2.30/1.42	WORST_CASE(?, O(n^1))
2.43/1.43	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.43/1.43	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.43/1.43	
2.43/1.43	
2.43/1.43	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).
2.43/1.43	
2.43/1.43	(0) CpxIntTrs
2.43/1.43	(1) Koat Proof [FINISHED, 178 ms]
2.43/1.43	(2) BOUNDS(1, n^1)
2.43/1.43	
2.43/1.43	
2.43/1.43	----------------------------------------
2.43/1.43	
2.43/1.43	(0)
2.43/1.43	Obligation:
2.43/1.43	Complexity Int TRS consisting of the following rules:
2.43/1.43	eval_peed_pldi09_fig4_4_start(v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_4_bb0_in(v_i.0, v_m, v_n)) :|: TRUE
2.43/1.43	eval_peed_pldi09_fig4_4_bb0_in(v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_4_bb3_in(v_i.0, v_m, v_n)) :|: 0 >= v_m
2.43/1.43	eval_peed_pldi09_fig4_4_bb0_in(v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_4_bb1_in(v_n, v_m, v_n)) :|: 0 < v_m
2.43/1.43	eval_peed_pldi09_fig4_4_bb1_in(v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_4_bb2_in(v_i.0, v_m, v_n)) :|: v_i.0 > 0
2.43/1.43	eval_peed_pldi09_fig4_4_bb1_in(v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_4_bb3_in(v_i.0, v_m, v_n)) :|: v_i.0 <= 0
2.43/1.43	eval_peed_pldi09_fig4_4_bb2_in(v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_4_bb1_in(v_i.0 - 1, v_m, v_n)) :|: v_i.0 < v_m
2.43/1.43	eval_peed_pldi09_fig4_4_bb2_in(v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_4_bb1_in(v_i.0 - v_m, v_m, v_n)) :|: v_i.0 >= v_m
2.43/1.43	eval_peed_pldi09_fig4_4_bb3_in(v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_4_stop(v_i.0, v_m, v_n)) :|: TRUE
2.43/1.43	
2.43/1.43	The start-symbols are:[eval_peed_pldi09_fig4_4_start_3]
2.43/1.43	
2.43/1.43	
2.43/1.43	----------------------------------------
2.43/1.43	
2.43/1.43	(1) Koat Proof (FINISHED)
2.43/1.43	YES(?, 6*ar_2 + 7)
2.43/1.43	
2.43/1.43	
2.43/1.43	
2.43/1.43	Initial complexity problem:
2.43/1.43	
2.43/1.43	1:	T:
2.43/1.43	
2.43/1.43			(Comp: ?, Cost: 1)    evalpeedpldi09fig44start(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb0in(ar_0, ar_1, ar_2))
2.43/1.43	
2.43/1.43			(Comp: ?, Cost: 1)    evalpeedpldi09fig44bb0in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.43/1.43	
2.43/1.43			(Comp: ?, Cost: 1)    evalpeedpldi09fig44bb0in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb1in(ar_0, ar_2, ar_2)) [ ar_0 >= 1 ]
2.43/1.43	
2.43/1.43			(Comp: ?, Cost: 1)    evalpeedpldi09fig44bb1in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 1 ]
2.43/1.43	
2.43/1.43			(Comp: ?, Cost: 1)    evalpeedpldi09fig44bb1in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 ]
2.43/1.43	
2.43/1.43			(Comp: ?, Cost: 1)    evalpeedpldi09fig44bb2in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb1in(ar_0, ar_1 - 1, ar_2)) [ ar_0 >= ar_1 + 1 ]
2.43/1.43	
2.43/1.43			(Comp: ?, Cost: 1)    evalpeedpldi09fig44bb2in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb1in(ar_0, ar_1 - ar_0, ar_2)) [ ar_1 >= ar_0 ]
2.43/1.43	
2.43/1.43			(Comp: ?, Cost: 1)    evalpeedpldi09fig44bb3in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44stop(ar_0, ar_1, ar_2))
2.43/1.43	
2.43/1.43			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.43/1.43	
2.43/1.43		start location:	koat_start
2.43/1.43	
2.43/1.43		leaf cost:	0
2.43/1.43	
2.43/1.43	
2.43/1.43	
2.43/1.43	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.43/1.43	
2.43/1.43	2:	T:
2.43/1.43	
