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


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YES

Problem 1: 

(VAR X X1 X2 X3)
(RULES
a__c -> a
a__c -> b
a__c -> c
a__f(a,b,X) -> a__f(X,X,mark(X))
a__f(X1,X2,X3) -> f(X1,X2,X3)
mark(a) -> a
mark(b) -> b
mark(c) -> a__c
mark(f(X1,X2,X3)) -> a__f(X1,X2,mark(X3))
) 
(STRATEGY INNERMOST)

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

The problem is finite.