2.18/1.50	WORST_CASE(?, O(n^1))
2.18/1.51	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.18/1.51	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.18/1.51	
2.18/1.51	
2.18/1.51	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).
2.18/1.51	
2.18/1.51	(0) CpxIntTrs
2.18/1.51	(1) Koat Proof [FINISHED, 278 ms]
2.18/1.51	(2) BOUNDS(1, n^1)
2.18/1.51	
2.18/1.51	
2.18/1.51	----------------------------------------
2.18/1.51	
2.18/1.51	(0)
2.18/1.51	Obligation:
2.18/1.51	Complexity Int TRS consisting of the following rules:
2.18/1.51	eval_gcd_start(v_.0, v_.01, v_x, v_y) -> Com_1(eval_gcd_bb0_in(v_.0, v_.01, v_x, v_y)) :|: TRUE
2.18/1.51	eval_gcd_bb0_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_gcd_bb1_in(v_x, v_y, v_x, v_y)) :|: TRUE
2.18/1.51	eval_gcd_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_gcd_bb2_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 > 0 && v_.01 > 0
2.18/1.51	eval_gcd_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_gcd_bb3_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 <= 0
2.18/1.51	eval_gcd_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_gcd_bb3_in(v_.0, v_.01, v_x, v_y)) :|: v_.01 <= 0
2.18/1.51	eval_gcd_bb2_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_gcd_bb1_in(v_.0 - v_.01, v_.01, v_x, v_y)) :|: v_.0 > v_.01
2.18/1.51	eval_gcd_bb2_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_gcd_bb1_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 > v_.01 && v_.0 <= v_.01
2.18/1.51	eval_gcd_bb2_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_gcd_bb1_in(v_.0 - v_.01, v_.01 - v_.0, v_x, v_y)) :|: v_.0 <= v_.01 && v_.0 > v_.01
2.18/1.51	eval_gcd_bb2_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_gcd_bb1_in(v_.0, v_.01 - v_.0, v_x, v_y)) :|: v_.0 <= v_.01
2.18/1.51	eval_gcd_bb3_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_gcd_stop(v_.0, v_.01, v_x, v_y)) :|: TRUE
2.18/1.51	
2.18/1.51	The start-symbols are:[eval_gcd_start_4]
2.18/1.51	
2.18/1.51	
2.18/1.51	----------------------------------------
2.18/1.51	
2.18/1.51	(1) Koat Proof (FINISHED)
2.18/1.51	YES(?, 6*ar_1 + 6*ar_3 + 8)
2.18/1.51	
2.18/1.51	
2.18/1.51	
2.18/1.51	Initial complexity problem:
2.18/1.51	
2.18/1.51	1:	T:
2.18/1.51	
2.18/1.51			(Comp: ?, Cost: 1)    evalgcdstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb0in(ar_0, ar_1, ar_2, ar_3))
2.18/1.51	
2.18/1.51			(Comp: ?, Cost: 1)    evalgcdbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb1in(ar_1, ar_1, ar_3, ar_3))
2.18/1.51	
2.18/1.51			(Comp: ?, Cost: 1)    evalgcdbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 /\ ar_2 >= 1 ]
2.18/1.51	
2.18/1.51			(Comp: ?, Cost: 1)    evalgcdbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.18/1.51	
2.18/1.51			(Comp: ?, Cost: 1)    evalgcdbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]
2.18/1.51	
2.18/1.51			(Comp: ?, Cost: 1)    evalgcdbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb1in(ar_0 - ar_2, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.18/1.51	
2.18/1.51			(Comp: ?, Cost: 1)    evalgcdbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 /\ ar_2 >= ar_0 ]
2.18/1.51	
2.18/1.51			(Comp: ?, Cost: 1)    evalgcdbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb1in(ar_0 - ar_2, ar_1, ar_2 - ar_0, ar_3)) [ ar_2 >= ar_0 /\ ar_0 >= ar_2 + 1 ]
2.18/1.51	
2.18/1.51			(Comp: ?, Cost: 1)    evalgcdbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb1in(ar_0, ar_1, ar_2 - ar_0, ar_3)) [ ar_2 >= ar_0 ]
2.18/1.51	
