MAYBE
* Step 1: DependencyPairs MAYBE
+ Considered Problem:
- Strict TRS:
del(x,cons(y,xs)) -> if2(eq(x,y),x,y,xs)
del(x,nil()) -> nil()
eq(0(),0()) -> true()
eq(0(),s(y)) -> false()
eq(s(x),0()) -> false()
eq(s(x),s(y)) -> eq(x,y)
ge(0(),0()) -> true()
ge(0(),s(x)) -> false()
ge(s(x),0()) -> true()
ge(s(x),s(y)) -> ge(x,y)
h(cons(x,xs)) -> cons(x,h(xs))
h(nil()) -> nil()
if1(false(),x,y,xs) -> max(cons(y,xs))
if1(true(),x,y,xs) -> max(cons(x,xs))
if2(false(),x,y,xs) -> cons(y,del(x,xs))
if2(true(),x,y,xs) -> xs
max(cons(x,cons(y,xs))) -> if1(ge(x,y),x,y,xs)
max(cons(x,nil())) -> x
max(nil()) -> 0()
sort(cons(x,xs)) -> cons(max(cons(x,xs)),sort(h(del(max(cons(x,xs)),cons(x,xs)))))
sort(nil()) -> nil()
- Signature:
{del/2,eq/2,ge/2,h/1,if1/4,if2/4,max/1,sort/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {del,eq,ge,h,if1,if2,max,sort} and constructors {0,cons
,false,nil,s,true}
+ Applied Processor:
DependencyPairs {dpKind_ = DT}
+ Details:
We add the following dependency tuples:
Strict DPs
del#(x,cons(y,xs)) -> c_1(if2#(eq(x,y),x,y,xs),eq#(x,y))
del#(x,nil()) -> c_2()
eq#(0(),0()) -> c_3()
eq#(0(),s(y)) -> c_4()
eq#(s(x),0()) -> c_5()
eq#(s(x),s(y)) -> c_6(eq#(x,y))
ge#(0(),0()) -> c_7()
ge#(0(),s(x)) -> c_8()
ge#(s(x),0()) -> c_9()
ge#(s(x),s(y)) -> c_10(ge#(x,y))
h#(cons(x,xs)) -> c_11(h#(xs))
h#(nil()) -> c_12()
if1#(false(),x,y,xs) -> c_13(max#(cons(y,xs)))
if1#(true(),x,y,xs) -> c_14(max#(cons(x,xs)))
if2#(false(),x,y,xs) -> c_15(del#(x,xs))
if2#(true(),x,y,xs) -> c_16()
max#(cons(x,cons(y,xs))) -> c_17(if1#(ge(x,y),x,y,xs),ge#(x,y))
max#(cons(x,nil())) -> c_18()
max#(nil()) -> c_19()
sort#(cons(x,xs)) -> c_20(max#(cons(x,xs))
,sort#(h(del(max(cons(x,xs)),cons(x,xs))))
,h#(del(max(cons(x,xs)),cons(x,xs)))
,del#(max(cons(x,xs)),cons(x,xs))
,max#(cons(x,xs)))
sort#(nil()) -> c_21()
Weak DPs
and mark the set of starting terms.
