/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


YES

Problem 1: 

(VAR X X1 X2 X3 Y)
(RULES
a__f(X) -> a__if(mark(X),c,f(true))
a__f(X) -> f(X)
a__if(false,X,Y) -> mark(Y)
a__if(true,X,Y) -> mark(X)
a__if(X1,X2,X3) -> if(X1,X2,X3)
mark(c) -> c
mark(f(X)) -> a__f(mark(X))
mark(false) -> false
mark(if(X1,X2,X3)) -> a__if(mark(X1),mark(X2),X3)
mark(true) -> true
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 A__F(X) -> A__IF(mark(X),c,f(true))
 A__F(X) -> MARK(X)
 A__IF(false,X,Y) -> MARK(Y)
 A__IF(true,X,Y) -> MARK(X)
 MARK(f(X)) -> A__F(mark(X))
 MARK(f(X)) -> MARK(X)
 MARK(if(X1,X2,X3)) -> A__IF(mark(X1),mark(X2),X3)
 MARK(if(X1,X2,X3)) -> MARK(X1)
 MARK(if(X1,X2,X3)) -> MARK(X2)
-> Rules:
 a__f(X) -> a__if(mark(X),c,f(true))
 a__f(X) -> f(X)
 a__if(false,X,Y) -> mark(Y)
 a__if(true,X,Y) -> mark(X)
 a__if(X1,X2,X3) -> if(X1,X2,X3)
 mark(c) -> c
 mark(f(X)) -> a__f(mark(X))
 mark(false) -> false
 mark(if(X1,X2,X3)) -> a__if(mark(X1),mark(X2),X3)
 mark(true) -> true

Problem 1: 

SCC Processor:
-> Pairs:
 A__F(X) -> A__IF(mark(X),c,f(true))
 A__F(X) -> MARK(X)
 A__IF(false,X,Y) -> MARK(Y)
 A__IF(true,X,Y) -> MARK(X)
 MARK(f(X)) -> A__F(mark(X))
 MARK(f(X)) -> MARK(X)
 MARK(if(X1,X2,X3)) -> A__IF(mark(X1),mark(X2),X3)
 MARK(if(X1,X2,X3)) -> MARK(X1)
 MARK(if(X1,X2,X3)) -> MARK(X2)
-> Rules:
 a__f(X) -> a__if(mark(X),c,f(true))
 a__f(X) -> f(X)
 a__if(false,X,Y) -> mark(Y)
 a__if(true,X,Y) -> mark(X)
 a__if(X1,X2,X3) -> if(X1,X2,X3)
 mark(c) -> c
 mark(f(X)) -> a__f(mark(X))
 mark(false) -> false
 mark(if(X1,X2,X3)) -> a__if(mark(X1),mark(X2),X3)
 mark(true) -> true
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A__F(X) -> A__IF(mark(X),c,f(true))
 A__F(X) -> MARK(X)
 A__IF(false,X,Y) -> MARK(Y)
 A__IF(true,X,Y) -> MARK(X)
 MARK(f(X)) -> A__F(mark(X))
 MARK(f(X)) -> MARK(X)
 MARK(if(X1,X2,X3)) -> A__IF(mark(X1),mark(X2),X3)
 MARK(if(X1,X2,X3)) -> MARK(X1)
 MARK(if(X1,X2,X3)) -> MARK(X2)
->->-> Rules:
 a__f(X) -> a__if(mark(X),c,f(true))
 a__f(X) -> f(X)
 a__if(false,X,Y) -> mark(Y)
 a__if(true,X,Y) -> mark(X)
 a__if(X1,X2,X3) -> if(X1,X2,X3)
 mark(c) -> c
 mark(f(X)) -> a__f(mark(X))
 mark(false) -> false
 mark(if(X1,X2,X3)) -> a__if(mark(X1),mark(X2),X3)
 mark(true) -> true

