/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)
(RULES
ack_in(0,n) -> ack_out(s(n))
ack_in(s(m),0) -> u11(ack_in(m,s(0)))
ack_in(s(m),s(n)) -> u21(ack_in(s(m),n),m)
u11(ack_out(n)) -> ack_out(n)
u21(ack_out(n),m) -> u22(ack_in(m,n))
u22(ack_out(n)) -> ack_out(n)
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 ack_in(0,n) -> ack_out(s(n))
 ack_in(s(m),0) -> u11(ack_in(m,s(0)))
 ack_in(s(m),s(n)) -> u21(ack_in(s(m),n),m)
 u11(ack_out(n)) -> ack_out(n)
 u21(ack_out(n),m) -> u22(ack_in(m,n))
 u22(ack_out(n)) -> ack_out(n)
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 ACK_IN(s(m),0) -> ACK_IN(m,s(0))
 ACK_IN(s(m),0) -> U11(ack_in(m,s(0)))
 ACK_IN(s(m),s(n)) -> ACK_IN(s(m),n)
 ACK_IN(s(m),s(n)) -> U21(ack_in(s(m),n),m)
 U21(ack_out(n),m) -> ACK_IN(m,n)
 U21(ack_out(n),m) -> U22(ack_in(m,n))
-> Rules:
 ack_in(0,n) -> ack_out(s(n))
 ack_in(s(m),0) -> u11(ack_in(m,s(0)))
 ack_in(s(m),s(n)) -> u21(ack_in(s(m),n),m)
 u11(ack_out(n)) -> ack_out(n)
 u21(ack_out(n),m) -> u22(ack_in(m,n))
 u22(ack_out(n)) -> ack_out(n)

Problem 1: 

SCC Processor:
-> Pairs:
 ACK_IN(s(m),0) -> ACK_IN(m,s(0))
 ACK_IN(s(m),0) -> U11(ack_in(m,s(0)))
 ACK_IN(s(m),s(n)) -> ACK_IN(s(m),n)
 ACK_IN(s(m),s(n)) -> U21(ack_in(s(m),n),m)
 U21(ack_out(n),m) -> ACK_IN(m,n)
 U21(ack_out(n),m) -> U22(ack_in(m,n))
-> Rules:
 ack_in(0,n) -> ack_out(s(n))
 ack_in(s(m),0) -> u11(ack_in(m,s(0)))
 ack_in(s(m),s(n)) -> u21(ack_in(s(m),n),m)
 u11(ack_out(n)) -> ack_out(n)
 u21(ack_out(n),m) -> u22(ack_in(m,n))
 u22(ack_out(n)) -> ack_out(n)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACK_IN(s(m),0) -> ACK_IN(m,s(0))
 ACK_IN(s(m),s(n)) -> ACK_IN(s(m),n)
 ACK_IN(s(m),s(n)) -> U21(ack_in(s(m),n),m)
 U21(ack_out(n),m) -> ACK_IN(m,n)
->->-> Rules:
 ack_in(0,n) -> ack_out(s(n))
 ack_in(s(m),0) -> u11(ack_in(m,s(0)))
 ack_in(s(m),s(n)) -> u21(ack_in(s(m),n),m)
 u11(ack_out(n)) -> ack_out(n)
 u21(ack_out(n),m) -> u22(ack_in(m,n))
 u22(ack_out(n)) -> ack_out(n)

Problem 1: 

Subterm Processor:
-> Pairs:
 ACK_IN(s(m),0) -> ACK_IN(m,s(0))
 ACK_IN(s(m),s(n)) -> ACK_IN(s(m),n)
 ACK_IN(s(m),s(n)) -> U21(ack_in(s(m),n),m)
 U21(ack_out(n),m) -> ACK_IN(m,n)
-> Rules:
 ack_in(0,n) -> ack_out(s(n))
 ack_in(s(m),0) -> u11(ack_in(m,s(0)))
 ack_in(s(m),s(n)) -> u21(ack_in(s(m),n),m)
 u11(ack_out(n)) -> ack_out(n)
 u21(ack_out(n),m) -> u22(ack_in(m,n))
 u22(ack_out(n)) -> ack_out(n)
->Projection:
 pi(ACK_IN) = 1
 pi(U21) = 2

Problem 1: 

SCC Processor:
-> Pairs:
 ACK_IN(s(m),s(n)) -> ACK_IN(s(m),n)
 U21(ack_out(n),m) -> ACK_IN(m,n)
-> Rules:
 ack_in(0,n) -> ack_out(s(n))
 ack_in(s(m),0) -> u11(ack_in(m,s(0)))
 ack_in(s(m),s(n)) -> u21(ack_in(s(m),n),m)
 u11(ack_out(n)) -> ack_out(n)
 u21(ack_out(n),m) -> u22(ack_in(m,n))
 u22(ack_out(n)) -> ack_out(n)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACK_IN(s(m),s(n)) -> ACK_IN(s(m),n)
->->-> Rules:
 ack_in(0,n) -> ack_out(s(n))
 ack_in(s(m),0) -> u11(ack_in(m,s(0)))
 ack_in(s(m),s(n)) -> u21(ack_in(s(m),n),m)
 u11(ack_out(n)) -> ack_out(n)
 u21(ack_out(n),m) -> u22(ack_in(m,n))
 u22(ack_out(n)) -> ack_out(n)

Problem 1: 

Subterm Processor:
-> Pairs:
 ACK_IN(s(m),s(n)) -> ACK_IN(s(m),n)
-> Rules:
 ack_in(0,n) -> ack_out(s(n))
 ack_in(s(m),0) -> u11(ack_in(m,s(0)))
 ack_in(s(m),s(n)) -> u21(ack_in(s(m),n),m)
 u11(ack_out(n)) -> ack_out(n)
 u21(ack_out(n),m) -> u22(ack_in(m,n))
 u22(ack_out(n)) -> ack_out(n)
->Projection:
 pi(ACK_IN) = 2

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 ack_in(0,n) -> ack_out(s(n))
 ack_in(s(m),0) -> u11(ack_in(m,s(0)))
 ack_in(s(m),s(n)) -> u21(ack_in(s(m),n),m)
 u11(ack_out(n)) -> ack_out(n)
 u21(ack_out(n),m) -> u22(ack_in(m,n))
 u22(ack_out(n)) -> ack_out(n)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.