_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 >= v_.01 && v_.0 <= v_.01
2.23/1.34	eval_foo_bb2_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0, v_.01 + 1, v_x, v_y)) :|: v_.0 > v_.01
2.23/1.34	eval_foo_bb2_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0 + 1, v_.01 + 1, v_x, v_y)) :|: v_.0 > v_.01 && v_.0 <= v_.01
2.23/1.34	eval_foo_bb2_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 <= v_.01 && v_.0 > v_.01
2.23/1.34	eval_foo_bb2_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0 + 1, v_.01, v_x, v_y)) :|: v_.0 <= v_.01
2.23/1.34	eval_foo_bb3_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_stop(v_.0, v_.01, v_x, v_y)) :|: TRUE
2.23/1.34	
2.23/1.34	The start-symbols are:[eval_foo_start_4]
2.23/1.34	
2.23/1.34	
2.23/1.34	----------------------------------------
2.23/1.34	
2.23/1.34	(1) Koat Proof (FINISHED)
2.23/1.34	YES(?, 24*ar_1^2 + 56*ar_1*ar_3 + 32*ar_3^2 + 176*ar_1 + 184*ar_3 + 154)
2.23/1.34	
2.23/1.34	
2.23/1.34	
2.23/1.34	Initial complexity problem:
2.23/1.34	
2.23/1.34	1:	T:
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ]
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2 + 1, ar_3)) [ ar_0 >= ar_2 + 1 /\ ar_2 >= ar_0 ]
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 /\ ar_0 >= ar_2 + 1 ]
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.23/1.34	
2.23/1.34			(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 ]
2.23/1.34	
2.23/1.34		start location:	koat_start
2.23/1.34	
2.23/1.34		leaf cost:	0
2.23/1.34	
2.23/1.34	
2.23/1.34	
2.23/1.34	Testing for reachability in the complexity graph removes the following transitions from problem 1:
2.23/1.34	
2.23/1.34		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2 + 1, ar_3)) [ ar_0 >= ar_2 + 1 /\ ar_2 >= ar_0 ]
2.23/1.34	
2.23/1.34		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 /\ ar_0 >= ar_2 + 1 ]
2.23/1.34	
2.23/1.34	We thus obtain the following problem:
2.23/1.34	
2.23/1.34	2:	T:
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ]
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.23/1.34	
2.23/1.34			(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 ]
2.23/1.34	
2.23/1.34		start location:	koat_start
2.23/1.34	
2.23/1.34		leaf cost:	0
2.23/1.34	
2.23/1.34	
2.23/1.34	
2.23/1.34	Repeatedly propagating knowledge in problem 2 produces the following problem:
2.23/1.34	
2.23/1.34	3:	T:
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ]
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.23/1.34	
2.23/1.34			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.23/1.34	
2.23/1.34			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.23/1.34	
2.23/1.34			(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 ]
2.23/1.34	
2.23/1.34		start location:	koat_start
2.23/1.34	
2.23/1.34		leaf cost:	0
2.23/1.34	
2.23/1.34	
2.23/1.34	
2.23/1.34	A polynomial rank function with
2.23/1.34	
2.23/1.34		Pol(evalfoobb3in) = 1
2.23/1.34	
2.23/1.34		Pol(evalfoostop) = 0
2.23/1.34	
2.23/1.34		Pol(evalfoobb2in) = 2
2.23/1.34	
2.23/1.34		Pol(evalfoobb1in) = 2
2.23/1.34	
2.23/1.34		Pol(evalfoobb0in) = 2
2.23/1.34	
2.23/1.34		Pol(evalfoostart) = 2
2.23/1.34	
2.23/1.34		Pol(koat_start) = 2
2.23/1.34	
2.23/1.34	orients all transitions weakly and the transitions
2.23/1.34	
2.23/1.34		evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.23/1.34	
2.23/1.34		evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ]
2.23/1.34	
2.23/1.34	strictly and produces the following problem:
2.23/1.34	
2.23/1.34	4:	T:
2.23/1.34	
2.23/1.34			(Comp: 2, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]
2.23/1.34	
2.23/1.34			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ]
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.23/1.34	
2.23/1.34			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.23/1.34	
2.23/1.34			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.23/1.34	
2.23/1.34			(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 ]
2.23/1.34	
2.23/1.34		start location:	koat_start
2.23/1.34	
2.23/1.34		leaf cost:	0
2.23/1.34	
2.23/1.34	
2.23/1.34	
2.23/1.34	A polynomial rank function with
2.23/1.34	
2.23/1.34		Pol(evalfoobb1in) = -2*V_1 + 2*V_3 + 2
2.23/1.34	
2.23/1.34		Pol(evalfoobb2in) = -2*V_1 + 2*V_3 + 1
2.23/1.34	
2.23/1.34	and size complexities
2.23/1.34	
2.23/1.34		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
2.23/1.34	
2.23/1.34		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
2.23/1.34	
2.23/1.34		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
2.23/1.34	
2.23/1.34		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
2.23/1.34	
2.23/1.34		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
2.23/1.34	
2.23/1.34		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
2.23/1.34	
2.23/1.34		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
2.23/1.34	
2.23/1.34		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
2.23/1.34	
2.23/1.34		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))", 0-0) = ar_1
2.23/1.34	
2.23/1.34		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))", 0-1) = ar_1
2.23/1.34	
2.23/1.34		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))", 0-2) = ar_3
2.23/1.34	
2.23/1.34		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))", 0-3) = ar_3
2.23/1.34	
2.23/1.34		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]", 0-0) = ?