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A__F(X) -> A__IF(mark(X),c,f(true))
 A__F(X) -> MARK(X)
 A__IF(false,X,Y) -> MARK(Y)
 A__IF(true,X,Y) -> MARK(X)
 MARK(f(X)) -> A__F(mark(X))
 MARK(f(X)) -> MARK(X)
 MARK(if(X1,X2,X3)) -> A__IF(mark(X1),mark(X2),X3)
 MARK(if(X1,X2,X3)) -> MARK(X1)
 MARK(if(X1,X2,X3)) -> MARK(X2)
-> Rules:
 a__f(X) -> a__if(mark(X),c,f(true))
 a__f(X) -> f(X)
 a__if(false,X,Y) -> mark(Y)
 a__if(true,X,Y) -> mark(X)
 a__if(X1,X2,X3) -> if(X1,X2,X3)
 mark(c) -> c
 mark(f(X)) -> a__f(mark(X))
 mark(false) -> false
 mark(if(X1,X2,X3)) -> a__if(mark(X1),mark(X2),X3)
 mark(true) -> true
-> Usable rules:
 a__f(X) -> a__if(mark(X),c,f(true))
 a__f(X) -> f(X)
 a__if(false,X,Y) -> mark(Y)
 a__if(true,X,Y) -> mark(X)
 a__if(X1,X2,X3) -> if(X1,X2,X3)
 mark(c) -> c
 mark(f(X)) -> a__f(mark(X))
 mark(false) -> false
 mark(if(X1,X2,X3)) -> a__if(mark(X1),mark(X2),X3)
 mark(true) -> true
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a__f](X) = 2.X + 2
[a__if](X1,X2,X3) = X1 + 2.X2 + 2.X3
[mark](X) = 2.X
[c] = 0
[f](X) = 2.X + 1
[false] = 1
[if](X1,X2,X3) = X1 + 2.X2 + 2.X3
[true] = 0
[A__F](X) = 2.X + 2
[A__IF](X1,X2,X3) = X1 + 2.X2 + 2.X3
[MARK](X) = 2.X

Problem 1: 

SCC Processor:
-> Pairs:
 A__F(X) -> A__IF(mark(X),c,f(true))
 A__IF(false,X,Y) -> MARK(Y)
 A__IF(true,X,Y) -> MARK(X)
 MARK(f(X)) -> A__F(mark(X))
 MARK(f(X)) -> MARK(X)
 MARK(if(X1,X2,X3)) -> A__IF(mark(X1),mark(X2),X3)
 MARK(if(X1,X2,X3)) -> MARK(X1)
 MARK(if(X1,X2,X3)) -> MARK(X2)
-> Rules:
 a__f(X) -> a__if(mark(X),c,f(true))
 a__f(X) -> f(X)
 a__if(false,X,Y) -> mark(Y)
 a__if(true,X,Y) -> mark(X)
 a__if(X1,X2,X3) -> if(X1,X2,X3)
 mark(c) -> c
 mark(f(X)) -> a__f(mark(X))
 mark(false) -> false
 mark(if(X1,X2,X3)) -> a__if(mark(X1),mark(X2),X3)
 mark(true) -> true
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A__F(X) -> A__IF(mark(X),c,f(true))
 A__IF(false,X,Y) -> MARK(Y)
 A__IF(true,X,Y) -> MARK(X)
 MARK(f(X)) -> A__F(mark(X))
 MARK(f(X)) -> MARK(X)
 MARK(if(X1,X2,X3)) -> A__IF(mark(X1),mark(X2),X3)
 MARK(if(X1,X2,X3)) -> MARK(X1)
 MARK(if(X1,X2,X3)) -> MARK(X2)
->->-> Rules:
 a__f(X) -> a__if(mark(X),c,f(true))
 a__f(X) -> f(X)
 a__if(false,X,Y) -> mark(Y)
 a__if(true,X,Y) -> mark(X)
 a__if(X1,X2,X3) -> if(X1,X2,X3)
 mark(c) -> c
 mark(f(X)) -> a__f(mark(X))
 mark(false) -> false
 mark(if(X1,X2,X3)) -> a__if(mark(X1),mark(X2),X3)
 mark(true) -> true