2.18/1.51			(Comp: ?, Cost: 1)    evalgcdbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdstop(ar_0, ar_1, ar_2, ar_3))
2.18/1.51	
2.18/1.51			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.18/1.51	
2.18/1.51		start location:	koat_start
2.18/1.51	
2.18/1.51		leaf cost:	0
2.18/1.51	
2.18/1.51	
2.18/1.51	
2.18/1.51	Testing for reachability in the complexity graph removes the following transitions from problem 1:
2.18/1.51	
2.18/1.51		evalgcdbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 /\ ar_2 >= ar_0 ]
2.18/1.51	
2.18/1.51		evalgcdbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb1in(ar_0 - ar_2, ar_1, ar_2 - ar_0, ar_3)) [ ar_2 >= ar_0 /\ ar_0 >= ar_2 + 1 ]
2.18/1.51	
2.18/1.51	We thus obtain the following problem:
2.18/1.51	
2.18/1.51	2:	T:
2.18/1.51	
2.18/1.51			(Comp: ?, Cost: 1)    evalgcdbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdstop(ar_0, ar_1, ar_2, ar_3))
2.18/1.51	
2.18/1.51			(Comp: ?, Cost: 1)    evalgcdbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb1in(ar_0, ar_1, ar_2 - ar_0, ar_3)) [ ar_2 >= ar_0 ]
2.18/1.51	
2.18/1.51			(Comp: ?, Cost: 1)    evalgcdbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb1in(ar_0 - ar_2, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.18/1.51	
2.18/1.51			(Comp: ?, Cost: 1)    evalgcdbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]
2.18/1.51	
2.18/1.51			(Comp: ?, Cost: 1)    evalgcdbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.18/1.51	
2.18/1.51			(Comp: ?, Cost: 1)    evalgcdbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 /\ ar_2 >= 1 ]
2.18/1.51	
2.18/1.51			(Comp: ?, Cost: 1)    evalgcdbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb1in(ar_1, ar_1, ar_3, ar_3))
2.18/1.51	
2.18/1.51			(Comp: ?, Cost: 1)    evalgcdstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb0in(ar_0, ar_1, ar_2, ar_3))
2.18/1.51	
2.18/1.51			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.18/1.51	
2.18/1.51		start location:	koat_start
2.18/1.51	
2.18/1.51		leaf cost:	0
2.18/1.51	
2.18/1.51	
2.18/1.51	
2.18/1.51	Repeatedly propagating knowledge in problem 2 produces the following problem:
2.18/1.51	
2.18/1.51	3:	T:
2.18/1.51	
2.18/1.51			(Comp: ?, Cost: 1)    evalgcdbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdstop(ar_0, ar_1, ar_2, ar_3))
2.18/1.51	
2.18/1.51			(Comp: ?, Cost: 1)    evalgcdbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb1in(ar_0, ar_1, ar_2 - ar_0, ar_3)) [ ar_2 >= ar_0 ]
2.18/1.51	
2.18/1.51			(Comp: ?, Cost: 1)    evalgcdbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb1in(ar_0 - ar_2, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.18/1.51	
2.18/1.51			(Comp: ?, Cost: 1)    evalgcdbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]
2.18/1.51	
2.18/1.51			(Comp: ?, Cost: 1)    evalgcdbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.18/1.51	
2.18/1.51			(Comp: ?, Cost: 1)    evalgcdbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 /\ ar_2 >= 1 ]
2.18/1.51	
2.18/1.51			(Comp: 1, Cost: 1)    evalgcdbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb1in(ar_1, ar_1, ar_3, ar_3))
2.18/1.51	
2.18/1.51			(Comp: 1, Cost: 1)    evalgcdstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb0in(ar_0, ar_1, ar_2, ar_3))
2.18/1.51	
2.18/1.51			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.18/1.51	
2.18/1.51		start location:	koat_start
2.18/1.51	
2.18/1.51		leaf cost:	0
2.18/1.51	
2.18/1.51	
2.18/1.51	
2.18/1.51	A polynomial rank function with
2.18/1.51	
2.18/1.51		Pol(evalgcdbb3in) = 1
2.18/1.51	
2.18/1.51		Pol(evalgcdstop) = 0
