YES(O(1), O(n^1)) 0.00/0.89 YES(O(1), O(n^1)) 0.00/0.92 0.00/0.92 0.00/0.92
0.00/0.92 0.00/0.920 CpxTRS0.00/0.92
↳1 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))0.00/0.92
↳2 CdtProblem0.00/0.92
↳3 CdtLeafRemovalProof (ComplexityIfPolyImplication)0.00/0.92
↳4 CdtProblem0.00/0.92
↳5 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))0.00/0.92
↳6 CdtProblem0.00/0.92
↳7 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))0.00/0.92
↳8 CdtProblem0.00/0.92
↳9 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))0.00/0.92
↳10 CdtProblem0.00/0.92
↳11 SIsEmptyProof (BOTH BOUNDS(ID, ID))0.00/0.92
↳12 BOUNDS(O(1), O(1))0.00/0.92
@(Cons(x, xs), ys) → Cons(x, @(xs, ys)) 0.00/0.92
@(Nil, ys) → ys 0.00/0.92
game(p1, p2, Cons(Capture, xs)) → game[Ite][False][Ite][False][Ite](True, p1, p2, Cons(Capture, xs)) 0.00/0.92
game(p1, p2, Cons(Swap, xs)) → game(p2, p1, xs) 0.00/0.92
equal(Capture, Capture) → True 0.00/0.92
equal(Capture, Swap) → False 0.00/0.92
equal(Swap, Capture) → False 0.00/0.92
equal(Swap, Swap) → True 0.00/0.92
game(p1, p2, Nil) → @(p1, p2) 0.00/0.92
goal(p1, p2, moves) → game(p1, p2, moves)
Tuples:
@(Cons(z0, z1), z2) → Cons(z0, @(z1, z2)) 0.00/0.92
@(Nil, z0) → z0 0.00/0.92
game(z0, z1, Cons(Capture, z2)) → game[Ite][False][Ite][False][Ite](True, z0, z1, Cons(Capture, z2)) 0.00/0.92
game(z0, z1, Cons(Swap, z2)) → game(z1, z0, z2) 0.00/0.92
game(z0, z1, Nil) → @(z0, z1) 0.00/0.92
equal(Capture, Capture) → True 0.00/0.92
equal(Capture, Swap) → False 0.00/0.92
equal(Swap, Capture) → False 0.00/0.92
equal(Swap, Swap) → True 0.00/0.92
goal(z0, z1, z2) → game(z0, z1, z2)
S tuples:
@'(Cons(z0, z1), z2) → c(@'(z1, z2)) 0.00/0.92
GAME(z0, z1, Cons(Swap, z2)) → c3(GAME(z1, z0, z2)) 0.00/0.92
GAME(z0, z1, Nil) → c4(@'(z0, z1)) 0.00/0.92
GOAL(z0, z1, z2) → c9(GAME(z0, z1, z2))
K tuples:none
@'(Cons(z0, z1), z2) → c(@'(z1, z2)) 0.00/0.92
GAME(z0, z1, Cons(Swap, z2)) → c3(GAME(z1, z0, z2)) 0.00/0.92
GAME(z0, z1, Nil) → c4(@'(z0, z1)) 0.00/0.92
GOAL(z0, z1, z2) → c9(GAME(z0, z1, z2))
@, game, equal, goal
@', GAME, GOAL
c, c3, c4, c9
GOAL(z0, z1, z2) → c9(GAME(z0, z1, z2))
Tuples:
@(Cons(z0, z1), z2) → Cons(z0, @(z1, z2)) 0.00/0.92
@(Nil, z0) → z0 0.00/0.92
game(z0, z1, Cons(Capture, z2)) → game[Ite][False][Ite][False][Ite](True, z0, z1, Cons(Capture, z2)) 0.00/0.92
game(z0, z1, Cons(Swap, z2)) → game(z1, z0, z2) 0.00/0.92