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A__F(X) -> A__IF(mark(X),c,f(true))
 A__IF(false,X,Y) -> MARK(Y)
 A__IF(true,X,Y) -> MARK(X)
 MARK(f(X)) -> A__F(mark(X))
 MARK(f(X)) -> MARK(X)
 MARK(if(X1,X2,X3)) -> A__IF(mark(X1),mark(X2),X3)
 MARK(if(X1,X2,X3)) -> MARK(X1)
 MARK(if(X1,X2,X3)) -> MARK(X2)
-> Rules:
 a__f(X) -> a__if(mark(X),c,f(true))
 a__f(X) -> f(X)
 a__if(false,X,Y) -> mark(Y)
 a__if(true,X,Y) -> mark(X)
 a__if(X1,X2,X3) -> if(X1,X2,X3)
 mark(c) -> c
 mark(f(X)) -> a__f(mark(X))
 mark(false) -> false
 mark(if(X1,X2,X3)) -> a__if(mark(X1),mark(X2),X3)
 mark(true) -> true
-> Usable rules:
 a__f(X) -> a__if(mark(X),c,f(true))
 a__f(X) -> f(X)
 a__if(false,X,Y) -> mark(Y)
 a__if(true,X,Y) -> mark(X)
 a__if(X1,X2,X3) -> if(X1,X2,X3)
 mark(c) -> c
 mark(f(X)) -> a__f(mark(X))
 mark(false) -> false
 mark(if(X1,X2,X3)) -> a__if(mark(X1),mark(X2),X3)
 mark(true) -> true
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a__f](X) = 2.X
[a__if](X1,X2,X3) = X1 + 2.X2 + 2.X3
[mark](X) = 2.X
[c] = 0
[f](X) = 2.X
[false] = 1
[if](X1,X2,X3) = X1 + 2.X2 + 2.X3
[true] = 0
[A__F](X) = 2.X + 2
[A__IF](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2
[MARK](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 A__F(X) -> A__IF(mark(X),c,f(true))
 A__IF(true,X,Y) -> MARK(X)
 MARK(f(X)) -> A__F(mark(X))
 MARK(f(X)) -> MARK(X)
 MARK(if(X1,X2,X3)) -> A__IF(mark(X1),mark(X2),X3)
 MARK(if(X1,X2,X3)) -> MARK(X1)
 MARK(if(X1,X2,X3)) -> MARK(X2)
-> Rules:
 a__f(X) -> a__if(mark(X),c,f(true))
 a__f(X) -> f(X)
 a__if(false,X,Y) -> mark(Y)
 a__if(true,X,Y) -> mark(X)
 a__if(X1,X2,X3) -> if(X1,X2,X3)
 mark(c) -> c
 mark(f(X)) -> a__f(mark(X))
 mark(false) -> false
 mark(if(X1,X2,X3)) -> a__if(mark(X1),mark(X2),X3)
 mark(true) -> true
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A__F(X) -> A__IF(mark(X),c,f(true))
 A__IF(true,X,Y) -> MARK(X)
 MARK(f(X)) -> A__F(mark(X))
 MARK(f(X)) -> MARK(X)
 MARK(if(X1,X2,X3)) -> A__IF(mark(X1),mark(X2),X3)
 MARK(if(X1,X2,X3)) -> MARK(X1)
 MARK(if(X1,X2,X3)) -> MARK(X2)
->->-> Rules:
 a__f(X) -> a__if(mark(X),c,f(true))
 a__f(X) -> f(X)
 a__if(false,X,Y) -> mark(Y)
 a__if(true,X,Y) -> mark(X)
 a__if(X1,X2,X3) -> if(X1,X2,X3)
 mark(c) -> c
 mark(f(X)) -> a__f(mark(X))
 mark(false) -> false
 mark(if(X1,X2,X3)) -> a__if(mark(X1),mark(X2),X3)
 mark(true) -> true