2.18/1.51	
2.18/1.51		Pol(evalgcdbb2in) = 2
2.18/1.51	
2.18/1.51		Pol(evalgcdbb1in) = 2
2.18/1.51	
2.18/1.51		Pol(evalgcdbb0in) = 2
2.18/1.51	
2.18/1.51		Pol(evalgcdstart) = 2
2.18/1.51	
2.18/1.51		Pol(koat_start) = 2
2.18/1.51	
2.18/1.51	orients all transitions weakly and the transitions
2.18/1.51	
2.18/1.51		evalgcdbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdstop(ar_0, ar_1, ar_2, ar_3))
2.18/1.51	
2.18/1.51		evalgcdbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]
2.18/1.51	
2.18/1.51		evalgcdbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.18/1.51	
2.18/1.51	strictly and produces the following problem:
2.18/1.51	
2.18/1.51	4:	T:
2.18/1.51	
2.18/1.51			(Comp: 2, Cost: 1)    evalgcdbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdstop(ar_0, ar_1, ar_2, ar_3))
2.18/1.51	
2.18/1.51			(Comp: ?, Cost: 1)    evalgcdbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb1in(ar_0, ar_1, ar_2 - ar_0, ar_3)) [ ar_2 >= ar_0 ]
2.18/1.51	
2.18/1.51			(Comp: ?, Cost: 1)    evalgcdbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb1in(ar_0 - ar_2, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]
2.18/1.51	
2.18/1.51			(Comp: 2, Cost: 1)    evalgcdbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]
2.18/1.51	
2.18/1.51			(Comp: 2, Cost: 1)    evalgcdbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
2.18/1.51	
2.18/1.51			(Comp: ?, Cost: 1)    evalgcdbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 1 /\ ar_2 >= 1 ]
2.18/1.51	
2.18/1.51			(Comp: 1, Cost: 1)    evalgcdbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb1in(ar_1, ar_1, ar_3, ar_3))
2.18/1.51	
2.18/1.51			(Comp: 1, Cost: 1)    evalgcdstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb0in(ar_0, ar_1, ar_2, ar_3))
2.18/1.51	
2.18/1.51			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.18/1.51	
2.18/1.51		start location:	koat_start
2.18/1.51	
2.18/1.51		leaf cost:	0
2.18/1.51	
2.18/1.51	
2.18/1.51	
2.18/1.51	Applied AI with 'oct' on problem 4 to obtain the following invariants:
2.18/1.51	
2.18/1.51	  For symbol evalgcdbb1in: -X_3 + X_4 >= 0 /\ -X_1 + X_2 >= 0
2.18/1.51	
2.18/1.51	  For symbol evalgcdbb2in: X_4 - 1 >= 0 /\ X_3 + X_4 - 2 >= 0 /\ -X_3 + X_4 >= 0 /\ X_2 + X_4 - 2 >= 0 /\ X_1 + X_4 - 2 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ X_1 + X_3 - 2 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 - 1 >= 0
2.18/1.51	
2.18/1.51	  For symbol evalgcdbb3in: -X_3 + X_4 >= 0 /\ -X_1 + X_2 >= 0
2.18/1.51	
2.18/1.51	
2.18/1.51	
2.18/1.51	
2.18/1.51	
2.18/1.51	This yielded the following problem:
2.18/1.51	
2.18/1.51	5:	T:
2.18/1.51	
2.18/1.51			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.18/1.51	
2.18/1.51			(Comp: 1, Cost: 1)    evalgcdstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb0in(ar_0, ar_1, ar_2, ar_3))
2.18/1.51	
2.18/1.51			(Comp: 1, Cost: 1)    evalgcdbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb1in(ar_1, ar_1, ar_3, ar_3))
2.18/1.51	
2.18/1.51			(Comp: ?, Cost: 1)    evalgcdbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 /\ ar_2 >= 1 ]
2.18/1.51	
2.18/1.51			(Comp: 2, Cost: 1)    evalgcdbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb3in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 ]
2.18/1.51	
2.18/1.51			(Comp: 2, Cost: 1)    evalgcdbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb3in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_2 ]
2.18/1.51	
2.18/1.51			(Comp: ?, Cost: 1)    evalgcdbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb1in(ar_0 - ar_2, ar_1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_2 + 1 ]
