/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 X Y)
(RULES
ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X)
u21(ackout(X),Y) -> u22(ackin(Y,X))
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X)
 u21(ackout(X),Y) -> u22(ackin(Y,X))
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 ACKIN(s(X),s(Y)) -> ACKIN(s(X),Y)
 ACKIN(s(X),s(Y)) -> U21(ackin(s(X),Y),X)
 U21(ackout(X),Y) -> ACKIN(Y,X)
-> Rules:
 ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X)
 u21(ackout(X),Y) -> u22(ackin(Y,X))

Problem 1: 

SCC Processor:
-> Pairs:
 ACKIN(s(X),s(Y)) -> ACKIN(s(X),Y)
 ACKIN(s(X),s(Y)) -> U21(ackin(s(X),Y),X)
 U21(ackout(X),Y) -> ACKIN(Y,X)
-> Rules:
 ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X)
 u21(ackout(X),Y) -> u22(ackin(Y,X))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACKIN(s(X),s(Y)) -> ACKIN(s(X),Y)
 ACKIN(s(X),s(Y)) -> U21(ackin(s(X),Y),X)
 U21(ackout(X),Y) -> ACKIN(Y,X)
->->-> Rules:
 ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X)
 u21(ackout(X),Y) -> u22(ackin(Y,X))

Problem 1: 

Subterm Processor:
-> Pairs:
 ACKIN(s(X),s(Y)) -> ACKIN(s(X),Y)
 ACKIN(s(X),s(Y)) -> U21(ackin(s(X),Y),X)
 U21(ackout(X),Y) -> ACKIN(Y,X)
-> Rules:
 ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X)
 u21(ackout(X),Y) -> u22(ackin(Y,X))
->Projection:
 pi(ACKIN) = 1
 pi(U21) = 2

Problem 1: 

SCC Processor:
-> Pairs:
 ACKIN(s(X),s(Y)) -> ACKIN(s(X),Y)
 U21(ackout(X),Y) -> ACKIN(Y,X)
-> Rules:
 ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X)
 u21(ackout(X),Y) -> u22(ackin(Y,X))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACKIN(s(X),s(Y)) -> ACKIN(s(X),Y)
->->-> Rules:
 ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X)
 u21(ackout(X),Y) -> u22(ackin(Y,X))

Problem 1: 

Subterm Processor:
-> Pairs:
 ACKIN(s(X),s(Y)) -> ACKIN(s(X),Y)
-> Rules:
 ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X)
 u21(ackout(X),Y) -> u22(ackin(Y,X))
->Projection:
 pi(ACKIN) = 2

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X)
 u21(ackout(X),Y) -> u22(ackin(Y,X))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.