*** 1 Progress [(O(1),O(n^1))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
@(Cons(x,xs),ys) -> Cons(x,@(xs,ys))
@(Nil(),ys) -> ys
equal(Capture(),Capture()) -> True()
equal(Capture(),Swap()) -> False()
equal(Swap(),Capture()) -> False()
equal(Swap(),Swap()) -> True()
game(p1,p2,Cons(Swap(),xs)) -> game(p2,p1,xs)
game(p1,p2,Nil()) -> @(p1,p2)
game(p1,Cons(x',xs'),Cons(Capture(),xs)) -> game(Cons(x',p1),xs',xs)
goal(p1,p2,moves) -> game(p1,p2,moves)
Weak DP Rules:
Weak TRS Rules:
Signature:
{@/2,equal/2,game/3,goal/3} / {Capture/0,Cons/2,False/0,Nil/0,Swap/0,True/0}
Obligation:
Innermost
basic terms: {@,equal,game,goal}/{Capture,Cons,False,Nil,Swap,True}
Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
Proof:
The problem is match-bounded by 2.
The enriched problem is compatible with follwoing automaton.
@_0(2,2) -> 1
@_1(2,2) -> 1
@_1(2,2) -> 3
@_2(2,2) -> 4
Capture_0() -> 1
Capture_0() -> 2
Capture_0() -> 3
Capture_0() -> 4
Cons_0(2,2) -> 1
Cons_0(2,2) -> 2
Cons_0(2,2) -> 3
Cons_0(2,2) -> 4
Cons_1(2,2) -> 1
Cons_1(2,2) -> 2
Cons_1(2,2) -> 3
Cons_1(2,2) -> 4
Cons_1(2,3) -> 1
Cons_1(2,3) -> 3
Cons_1(2,3) -> 4
Cons_2(2,4) -> 1
Cons_2(2,4) -> 3
Cons_2(2,4) -> 4
False_0() -> 1
False_0() -> 2
False_0() -> 3
False_0() -> 4
False_1() -> 1
Nil_0() -> 1
Nil_0() -> 2
Nil_0() -> 3
Nil_0() -> 4
Swap_0() -> 1
Swap_0() -> 2
Swap_0() -> 3
Swap_0() -> 4
True_0() -> 1
True_0() -> 2
True_0() -> 3
True_0() -> 4
True_1() -> 1
equal_0(2,2) -> 1
game_0(2,2,2) -> 1
game_1(2,2,2) -> 1
goal_0(2,2,2) -> 1
2 -> 1
2 -> 3
2 -> 4
*** 1.1 Progress [(O(1),O(1))] ***
Considered Problem:
Strict DP Rules:
Strict TRS Rules:
Weak DP Rules:
Weak TRS Rules:
@(Cons(x,xs),ys) -> Cons(x,@(xs,ys))
@(Nil(),ys) -> ys
equal(Capture(),Capture()) -> True()
equal(Capture(),Swap()) -> False()
equal(Swap(),Capture()) -> False()
equal(Swap(),Swap()) -> True()
game(p1,p2,Cons(Swap(),xs)) -> game(p2,p1,xs)
game(p1,p2,Nil()) -> @(p1,p2)
game(p1,Cons(x',xs'),Cons(Capture(),xs)) -> game(Cons(x',p1),xs',xs)
goal(p1,p2,moves) -> game(p1,p2,moves)
Signature:
{@/2,equal/2,game/3,goal/3} / {Capture/0,Cons/2,False/0,Nil/0,Swap/0,True/0}
Obligation:
Innermost
basic terms: {@,equal,game,goal}/{Capture,Cons,False,Nil,Swap,True}
Applied Processor:
EmptyProcessor
Proof:
The problem is already closed. The intended complexity is O(1).