/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 M N X)
(RULES
activate(X) -> X
and(tt,X) -> activate(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:
 activate(X) -> X
 and(tt,X) -> activate(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 term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 AND(tt,X) -> ACTIVATE(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:
 activate(X) -> X
 and(tt,X) -> activate(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: 

SCC Processor:
-> Pairs:
 AND(tt,X) -> ACTIVATE(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:
 activate(X) -> X
 and(tt,X) -> activate(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)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 PLUS(N,s(M)) -> PLUS(N,M)
->->-> Rules:
 activate(X) -> X
 and(tt,X) -> activate(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)
->->Cycle:
->->-> Pairs:
 X(N,s(M)) -> X(N,M)
->->-> Rules:
 activate(X) -> X
 and(tt,X) -> activate(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 problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 PLUS(N,s(M)) -> PLUS(N,M)
-> Rules:
 activate(X) -> X
 and(tt,X) -> activate(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)
->Projection:
 pi(PLUS) = 2

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 activate(X) -> X
 and(tt,X) -> activate(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)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 X(N,s(M)) -> X(N,M)
-> Rules:
 activate(X) -> X
 and(tt,X) -> activate(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)
->Projection:
 pi(X) = 2

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 activate(X) -> X
 and(tt,X) -> activate(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)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.