2.12/1.43	WORST_CASE(?, O(n^2))
2.39/1.44	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.39/1.44	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.39/1.44	
2.39/1.44	
2.39/1.44	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2).
2.39/1.44	
2.39/1.44	(0) CpxIntTrs
2.39/1.44	(1) Koat Proof [FINISHED, 269 ms]
2.39/1.44	(2) BOUNDS(1, n^2)
2.39/1.44	
2.39/1.44	
2.39/1.44	----------------------------------------
2.39/1.44	
2.39/1.44	(0)
2.39/1.44	Obligation:
2.39/1.44	Complexity Int TRS consisting of the following rules:
2.39/1.44	eval_foo_start(v_.0, v_.01, v_N, v_i, v_j) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_N, v_i, v_j)) :|: TRUE
2.39/1.44	eval_foo_bb0_in(v_.0, v_.01, v_N, v_i, v_j) -> Com_1(eval_foo_bb1_in(v_N, v_j, v_N, v_i, v_j)) :|: TRUE
2.39/1.44	eval_foo_bb1_in(v_.0, v_.01, v_N, v_i, v_j) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_N, v_i, v_j)) :|: v_.0 > 0
2.39/1.44	eval_foo_bb1_in(v_.0, v_.01, v_N, v_i, v_j) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_N, v_i, v_j)) :|: v_.0 <= 0
2.39/1.44	eval_foo_bb2_in(v_.0, v_.01, v_N, v_i, v_j) -> Com_1(eval_foo_bb1_in(v_.0, v_.01 - 1, v_N, v_i, v_j)) :|: v_.01 > 0
2.39/1.44	eval_foo_bb2_in(v_.0, v_.01, v_N, v_i, v_j) -> Com_1(eval_foo_bb1_in(v_.0 - 1, v_.01 - 1, v_N, v_i, v_j)) :|: v_.01 > 0 && v_.01 <= 0
2.39/1.44	eval_foo_bb2_in(v_.0, v_.01, v_N, v_i, v_j) -> Com_1(eval_foo_bb1_in(v_.0, v_N, v_N, v_i, v_j)) :|: v_.01 <= 0 && v_.01 > 0
2.39/1.44	eval_foo_bb2_in(v_.0, v_.01, v_N, v_i, v_j) -> Com_1(eval_foo_bb1_in(v_.0 - 1, v_N, v_N, v_i, v_j)) :|: v_.01 <= 0
2.39/1.44	eval_foo_bb3_in(v_.0, v_.01, v_N, v_i, v_j) -> Com_1(eval_foo_stop(v_.0, v_.01, v_N, v_i, v_j)) :|: TRUE
2.39/1.44	
2.39/1.44	The start-symbols are:[eval_foo_start_5]
2.39/1.44	
2.39/1.44	
2.39/1.44	----------------------------------------
2.39/1.44	
2.39/1.44	(1) Koat Proof (FINISHED)
2.39/1.44	YES(?, 2*ar_1 + 2*ar_1^2 + 2*ar_3 + 7)
2.39/1.44	
2.39/1.44	
2.39/1.44	
2.39/1.44	Initial complexity problem:
2.39/1.44	
2.39/1.44	1:	T:
2.39/1.44	
2.39/1.44			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.39/1.44	
2.39/1.44			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.39/1.44	
2.39/1.44			(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 >= 1 ]
2.39/1.44	
2.39/1.44			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.39/1.44	
2.39/1.44			(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_2 >= 1 ]
2.39/1.44	
2.39/1.44			(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_2 >= 1 /\ 0 >= ar_2 ]
2.39/1.44	
2.39/1.44			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_1, ar_3)) [ 0 >= ar_2 /\ ar_2 >= 1 ]
2.39/1.44	
2.39/1.44			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_1, ar_3)) [ 0 >= ar_2 ]
2.39/1.44	
2.39/1.44			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.39/1.44	
2.39/1.44			(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 ]
2.39/1.44	
2.39/1.44		start location:	koat_start
2.39/1.44	
2.39/1.44		leaf cost:	0
2.39/1.44	
2.39/1.44	
2.39/1.44	
2.39/1.44	Testing for reachability in the complexity graph removes the following transitions from problem 1:
2.39/1.44	
2.39/1.44		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3)) [ ar_2 >= 1 /\ 0 >= ar_2 ]
2.39/1.44	
2.39/1.44		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_1, ar_3)) [ 0 >= ar_2 /\ ar_2 >= 1 ]
2.39/1.44	
2.39/1.44	We thus obtain the following problem:
2.39/1.44	
2.39/1.44	2:	T:
2.39/1.44	
2.39/1.44			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.39/1.44	
2.39/1.44			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_1, ar_3)) [ 0 >= ar_2 ]
2.39/1.44	
2.39/1.44			(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_2 >= 1 ]
2.39/1.44	
2.39/1.44			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.39/1.44	
2.39/1.44			(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 >= 1 ]
2.39/1.44	
2.39/1.44			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.39/1.44	
2.39/1.44			(Comp: ?, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.39/1.44	
