YES(?,O(n^1))
0.16/0.33	YES(?,O(n^1))
0.16/0.33	
0.16/0.33	Problem:
0.16/0.33	 f(0()) -> s(0())
0.16/0.33	 f(s(0())) -> s(s(0()))
0.16/0.33	 f(s(0())) -> *(s(s(0())),f(0()))
0.16/0.33	 f(+(x,s(0()))) -> +(s(s(0())),f(x))
0.16/0.33	 f(+(x,y)) -> *(f(x),f(y))
0.16/0.33	
0.16/0.33	Proof:
0.16/0.33	 Bounds Processor:
0.16/0.33	  bound: 3
0.16/0.33	  enrichment: match
0.16/0.33	  automaton:
0.16/0.33	   final states: {5,4,3,2,1}
0.16/0.33	   transitions:
0.16/0.33	    s3(20) -> 16*
0.16/0.33	    *1(1,9) -> 12,1
0.16/0.33	    *1(12,12) -> 12,1
0.16/0.33	    03() -> 20*
0.16/0.33	    f1(5) -> 12*
0.16/0.33	    f1(12) -> 12*
0.16/0.33	    f1(7) -> 9*
0.16/0.33	    f1(2) -> 12*
0.16/0.33	    f1(4) -> 12*
0.16/0.33	    f1(1) -> 12*
0.16/0.33	    f1(3) -> 12*
0.16/0.33	    *3(25,24) -> 25,23,24,18
0.16/0.33	    +1(1,12) -> 12,1
0.16/0.33	    f3(12) -> 25*
0.16/0.33	    f3(19) -> 24*
0.16/0.33	    s1(7) -> 12,1
0.16/0.33	    s1(1) -> 12,1
0.16/0.33	    01() -> 7*
0.16/0.33	    *2(12,16) -> 25,18,19,12
0.16/0.33	    *2(18,23) -> 12*
0.16/0.33	    *2(19,18) -> 25,18,19,12
0.16/0.33	    f0(5) -> 1*
0.16/0.33	    f0(2) -> 1*
0.16/0.33	    f0(4) -> 1*
0.16/0.33	    f0(1) -> 1*
0.16/0.33	    f0(3) -> 1*
0.16/0.33	    f2(12) -> 18*
0.16/0.33	    f2(19) -> 23*
0.16/0.33	    f2(14) -> 16*
0.16/0.33	    f2(1) -> 19*
0.16/0.33	    00() -> 2*
0.16/0.33	    s2(14) -> 9*
0.16/0.33	    s2(9) -> 25,18,19,12
0.16/0.33	    s0(5) -> 3*
0.16/0.33	    s0(2) -> 3*
0.16/0.33	    s0(4) -> 3*
0.16/0.33	    s0(1) -> 3*
0.16/0.33	    s0(3) -> 3*
0.16/0.33	    02() -> 14*
0.16/0.33	    *0(3,1) -> 4*
0.16/0.33	    *0(3,3) -> 4*
0.16/0.33	    *0(3,5) -> 4*
0.16/0.33	    *0(4,2) -> 4*
0.16/0.33	    *0(4,4) -> 4*
0.16/0.33	    *0(5,1) -> 4*
0.16/0.33	    *0(5,3) -> 4*
0.16/0.33	    *0(5,5) -> 4*
0.16/0.33	    *0(1,2) -> 4*
0.16/0.33	    *0(1,4) -> 4*
0.16/0.33	    *0(2,1) -> 4*
0.16/0.33	    *0(2,3) -> 4*
0.16/0.33	    *0(2,5) -> 4*
0.16/0.33	    *0(3,2) -> 4*
0.16/0.33	    *0(3,4) -> 4*
0.16/0.33	    *0(4,1) -> 4*
0.16/0.33	    *0(4,3) -> 4*
0.16/0.33	    *0(4,5) -> 4*
0.16/0.33	    *0(5,2) -> 4*
0.16/0.33	    *0(5,4) -> 4*
0.16/0.33	    *0(1,1) -> 4*
0.16/0.33	    *0(1,3) -> 4*
0.16/0.33	    *0(1,5) -> 4*
0.16/0.33	    *0(2,2) -> 4*
0.16/0.33	    *0(2,4) -> 4*
0.16/0.33	    +2(12,19) -> 25,18,12,19
0.16/0.33	    +0(3,1) -> 5*
0.16/0.33	    +0(3,3) -> 5*
0.16/0.33	    +0(3,5) -> 5*
0.16/0.33	    +0(4,2) -> 5*
0.16/0.33	    +0(4,4) -> 5*
0.16/0.33	    +0(5,1) -> 5*
0.16/0.33	    +0(5,3) -> 5*
0.16/0.33	    +0(5,5) -> 5*
0.16/0.33	    +0(1,2) -> 5*
0.16/0.33	    +0(1,4) -> 5*
0.16/0.33	    +0(2,1) -> 5*
0.16/0.33	    +0(2,3) -> 5*
0.16/0.33	    +0(2,5) -> 5*
0.16/0.33	    +0(3,2) -> 5*
0.16/0.33	    +0(3,4) -> 5*
0.16/0.33	    +0(4,1) -> 5*
0.16/0.33	    +0(4,3) -> 5*
0.16/0.33	    +0(4,5) -> 5*
0.16/0.33	    +0(5,2) -> 5*
0.16/0.33	    +0(5,4) -> 5*
0.16/0.33	    +0(1,1) -> 5*
0.16/0.33	    +0(1,3) -> 5*
0.16/0.33	    +0(1,5) -> 5*
0.16/0.33	    +0(2,2) -> 5*
0.16/0.33	    +0(2,4) -> 5*
0.16/0.33	  problem:
0.16/0.33	   
0.16/0.33	  Qed
0.16/0.34	EOF