2.16/1.29	WORST_CASE(?, O(1))
2.16/1.30	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.16/1.30	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.16/1.30	
2.16/1.30	
2.16/1.30	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
2.16/1.30	
2.16/1.30	(0) CpxIntTrs
2.16/1.30	(1) Koat Proof [FINISHED, 49 ms]
2.16/1.30	(2) BOUNDS(1, 1)
2.16/1.30	
2.16/1.30	
2.16/1.30	----------------------------------------
2.16/1.30	
2.16/1.30	(0)
2.16/1.30	Obligation:
2.16/1.30	Complexity Int TRS consisting of the following rules:
2.16/1.30	eval_foo_start(v_.0, v_x) -> Com_1(eval_foo_bb0_in(v_.0, v_x)) :|: TRUE
2.16/1.30	eval_foo_bb0_in(v_.0, v_x) -> Com_1(eval_foo_bb1_in(0, v_x)) :|: TRUE
2.16/1.30	eval_foo_bb1_in(v_.0, v_x) -> Com_1(eval_foo_bb2_in(v_.0, v_x)) :|: v_.0 >= 0
2.16/1.30	eval_foo_bb1_in(v_.0, v_x) -> Com_1(eval_foo_bb3_in(v_.0, v_x)) :|: v_.0 < 0
2.16/1.30	eval_foo_bb2_in(v_.0, v_x) -> Com_1(eval_foo_bb1_in(v_.0 - 1, v_x)) :|: TRUE
2.16/1.30	eval_foo_bb3_in(v_.0, v_x) -> Com_1(eval_foo_stop(v_.0, v_x)) :|: TRUE
2.16/1.30	
2.16/1.30	The start-symbols are:[eval_foo_start_2]
2.16/1.30	
2.16/1.30	
2.16/1.30	----------------------------------------
2.16/1.30	
2.16/1.30	(1) Koat Proof (FINISHED)
2.16/1.30	YES(?, 8)
2.16/1.30	
2.16/1.30	
2.16/1.30	
2.16/1.30	Initial complexity problem:
2.16/1.30	
2.16/1.30	1:	T:
2.16/1.30	
2.16/1.30			(Comp: ?, Cost: 1)    evalfoostart(ar_0) -> Com_1(evalfoobb0in(ar_0))
2.16/1.30	
2.16/1.30			(Comp: ?, Cost: 1)    evalfoobb0in(ar_0) -> Com_1(evalfoobb1in(0))
2.16/1.30	
2.16/1.30			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0) -> Com_1(evalfoobb2in(ar_0)) [ ar_0 >= 0 ]
2.16/1.30	
2.16/1.30			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0) -> Com_1(evalfoobb3in(ar_0)) [ 0 >= ar_0 + 1 ]
2.16/1.30	
2.16/1.30			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0) -> Com_1(evalfoobb1in(ar_0 - 1))
2.16/1.30	
2.16/1.30			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0) -> Com_1(evalfoostop(ar_0))
2.16/1.30	
2.16/1.30			(Comp: 1, Cost: 0)    koat_start(ar_0) -> Com_1(evalfoostart(ar_0)) [ 0 <= 0 ]
2.16/1.30	
2.16/1.30		start location:	koat_start
2.16/1.30	
2.16/1.30		leaf cost:	0
2.16/1.30	
2.16/1.30	
2.16/1.30	
2.16/1.30	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.16/1.30	
2.16/1.30	2:	T:
2.16/1.30	
2.16/1.30			(Comp: 1, Cost: 1)    evalfoostart(ar_0) -> Com_1(evalfoobb0in(ar_0))
2.16/1.30	
2.16/1.30			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0) -> Com_1(evalfoobb1in(0))
2.16/1.30	
2.16/1.30			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0) -> Com_1(evalfoobb2in(ar_0)) [ ar_0 >= 0 ]
2.16/1.30	
2.16/1.30			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0) -> Com_1(evalfoobb3in(ar_0)) [ 0 >= ar_0 + 1 ]
2.16/1.30	
2.16/1.30			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0) -> Com_1(evalfoobb1in(ar_0 - 1))
2.16/1.30	
2.16/1.30			(Comp: ?, Cost: 1)    evalfoobb3in(ar_0) -> Com_1(evalfoostop(ar_0))
2.16/1.30	
2.16/1.30			(Comp: 1, Cost: 0)    koat_start(ar_0) -> Com_1(evalfoostart(ar_0)) [ 0 <= 0 ]
2.16/1.30	
2.16/1.30		start location:	koat_start
2.16/1.30	
2.16/1.30		leaf cost:	0
2.16/1.30	
2.16/1.30	
2.16/1.30	
2.16/1.30	A polynomial rank function with
2.16/1.30	
2.16/1.30		Pol(evalfoostart) = 2
2.16/1.30	
2.16/1.30		Pol(evalfoobb0in) = 2
2.16/1.30	
2.16/1.30		Pol(evalfoobb1in) = 2
2.16/1.30	
2.16/1.30		Pol(evalfoobb2in) = 2
2.16/1.30	
2.16/1.30		Pol(evalfoobb3in) = 1
2.16/1.30	
2.16/1.30		Pol(evalfoostop) = 0
2.16/1.30	
2.16/1.30		Pol(koat_start) = 2
2.16/1.30	
2.16/1.30	orients all transitions weakly and the transitions
2.16/1.30	
2.16/1.30		evalfoobb3in(ar_0) -> Com_1(evalfoostop(ar_0))
