/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)
(U21 1)
(U22 1)
(plus 1 2)
(x 1 2)
(0)
(s 1)
(tt)
)
(RULES
U11(tt,M,N) -> U12(tt,M,N)
U12(tt,M,N) -> s(plus(N,M))
U21(tt,M,N) -> U22(tt,M,N)
U22(tt,M,N) -> plus(x(N,M),N)
plus(N,0) -> N
plus(N,s(M)) -> U11(tt,M,N)
x(N,0) -> 0
x(N,s(M)) -> U21(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))
 U21(tt,M,N) -> U22(tt,M,N)
 U22(tt,M,N) -> plus(x(N,M),N)
 plus(N,0) -> N
 plus(N,s(M)) -> U11(tt,M,N)
 x(N,0) -> 0
 x(N,s(M)) -> U21(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
 U21#(tt,M,N) -> U22#(tt,M,N)
 U22#(tt,M,N) -> PLUS(x(N,M),N)
 U22#(tt,M,N) -> X(N,M)
 U22#(tt,M,N) -> M
 U22#(tt,M,N) -> N
 PLUS(N,s(M)) -> U11#(tt,M,N)
 X(N,s(M)) -> U21#(tt,M,N)
-> Rules:
 U11(tt,M,N) -> U12(tt,M,N)
 U12(tt,M,N) -> s(plus(N,M))
 U21(tt,M,N) -> U22(tt,M,N)
 U22(tt,M,N) -> plus(x(N,M),N)
 plus(N,0) -> N
 plus(N,s(M)) -> U11(tt,M,N)
 x(N,0) -> 0
 x(N,s(M)) -> U21(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
 U21#(tt,M,N) -> U22#(tt,M,N)
 U22#(tt,M,N) -> PLUS(x(N,M),N)
 U22#(tt,M,N) -> X(N,M)
 U22#(tt,M,N) -> M
 U22#(tt,M,N) -> N
 PLUS(N,s(M)) -> U11#(tt,M,N)
 X(N,s(M)) -> U21#(tt,M,N)
-> Rules:
 U11(tt,M,N) -> U12(tt,M,N)
 U12(tt,M,N) -> s(plus(N,M))
 U21(tt,M,N) -> U22(tt,M,N)
 U22(tt,M,N) -> plus(x(N,M),N)
 plus(N,0) -> N
 plus(N,s(M)) -> U11(tt,M,N)
 x(N,0) -> 0
 x(N,s(M)) -> U21(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))
 U21(tt,M,N) -> U22(tt,M,N)
 U22(tt,M,N) -> plus(x(N,M),N)
 plus(N,0) -> N
 plus(N,s(M)) -> U11(tt,M,N)
 x(N,0) -> 0
 x(N,s(M)) -> U21(tt,M,N)
->->-> Unhiding rules:
 Empty
->->Cycle:
->->-> Pairs:
 U21#(tt,M,N) -> U22#(tt,M,N)
 U22#(tt,M,N) -> X(N,M)
 X(N,s(M)) -> U21#(tt,M,N)
->->-> Rules:
 U11(tt,M,N) -> U12(tt,M,N)
 U12(tt,M,N) -> s(plus(N,M))
 U21(tt,M,N) -> U22(tt,M,N)
 U22(tt,M,N) -> plus(x(N,M),N)
 plus(N,0) -> N
 plus(N,s(M)) -> U11(tt,M,N)
 x(N,0) -> 0
 x(N,s(M)) -> U21(tt,M,N)
->->-> Unhiding rules:
 Empty


The problem is decomposed in 2 subproblems.

Problem 1.1: 

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))
 U21(tt,M,N) -> U22(tt,M,N)
 U22(tt,M,N) -> plus(x(N,M),N)
 plus(N,0) -> N
 plus(N,s(M)) -> U11(tt,M,N)
 x(N,0) -> 0
 x(N,s(M)) -> U21(tt,M,N)
-> Unhiding rules:
 Empty
->Projection:
 pi(U11#) = 2
 pi(U12#) = 2
 pi(PLUS) = 2

Problem 1.1: 

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))
 U21(tt,M,N) -> U22(tt,M,N)
 U22(tt,M,N) -> plus(x(N,M),N)
 plus(N,0) -> N
 plus(N,s(M)) -> U11(tt,M,N)
 x(N,0) -> 0
 x(N,s(M)) -> U21(tt,M,N)
-> Unhiding rules:
 Empty
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

SubNColl Processor:
-> Pairs:
 U21#(tt,M,N) -> U22#(tt,M,N)
 U22#(tt,M,N) -> X(N,M)
 X(N,s(M)) -> U21#(tt,M,N)
-> Rules:
 U11(tt,M,N) -> U12(tt,M,N)
 U12(tt,M,N) -> s(plus(N,M))
 U21(tt,M,N) -> U22(tt,M,N)
 U22(tt,M,N) -> plus(x(N,M),N)
 plus(N,0) -> N
 plus(N,s(M)) -> U11(tt,M,N)
 x(N,0) -> 0
 x(N,s(M)) -> U21(tt,M,N)
-> Unhiding rules:
 Empty
->Projection:
 pi(U21#) = 2
 pi(U22#) = 2
 pi(X) = 2

Problem 1.2: 

SCC Processor:
-> Pairs:
 U21#(tt,M,N) -> U22#(tt,M,N)
 U22#(tt,M,N) -> X(N,M)
-> Rules:
 U11(tt,M,N) -> U12(tt,M,N)
 U12(tt,M,N) -> s(plus(N,M))
 U21(tt,M,N) -> U22(tt,M,N)
 U22(tt,M,N) -> plus(x(N,M),N)
 plus(N,0) -> N
 plus(N,s(M)) -> U11(tt,M,N)
 x(N,0) -> 0
 x(N,s(M)) -> U21(tt,M,N)
-> Unhiding rules:
 Empty
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.