2.43/1.43			(Comp: 1, Cost: 1)    evalpeedpldi09fig44start(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb0in(ar_0, ar_1, ar_2))
2.43/1.43	
2.43/1.43			(Comp: 1, Cost: 1)    evalpeedpldi09fig44bb0in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.43/1.43	
2.43/1.43			(Comp: 1, Cost: 1)    evalpeedpldi09fig44bb0in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb1in(ar_0, ar_2, ar_2)) [ ar_0 >= 1 ]
2.43/1.43	
2.43/1.43			(Comp: ?, Cost: 1)    evalpeedpldi09fig44bb1in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 1 ]
2.43/1.43	
2.43/1.43			(Comp: ?, Cost: 1)    evalpeedpldi09fig44bb1in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 ]
2.43/1.43	
2.43/1.43			(Comp: ?, Cost: 1)    evalpeedpldi09fig44bb2in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb1in(ar_0, ar_1 - 1, ar_2)) [ ar_0 >= ar_1 + 1 ]
2.43/1.43	
2.43/1.43			(Comp: ?, Cost: 1)    evalpeedpldi09fig44bb2in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb1in(ar_0, ar_1 - ar_0, ar_2)) [ ar_1 >= ar_0 ]
2.43/1.43	
2.43/1.43			(Comp: ?, Cost: 1)    evalpeedpldi09fig44bb3in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44stop(ar_0, ar_1, ar_2))
2.43/1.43	
2.43/1.43			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.43/1.43	
2.43/1.43		start location:	koat_start
2.43/1.43	
2.43/1.43		leaf cost:	0
2.43/1.43	
2.43/1.43	
2.43/1.43	
2.43/1.43	A polynomial rank function with
2.43/1.43	
2.43/1.43		Pol(evalpeedpldi09fig44start) = 2
2.43/1.43	
2.43/1.43		Pol(evalpeedpldi09fig44bb0in) = 2
2.43/1.43	
2.43/1.43		Pol(evalpeedpldi09fig44bb3in) = 1
2.43/1.43	
2.43/1.43		Pol(evalpeedpldi09fig44bb1in) = 2
2.43/1.43	
2.43/1.43		Pol(evalpeedpldi09fig44bb2in) = 2
2.43/1.43	
2.43/1.43		Pol(evalpeedpldi09fig44stop) = 0
2.43/1.43	
2.43/1.43		Pol(koat_start) = 2
2.43/1.43	
2.43/1.43	orients all transitions weakly and the transitions
2.43/1.43	
2.43/1.43		evalpeedpldi09fig44bb3in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44stop(ar_0, ar_1, ar_2))
2.43/1.43	
2.43/1.43		evalpeedpldi09fig44bb1in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 ]
2.43/1.43	
2.43/1.43	strictly and produces the following problem:
2.43/1.43	
2.43/1.43	3:	T:
2.43/1.43	
2.43/1.43			(Comp: 1, Cost: 1)    evalpeedpldi09fig44start(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb0in(ar_0, ar_1, ar_2))
2.43/1.43	
2.43/1.43			(Comp: 1, Cost: 1)    evalpeedpldi09fig44bb0in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.43/1.43	
2.43/1.43			(Comp: 1, Cost: 1)    evalpeedpldi09fig44bb0in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb1in(ar_0, ar_2, ar_2)) [ ar_0 >= 1 ]
2.43/1.43	
2.43/1.43			(Comp: ?, Cost: 1)    evalpeedpldi09fig44bb1in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 1 ]
2.43/1.43	
2.43/1.43			(Comp: 2, Cost: 1)    evalpeedpldi09fig44bb1in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 ]
2.43/1.43	
2.43/1.43			(Comp: ?, Cost: 1)    evalpeedpldi09fig44bb2in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb1in(ar_0, ar_1 - 1, ar_2)) [ ar_0 >= ar_1 + 1 ]
2.43/1.43	
2.43/1.43			(Comp: ?, Cost: 1)    evalpeedpldi09fig44bb2in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb1in(ar_0, ar_1 - ar_0, ar_2)) [ ar_1 >= ar_0 ]
2.43/1.43	
2.43/1.43			(Comp: 2, Cost: 1)    evalpeedpldi09fig44bb3in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44stop(ar_0, ar_1, ar_2))
2.43/1.43	
2.43/1.43			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.43/1.43	
