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


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


YES

Problem 1: 

(VAR X X1 X2 X3)
(RULES
a__b -> a
a__b -> b
a__f(a,X,X) -> a__f(X,a__b,b)
a__f(X1,X2,X3) -> f(X1,X2,X3)
mark(a) -> a
mark(b) -> a__b
mark(f(X1,X2,X3)) -> a__f(X1,mark(X2),X3)
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 A__F(a,X,X) -> A__B
 A__F(a,X,X) -> A__F(X,a__b,b)
 MARK(b) -> A__B
 MARK(f(X1,X2,X3)) -> A__F(X1,mark(X2),X3)
 MARK(f(X1,X2,X3)) -> MARK(X2)
-> Rules:
 a__b -> a
 a__b -> b
 a__f(a,X,X) -> a__f(X,a__b,b)
 a__f(X1,X2,X3) -> f(X1,X2,X3)
 mark(a) -> a
 mark(b) -> a__b
 mark(f(X1,X2,X3)) -> a__f(X1,mark(X2),X3)

Problem 1: 

SCC Processor:
-> Pairs:
 A__F(a,X,X) -> A__B
 A__F(a,X,X) -> A__F(X,a__b,b)
 MARK(b) -> A__B
 MARK(f(X1,X2,X3)) -> A__F(X1,mark(X2),X3)
 MARK(f(X1,X2,X3)) -> MARK(X2)
-> Rules:
 a__b -> a
 a__b -> b
 a__f(a,X,X) -> a__f(X,a__b,b)
 a__f(X1,X2,X3) -> f(X1,X2,X3)
 mark(a) -> a
 mark(b) -> a__b
 mark(f(X1,X2,X3)) -> a__f(X1,mark(X2),X3)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A__F(a,X,X) -> A__F(X,a__b,b)
->->-> Rules:
 a__b -> a
 a__b -> b
 a__f(a,X,X) -> a__f(X,a__b,b)
 a__f(X1,X2,X3) -> f(X1,X2,X3)
 mark(a) -> a
 mark(b) -> a__b
 mark(f(X1,X2,X3)) -> a__f(X1,mark(X2),X3)
->->Cycle:
->->-> Pairs:
 MARK(f(X1,X2,X3)) -> MARK(X2)
->->-> Rules:
 a__b -> a
 a__b -> b
 a__f(a,X,X) -> a__f(X,a__b,b)
 a__f(X1,X2,X3) -> f(X1,X2,X3)
 mark(a) -> a
 mark(b) -> a__b
 mark(f(X1,X2,X3)) -> a__f(X1,mark(X2),X3)


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Reduction Pair Processor:
-> Pairs:
 A__F(a,X,X) -> A__F(X,a__b,b)
-> Rules:
 a__b -> a
 a__b -> b
 a__f(a,X,X) -> a__f(X,a__b,b)
 a__f(X1,X2,X3) -> f(X1,X2,X3)
 mark(a) -> a
 mark(b) -> a__b
 mark(f(X1,X2,X3)) -> a__f(X1,mark(X2),X3)
-> Usable rules:
 a__b -> a
 a__b -> b
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a__b] = 2
[a] = 2
[b] = 0
[A__F](X1,X2,X3) = X1 + 2.X3

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 a__b -> a
 a__b -> b
 a__f(a,X,X) -> a__f(X,a__b,b)
 a__f(X1,X2,X3) -> f(X1,X2,X3)
 mark(a) -> a
 mark(b) -> a__b
 mark(f(X1,X2,X3)) -> a__f(X1,mark(X2),X3)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 MARK(f(X1,X2,X3)) -> MARK(X2)
-> Rules:
 a__b -> a
 a__b -> b
 a__f(a,X,X) -> a__f(X,a__b,b)
 a__f(X1,X2,X3) -> f(X1,X2,X3)
 mark(a) -> a
 mark(b) -> a__b
 mark(f(X1,X2,X3)) -> a__f(X1,mark(X2),X3)
->Projection:
 pi(MARK) = 1

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 a__b -> a
 a__b -> b
 a__f(a,X,X) -> a__f(X,a__b,b)
 a__f(X1,X2,X3) -> f(X1,X2,X3)
 mark(a) -> a
 mark(b) -> a__b
 mark(f(X1,X2,X3)) -> a__f(X1,mark(X2),X3)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.