2.16/1.30	
2.16/1.30		evalfoobb1in(ar_0) -> Com_1(evalfoobb3in(ar_0)) [ 0 >= ar_0 + 1 ]
2.16/1.30	
2.16/1.30	strictly and produces the following problem:
2.16/1.30	
2.16/1.30	3:	T:
2.16/1.30	
2.16/1.30			(Comp: 1, Cost: 1)    evalfoostart(ar_0) -> Com_1(evalfoobb0in(ar_0))
2.16/1.30	
2.16/1.30			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0) -> Com_1(evalfoobb1in(0))
2.16/1.30	
2.16/1.30			(Comp: ?, Cost: 1)    evalfoobb1in(ar_0) -> Com_1(evalfoobb2in(ar_0)) [ ar_0 >= 0 ]
2.16/1.30	
2.16/1.30			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0) -> Com_1(evalfoobb3in(ar_0)) [ 0 >= ar_0 + 1 ]
2.16/1.30	
2.16/1.30			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0) -> Com_1(evalfoobb1in(ar_0 - 1))
2.16/1.30	
2.16/1.30			(Comp: 2, Cost: 1)    evalfoobb3in(ar_0) -> Com_1(evalfoostop(ar_0))
2.16/1.30	
2.16/1.30			(Comp: 1, Cost: 0)    koat_start(ar_0) -> Com_1(evalfoostart(ar_0)) [ 0 <= 0 ]
2.16/1.30	
2.16/1.30		start location:	koat_start
2.16/1.30	
2.16/1.30		leaf cost:	0
2.16/1.30	
2.16/1.30	
2.16/1.30	
2.16/1.30	A polynomial rank function with
2.16/1.30	
2.16/1.30		Pol(evalfoostart) = 1
2.16/1.30	
2.16/1.30		Pol(evalfoobb0in) = 1
2.16/1.30	
2.16/1.30		Pol(evalfoobb1in) = V_1 + 1
2.16/1.30	
2.16/1.30		Pol(evalfoobb2in) = V_1
2.16/1.30	
2.16/1.30		Pol(evalfoobb3in) = V_1
2.16/1.30	
2.16/1.30		Pol(evalfoostop) = V_1
2.16/1.30	
2.16/1.30		Pol(koat_start) = 1
2.16/1.30	
2.16/1.30	orients all transitions weakly and the transition
2.16/1.30	
2.16/1.30		evalfoobb1in(ar_0) -> Com_1(evalfoobb2in(ar_0)) [ ar_0 >= 0 ]
2.16/1.30	
2.16/1.30	strictly and produces the following problem:
2.16/1.30	
2.16/1.30	4:	T:
2.16/1.30	
2.16/1.30			(Comp: 1, Cost: 1)    evalfoostart(ar_0) -> Com_1(evalfoobb0in(ar_0))
2.16/1.30	
2.16/1.30			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0) -> Com_1(evalfoobb1in(0))
2.16/1.30	
2.16/1.30			(Comp: 1, Cost: 1)    evalfoobb1in(ar_0) -> Com_1(evalfoobb2in(ar_0)) [ ar_0 >= 0 ]
2.16/1.30	
2.16/1.30			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0) -> Com_1(evalfoobb3in(ar_0)) [ 0 >= ar_0 + 1 ]
2.16/1.30	
2.16/1.30			(Comp: ?, Cost: 1)    evalfoobb2in(ar_0) -> Com_1(evalfoobb1in(ar_0 - 1))
2.16/1.30	
2.16/1.30			(Comp: 2, Cost: 1)    evalfoobb3in(ar_0) -> Com_1(evalfoostop(ar_0))
2.16/1.30	
2.16/1.30			(Comp: 1, Cost: 0)    koat_start(ar_0) -> Com_1(evalfoostart(ar_0)) [ 0 <= 0 ]
2.16/1.30	
2.16/1.30		start location:	koat_start
2.16/1.30	
2.16/1.30		leaf cost:	0
2.16/1.30	
2.16/1.30	
2.16/1.30	
2.16/1.30	Repeatedly propagating knowledge in problem 4 produces the following problem:
2.16/1.30	
2.16/1.30	5:	T:
2.16/1.30	
2.16/1.30			(Comp: 1, Cost: 1)    evalfoostart(ar_0) -> Com_1(evalfoobb0in(ar_0))
2.16/1.30	
2.16/1.30			(Comp: 1, Cost: 1)    evalfoobb0in(ar_0) -> Com_1(evalfoobb1in(0))
2.16/1.30	
2.16/1.30			(Comp: 1, Cost: 1)    evalfoobb1in(ar_0) -> Com_1(evalfoobb2in(ar_0)) [ ar_0 >= 0 ]
2.16/1.30	
2.16/1.30			(Comp: 2, Cost: 1)    evalfoobb1in(ar_0) -> Com_1(evalfoobb3in(ar_0)) [ 0 >= ar_0 + 1 ]
2.16/1.30	
2.16/1.30			(Comp: 1, Cost: 1)    evalfoobb2in(ar_0) -> Com_1(evalfoobb1in(ar_0 - 1))
2.16/1.30	
2.16/1.30			(Comp: 2, Cost: 1)    evalfoobb3in(ar_0) -> Com_1(evalfoostop(ar_0))
2.16/1.30	
2.16/1.30			(Comp: 1, Cost: 0)    koat_start(ar_0) -> Com_1(evalfoostart(ar_0)) [ 0 <= 0 ]
2.16/1.30	
2.16/1.30		start location:	koat_start
2.16/1.30	
2.16/1.30		leaf cost:	0
2.16/1.30	
2.16/1.30	
2.16/1.30	
2.16/1.30	Complexity upper bound 8
2.16/1.30	
2.16/1.30	
2.16/1.30	
2.16/1.30	Time: 0.028 sec (SMT: 0.026 sec)
2.16/1.30	
2.16/1.30	
2.16/1.30	----------------------------------------
2.16/1.30	
2.16/1.30	(2)
2.16/1.30	BOUNDS(1, 1)
2.25/1.32	EOF