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TRS Standard pair #487069294
details
property
value
status
complete
benchmark
prov.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n192.star.cs.uiowa.edu
space
Rubio_04
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.017098 seconds
cpu usage
0.017648
user time
0.008467
system time
0.009181
max virtual memory
113188.0
max residence set size
4384.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S X:S Y:S) (RULES ackin(s(X:S),s(Y:S)) -> u21(ackin(s(X:S),Y:S),X:S) u21(ackout(X:S),Y:S) -> u22(ackin(Y:S,X:S)) ) Problem 1: Innermost Equivalent Processor: -> Rules: ackin(s(X:S),s(Y:S)) -> u21(ackin(s(X:S),Y:S),X:S) u21(ackout(X:S),Y:S) -> u22(ackin(Y:S,X:S)) -> 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),s(Y:S)) -> ACKIN(s(X:S),Y:S) ACKIN(s(X:S),s(Y:S)) -> U21(ackin(s(X:S),Y:S),X:S) U21(ackout(X:S),Y:S) -> ACKIN(Y:S,X:S) -> Rules: ackin(s(X:S),s(Y:S)) -> u21(ackin(s(X:S),Y:S),X:S) u21(ackout(X:S),Y:S) -> u22(ackin(Y:S,X:S)) Problem 1: SCC Processor: -> Pairs: ACKIN(s(X:S),s(Y:S)) -> ACKIN(s(X:S),Y:S) ACKIN(s(X:S),s(Y:S)) -> U21(ackin(s(X:S),Y:S),X:S) U21(ackout(X:S),Y:S) -> ACKIN(Y:S,X:S) -> Rules: ackin(s(X:S),s(Y:S)) -> u21(ackin(s(X:S),Y:S),X:S) u21(ackout(X:S),Y:S) -> u22(ackin(Y:S,X:S)) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACKIN(s(X:S),s(Y:S)) -> ACKIN(s(X:S),Y:S) ACKIN(s(X:S),s(Y:S)) -> U21(ackin(s(X:S),Y:S),X:S) U21(ackout(X:S),Y:S) -> ACKIN(Y:S,X:S) ->->-> Rules: ackin(s(X:S),s(Y:S)) -> u21(ackin(s(X:S),Y:S),X:S) u21(ackout(X:S),Y:S) -> u22(ackin(Y:S,X:S)) Problem 1: Subterm Processor: -> Pairs: ACKIN(s(X:S),s(Y:S)) -> ACKIN(s(X:S),Y:S) ACKIN(s(X:S),s(Y:S)) -> U21(ackin(s(X:S),Y:S),X:S) U21(ackout(X:S),Y:S) -> ACKIN(Y:S,X:S) -> Rules: ackin(s(X:S),s(Y:S)) -> u21(ackin(s(X:S),Y:S),X:S) u21(ackout(X:S),Y:S) -> u22(ackin(Y:S,X:S)) ->Projection: pi(ACKIN) = 1 pi(U21) = 2 Problem 1: SCC Processor: -> Pairs: ACKIN(s(X:S),s(Y:S)) -> ACKIN(s(X:S),Y:S) U21(ackout(X:S),Y:S) -> ACKIN(Y:S,X:S) -> Rules: ackin(s(X:S),s(Y:S)) -> u21(ackin(s(X:S),Y:S),X:S) u21(ackout(X:S),Y:S) -> u22(ackin(Y:S,X:S)) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACKIN(s(X:S),s(Y:S)) -> ACKIN(s(X:S),Y:S) ->->-> Rules: ackin(s(X:S),s(Y:S)) -> u21(ackin(s(X:S),Y:S),X:S) u21(ackout(X:S),Y:S) -> u22(ackin(Y:S,X:S)) Problem 1: Subterm Processor: -> Pairs: ACKIN(s(X:S),s(Y:S)) -> ACKIN(s(X:S),Y:S) -> Rules: ackin(s(X:S),s(Y:S)) -> u21(ackin(s(X:S),Y:S),X:S) u21(ackout(X:S),Y:S) -> u22(ackin(Y:S,X:S)) ->Projection: pi(ACKIN) = 2 Problem 1: SCC Processor: -> Pairs: Empty -> Rules: ackin(s(X:S),s(Y:S)) -> u21(ackin(s(X:S),Y:S),X:S) u21(ackout(X:S),Y:S) -> u22(ackin(Y:S,X:S))
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