2.43/1.43		start location:	koat_start
2.43/1.43	
2.43/1.43		leaf cost:	0
2.43/1.43	
2.43/1.43	
2.43/1.43	
2.43/1.43	Applied AI with 'oct' on problem 3 to obtain the following invariants:
2.43/1.43	
2.43/1.43	  For symbol evalpeedpldi09fig44bb1in: -X_2 + X_3 >= 0 /\ X_1 - 1 >= 0
2.43/1.43	
2.43/1.43	  For symbol evalpeedpldi09fig44bb2in: X_3 - 1 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ -X_2 + X_3 >= 0 /\ X_1 + X_3 - 2 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0
2.43/1.43	
2.43/1.43	
2.43/1.43	
2.43/1.43	
2.43/1.43	
2.43/1.43	This yielded the following problem:
2.43/1.43	
2.43/1.43	4:	T:
2.43/1.43	
2.43/1.43			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.43/1.43	
2.43/1.43			(Comp: 2, Cost: 1)    evalpeedpldi09fig44bb3in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44stop(ar_0, ar_1, ar_2))
2.43/1.43	
2.43/1.43			(Comp: ?, Cost: 1)    evalpeedpldi09fig44bb2in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb1in(ar_0, ar_1 - ar_0, ar_2)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 ]
2.43/1.43	
2.43/1.43			(Comp: ?, Cost: 1)    evalpeedpldi09fig44bb2in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb1in(ar_0, ar_1 - 1, ar_2)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 + 1 ]
2.43/1.43	
2.43/1.43			(Comp: 2, Cost: 1)    evalpeedpldi09fig44bb1in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb3in(ar_0, ar_1, ar_2)) [ -ar_1 + ar_2 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_1 ]
2.43/1.43	
2.43/1.43			(Comp: ?, Cost: 1)    evalpeedpldi09fig44bb1in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb2in(ar_0, ar_1, ar_2)) [ -ar_1 + ar_2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= 1 ]
2.43/1.43	
2.43/1.43			(Comp: 1, Cost: 1)    evalpeedpldi09fig44bb0in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb1in(ar_0, ar_2, ar_2)) [ ar_0 >= 1 ]
2.43/1.43	
2.43/1.43			(Comp: 1, Cost: 1)    evalpeedpldi09fig44bb0in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.43/1.43	
2.43/1.43			(Comp: 1, Cost: 1)    evalpeedpldi09fig44start(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb0in(ar_0, ar_1, ar_2))
2.43/1.43	
2.43/1.43		start location:	koat_start
2.43/1.43	
2.43/1.43		leaf cost:	0
2.43/1.43	
2.43/1.43	
2.43/1.43	
2.43/1.43	A polynomial rank function with
2.43/1.43	
2.43/1.43		Pol(evalpeedpldi09fig44bb2in) = 2*V_2 - 1
2.43/1.43	
2.43/1.43		Pol(evalpeedpldi09fig44bb1in) = 2*V_2
2.43/1.43	
2.43/1.43	and size complexities
2.43/1.43	
2.43/1.43		S("evalpeedpldi09fig44start(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb0in(ar_0, ar_1, ar_2))", 0-0) = ar_0
2.43/1.43	
2.43/1.43		S("evalpeedpldi09fig44start(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb0in(ar_0, ar_1, ar_2))", 0-1) = ar_1
2.43/1.43	
2.43/1.43		S("evalpeedpldi09fig44start(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb0in(ar_0, ar_1, ar_2))", 0-2) = ar_2
2.43/1.43	
2.43/1.43		S("evalpeedpldi09fig44bb0in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]", 0-0) = ar_0
2.43/1.43	
2.43/1.43		S("evalpeedpldi09fig44bb0in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]", 0-1) = ar_1
2.43/1.43	
2.43/1.43		S("evalpeedpldi09fig44bb0in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]", 0-2) = ar_2
2.43/1.43	
2.43/1.43		S("evalpeedpldi09fig44bb0in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb1in(ar_0, ar_2, ar_2)) [ ar_0 >= 1 ]", 0-0) = ar_0
2.43/1.43	
