/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)
(STRATEGY CONTEXTSENSITIVE
(U11 1)
(U12 1)
(plus 1 2)
(0)
(s 1)
(tt)
)
(RULES
U11(tt,M,N) -> U12(tt,M,N)
U12(tt,M,N) -> s(plus(N,M))
plus(N,0) -> N
plus(N,s(M)) -> U11(tt,M,N)
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 U11(tt,M,N) -> U12(tt,M,N)
 U12(tt,M,N) -> s(plus(N,M))
 plus(N,0) -> N
 plus(N,s(M)) -> U11(tt,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:
 U11#(tt,M,N) -> U12#(tt,M,N)
 U12#(tt,M,N) -> PLUS(N,M)
 U12#(tt,M,N) -> M
 U12#(tt,M,N) -> N
 PLUS(N,s(M)) -> U11#(tt,M,N)
-> Rules:
 U11(tt,M,N) -> U12(tt,M,N)
 U12(tt,M,N) -> s(plus(N,M))
 plus(N,0) -> N
 plus(N,s(M)) -> U11(tt,M,N)
-> Unhiding Rules:
 Empty

Problem 1: 

SCC Processor:
-> Pairs:
 U11#(tt,M,N) -> U12#(tt,M,N)
 U12#(tt,M,N) -> PLUS(N,M)
 U12#(tt,M,N) -> M
 U12#(tt,M,N) -> N
 PLUS(N,s(M)) -> U11#(tt,M,N)
-> Rules:
 U11(tt,M,N) -> U12(tt,M,N)
 U12(tt,M,N) -> s(plus(N,M))
 plus(N,0) -> N
 plus(N,s(M)) -> U11(tt,M,N)
-> Unhiding rules:
 Empty
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 U11#(tt,M,N) -> U12#(tt,M,N)
 U12#(tt,M,N) -> PLUS(N,M)
 PLUS(N,s(M)) -> U11#(tt,M,N)
->->-> Rules:
 U11(tt,M,N) -> U12(tt,M,N)
 U12(tt,M,N) -> s(plus(N,M))
 plus(N,0) -> N
 plus(N,s(M)) -> U11(tt,M,N)
->->-> Unhiding rules:
 Empty

Problem 1: 

SubNColl Processor:
-> Pairs:
 U11#(tt,M,N) -> U12#(tt,M,N)
 U12#(tt,M,N) -> PLUS(N,M)
 PLUS(N,s(M)) -> U11#(tt,M,N)
-> Rules:
 U11(tt,M,N) -> U12(tt,M,N)
 U12(tt,M,N) -> s(plus(N,M))
 plus(N,0) -> N
 plus(N,s(M)) -> U11(tt,M,N)
-> Unhiding rules:
 Empty
->Projection:
 pi(U11#) = 2
 pi(U12#) = 2
 pi(PLUS) = 2

Problem 1: 

SCC Processor:
-> Pairs:
 U11#(tt,M,N) -> U12#(tt,M,N)
 U12#(tt,M,N) -> PLUS(N,M)
-> Rules:
 U11(tt,M,N) -> U12(tt,M,N)
 U12(tt,M,N) -> s(plus(N,M))
 plus(N,0) -> N
 plus(N,s(M)) -> U11(tt,M,N)
-> Unhiding rules:
 Empty
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.