R
↳Dependency Pair Analysis
AF(X) -> AIF(mark(X), c, f(true))
AF(X) -> MARK(X)
AIF(true, X, Y) -> MARK(X)
AIF(false, X, Y) -> MARK(Y)
MARK(f(X)) -> AF(mark(X))
MARK(f(X)) -> MARK(X)
MARK(if(X1, X2, X3)) -> AIF(mark(X1), mark(X2), X3)
MARK(if(X1, X2, X3)) -> MARK(X1)
MARK(if(X1, X2, X3)) -> MARK(X2)
R
↳DPs
→DP Problem 1
↳Argument Filtering and Ordering
MARK(if(X1, X2, X3)) -> MARK(X2)
MARK(if(X1, X2, X3)) -> MARK(X1)
AIF(false, X, Y) -> MARK(Y)
MARK(if(X1, X2, X3)) -> AIF(mark(X1), mark(X2), X3)
MARK(f(X)) -> MARK(X)
AF(X) -> MARK(X)
MARK(f(X)) -> AF(mark(X))
AIF(true, X, Y) -> MARK(X)
AF(X) -> AIF(mark(X), c, f(true))
af(X) -> aif(mark(X), c, f(true))
af(X) -> f(X)
aif(true, X, Y) -> mark(X)
aif(false, X, Y) -> mark(Y)
aif(X1, X2, X3) -> if(X1, X2, X3)
mark(f(X)) -> af(mark(X))
mark(if(X1, X2, X3)) -> aif(mark(X1), mark(X2), X3)
mark(c) -> c
mark(true) -> true
mark(false) -> false
AIF(false, X, Y) -> MARK(Y)
aif(true, X, Y) -> mark(X)
aif(false, X, Y) -> mark(Y)
aif(X1, X2, X3) -> if(X1, X2, X3)
mark(f(X)) -> af(mark(X))
mark(if(X1, X2, X3)) -> aif(mark(X1), mark(X2), X3)
mark(c) -> c
mark(true) -> true
mark(false) -> false
af(X) -> aif(mark(X), c, f(true))
af(X) -> f(X)
POL(if(x1, x2, x3)) = x1 + x2 + x3 POL(c) = 0 POL(MARK(x1)) = x1 POL(false) = 1 POL(a__if(x1, x2, x3)) = x1 + x2 + x3 POL(A__F(x1)) = x1 POL(true) = 0 POL(mark(x1)) = x1 POL(f(x1)) = x1 POL(A__IF(x1, x2, x3)) = x1 + x2 + x3 POL(a__f(x1)) = x1
MARK(x1) -> MARK(x1)
if(x1, x2, x3) -> if(x1, x2, x3)
AF(x1) -> AF(x1)
AIF(x1, x2, x3) -> AIF(x1, x2, x3)
mark(x1) -> mark(x1)
f(x1) -> f(x1)
aif(x1, x2, x3) -> aif(x1, x2, x3)
af(x1) -> af(x1)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Argument Filtering and Ordering
MARK(if(X1, X2, X3)) -> MARK(X2)
MARK(if(X1, X2, X3)) -> MARK(X1)
MARK(if(X1, X2, X3)) -> AIF(mark(X1), mark(X2), X3)
MARK(f(X)) -> MARK(X)
AF(X) -> MARK(X)
MARK(f(X)) -> AF(mark(X))
AIF(true, X, Y) -> MARK(X)
AF(X) -> AIF(mark(X), c, f(true))
af(X) -> aif(mark(X), c, f(true))
af(X) -> f(X)
aif(true, X, Y) -> mark(X)
aif(false, X, Y) -> mark(Y)
aif(X1, X2, X3) -> if(X1, X2, X3)
mark(f(X)) -> af(mark(X))
mark(if(X1, X2, X3)) -> aif(mark(X1), mark(X2), X3)
mark(c) -> c
mark(true) -> true
mark(false) -> false
MARK(f(X)) -> MARK(X)
AF(X) -> MARK(X)
aif(true, X, Y) -> mark(X)
aif(false, X, Y) -> mark(Y)
aif(X1, X2, X3) -> if(X1, X2, X3)
mark(f(X)) -> af(mark(X))
mark(if(X1, X2, X3)) -> aif(mark(X1), mark(X2), X3)
mark(c) -> c
mark(true) -> true
mark(false) -> false
af(X) -> aif(mark(X), c, f(true))
af(X) -> f(X)
POL(if(x1, x2, x3)) = x1 + x2 + x3 POL(c) = 0 POL(MARK(x1)) = x1 POL(false) = 0 POL(a__if(x1, x2, x3)) = x1 + x2 + x3 POL(A__F(x1)) = 1 + x1 POL(true) = 0 POL(mark(x1)) = x1 POL(f(x1)) = 1 + x1 POL(A__IF(x1, x2, x3)) = x1 + x2 + x3 POL(a__f(x1)) = 1 + x1
MARK(x1) -> MARK(x1)
if(x1, x2, x3) -> if(x1, x2, x3)
AF(x1) -> AF(x1)
AIF(x1, x2, x3) -> AIF(x1, x2, x3)
mark(x1) -> mark(x1)
f(x1) -> f(x1)
aif(x1, x2, x3) -> aif(x1, x2, x3)
af(x1) -> af(x1)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳AFS
...
