WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: @(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 runtime complexity wrt. defined symbols {@,equal,game,goal} and constructors {Capture,Cons,False ,Nil,Swap,True} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = MiniSMT} + Details: Signatures used: ---------------- @ :: [A(1) x A(0)] -(1)-> A(0) Capture :: [] -(0)-> A(0) Cons :: [A(0) x A(1)] -(1)-> A(1) Cons :: [A(0) x A(5)] -(5)-> A(5) Cons :: [A(0) x A(0)] -(0)-> A(0) False :: [] -(0)-> A(0) Nil :: [] -(0)-> A(1) Nil :: [] -(0)-> A(5) Swap :: [] -(0)-> A(0) True :: [] -(0)-> A(0) equal :: [A(0) x A(0)] -(4)-> A(0) game :: [A(1) x A(1) x A(5)] -(2)-> A(0) goal :: [A(1) x A(1) x A(5)] -(3)-> A(0) Cost-free Signatures used: -------------------------- @ :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0) Capture :: [] -(0)-> A_cf(0) Cons :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0) Nil :: [] -(0)-> A_cf(0) Swap :: [] -(0)-> A_cf(0) game :: [A_cf(0) x A_cf(0) x A_cf(0)] -(0)-> A_cf(0) Base Constructor Signatures used: --------------------------------- Capture_A :: [] -(1)-> A(1) Cons_A :: [A(0) x A(1)] -(1)-> A(1) False_A :: [] -(0)-> A(1) Nil_A :: [] -(0)-> A(1) Swap_A :: [] -(0)-> A(1) True_A :: [] -(0)-> A(1) * Step 2: Open MAYBE - Strict TRS: @(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 runtime complexity wrt. defined symbols {@,equal,game,goal} and constructors {Capture,Cons,False ,Nil,Swap,True} Following problems could not be solved: - Strict TRS: @(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 runtime complexity wrt. defined symbols {@,equal,game,goal} and constructors {Capture,Cons,False ,Nil,Swap,True} WORST_CASE(?,O(n^1))