/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 M:S N:S X:S)
(RULES
activate(X:S) -> X:S
and(tt,X:S) -> activate(X:S)
plus(N:S,0) -> N:S
plus(N:S,s(M:S)) -> s(plus(N:S,M:S))
x(N:S,0) -> 0
x(N:S,s(M:S)) -> plus(x(N:S,M:S),N:S)
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 activate(X:S) -> X:S
 and(tt,X:S) -> activate(X:S)
 plus(N:S,0) -> N:S
 plus(N:S,s(M:S)) -> s(plus(N:S,M:S))
 x(N:S,0) -> 0
 x(N:S,s(M:S)) -> plus(x(N:S,M:S),N:S)
-> 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:S) -> ACTIVATE(X:S)
 PLUS(N:S,s(M:S)) -> PLUS(N:S,M:S)
 X(N:S,s(M:S)) -> PLUS(x(N:S,M:S),N:S)
 X(N:S,s(M:S)) -> X(N:S,M:S)
-> Rules:
 activate(X:S) -> X:S
 and(tt,X:S) -> activate(X:S)
 plus(N:S,0) -> N:S
 plus(N:S,s(M:S)) -> s(plus(N:S,M:S))
 x(N:S,0) -> 0
 x(N:S,s(M:S)) -> plus(x(N:S,M:S),N:S)

Problem 1: 

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


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 PLUS(N:S,s(M:S)) -> PLUS(N:S,M:S)
-> Rules:
 activate(X:S) -> X:S
 and(tt,X:S) -> activate(X:S)
 plus(N:S,0) -> N:S
 plus(N:S,s(M:S)) -> s(plus(N:S,M:S))
 x(N:S,0) -> 0
 x(N:S,s(M:S)) -> plus(x(N:S,M:S),N:S)
->Projection:
 pi(PLUS) = 2

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 activate(X:S) -> X:S
 and(tt,X:S) -> activate(X:S)
 plus(N:S,0) -> N:S
 plus(N:S,s(M:S)) -> s(plus(N:S,M:S))
 x(N:S,0) -> 0
 x(N:S,s(M:S)) -> plus(x(N:S,M:S),N:S)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 X(N:S,s(M:S)) -> X(N:S,M:S)
-> Rules:
 activate(X:S) -> X:S
 and(tt,X:S) -> activate(X:S)
 plus(N:S,0) -> N:S
 plus(N:S,s(M:S)) -> s(plus(N:S,M:S))
 x(N:S,0) -> 0
 x(N:S,s(M:S)) -> plus(x(N:S,M:S),N:S)
->Projection:
 pi(X) = 2

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 activate(X:S) -> X:S
 and(tt,X:S) -> activate(X:S)
 plus(N:S,0) -> N:S
 plus(N:S,s(M:S)) -> s(plus(N:S,M:S))
 x(N:S,0) -> 0
 x(N:S,s(M:S)) -> plus(x(N:S,M:S),N:S)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.