* Step 2: UsableRules MAYBE
+ Considered Problem:
- Strict DPs:
del#(x,cons(y,xs)) -> c_1(if2#(eq(x,y),x,y,xs),eq#(x,y))
del#(x,nil()) -> c_2()
eq#(0(),0()) -> c_3()
eq#(0(),s(y)) -> c_4()
eq#(s(x),0()) -> c_5()
eq#(s(x),s(y)) -> c_6(eq#(x,y))
ge#(0(),0()) -> c_7()
ge#(0(),s(x)) -> c_8()
ge#(s(x),0()) -> c_9()
ge#(s(x),s(y)) -> c_10(ge#(x,y))
h#(cons(x,xs)) -> c_11(h#(xs))
h#(nil()) -> c_12()
if1#(false(),x,y,xs) -> c_13(max#(cons(y,xs)))
if1#(true(),x,y,xs) -> c_14(max#(cons(x,xs)))
if2#(false(),x,y,xs) -> c_15(del#(x,xs))
if2#(true(),x,y,xs) -> c_16()
max#(cons(x,cons(y,xs))) -> c_17(if1#(ge(x,y),x,y,xs),ge#(x,y))
max#(cons(x,nil())) -> c_18()
max#(nil()) -> c_19()
sort#(cons(x,xs)) -> c_20(max#(cons(x,xs))
,sort#(h(del(max(cons(x,xs)),cons(x,xs))))
,h#(del(max(cons(x,xs)),cons(x,xs)))
,del#(max(cons(x,xs)),cons(x,xs))
,max#(cons(x,xs)))
sort#(nil()) -> c_21()
- Weak TRS:
del(x,cons(y,xs)) -> if2(eq(x,y),x,y,xs)
del(x,nil()) -> nil()
eq(0(),0()) -> true()
eq(0(),s(y)) -> false()
eq(s(x),0()) -> false()
eq(s(x),s(y)) -> eq(x,y)
ge(0(),0()) -> true()
ge(0(),s(x)) -> false()
ge(s(x),0()) -> true()
ge(s(x),s(y)) -> ge(x,y)
h(cons(x,xs)) -> cons(x,h(xs))
h(nil()) -> nil()
if1(false(),x,y,xs) -> max(cons(y,xs))
if1(true(),x,y,xs) -> max(cons(x,xs))
if2(false(),x,y,xs) -> cons(y,del(x,xs))
if2(true(),x,y,xs) -> xs
max(cons(x,cons(y,xs))) -> if1(ge(x,y),x,y,xs)
max(cons(x,nil())) -> x
max(nil()) -> 0()
sort(cons(x,xs)) -> cons(max(cons(x,xs)),sort(h(del(max(cons(x,xs)),cons(x,xs)))))
sort(nil()) -> nil()
- Signature:
{del/2,eq/2,ge/2,h/1,if1/4,if2/4,max/1,sort/1,del#/2,eq#/2,ge#/2,h#/1,if1#/4,if2#/4,max#/1,sort#/1} / {0/0
,cons/2,false/0,nil/0,s/1,true/0,c_1/2,c_2/0,c_3/0,c_4/0,c_5/0,c_6/1,c_7/0,c_8/0,c_9/0,c_10/1,c_11/1,c_12/0
,c_13/1,c_14/1,c_15/1,c_16/0,c_17/2,c_18/0,c_19/0,c_20/5,c_21/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {del#,eq#,ge#,h#,if1#,if2#,max#,sort#} and constructors {0
,cons,false,nil,s,true}
+ Applied Processor:
UsableRules
+ Details:
We replace rewrite rules by usable rules:
del(x,cons(y,xs)) -> if2(eq(x,y),x,y,xs)
del(x,nil()) -> nil()
eq(0(),0()) -> true()
eq(0(),s(y)) -> false()
eq(s(x),0()) -> false()
eq(s(x),s(y)) -> eq(x,y)
ge(0(),0()) -> true()
ge(0(),s(x)) -> false()
ge(s(x),0()) -> true()
ge(s(x),s(y)) -> ge(x,y)
h(cons(x,xs)) -> cons(x,h(xs))
h(nil()) -> nil()
if1(false(),x,y,xs) -> max(cons(y,xs))
if1(true(),x,y,xs) -> max(cons(x,xs))
if2(false(),x,y,xs) -> cons(y,del(x,xs))
if2(true(),x,y,xs) -> xs
max(cons(x,cons(y,xs))) -> if1(ge(x,y),x,y,xs)
max(cons(x,nil())) -> x
del#(x,cons(y,xs)) -> c_1(if2#(eq(x,y),x,y,xs),eq#(x,y))
del#(x,nil()) -> c_2()
eq#(0(),0()) -> c_3()
eq#(0(),s(y)) -> c_4()
eq#(s(x),0()) -> c_5()
eq#(s(x),s(y)) -> c_6(eq#(x,y))