2.39/1.44			(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 ]
2.39/1.44	
2.39/1.44		start location:	koat_start
2.39/1.44	
2.39/1.44		leaf cost:	0
2.39/1.44	
2.39/1.44	
2.39/1.44	
2.39/1.44	Repeatedly propagating knowledge in problem 2 produces the following problem:
2.39/1.44	
2.39/1.44	3:	T:
2.39/1.44	
2.39/1.44			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.39/1.44	
2.39/1.44			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_1, ar_3)) [ 0 >= ar_2 ]
2.39/1.44	
2.39/1.44			(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_2 >= 1 ]
2.39/1.44	
2.39/1.44			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.39/1.44	
2.39/1.44			(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 >= 1 ]
2.39/1.44	
2.39/1.44			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.39/1.44	
2.39/1.44			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.39/1.44	
2.39/1.44			(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 ]
2.39/1.44	
2.39/1.44		start location:	koat_start
2.39/1.44	
2.39/1.44		leaf cost:	0
2.39/1.44	
2.39/1.44	
2.39/1.44	
2.39/1.44	A polynomial rank function with
2.39/1.44	
2.39/1.44		Pol(evalfoobb3in) = 1
2.39/1.44	
2.39/1.44		Pol(evalfoostop) = 0
2.39/1.44	
2.39/1.44		Pol(evalfoobb2in) = 2
2.39/1.44	
2.39/1.44		Pol(evalfoobb1in) = 2
2.39/1.44	
2.39/1.44		Pol(evalfoobb0in) = 2
2.39/1.44	
2.39/1.44		Pol(evalfoostart) = 2
2.39/1.44	
2.39/1.44		Pol(koat_start) = 2
2.39/1.44	
2.39/1.44	orients all transitions weakly and the transitions
2.39/1.44	
2.39/1.44		evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.39/1.44	
2.39/1.44		evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.39/1.44	
2.39/1.44	strictly and produces the following problem:
2.39/1.44	
2.39/1.44	4:	T:
2.39/1.44	
2.39/1.44			(Comp: 2, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3))
2.39/1.44	
2.39/1.44			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_1, ar_3)) [ 0 >= ar_2 ]
2.39/1.44	
2.39/1.44			(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_2 >= 1 ]
2.39/1.44	
2.39/1.44			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.39/1.44	
2.39/1.44			(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 >= 1 ]
2.39/1.44	
2.39/1.44			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.39/1.44	
2.39/1.44			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.39/1.44	
2.39/1.44			(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 ]
2.39/1.44	
2.39/1.44		start location:	koat_start
2.39/1.44	
2.39/1.44		leaf cost:	0
2.39/1.44	
2.39/1.44	
2.39/1.44	
2.39/1.44	Applied AI with 'oct' on problem 4 to obtain the following invariants:
2.39/1.44	
2.39/1.44	  For symbol evalfoobb1in: -X_1 + X_2 >= 0
2.39/1.44	
2.39/1.44	  For symbol evalfoobb2in: X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 - 1 >= 0
2.39/1.44	
2.39/1.44	  For symbol evalfoobb3in: -X_1 + X_2 >= 0 /\ -X_1 >= 0
2.39/1.44	
2.39/1.44	
2.39/1.44	
2.39/1.44	
2.39/1.44	
2.39/1.44	This yielded the following problem:
2.39/1.44	
2.39/1.44	5:	T:
2.39/1.44	
2.39/1.44			(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 ]
2.39/1.44	
2.39/1.44			(Comp: 1, Cost: 1)    evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.39/1.44	
2.39/1.44			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.39/1.44	
2.39/1.44			(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_1 >= 0 /\ ar_0 >= 1 ]
2.39/1.44	
2.39/1.44			(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_1 >= 0 /\ 0 >= ar_0 ]
2.39/1.44	
2.39/1.44			(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_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 ]
2.39/1.44	
2.39/1.44			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_1, ar_3)) [ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ]
2.39/1.44	
2.39/1.44			(Comp: 2, Cost: 1)    evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\ -ar_0 >= 0 ]
2.39/1.44	
2.39/1.44		start location:	koat_start
2.39/1.44	
2.39/1.44		leaf cost:	0
2.39/1.44	
2.39/1.44	
2.39/1.44	
2.39/1.44	A polynomial rank function with
2.39/1.44	