2.43/1.43		S("evalpeedpldi09fig44bb0in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb1in(ar_0, ar_2, ar_2)) [ ar_0 >= 1 ]", 0-1) = ar_2
2.43/1.43	
2.43/1.43		S("evalpeedpldi09fig44bb0in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb1in(ar_0, ar_2, ar_2)) [ ar_0 >= 1 ]", 0-2) = ar_2
2.43/1.43	
2.43/1.43		S("evalpeedpldi09fig44bb1in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb2in(ar_0, ar_1, ar_2)) [ -ar_1 + ar_2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= 1 ]", 0-0) = ar_0
2.43/1.43	
2.43/1.43		S("evalpeedpldi09fig44bb1in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb2in(ar_0, ar_1, ar_2)) [ -ar_1 + ar_2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= 1 ]", 0-1) = ar_2
2.43/1.43	
2.43/1.43		S("evalpeedpldi09fig44bb1in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb2in(ar_0, ar_1, ar_2)) [ -ar_1 + ar_2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= 1 ]", 0-2) = ar_2
2.43/1.43	
2.43/1.43		S("evalpeedpldi09fig44bb1in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb3in(ar_0, ar_1, ar_2)) [ -ar_1 + ar_2 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_1 ]", 0-0) = ar_0
2.43/1.43	
2.43/1.43		S("evalpeedpldi09fig44bb1in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb3in(ar_0, ar_1, ar_2)) [ -ar_1 + ar_2 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_1 ]", 0-1) = ar_2
2.43/1.43	
2.43/1.43		S("evalpeedpldi09fig44bb1in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb3in(ar_0, ar_1, ar_2)) [ -ar_1 + ar_2 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_1 ]", 0-2) = ar_2
2.43/1.43	
2.43/1.43		S("evalpeedpldi09fig44bb2in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb1in(ar_0, ar_1 - 1, ar_2)) [ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_1 + 1 ]", 0-0) = ar_0
2.43/1.43	
2.43/1.43		S("evalpeedpldi09fig44bb2in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb1in(ar_0, ar_1 - 1, ar_2)) [ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_1 + 1 ]", 0-1) = ar_2
2.43/1.43	
2.43/1.43		S("evalpeedpldi09fig44bb2in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb1in(ar_0, ar_1 - 1, ar_2)) [ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_1 + 1 ]", 0-2) = ar_2
2.43/1.43	
2.43/1.43		S("evalpeedpldi09fig44bb2in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb1in(ar_0, ar_1 - ar_0, ar_2)) [ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_0 ]", 0-0) = ar_0
2.43/1.43	
2.43/1.43		S("evalpeedpldi09fig44bb2in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb1in(ar_0, ar_1 - ar_0, ar_2)) [ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_0 ]", 0-1) = ar_2
2.43/1.43	
2.43/1.43		S("evalpeedpldi09fig44bb2in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb1in(ar_0, ar_1 - ar_0, ar_2)) [ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ -ar_1 + ar_2 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_0 ]", 0-2) = ar_2
2.43/1.43	
2.43/1.43		S("evalpeedpldi09fig44bb3in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44stop(ar_0, ar_1, ar_2))", 0-0) = ar_0
2.43/1.43	
2.43/1.43		S("evalpeedpldi09fig44bb3in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44stop(ar_0, ar_1, ar_2))", 0-1) = ar_1 + ar_2
2.43/1.43	
2.43/1.43		S("evalpeedpldi09fig44bb3in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44stop(ar_0, ar_1, ar_2))", 0-2) = ar_2
2.43/1.43	
2.43/1.43		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
2.43/1.43	
2.43/1.43		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
