/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 v_NonEmpty:S X:S Y:S Z:S)
(RULES
plus(plus(X:S,Y:S),Z:S) -> plus(X:S,plus(Y:S,Z:S))
times(X:S,s(Y:S)) -> plus(X:S,times(Y:S,X:S))
)

Problem 1: 

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

Problem 1: 

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


The problem is decomposed in 2 subproblems.

Problem 1.1: 

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

Problem 1.1: 

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

The problem is finite.

Problem 1.2: 

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

The problem is finite.