2.39/1.44		Pol(koat_start) = V_2
2.39/1.44	
2.39/1.44		Pol(evalfoostart) = V_2
2.39/1.44	
2.39/1.44		Pol(evalfoobb0in) = V_2
2.39/1.44	
2.39/1.44		Pol(evalfoobb1in) = V_1
2.39/1.44	
2.39/1.44		Pol(evalfoobb2in) = V_1
2.39/1.44	
2.39/1.44		Pol(evalfoobb3in) = V_1
2.39/1.44	
2.39/1.44		Pol(evalfoostop) = V_1
2.39/1.44	
2.39/1.44	orients all transitions weakly and the transition
2.39/1.44	
2.39/1.44		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_1, ar_3)) [ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ]
2.39/1.44	
2.39/1.44	strictly and produces the following problem:
2.39/1.44	
2.39/1.44	6:	T:
2.39/1.44	
2.39/1.44			(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 ]
2.39/1.44	
2.39/1.44			(Comp: 1, Cost: 1)       evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.39/1.44	
2.39/1.44			(Comp: 1, Cost: 1)       evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.39/1.44	
2.39/1.44			(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_1 >= 0 /\ ar_0 >= 1 ]
2.39/1.44	
2.39/1.44			(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_1 >= 0 /\ 0 >= ar_0 ]
2.39/1.44	
2.39/1.44			(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_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 ]
2.39/1.44	
2.39/1.44			(Comp: ar_1, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_1, ar_3)) [ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ]
2.39/1.44	
2.39/1.44			(Comp: 2, Cost: 1)       evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\ -ar_0 >= 0 ]
2.39/1.44	
2.39/1.44		start location:	koat_start
2.39/1.44	
2.39/1.44		leaf cost:	0
2.39/1.44	
2.39/1.44	
2.39/1.44	
2.39/1.44	A polynomial rank function with
2.39/1.44	
2.39/1.44		Pol(evalfoobb2in) = V_3
2.39/1.44	
2.39/1.44		Pol(evalfoobb1in) = V_3
2.39/1.44	
2.39/1.44	and size complexities
2.39/1.44	
2.39/1.44		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\\ -ar_0 >= 0 ]", 0-0) = ar_1
2.39/1.44	
2.39/1.44		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\\ -ar_0 >= 0 ]", 0-1) = ar_1
2.39/1.44	
2.39/1.44		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\\ -ar_0 >= 0 ]", 0-2) = ar_1 + ar_3
2.39/1.44	
2.39/1.44		S("evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\\ -ar_0 >= 0 ]", 0-3) = ar_3
2.39/1.44	
2.39/1.44		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_1, ar_3)) [ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 ]", 0-0) = ar_1
2.39/1.44	
2.39/1.44		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_1, ar_3)) [ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 ]", 0-1) = ar_1
2.39/1.44	
2.39/1.44		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_1, ar_3)) [ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 ]", 0-2) = ar_1
2.39/1.44	
2.39/1.44		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_1, ar_3)) [ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_2 ]", 0-3) = ar_3
2.39/1.44	
2.39/1.44		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 ]", 0-0) = ar_1
2.39/1.44	
2.39/1.44		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 ]", 0-1) = ar_1
2.39/1.44	
2.39/1.44		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 ]", 0-2) = ar_1 + ar_3
2.39/1.44	
2.39/1.44		S("evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= 1 ]", 0-3) = ar_3
2.39/1.44	
2.39/1.44		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\\ 0 >= ar_0 ]", 0-0) = ar_1
2.39/1.44	
2.39/1.44		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\\ 0 >= ar_0 ]", 0-1) = ar_1
2.39/1.44	
2.39/1.44		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\\ 0 >= ar_0 ]", 0-2) = ar_1 + ar_3
2.39/1.44	
2.39/1.44		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\\ 0 >= ar_0 ]", 0-3) = ar_3
2.39/1.44	
2.39/1.44		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\\ ar_0 >= 1 ]", 0-0) = ar_1
2.39/1.44	
2.39/1.44		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\\ ar_0 >= 1 ]", 0-1) = ar_1
2.39/1.44	
2.39/1.44		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\\ ar_0 >= 1 ]", 0-2) = ar_1 + ar_3
2.39/1.44	
