/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 M N X)
(STRATEGY CONTEXTSENSITIVE
(and 1)
(plus 1 2)
(x 1 2)
(0)
(s 1)
(tt)
)
(RULES
and(tt,X) -> X
plus(N,0) -> N
plus(N,s(M)) -> s(plus(N,M))
x(N,0) -> 0
x(N,s(M)) -> plus(x(N,M),N)
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 and(tt,X) -> X
 plus(N,0) -> N
 plus(N,s(M)) -> s(plus(N,M))
 x(N,0) -> 0
 x(N,s(M)) -> plus(x(N,M),N)
-> The context-sensitive term rewriting system is an orthogonal system. Therefore, innermost cs-termination implies cs-termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 AND(tt,X) -> X
 PLUS(N,s(M)) -> PLUS(N,M)
 X(N,s(M)) -> PLUS(x(N,M),N)
 X(N,s(M)) -> X(N,M)
-> Rules:
 and(tt,X) -> X
 plus(N,0) -> N
 plus(N,s(M)) -> s(plus(N,M))
 x(N,0) -> 0
 x(N,s(M)) -> plus(x(N,M),N)
-> Unhiding Rules:
 Empty

Problem 1: 

SCC Processor:
-> Pairs:
 AND(tt,X) -> X
 PLUS(N,s(M)) -> PLUS(N,M)
 X(N,s(M)) -> PLUS(x(N,M),N)
 X(N,s(M)) -> X(N,M)
-> Rules:
 and(tt,X) -> X
 plus(N,0) -> N
 plus(N,s(M)) -> s(plus(N,M))
 x(N,0) -> 0
 x(N,s(M)) -> plus(x(N,M),N)
-> Unhiding rules:
 Empty
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 PLUS(N,s(M)) -> PLUS(N,M)
->->-> Rules:
 and(tt,X) -> X
 plus(N,0) -> N
 plus(N,s(M)) -> s(plus(N,M))
 x(N,0) -> 0
 x(N,s(M)) -> plus(x(N,M),N)
->->-> Unhiding rules:
 Empty
->->Cycle:
->->-> Pairs:
 X(N,s(M)) -> X(N,M)
->->-> Rules:
 and(tt,X) -> X
 plus(N,0) -> N
 plus(N,s(M)) -> s(plus(N,M))
 x(N,0) -> 0
 x(N,s(M)) -> plus(x(N,M),N)
->->-> Unhiding rules:
 Empty


The problem is decomposed in 2 subproblems.

Problem 1.1: 

SubNColl Processor:
-> Pairs:
 PLUS(N,s(M)) -> PLUS(N,M)
-> Rules:
 and(tt,X) -> X
 plus(N,0) -> N
 plus(N,s(M)) -> s(plus(N,M))
 x(N,0) -> 0
 x(N,s(M)) -> plus(x(N,M),N)
-> Unhiding rules:
 Empty
->Projection:
 pi(PLUS) = 2

Problem 1.1: 

Basic Processor:
-> Pairs:
 Empty
-> Rules:
 and(tt,X) -> X
 plus(N,0) -> N
 plus(N,s(M)) -> s(plus(N,M))
 x(N,0) -> 0
 x(N,s(M)) -> plus(x(N,M),N)
-> Unhiding rules:
 Empty
-> Result:
 Set P is empty

The problem is finite.

Problem 1.2: 

SubNColl Processor:
-> Pairs:
 X(N,s(M)) -> X(N,M)
-> Rules:
 and(tt,X) -> X
 plus(N,0) -> N
 plus(N,s(M)) -> s(plus(N,M))
 x(N,0) -> 0
 x(N,s(M)) -> plus(x(N,M),N)
-> Unhiding rules:
 Empty
->Projection:
 pi(X) = 2

Problem 1.2: 

Basic Processor:
-> Pairs:
 Empty
-> Rules:
 and(tt,X) -> X
 plus(N,0) -> N
 plus(N,s(M)) -> s(plus(N,M))
 x(N,0) -> 0
 x(N,s(M)) -> plus(x(N,M),N)
-> Unhiding rules:
 Empty
-> Result:
 Set P is empty

The problem is finite.