2.18/1.51	
2.18/1.51			(Comp: ?, Cost: 1)    evalgcdbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb1in(ar_0, ar_1, ar_2 - ar_0, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_0 ]
2.18/1.51	
2.18/1.51			(Comp: 2, Cost: 1)    evalgcdbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 ]
2.18/1.51	
2.18/1.51		start location:	koat_start
2.18/1.51	
2.18/1.51		leaf cost:	0
2.18/1.51	
2.18/1.51	
2.18/1.51	
2.18/1.51	A polynomial rank function with
2.18/1.51	
2.18/1.51		Pol(koat_start) = 2*V_2 + 2*V_4
2.18/1.51	
2.18/1.51		Pol(evalgcdstart) = 2*V_2 + 2*V_4
2.18/1.51	
2.18/1.51		Pol(evalgcdbb0in) = 2*V_2 + 2*V_4
2.18/1.51	
2.18/1.51		Pol(evalgcdbb1in) = 2*V_1 + 2*V_3
2.18/1.51	
2.18/1.51		Pol(evalgcdbb2in) = 2*V_1 + 2*V_3 - 1
2.18/1.51	
2.18/1.51		Pol(evalgcdbb3in) = 2*V_1 + 2*V_3
2.18/1.51	
2.18/1.51		Pol(evalgcdstop) = 2*V_1 + 2*V_3
2.18/1.51	
2.18/1.51	orients all transitions weakly and the transitions
2.18/1.51	
2.18/1.51		evalgcdbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb1in(ar_0 - ar_2, ar_1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_2 + 1 ]
2.18/1.51	
2.18/1.51		evalgcdbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb1in(ar_0, ar_1, ar_2 - ar_0, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_0 ]
2.18/1.51	
2.18/1.51		evalgcdbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 /\ ar_2 >= 1 ]
2.18/1.51	
2.18/1.51	strictly and produces the following problem:
2.18/1.51	
2.18/1.51	6:	T:
2.18/1.51	
2.18/1.51			(Comp: 1, Cost: 0)                  koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
2.18/1.51	
2.18/1.51			(Comp: 1, Cost: 1)                  evalgcdstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb0in(ar_0, ar_1, ar_2, ar_3))
2.18/1.51	
2.18/1.51			(Comp: 1, Cost: 1)                  evalgcdbb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb1in(ar_1, ar_1, ar_3, ar_3))
2.18/1.51	
2.18/1.51			(Comp: 2*ar_1 + 2*ar_3, Cost: 1)    evalgcdbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb2in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 1 /\ ar_2 >= 1 ]
2.18/1.51	
2.18/1.51			(Comp: 2, Cost: 1)                  evalgcdbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb3in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_0 ]
2.18/1.51	
2.18/1.51			(Comp: 2, Cost: 1)                  evalgcdbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb3in(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ 0 >= ar_2 ]
2.18/1.51	
2.18/1.51			(Comp: 2*ar_1 + 2*ar_3, Cost: 1)    evalgcdbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb1in(ar_0 - ar_2, ar_1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_2 + 1 ]
2.18/1.51	
2.18/1.51			(Comp: 2*ar_1 + 2*ar_3, Cost: 1)    evalgcdbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdbb1in(ar_0, ar_1, ar_2 - ar_0, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_0 ]
2.18/1.51	
2.18/1.51			(Comp: 2, Cost: 1)                  evalgcdbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalgcdstop(ar_0, ar_1, ar_2, ar_3)) [ -ar_2 + ar_3 >= 0 /\ -ar_0 + ar_1 >= 0 ]
2.18/1.51	
2.18/1.51		start location:	koat_start
2.18/1.51	
2.18/1.51		leaf cost:	0
2.18/1.51	
2.18/1.51	
2.18/1.51	
2.18/1.51	Complexity upper bound 6*ar_1 + 6*ar_3 + 8
2.18/1.51	
2.18/1.51	
2.18/1.51	
2.18/1.51	Time: 0.284 sec (SMT: 0.247 sec)
2.18/1.51	
2.18/1.51	
2.18/1.51	----------------------------------------
2.18/1.51	
2.18/1.51	(2)
2.18/1.51	BOUNDS(1, n^1)
2.50/1.85	EOF