ge#(0(),0()) -> c_7()
ge#(0(),s(x)) -> c_8()
ge#(s(x),0()) -> c_9()
ge#(s(x),s(y)) -> c_10(ge#(x,y))
h#(cons(x,xs)) -> c_11(h#(xs))
h#(nil()) -> c_12()
if1#(false(),x,y,xs) -> c_13(max#(cons(y,xs)))
if1#(true(),x,y,xs) -> c_14(max#(cons(x,xs)))
if2#(false(),x,y,xs) -> c_15(del#(x,xs))
if2#(true(),x,y,xs) -> c_16()
max#(cons(x,cons(y,xs))) -> c_17(if1#(ge(x,y),x,y,xs),ge#(x,y))
max#(cons(x,nil())) -> c_18()
max#(nil()) -> c_19()
sort#(cons(x,xs)) -> c_20(max#(cons(x,xs))
,sort#(h(del(max(cons(x,xs)),cons(x,xs))))
,h#(del(max(cons(x,xs)),cons(x,xs)))
,del#(max(cons(x,xs)),cons(x,xs))
,max#(cons(x,xs)))
sort#(nil()) -> c_21()
* Step 3: PredecessorEstimation MAYBE
+ Considered Problem:
- Strict DPs:
del#(x,cons(y,xs)) -> c_1(if2#(eq(x,y),x,y,xs),eq#(x,y))
del#(x,nil()) -> c_2()
eq#(0(),0()) -> c_3()
eq#(0(),s(y)) -> c_4()
eq#(s(x),0()) -> c_5()
eq#(s(x),s(y)) -> c_6(eq#(x,y))
ge#(0(),0()) -> c_7()
ge#(0(),s(x)) -> c_8()
ge#(s(x),0()) -> c_9()
ge#(s(x),s(y)) -> c_10(ge#(x,y))
h#(cons(x,xs)) -> c_11(h#(xs))
h#(nil()) -> c_12()
if1#(false(),x,y,xs) -> c_13(max#(cons(y,xs)))
if1#(true(),x,y,xs) -> c_14(max#(cons(x,xs)))
if2#(false(),x,y,xs) -> c_15(del#(x,xs))
if2#(true(),x,y,xs) -> c_16()
max#(cons(x,cons(y,xs))) -> c_17(if1#(ge(x,y),x,y,xs),ge#(x,y))
max#(cons(x,nil())) -> c_18()
max#(nil()) -> c_19()
sort#(cons(x,xs)) -> c_20(max#(cons(x,xs))
,sort#(h(del(max(cons(x,xs)),cons(x,xs))))
,h#(del(max(cons(x,xs)),cons(x,xs)))
,del#(max(cons(x,xs)),cons(x,xs))
,max#(cons(x,xs)))
sort#(nil()) -> c_21()
- Weak TRS:
del(x,cons(y,xs)) -> if2(eq(x,y),x,y,xs)
del(x,nil()) -> nil()
eq(0(),0()) -> true()
eq(0(),s(y)) -> false()
eq(s(x),0()) -> false()
eq(s(x),s(y)) -> eq(x,y)
ge(0(),0()) -> true()
ge(0(),s(x)) -> false()
ge(s(x),0()) -> true()
ge(s(x),s(y)) -> ge(x,y)
h(cons(x,xs)) -> cons(x,h(xs))
h(nil()) -> nil()
if1(false(),x,y,xs) -> max(cons(y,xs))
if1(true(),x,y,xs) -> max(cons(x,xs))
if2(false(),x,y,xs) -> cons(y,del(x,xs))
if2(true(),x,y,xs) -> xs
max(cons(x,cons(y,xs))) -> if1(ge(x,y),x,y,xs)
max(cons(x,nil())) -> x
- Signature:
{del/2,eq/2,ge/2,h/1,if1/4,if2/4,max/1,sort/1,del#/2,eq#/2,ge#/2,h#/1,if1#/4,if2#/4,max#/1,sort#/1} / {0/0
,cons/2,false/0,nil/0,s/1,true/0,c_1/2,c_2/0,c_3/0,c_4/0,c_5/0,c_6/1,c_7/0,c_8/0,c_9/0,c_10/1,c_11/1,c_12/0
,c_13/1,c_14/1,c_15/1,c_16/0,c_17/2,c_18/0,c_19/0,c_20/5,c_21/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {del#,eq#,ge#,h#,if1#,if2#,max#,sort#} and constructors {0
,cons,false,nil,s,true}
+ Applied Processor:
PredecessorEstimation {onSelection = all simple predecessor estimation selector}
+ Details:
We estimate the number of application of
{2,3,4,5,7,8,9,12,16,18,19,21}
by application of
Pre({2,3,4,5,7,8,9,12,16,18,19,21}) = {1,6,10,11,13,14,15,17,20}.