2.39/1.44		S("evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\\ ar_0 >= 1 ]", 0-3) = ar_3
2.39/1.44	
2.39/1.44		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
2.39/1.44	
2.39/1.44		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
2.39/1.44	
2.39/1.44		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
2.39/1.44	
2.39/1.44		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
2.39/1.44	
2.39/1.44		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
2.39/1.44	
2.39/1.44		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
2.39/1.44	
2.39/1.44		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
2.39/1.44	
2.39/1.44		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
2.39/1.44	
2.39/1.44		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
2.39/1.44	
2.39/1.44		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
2.39/1.44	
2.39/1.44		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
2.39/1.44	
2.39/1.44		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
2.39/1.44	
2.39/1.44	orients the transitions
2.39/1.44	
2.39/1.44		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 ]
2.39/1.44	
2.39/1.44		evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 ]
2.39/1.44	
2.39/1.44	weakly and the transition
2.39/1.44	
2.39/1.44		evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 ]
2.39/1.44	
2.39/1.44	strictly and produces the following problem:
2.39/1.44	
2.39/1.44	7:	T:
2.39/1.44	
2.39/1.44			(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 ]
2.39/1.44	
2.39/1.44			(Comp: 1, Cost: 1)                evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.39/1.44	
2.39/1.44			(Comp: 1, Cost: 1)                evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.39/1.44	
2.39/1.44			(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_1 >= 0 /\ ar_0 >= 1 ]
2.39/1.44	
2.39/1.44			(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_1 >= 0 /\ 0 >= ar_0 ]
2.39/1.44	
2.39/1.44			(Comp: ar_1^2 + ar_3, Cost: 1)    evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 ]
2.39/1.44	
2.39/1.44			(Comp: ar_1, Cost: 1)             evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_1, ar_3)) [ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ]
2.39/1.44	
2.39/1.44			(Comp: 2, Cost: 1)                evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\ -ar_0 >= 0 ]
2.39/1.44	
2.39/1.44		start location:	koat_start
2.39/1.44	
2.39/1.44		leaf cost:	0
2.39/1.44	
2.39/1.44	
2.39/1.44	
2.39/1.44	Repeatedly propagating knowledge in problem 7 produces the following problem:
2.39/1.44	
2.39/1.44	8:	T:
2.39/1.44	
2.39/1.44			(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 ]
2.39/1.44	
2.39/1.44			(Comp: 1, Cost: 1)                           evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3))
2.39/1.44	
2.39/1.44			(Comp: 1, Cost: 1)                           evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3))
2.39/1.44	
2.39/1.44			(Comp: ar_1 + ar_1^2 + ar_3 + 1, 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_1 >= 0 /\ ar_0 >= 1 ]
2.39/1.44	
2.39/1.44			(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_1 >= 0 /\ 0 >= ar_0 ]
2.39/1.44	
2.39/1.44			(Comp: ar_1^2 + ar_3, Cost: 1)               evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= 1 ]
2.39/1.44	
2.39/1.44			(Comp: ar_1, Cost: 1)                        evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_1, ar_3)) [ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_2 ]
2.39/1.44	
2.39/1.44			(Comp: 2, Cost: 1)                           evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) [ -ar_0 + ar_1 >= 0 /\ -ar_0 >= 0 ]
2.39/1.44	
2.39/1.44		start location:	koat_start
2.39/1.44	
2.39/1.44		leaf cost:	0
2.39/1.44	
2.39/1.44	
2.39/1.44	
2.39/1.44	Complexity upper bound 2*ar_1 + 2*ar_1^2 + 2*ar_3 + 7
2.39/1.44	
2.39/1.44	
2.39/1.44	
2.39/1.44	Time: 0.211 sec (SMT: 0.189 sec)
2.39/1.44	
2.39/1.44	
2.39/1.44	----------------------------------------
2.39/1.44	
2.39/1.44	(2)
2.39/1.44	BOUNDS(1, n^2)
2.39/1.45	EOF