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TRS Standard pair #516964701
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
n074.star.cs.uiowa.edu
space
Rubio_04
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0919599533081 seconds
cpu usage
0.01908864
max memory
1658880.0
stage attributes
key
value
output-size
2805
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- 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:
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