Here rules are labelled as follows:
1: del#(x,cons(y,xs)) -> c_1(if2#(eq(x,y),x,y,xs),eq#(x,y))
2: del#(x,nil()) -> c_2()
3: eq#(0(),0()) -> c_3()
4: eq#(0(),s(y)) -> c_4()
5: eq#(s(x),0()) -> c_5()
6: eq#(s(x),s(y)) -> c_6(eq#(x,y))
7: ge#(0(),0()) -> c_7()
8: ge#(0(),s(x)) -> c_8()
9: ge#(s(x),0()) -> c_9()
10: ge#(s(x),s(y)) -> c_10(ge#(x,y))
11: h#(cons(x,xs)) -> c_11(h#(xs))
12: h#(nil()) -> c_12()
13: if1#(false(),x,y,xs) -> c_13(max#(cons(y,xs)))
14: if1#(true(),x,y,xs) -> c_14(max#(cons(x,xs)))
15: if2#(false(),x,y,xs) -> c_15(del#(x,xs))
16: if2#(true(),x,y,xs) -> c_16()
17: max#(cons(x,cons(y,xs))) -> c_17(if1#(ge(x,y),x,y,xs),ge#(x,y))
18: max#(cons(x,nil())) -> c_18()
19: max#(nil()) -> c_19()
20: sort#(cons(x,xs)) -> c_20(max#(cons(x,xs))
,sort#(h(del(max(cons(x,xs)),cons(x,xs))))
,h#(del(max(cons(x,xs)),cons(x,xs)))
,del#(max(cons(x,xs)),cons(x,xs))
,max#(cons(x,xs)))
21: sort#(nil()) -> c_21()
* Step 4: RemoveWeakSuffixes MAYBE
+ Considered Problem:
- Strict DPs:
del#(x,cons(y,xs)) -> c_1(if2#(eq(x,y),x,y,xs),eq#(x,y))
eq#(s(x),s(y)) -> c_6(eq#(x,y))
ge#(s(x),s(y)) -> c_10(ge#(x,y))
h#(cons(x,xs)) -> c_11(h#(xs))
if1#(false(),x,y,xs) -> c_13(max#(cons(y,xs)))
if1#(true(),x,y,xs) -> c_14(max#(cons(x,xs)))
if2#(false(),x,y,xs) -> c_15(del#(x,xs))
max#(cons(x,cons(y,xs))) -> c_17(if1#(ge(x,y),x,y,xs),ge#(x,y))
sort#(cons(x,xs)) -> c_20(max#(cons(x,xs))
,sort#(h(del(max(cons(x,xs)),cons(x,xs))))
,h#(del(max(cons(x,xs)),cons(x,xs)))
,del#(max(cons(x,xs)),cons(x,xs))
,max#(cons(x,xs)))
- Weak DPs:
del#(x,nil()) -> c_2()
eq#(0(),0()) -> c_3()
eq#(0(),s(y)) -> c_4()
eq#(s(x),0()) -> c_5()
ge#(0(),0()) -> c_7()
ge#(0(),s(x)) -> c_8()
ge#(s(x),0()) -> c_9()
h#(nil()) -> c_12()
if2#(true(),x,y,xs) -> c_16()
max#(cons(x,nil())) -> c_18()
max#(nil()) -> c_19()
sort#(nil()) -> c_21()
- Weak TRS:
del(x,cons(y,xs)) -> if2(eq(x,y),x,y,xs)
del(x,nil()) -> nil()
eq(0(),0()) -> true()
eq(0(),s(y)) -> false()
eq(s(x),0()) -> false()
eq(s(x),s(y)) -> eq(x,y)
ge(0(),0()) -> true()
ge(0(),s(x)) -> false()
ge(s(x),0()) -> true()
ge(s(x),s(y)) -> ge(x,y)
h(cons(x,xs)) -> cons(x,h(xs))
h(nil()) -> nil()
if1(false(),x,y,xs) -> max(cons(y,xs))
if1(true(),x,y,xs) -> max(cons(x,xs))
if2(false(),x,y,xs) -> cons(y,del(x,xs))
if2(true(),x,y,xs) -> xs
max(cons(x,cons(y,xs))) -> if1(ge(x,y),x,y,xs)
max(cons(x,nil())) -> x
- Signature:
{del/2,eq/2,ge/2,h/1,if1/4,if2/4,max/1,sort/1,del#/2,eq#/2,ge#/2,h#/1,if1#/4,if2#/4,max#/1,sort#/1} / {0/0