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A__F(X) -> A__IF(mark(X),c,f(true))
 A__IF(true,X,Y) -> MARK(X)
 MARK(f(X)) -> A__F(mark(X))
 MARK(f(X)) -> MARK(X)
 MARK(if(X1,X2,X3)) -> A__IF(mark(X1),mark(X2),X3)
 MARK(if(X1,X2,X3)) -> MARK(X1)
 MARK(if(X1,X2,X3)) -> MARK(X2)
-> Rules:
 a__f(X) -> a__if(mark(X),c,f(true))
 a__f(X) -> f(X)
 a__if(false,X,Y) -> mark(Y)
 a__if(true,X,Y) -> mark(X)
 a__if(X1,X2,X3) -> if(X1,X2,X3)
 mark(c) -> c
 mark(f(X)) -> a__f(mark(X))
 mark(false) -> false
 mark(if(X1,X2,X3)) -> a__if(mark(X1),mark(X2),X3)
 mark(true) -> true
-> Usable rules:
 a__f(X) -> a__if(mark(X),c,f(true))
 a__f(X) -> f(X)
 a__if(false,X,Y) -> mark(Y)
 a__if(true,X,Y) -> mark(X)
 a__if(X1,X2,X3) -> if(X1,X2,X3)
 mark(c) -> c
 mark(f(X)) -> a__f(mark(X))
 mark(false) -> false
 mark(if(X1,X2,X3)) -> a__if(mark(X1),mark(X2),X3)
 mark(true) -> true
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a__f](X) = 2.X + 2
[a__if](X1,X2,X3) = X1 + 2.X2 + 2.X3
[mark](X) = 2.X
[c] = 0
[f](X) = 2.X + 1
[false] = 1
[if](X1,X2,X3) = X1 + 2.X2 + X3
[true] = 0
[A__F](X) = 2.X + 2
[A__IF](X1,X2,X3) = X1 + 2.X2
[MARK](X) = 2.X

Problem 1: 

SCC Processor:
-> Pairs:
 A__IF(true,X,Y) -> MARK(X)
 MARK(f(X)) -> A__F(mark(X))
 MARK(f(X)) -> MARK(X)
 MARK(if(X1,X2,X3)) -> A__IF(mark(X1),mark(X2),X3)
 MARK(if(X1,X2,X3)) -> MARK(X1)
 MARK(if(X1,X2,X3)) -> MARK(X2)
-> Rules:
 a__f(X) -> a__if(mark(X),c,f(true))
 a__f(X) -> f(X)
 a__if(false,X,Y) -> mark(Y)
 a__if(true,X,Y) -> mark(X)
 a__if(X1,X2,X3) -> if(X1,X2,X3)
 mark(c) -> c
 mark(f(X)) -> a__f(mark(X))
 mark(false) -> false
 mark(if(X1,X2,X3)) -> a__if(mark(X1),mark(X2),X3)
 mark(true) -> true
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A__IF(true,X,Y) -> MARK(X)
 MARK(f(X)) -> MARK(X)
 MARK(if(X1,X2,X3)) -> A__IF(mark(X1),mark(X2),X3)
 MARK(if(X1,X2,X3)) -> MARK(X1)
 MARK(if(X1,X2,X3)) -> MARK(X2)
->->-> Rules:
 a__f(X) -> a__if(mark(X),c,f(true))
 a__f(X) -> f(X)
 a__if(false,X,Y) -> mark(Y)
 a__if(true,X,Y) -> mark(X)
 a__if(X1,X2,X3) -> if(X1,X2,X3)
 mark(c) -> c
 mark(f(X)) -> a__f(mark(X))
 mark(false) -> false
 mark(if(X1,X2,X3)) -> a__if(mark(X1),mark(X2),X3)
 mark(true) -> true