→DP Problem 3
↳Argument Filtering and Ordering
MARK(if(X1, X2, X3)) -> MARK(X2)
MARK(if(X1, X2, X3)) -> MARK(X1)
MARK(if(X1, X2, X3)) -> AIF(mark(X1), mark(X2), X3)
MARK(f(X)) -> AF(mark(X))
AIF(true, X, Y) -> MARK(X)
AF(X) -> AIF(mark(X), c, f(true))
af(X) -> aif(mark(X), c, f(true))
af(X) -> f(X)
aif(true, X, Y) -> mark(X)
aif(false, X, Y) -> mark(Y)
aif(X1, X2, X3) -> if(X1, X2, X3)
mark(f(X)) -> af(mark(X))
mark(if(X1, X2, X3)) -> aif(mark(X1), mark(X2), X3)
mark(c) -> c
mark(true) -> true
mark(false) -> false
AF(X) -> AIF(mark(X), c, f(true))
aif(true, X, Y) -> mark(X)
aif(false, X, Y) -> mark(Y)
aif(X1, X2, X3) -> if(X1, X2, X3)
mark(f(X)) -> af(mark(X))
mark(if(X1, X2, X3)) -> aif(mark(X1), mark(X2), X3)
mark(c) -> c
mark(true) -> true
mark(false) -> false
af(X) -> aif(mark(X), c, f(true))
af(X) -> f(X)
POL(if(x1, x2, x3)) = x1 + x2 + x3 POL(c) = 0 POL(MARK(x1)) = x1 POL(false) = 0 POL(a__if(x1, x2, x3)) = x1 + x2 + x3 POL(A__F(x1)) = 1 + x1 POL(true) = 0 POL(mark(x1)) = x1 POL(f(x1)) = 1 + x1 POL(a__f(x1)) = 1 + x1
MARK(x1) -> MARK(x1)
if(x1, x2, x3) -> if(x1, x2, x3)
AF(x1) -> AF(x1)
AIF(x1, x2, x3) -> x2
mark(x1) -> mark(x1)
f(x1) -> f(x1)
aif(x1, x2, x3) -> aif(x1, x2, x3)
af(x1) -> af(x1)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳AFS
...
→DP Problem 4
↳Dependency Graph
MARK(if(X1, X2, X3)) -> MARK(X2)
MARK(if(X1, X2, X3)) -> MARK(X1)
MARK(if(X1, X2, X3)) -> AIF(mark(X1), mark(X2), X3)
MARK(f(X)) -> AF(mark(X))
AIF(true, X, Y) -> MARK(X)
af(X) -> aif(mark(X), c, f(true))
af(X) -> f(X)
aif(true, X, Y) -> mark(X)
aif(false, X, Y) -> mark(Y)
aif(X1, X2, X3) -> if(X1, X2, X3)
mark(f(X)) -> af(mark(X))
mark(if(X1, X2, X3)) -> aif(mark(X1), mark(X2), X3)
mark(c) -> c
mark(true) -> true
mark(false) -> false
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳AFS
...
→DP Problem 5
↳Remaining Obligation(s)
MARK(if(X1, X2, X3)) -> MARK(X1)
AIF(true, X, Y) -> MARK(X)
MARK(if(X1, X2, X3)) -> AIF(mark(X1), mark(X2), X3)
MARK(if(X1, X2, X3)) -> MARK(X2)
af(X) -> aif(mark(X), c, f(true))
af(X) -> f(X)
aif(true, X, Y) -> mark(X)
aif(false, X, Y) -> mark(Y)
aif(X1, X2, X3) -> if(X1, X2, X3)
mark(f(X)) -> af(mark(X))
mark(if(X1, X2, X3)) -> aif(mark(X1), mark(X2), X3)
mark(c) -> c
mark(true) -> true
mark(false) -> false