,cons/2,false/0,nil/0,s/1,true/0,c_1/2,c_2/0,c_3/0,c_4/0,c_5/0,c_6/1,c_7/0,c_8/0,c_9/0,c_10/1,c_11/1,c_12/0
,c_13/1,c_14/1,c_15/1,c_16/0,c_17/2,c_18/0,c_19/0,c_20/5,c_21/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {del#,eq#,ge#,h#,if1#,if2#,max#,sort#} and constructors {0
,cons,false,nil,s,true}
+ Applied Processor:
RemoveWeakSuffixes
+ Details:
Consider the dependency graph
1:S:del#(x,cons(y,xs)) -> c_1(if2#(eq(x,y),x,y,xs),eq#(x,y))
-->_1 if2#(false(),x,y,xs) -> c_15(del#(x,xs)):7
-->_2 eq#(s(x),s(y)) -> c_6(eq#(x,y)):2
-->_1 if2#(true(),x,y,xs) -> c_16():18
-->_2 eq#(s(x),0()) -> c_5():13
-->_2 eq#(0(),s(y)) -> c_4():12
-->_2 eq#(0(),0()) -> c_3():11
2:S:eq#(s(x),s(y)) -> c_6(eq#(x,y))
-->_1 eq#(s(x),0()) -> c_5():13
-->_1 eq#(0(),s(y)) -> c_4():12
-->_1 eq#(0(),0()) -> c_3():11
-->_1 eq#(s(x),s(y)) -> c_6(eq#(x,y)):2
3:S:ge#(s(x),s(y)) -> c_10(ge#(x,y))
-->_1 ge#(s(x),0()) -> c_9():16
-->_1 ge#(0(),s(x)) -> c_8():15
-->_1 ge#(0(),0()) -> c_7():14
-->_1 ge#(s(x),s(y)) -> c_10(ge#(x,y)):3
4:S:h#(cons(x,xs)) -> c_11(h#(xs))
-->_1 h#(nil()) -> c_12():17
-->_1 h#(cons(x,xs)) -> c_11(h#(xs)):4
5:S:if1#(false(),x,y,xs) -> c_13(max#(cons(y,xs)))
-->_1 max#(cons(x,cons(y,xs))) -> c_17(if1#(ge(x,y),x,y,xs),ge#(x,y)):8
-->_1 max#(cons(x,nil())) -> c_18():19
6:S:if1#(true(),x,y,xs) -> c_14(max#(cons(x,xs)))
-->_1 max#(cons(x,cons(y,xs))) -> c_17(if1#(ge(x,y),x,y,xs),ge#(x,y)):8
-->_1 max#(cons(x,nil())) -> c_18():19
7:S:if2#(false(),x,y,xs) -> c_15(del#(x,xs))
-->_1 del#(x,nil()) -> c_2():10
-->_1 del#(x,cons(y,xs)) -> c_1(if2#(eq(x,y),x,y,xs),eq#(x,y)):1
8:S:max#(cons(x,cons(y,xs))) -> c_17(if1#(ge(x,y),x,y,xs),ge#(x,y))
-->_2 ge#(s(x),0()) -> c_9():16
-->_2 ge#(0(),s(x)) -> c_8():15
-->_2 ge#(0(),0()) -> c_7():14
-->_1 if1#(true(),x,y,xs) -> c_14(max#(cons(x,xs))):6
-->_1 if1#(false(),x,y,xs) -> c_13(max#(cons(y,xs))):5
-->_2 ge#(s(x),s(y)) -> c_10(ge#(x,y)):3
9:S:sort#(cons(x,xs)) -> c_20(max#(cons(x,xs))
,sort#(h(del(max(cons(x,xs)),cons(x,xs))))
,h#(del(max(cons(x,xs)),cons(x,xs)))
,del#(max(cons(x,xs)),cons(x,xs))
,max#(cons(x,xs)))
-->_2 sort#(nil()) -> c_21():21
-->_5 max#(cons(x,nil())) -> c_18():19
-->_1 max#(cons(x,nil())) -> c_18():19
-->_3 h#(nil()) -> c_12():17
-->_2 sort#(cons(x,xs)) -> c_20(max#(cons(x,xs))
,sort#(h(del(max(cons(x,xs)),cons(x,xs))))
,h#(del(max(cons(x,xs)),cons(x,xs)))
,del#(max(cons(x,xs)),cons(x,xs))
,max#(cons(x,xs))):9
-->_5 max#(cons(x,cons(y,xs))) -> c_17(if1#(ge(x,y),x,y,xs),ge#(x,y)):8