2.23/1.34	
2.23/1.34		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]", 0-1) = ar_1
2.23/1.34	
2.23/1.34		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]", 0-2) = ar_3
2.23/1.34	
2.23/1.34		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]", 0-3) = ar_3
2.23/1.34	
2.23/1.34		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]", 0-0) = ?
2.23/1.34	
2.23/1.34		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]", 0-1) = ar_1
2.23/1.34	
2.23/1.34		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]", 0-2) = ?
2.23/1.34	
2.23/1.34		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]", 0-3) = ar_3
2.23/1.34	
2.23/1.34		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ]", 0-0) = ?
2.23/1.34	
2.23/1.34		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ]", 0-1) = ar_1
2.23/1.34	
2.23/1.34		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ]", 0-2) = ?
2.23/1.34	
2.23/1.34		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ]", 0-3) = ar_3
2.23/1.34	
2.23/1.34		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]", 0-0) = ?
2.23/1.34	
2.23/1.34		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]", 0-1) = ar_1
2.23/1.34	
2.23/1.34		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]", 0-2) = ar_3
2.23/1.34	
2.23/1.34		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]", 0-3) = ar_3
2.23/1.34	
2.23/1.34		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_0 >= ar_2 + 1 ]", 0-0) = ?
2.23/1.34	
2.23/1.34		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_0 >= ar_2 + 1 ]", 0-1) = ar_1
2.23/1.34	
2.23/1.34		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_0 >= ar_2 + 1 ]", 0-2) = ?
2.23/1.34	
2.23/1.34		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_0 >= ar_2 + 1 ]", 0-3) = ar_3
2.23/1.34	
2.23/1.34		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-0) = ?
2.23/1.34	
2.23/1.34		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.23/1.34	
2.23/1.34		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ?
2.23/1.34	
2.23/1.34		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
2.23/1.34	
2.23/1.34	orients the transitions
2.23/1.34	
2.23/1.34		evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.23/1.34	
2.23/1.34		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]
2.23/1.34	
2.23/1.34	weakly and the transitions
2.23/1.34	
2.23/1.34		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]
2.23/1.34	
2.23/1.34		evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.23/1.34	
2.23/1.34	strictly and produces the following problem:
2.23/1.34	
2.23/1.34	5:	T:
2.23/1.34	
2.23/1.34			(Comp: 2, Cost: 1)                      evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)                      evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.23/1.34	
2.23/1.34			(Comp: 2*ar_1 + 2*ar_3 + 2, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]
2.23/1.34	
2.23/1.34			(Comp: 2, Cost: 1)                      evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ]
2.23/1.34	
2.23/1.34			(Comp: ?, Cost: 1)                      evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.23/1.34	
2.23/1.34			(Comp: 2*ar_1 + 2*ar_3 + 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.23/1.34	
2.23/1.34			(Comp: 1, Cost: 1)                      evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.23/1.34	
2.23/1.34			(Comp: 1, Cost: 1)                      evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.23/1.34	
2.23/1.34			(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 ]
2.23/1.34	
2.23/1.34		start location:	koat_start
2.23/1.34	
2.23/1.34		leaf cost:	0
2.23/1.34	
2.23/1.34	
2.23/1.34	
2.23/1.34	A polynomial rank function with
2.23/1.34	
2.23/1.34		Pol(evalfoobb2in) = 2*V_1 - 2*V_3 - 1
2.23/1.34	
2.23/1.34		Pol(evalfoobb1in) = 2*V_1 - 2*V_3
2.23/1.34	
2.23/1.34	and size complexities
2.23/1.34	
2.23/1.34		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
2.23/1.34	
2.23/1.34		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
2.23/1.34	
2.23/1.34		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
2.23/1.34	
2.23/1.34		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
2.23/1.34	
2.23/1.34		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
2.23/1.34	
2.23/1.34		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
2.23/1.34	
2.23/1.34		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
2.23/1.34	
2.23/1.34		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
2.23/1.34	
2.23/1.34		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))", 0-0) = ar_1
2.23/1.34	
2.23/1.34		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))", 0-1) = ar_1
2.23/1.34	
2.23/1.34		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))", 0-2) = ar_3
2.23/1.34	
2.23/1.34		S("evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))", 0-3) = ar_3
2.23/1.34	
2.23/1.34		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]", 0-0) = 3*ar_1 + 3*ar_3 + 18
2.23/1.34	
2.23/1.34		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]", 0-1) = ar_1
2.23/1.34	
2.23/1.34		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]", 0-2) = ar_3
2.23/1.34	
2.23/1.34		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]", 0-3) = ar_3
2.23/1.34	
2.23/1.34		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]", 0-0) = 3*ar_1 + 3*ar_3 + 54
2.23/1.34	
2.23/1.34		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]", 0-1) = ar_1
2.23/1.34	
2.23/1.34		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]", 0-2) = ?