2.43/1.43	
2.43/1.43		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
2.43/1.43	
2.43/1.43	orients the transitions
2.43/1.43	
2.43/1.43		evalpeedpldi09fig44bb2in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb1in(ar_0, ar_1 - ar_0, ar_2)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 ]
2.43/1.43	
2.43/1.43		evalpeedpldi09fig44bb2in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb1in(ar_0, ar_1 - 1, ar_2)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 + 1 ]
2.43/1.43	
2.43/1.43		evalpeedpldi09fig44bb1in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb2in(ar_0, ar_1, ar_2)) [ -ar_1 + ar_2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= 1 ]
2.43/1.43	
2.43/1.43	weakly and the transitions
2.43/1.43	
2.43/1.43		evalpeedpldi09fig44bb2in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb1in(ar_0, ar_1 - ar_0, ar_2)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 ]
2.43/1.43	
2.43/1.43		evalpeedpldi09fig44bb2in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb1in(ar_0, ar_1 - 1, ar_2)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 + 1 ]
2.43/1.43	
2.43/1.43		evalpeedpldi09fig44bb1in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb2in(ar_0, ar_1, ar_2)) [ -ar_1 + ar_2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= 1 ]
2.43/1.43	
2.43/1.43	strictly and produces the following problem:
2.43/1.43	
2.43/1.43	5:	T:
2.43/1.43	
2.43/1.43			(Comp: 1, Cost: 0)         koat_start(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.43/1.43	
2.43/1.43			(Comp: 2, Cost: 1)         evalpeedpldi09fig44bb3in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44stop(ar_0, ar_1, ar_2))
2.43/1.43	
2.43/1.43			(Comp: 2*ar_2, Cost: 1)    evalpeedpldi09fig44bb2in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb1in(ar_0, ar_1 - ar_0, ar_2)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_0 ]
2.43/1.43	
2.43/1.43			(Comp: 2*ar_2, Cost: 1)    evalpeedpldi09fig44bb2in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb1in(ar_0, ar_1 - 1, ar_2)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ -ar_1 + ar_2 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_1 + 1 ]
2.43/1.43	
2.43/1.43			(Comp: 2, Cost: 1)         evalpeedpldi09fig44bb1in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb3in(ar_0, ar_1, ar_2)) [ -ar_1 + ar_2 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_1 ]
2.43/1.43	
2.43/1.43			(Comp: 2*ar_2, Cost: 1)    evalpeedpldi09fig44bb1in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb2in(ar_0, ar_1, ar_2)) [ -ar_1 + ar_2 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= 1 ]
2.43/1.43	
2.43/1.43			(Comp: 1, Cost: 1)         evalpeedpldi09fig44bb0in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb1in(ar_0, ar_2, ar_2)) [ ar_0 >= 1 ]
2.43/1.43	
2.43/1.43			(Comp: 1, Cost: 1)         evalpeedpldi09fig44bb0in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.43/1.43	
2.43/1.43			(Comp: 1, Cost: 1)         evalpeedpldi09fig44start(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb0in(ar_0, ar_1, ar_2))
2.43/1.43	
2.43/1.43		start location:	koat_start
2.43/1.43	
2.43/1.43		leaf cost:	0
2.43/1.43	
2.43/1.43	
2.43/1.43	
2.43/1.43	Complexity upper bound 6*ar_2 + 7
2.43/1.43	
2.43/1.43	
2.43/1.43	
2.43/1.43	Time: 0.204 sec (SMT: 0.184 sec)
2.43/1.43	
2.43/1.43	
2.43/1.43	----------------------------------------
2.43/1.43	
2.43/1.43	(2)
2.43/1.43	BOUNDS(1, n^1)
2.43/1.45	EOF