-->_1 max#(cons(x,cons(y,xs))) -> c_17(if1#(ge(x,y),x,y,xs),ge#(x,y)):8
-->_3 h#(cons(x,xs)) -> c_11(h#(xs)):4
-->_4 del#(x,cons(y,xs)) -> c_1(if2#(eq(x,y),x,y,xs),eq#(x,y)):1
10:W:del#(x,nil()) -> c_2()
11:W:eq#(0(),0()) -> c_3()
12:W:eq#(0(),s(y)) -> c_4()
13:W:eq#(s(x),0()) -> c_5()
14:W:ge#(0(),0()) -> c_7()
15:W:ge#(0(),s(x)) -> c_8()
16:W:ge#(s(x),0()) -> c_9()
17:W:h#(nil()) -> c_12()
18:W:if2#(true(),x,y,xs) -> c_16()
19:W:max#(cons(x,nil())) -> c_18()
20:W:max#(nil()) -> c_19()
21:W:sort#(nil()) -> c_21()
The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
20: max#(nil()) -> c_19()
21: sort#(nil()) -> c_21()
19: max#(cons(x,nil())) -> c_18()
17: h#(nil()) -> c_12()
14: ge#(0(),0()) -> c_7()
15: ge#(0(),s(x)) -> c_8()
16: ge#(s(x),0()) -> c_9()
18: if2#(true(),x,y,xs) -> c_16()
11: eq#(0(),0()) -> c_3()
12: eq#(0(),s(y)) -> c_4()
13: eq#(s(x),0()) -> c_5()
10: del#(x,nil()) -> c_2()
* Step 5: Failure MAYBE
+ Considered Problem:
- Strict DPs:
del#(x,cons(y,xs)) -> c_1(if2#(eq(x,y),x,y,xs),eq#(x,y))
eq#(s(x),s(y)) -> c_6(eq#(x,y))
ge#(s(x),s(y)) -> c_10(ge#(x,y))
h#(cons(x,xs)) -> c_11(h#(xs))
if1#(false(),x,y,xs) -> c_13(max#(cons(y,xs)))
if1#(true(),x,y,xs) -> c_14(max#(cons(x,xs)))
if2#(false(),x,y,xs) -> c_15(del#(x,xs))
max#(cons(x,cons(y,xs))) -> c_17(if1#(ge(x,y),x,y,xs),ge#(x,y))
sort#(cons(x,xs)) -> c_20(max#(cons(x,xs))
,sort#(h(del(max(cons(x,xs)),cons(x,xs))))
,h#(del(max(cons(x,xs)),cons(x,xs)))
,del#(max(cons(x,xs)),cons(x,xs))
,max#(cons(x,xs)))
- Weak TRS:
del(x,cons(y,xs)) -> if2(eq(x,y),x,y,xs)
del(x,nil()) -> nil()
eq(0(),0()) -> true()
eq(0(),s(y)) -> false()
eq(s(x),0()) -> false()
eq(s(x),s(y)) -> eq(x,y)
ge(0(),0()) -> true()
ge(0(),s(x)) -> false()
ge(s(x),0()) -> true()
ge(s(x),s(y)) -> ge(x,y)
h(cons(x,xs)) -> cons(x,h(xs))
h(nil()) -> nil()
if1(false(),x,y,xs) -> max(cons(y,xs))
if1(true(),x,y,xs) -> max(cons(x,xs))
if2(false(),x,y,xs) -> cons(y,del(x,xs))
if2(true(),x,y,xs) -> xs
max(cons(x,cons(y,xs))) -> if1(ge(x,y),x,y,xs)
max(cons(x,nil())) -> x
- Signature:
{del/2,eq/2,ge/2,h/1,if1/4,if2/4,max/1,sort/1,del#/2,eq#/2,ge#/2,h#/1,if1#/4,if2#/4,max#/1,sort#/1} / {0/0
,cons/2,false/0,nil/0,s/1,true/0,c_1/2,c_2/0,c_3/0,c_4/0,c_5/0,c_6/1,c_7/0,c_8/0,c_9/0,c_10/1,c_11/1,c_12/0
,c_13/1,c_14/1,c_15/1,c_16/0,c_17/2,c_18/0,c_19/0,c_20/5,c_21/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {del#,eq#,ge#,h#,if1#,if2#,max#,sort#} and constructors {0
,cons,false,nil,s,true}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is still open.
MAYBE