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A__IF(true,X,Y) -> MARK(X)
 MARK(f(X)) -> MARK(X)
 MARK(if(X1,X2,X3)) -> A__IF(mark(X1),mark(X2),X3)
 MARK(if(X1,X2,X3)) -> MARK(X1)
 MARK(if(X1,X2,X3)) -> MARK(X2)
-> Rules:
 a__f(X) -> a__if(mark(X),c,f(true))
 a__f(X) -> f(X)
 a__if(false,X,Y) -> mark(Y)
 a__if(true,X,Y) -> mark(X)
 a__if(X1,X2,X3) -> if(X1,X2,X3)
 mark(c) -> c
 mark(f(X)) -> a__f(mark(X))
 mark(false) -> false
 mark(if(X1,X2,X3)) -> a__if(mark(X1),mark(X2),X3)
 mark(true) -> true
-> Usable rules:
 a__f(X) -> a__if(mark(X),c,f(true))
 a__f(X) -> f(X)
 a__if(false,X,Y) -> mark(Y)
 a__if(true,X,Y) -> mark(X)
 a__if(X1,X2,X3) -> if(X1,X2,X3)
 mark(c) -> c
 mark(f(X)) -> a__f(mark(X))
 mark(false) -> false
 mark(if(X1,X2,X3)) -> a__if(mark(X1),mark(X2),X3)
 mark(true) -> true
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a__f](X) = 2.X + 2
[a__if](X1,X2,X3) = X1 + 2.X2 + 2.X3
[mark](X) = 2.X
[c] = 0
[f](X) = 2.X + 1
[false] = 1
[if](X1,X2,X3) = X1 + 2.X2 + 2.X3
[true] = 0
[A__IF](X1,X2,X3) = X1 + 2.X2 + 2.X3
[MARK](X) = 2.X

Problem 1: 

SCC Processor:
-> Pairs:
 A__IF(true,X,Y) -> MARK(X)
 MARK(if(X1,X2,X3)) -> A__IF(mark(X1),mark(X2),X3)
 MARK(if(X1,X2,X3)) -> MARK(X1)
 MARK(if(X1,X2,X3)) -> MARK(X2)
-> Rules:
 a__f(X) -> a__if(mark(X),c,f(true))
 a__f(X) -> f(X)
 a__if(false,X,Y) -> mark(Y)
 a__if(true,X,Y) -> mark(X)
 a__if(X1,X2,X3) -> if(X1,X2,X3)
 mark(c) -> c
 mark(f(X)) -> a__f(mark(X))
 mark(false) -> false
 mark(if(X1,X2,X3)) -> a__if(mark(X1),mark(X2),X3)
 mark(true) -> true
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A__IF(true,X,Y) -> MARK(X)
 MARK(if(X1,X2,X3)) -> A__IF(mark(X1),mark(X2),X3)
 MARK(if(X1,X2,X3)) -> MARK(X1)
 MARK(if(X1,X2,X3)) -> MARK(X2)
->->-> Rules:
 a__f(X) -> a__if(mark(X),c,f(true))
 a__f(X) -> f(X)
 a__if(false,X,Y) -> mark(Y)
 a__if(true,X,Y) -> mark(X)
 a__if(X1,X2,X3) -> if(X1,X2,X3)
 mark(c) -> c
 mark(f(X)) -> a__f(mark(X))
 mark(false) -> false
 mark(if(X1,X2,X3)) -> a__if(mark(X1),mark(X2),X3)
 mark(true) -> true