game(z0, z1, Nil) → @(z0, z1) 0.00/0.92
equal(Capture, Capture) → True 0.00/0.92
equal(Capture, Swap) → False 0.00/0.92
equal(Swap, Capture) → False 0.00/0.92
equal(Swap, Swap) → True 0.00/0.92
goal(z0, z1, z2) → game(z0, z1, z2)
S tuples:
@'(Cons(z0, z1), z2) → c(@'(z1, z2)) 0.00/0.92
GAME(z0, z1, Cons(Swap, z2)) → c3(GAME(z1, z0, z2)) 0.00/0.92
GAME(z0, z1, Nil) → c4(@'(z0, z1))
K tuples:none
@'(Cons(z0, z1), z2) → c(@'(z1, z2)) 0.00/0.92
GAME(z0, z1, Cons(Swap, z2)) → c3(GAME(z1, z0, z2)) 0.00/0.92
GAME(z0, z1, Nil) → c4(@'(z0, z1))
@, game, equal, goal
@', GAME
c, c3, c4
We considered the (Usable) Rules:none
GAME(z0, z1, Nil) → c4(@'(z0, z1))
The order we found is given by the following interpretation:
@'(Cons(z0, z1), z2) → c(@'(z1, z2)) 0.00/0.92
GAME(z0, z1, Cons(Swap, z2)) → c3(GAME(z1, z0, z2)) 0.00/0.92
GAME(z0, z1, Nil) → c4(@'(z0, z1))
POL(@'(x1, x2)) = [3] + x1 + [2]x2 0.00/0.92
POL(Cons(x1, x2)) = x2 0.00/0.92
POL(GAME(x1, x2, x3)) = [3] + [3]x1 + [3]x2 + [4]x3 0.00/0.92
POL(Nil) = [2] 0.00/0.92
POL(Swap) = 0 0.00/0.92
POL(c(x1)) = x1 0.00/0.92
POL(c3(x1)) = x1 0.00/0.92
POL(c4(x1)) = x1
Tuples:
@(Cons(z0, z1), z2) → Cons(z0, @(z1, z2)) 0.00/0.92
@(Nil, z0) → z0 0.00/0.92
game(z0, z1, Cons(Capture, z2)) → game[Ite][False][Ite][False][Ite](True, z0, z1, Cons(Capture, z2)) 0.00/0.92
game(z0, z1, Cons(Swap, z2)) → game(z1, z0, z2) 0.00/0.92
game(z0, z1, Nil) → @(z0, z1) 0.00/0.92
equal(Capture, Capture) → True 0.00/0.92
equal(Capture, Swap) → False 0.00/0.92
equal(Swap, Capture) → False 0.00/0.92
equal(Swap, Swap) → True 0.00/0.92
goal(z0, z1, z2) → game(z0, z1, z2)
S tuples:
@'(Cons(z0, z1), z2) → c(@'(z1, z2)) 0.00/0.92
GAME(z0, z1, Cons(Swap, z2)) → c3(GAME(z1, z0, z2)) 0.00/0.92
GAME(z0, z1, Nil) → c4(@'(z0, z1))
K tuples:
@'(Cons(z0, z1), z2) → c(@'(z1, z2)) 0.00/0.92
GAME(z0, z1, Cons(Swap, z2)) → c3(GAME(z1, z0, z2))
Defined Rule Symbols:
GAME(z0, z1, Nil) → c4(@'(z0, z1))
@, game, equal, goal
@', GAME
c, c3, c4
We considered the (Usable) Rules:none
@'(Cons(z0, z1), z2) → c(@'(z1, z2))
The order we found is given by the following interpretation:
@'(Cons(z0, z1), z2) → c(@'(z1, z2)) 0.00/0.92
GAME(z0, z1, Cons(Swap, z2)) → c3(GAME(z1, z0, z2)) 0.00/0.92
GAME(z0, z1, Nil) → c4(@'(z0, z1))
POL(@'(x1, x2)) = [3] + x1 + x2 0.00/0.92
POL(Cons(x1, x2)) = [2] + x2 0.00/0.92
POL(GAME(x1, x2, x3)) = [5] + [5]x1 + [5]x2 0.00/0.92
