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


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YES

Problem 1: 

(VAR X Y Z)
(RULES
plus(plus(X,Y),Z) -> plus(X,plus(Y,Z))
times(X,s(Y)) -> plus(X,times(Y,X))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 PLUS(plus(X,Y),Z) -> PLUS(X,plus(Y,Z))
 PLUS(plus(X,Y),Z) -> PLUS(Y,Z)
 TIMES(X,s(Y)) -> PLUS(X,times(Y,X))
 TIMES(X,s(Y)) -> TIMES(Y,X)
-> Rules:
 plus(plus(X,Y),Z) -> plus(X,plus(Y,Z))
 times(X,s(Y)) -> plus(X,times(Y,X))

Problem 1: 

SCC Processor:
-> Pairs:
 PLUS(plus(X,Y),Z) -> PLUS(X,plus(Y,Z))
 PLUS(plus(X,Y),Z) -> PLUS(Y,Z)
 TIMES(X,s(Y)) -> PLUS(X,times(Y,X))
 TIMES(X,s(Y)) -> TIMES(Y,X)
-> Rules:
 plus(plus(X,Y),Z) -> plus(X,plus(Y,Z))
 times(X,s(Y)) -> plus(X,times(Y,X))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 PLUS(plus(X,Y),Z) -> PLUS(X,plus(Y,Z))
 PLUS(plus(X,Y),Z) -> PLUS(Y,Z)
->->-> Rules:
 plus(plus(X,Y),Z) -> plus(X,plus(Y,Z))
 times(X,s(Y)) -> plus(X,times(Y,X))
->->Cycle:
->->-> Pairs:
 TIMES(X,s(Y)) -> TIMES(Y,X)
->->-> Rules:
 plus(plus(X,Y),Z) -> plus(X,plus(Y,Z))
 times(X,s(Y)) -> plus(X,times(Y,X))


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 PLUS(plus(X,Y),Z) -> PLUS(X,plus(Y,Z))
 PLUS(plus(X,Y),Z) -> PLUS(Y,Z)
-> Rules:
 plus(plus(X,Y),Z) -> plus(X,plus(Y,Z))
 times(X,s(Y)) -> plus(X,times(Y,X))
->Projection:
 pi(PLUS) = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 plus(plus(X,Y),Z) -> plus(X,plus(Y,Z))
 times(X,s(Y)) -> plus(X,times(Y,X))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Reduction Pair Processor:
-> Pairs:
 TIMES(X,s(Y)) -> TIMES(Y,X)
-> Rules:
 plus(plus(X,Y),Z) -> plus(X,plus(Y,Z))
 times(X,s(Y)) -> plus(X,times(Y,X))
-> Usable rules:
 Empty
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[s](X) = 2.X + 2
[TIMES](X1,X2) = 2.X1 + 2.X2

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 plus(plus(X,Y),Z) -> plus(X,plus(Y,Z))
 times(X,s(Y)) -> plus(X,times(Y,X))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.