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A__IF(true,X,Y) -> MARK(X)
 MARK(if(X1,X2,X3)) -> A__IF(mark(X1),mark(X2),X3)
 MARK(if(X1,X2,X3)) -> MARK(X1)
 MARK(if(X1,X2,X3)) -> MARK(X2)
-> Rules:
 a__f(X) -> a__if(mark(X),c,f(true))
 a__f(X) -> f(X)
 a__if(false,X,Y) -> mark(Y)
 a__if(true,X,Y) -> mark(X)
 a__if(X1,X2,X3) -> if(X1,X2,X3)
 mark(c) -> c
 mark(f(X)) -> a__f(mark(X))
 mark(false) -> false
 mark(if(X1,X2,X3)) -> a__if(mark(X1),mark(X2),X3)
 mark(true) -> true
-> Usable rules:
 a__f(X) -> a__if(mark(X),c,f(true))
 a__f(X) -> f(X)
 a__if(false,X,Y) -> mark(Y)
 a__if(true,X,Y) -> mark(X)
 a__if(X1,X2,X3) -> if(X1,X2,X3)
 mark(c) -> c
 mark(f(X)) -> a__f(mark(X))
 mark(false) -> false
 mark(if(X1,X2,X3)) -> a__if(mark(X1),mark(X2),X3)
 mark(true) -> true
->Interpretation type:
 Simple mixed
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a__f](X) = 2.X + 1
[a__if](X1,X2,X3) = 2.X1.X2.X3 + 2.X1.X2 + X1.X3 + 2.X2.X3 + X1 + 2.X2 + 1
[mark](X) = X
[c] = 0
[f](X) = 2.X + 1
[false] = 2
[if](X1,X2,X3) = 2.X1.X2.X3 + 2.X1.X2 + X1.X3 + 2.X2.X3 + X1 + 2.X2 + 1
[true] = 0
[A__IF](X1,X2,X3) = 2.X1.X2.X3 + X1.X2 + 2.X1.X3 + 2.X2 + 2
[MARK](X) = 2.X

Problem 1: 

SCC Processor:
-> Pairs:
 MARK(if(X1,X2,X3)) -> A__IF(mark(X1),mark(X2),X3)
 MARK(if(X1,X2,X3)) -> MARK(X1)
 MARK(if(X1,X2,X3)) -> MARK(X2)
-> Rules:
 a__f(X) -> a__if(mark(X),c,f(true))
 a__f(X) -> f(X)
 a__if(false,X,Y) -> mark(Y)
 a__if(true,X,Y) -> mark(X)
 a__if(X1,X2,X3) -> if(X1,X2,X3)
 mark(c) -> c
 mark(f(X)) -> a__f(mark(X))
 mark(false) -> false
 mark(if(X1,X2,X3)) -> a__if(mark(X1),mark(X2),X3)
 mark(true) -> true
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 MARK(if(X1,X2,X3)) -> MARK(X1)
 MARK(if(X1,X2,X3)) -> MARK(X2)
->->-> Rules:
 a__f(X) -> a__if(mark(X),c,f(true))
 a__f(X) -> f(X)
 a__if(false,X,Y) -> mark(Y)
 a__if(true,X,Y) -> mark(X)
 a__if(X1,X2,X3) -> if(X1,X2,X3)
 mark(c) -> c
 mark(f(X)) -> a__f(mark(X))
 mark(false) -> false
 mark(if(X1,X2,X3)) -> a__if(mark(X1),mark(X2),X3)
 mark(true) -> true

Problem 1: 

Subterm Processor:
-> Pairs:
 MARK(if(X1,X2,X3)) -> MARK(X1)
 MARK(if(X1,X2,X3)) -> MARK(X2)
-> Rules:
 a__f(X) -> a__if(mark(X),c,f(true))
 a__f(X) -> f(X)
 a__if(false,X,Y) -> mark(Y)
 a__if(true,X,Y) -> mark(X)
 a__if(X1,X2,X3) -> if(X1,X2,X3)
 mark(c) -> c
 mark(f(X)) -> a__f(mark(X))
 mark(false) -> false
 mark(if(X1,X2,X3)) -> a__if(mark(X1),mark(X2),X3)
 mark(true) -> true
->Projection:
 pi(MARK) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 a__f(X) -> a__if(mark(X),c,f(true))
 a__f(X) -> f(X)
 a__if(false,X,Y) -> mark(Y)
 a__if(true,X,Y) -> mark(X)
 a__if(X1,X2,X3) -> if(X1,X2,X3)
 mark(c) -> c
 mark(f(X)) -> a__f(mark(X))
 mark(false) -> false
 mark(if(X1,X2,X3)) -> a__if(mark(X1),mark(X2),X3)
 mark(true) -> true
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.