2.23/1.34	
2.23/1.34		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]", 0-3) = ar_3
2.23/1.34	
2.23/1.34		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ]", 0-0) = 3*ar_1 + 3*ar_3 + 162
2.23/1.34	
2.23/1.34		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ]", 0-1) = ar_1
2.23/1.34	
2.23/1.34		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ]", 0-2) = ?
2.23/1.34	
2.23/1.34		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ]", 0-3) = ar_3
2.23/1.34	
2.23/1.34		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]", 0-0) = 3*ar_1 + 3*ar_3 + 18
2.23/1.34	
2.23/1.34		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]", 0-1) = ar_1
2.23/1.34	
2.23/1.34		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]", 0-2) = ar_3
2.23/1.34	
2.23/1.34		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]", 0-3) = ar_3
2.23/1.34	
2.23/1.34		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_0 >= ar_2 + 1 ]", 0-0) = 3*ar_1 + 3*ar_3 + 54
2.23/1.34	
2.23/1.34		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_0 >= ar_2 + 1 ]", 0-1) = ar_1
2.23/1.34	
2.23/1.34		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_0 >= ar_2 + 1 ]", 0-2) = ?
2.23/1.34	
2.23/1.34		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_0 >= ar_2 + 1 ]", 0-3) = ar_3
2.23/1.34	
2.23/1.34		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-0) = 3*ar_1 + 3*ar_3 + 486
2.23/1.34	
2.23/1.34		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
2.23/1.34	
2.23/1.34		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ?
2.23/1.34	
2.23/1.34		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
2.23/1.34	
2.23/1.34	orients the transitions
2.23/1.34	
2.23/1.34		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.23/1.34	
2.23/1.34		evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.23/1.34	
2.23/1.34	weakly and the transitions
2.23/1.34	
2.23/1.34		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.23/1.34	
2.23/1.34		evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.23/1.34	
2.23/1.34	strictly and produces the following problem:
2.23/1.34	
2.23/1.34	6:	T:
2.23/1.34	
2.23/1.34			(Comp: 2, Cost: 1)                                                                evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.23/1.34	
2.23/1.34			(Comp: 12*ar_1^2 + 28*ar_1*ar_3 + 16*ar_3^2 + 86*ar_1 + 90*ar_3 + 72, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.23/1.34	
2.23/1.34			(Comp: 2*ar_1 + 2*ar_3 + 2, Cost: 1)                                              evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]
2.23/1.34	
2.23/1.34			(Comp: 2, Cost: 1)                                                                evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ]
2.23/1.34	
2.23/1.34			(Comp: 12*ar_1^2 + 28*ar_1*ar_3 + 16*ar_3^2 + 86*ar_1 + 90*ar_3 + 72, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.23/1.34	
2.23/1.34			(Comp: 2*ar_1 + 2*ar_3 + 2, Cost: 1)                                              evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ]
2.23/1.34	
2.23/1.34			(Comp: 1, Cost: 1)                                                                evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.23/1.34	
2.23/1.34			(Comp: 1, Cost: 1)                                                                evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.23/1.34	
2.23/1.34			(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 ]
2.23/1.34	
2.23/1.34		start location:	koat_start
2.23/1.34	
2.23/1.34		leaf cost:	0
2.23/1.34	
2.23/1.34	
2.23/1.34	
2.23/1.34	Complexity upper bound 24*ar_1^2 + 56*ar_1*ar_3 + 32*ar_3^2 + 176*ar_1 + 184*ar_3 + 154
2.23/1.34	
2.23/1.34	
2.23/1.34	
2.23/1.34	Time: 0.114 sec (SMT: 0.098 sec)
2.23/1.34	
2.23/1.34	
2.23/1.34	----------------------------------------
2.23/1.34	
2.23/1.34	(2)
2.23/1.34	BOUNDS(1, n^2)
2.25/1.45	EOF