POL(Nil) = [3] 0.00/0.92
POL(Swap) = [1] 0.00/0.92
POL(c(x1)) = x1 0.00/0.92
POL(c3(x1)) = x1 0.00/0.92
POL(c4(x1)) = x1
Tuples:
@(Cons(z0, z1), z2) → Cons(z0, @(z1, z2)) 0.00/0.92
@(Nil, z0) → z0 0.00/0.92
game(z0, z1, Cons(Capture, z2)) → game[Ite][False][Ite][False][Ite](True, z0, z1, Cons(Capture, z2)) 0.00/0.92
game(z0, z1, Cons(Swap, z2)) → game(z1, z0, z2) 0.00/0.92
game(z0, z1, Nil) → @(z0, z1) 0.00/0.92
equal(Capture, Capture) → True 0.00/0.92
equal(Capture, Swap) → False 0.00/0.92
equal(Swap, Capture) → False 0.00/0.92
equal(Swap, Swap) → True 0.00/0.92
goal(z0, z1, z2) → game(z0, z1, z2)
S tuples:
@'(Cons(z0, z1), z2) → c(@'(z1, z2)) 0.00/0.92
GAME(z0, z1, Cons(Swap, z2)) → c3(GAME(z1, z0, z2)) 0.00/0.92
GAME(z0, z1, Nil) → c4(@'(z0, z1))
K tuples:
GAME(z0, z1, Cons(Swap, z2)) → c3(GAME(z1, z0, z2))
Defined Rule Symbols:
GAME(z0, z1, Nil) → c4(@'(z0, z1)) 0.00/0.92
@'(Cons(z0, z1), z2) → c(@'(z1, z2))
@, game, equal, goal
@', GAME
c, c3, c4
We considered the (Usable) Rules:none
GAME(z0, z1, Cons(Swap, z2)) → c3(GAME(z1, z0, z2))
The order we found is given by the following interpretation:
@'(Cons(z0, z1), z2) → c(@'(z1, z2)) 0.00/0.92
GAME(z0, z1, Cons(Swap, z2)) → c3(GAME(z1, z0, z2)) 0.00/0.92
GAME(z0, z1, Nil) → c4(@'(z0, z1))
POL(@'(x1, x2)) = [5] + [3]x1 + [3]x2 0.00/0.92
POL(Cons(x1, x2)) = x1 + x2 0.00/0.92
POL(GAME(x1, x2, x3)) = [3] + [3]x1 + [3]x2 + [2]x3 0.00/0.92
POL(Nil) = [3] 0.00/0.92
POL(Swap) = [1] 0.00/0.92
POL(c(x1)) = x1 0.00/0.92
POL(c3(x1)) = x1 0.00/0.92
POL(c4(x1)) = x1
Tuples:
@(Cons(z0, z1), z2) → Cons(z0, @(z1, z2)) 0.00/0.92
@(Nil, z0) → z0 0.00/0.92
game(z0, z1, Cons(Capture, z2)) → game[Ite][False][Ite][False][Ite](True, z0, z1, Cons(Capture, z2)) 0.00/0.92
game(z0, z1, Cons(Swap, z2)) → game(z1, z0, z2) 0.00/0.92
game(z0, z1, Nil) → @(z0, z1) 0.00/0.92
equal(Capture, Capture) → True 0.00/0.92
equal(Capture, Swap) → False 0.00/0.92
equal(Swap, Capture) → False 0.00/0.92
equal(Swap, Swap) → True 0.00/0.92
goal(z0, z1, z2) → game(z0, z1, z2)
S tuples:none
@'(Cons(z0, z1), z2) → c(@'(z1, z2)) 0.00/0.92
GAME(z0, z1, Cons(Swap, z2)) → c3(GAME(z1, z0, z2)) 0.00/0.92
GAME(z0, z1, Nil) → c4(@'(z0, z1))
Defined Rule Symbols:
GAME(z0, z1, Nil) → c4(@'(z0, z1)) 0.00/0.92
@'(Cons(z0, z1), z2) → c(@'(z1, z2)) 0.00/0.92
GAME(z0, z1, Cons(Swap, z2)) → c3(GAME(z1, z0, z2))
@, game, equal, goal
@', GAME
c, c3, c4