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TRS Standard pair #516967886
details
property
value
status
complete
benchmark
ack_prolog.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n053.star.cs.uiowa.edu
space
CiME_04
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0736019611359 seconds
cpu usage
0.020800527
max memory
1998848.0
stage attributes
key
value
output-size
4677
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 m:S n:S) (RULES ack_in(0,n:S) -> ack_out(s(n:S)) ack_in(s(m:S),0) -> u11(ack_in(m:S,s(0))) ack_in(s(m:S),s(n:S)) -> u21(ack_in(s(m:S),n:S),m:S) u11(ack_out(n:S)) -> ack_out(n:S) u21(ack_out(n:S),m:S) -> u22(ack_in(m:S,n:S)) u22(ack_out(n:S)) -> ack_out(n:S) ) Problem 1: Innermost Equivalent Processor: -> Rules: ack_in(0,n:S) -> ack_out(s(n:S)) ack_in(s(m:S),0) -> u11(ack_in(m:S,s(0))) ack_in(s(m:S),s(n:S)) -> u21(ack_in(s(m:S),n:S),m:S) u11(ack_out(n:S)) -> ack_out(n:S) u21(ack_out(n:S),m:S) -> u22(ack_in(m:S,n:S)) u22(ack_out(n:S)) -> ack_out(n:S) -> 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:S),0) -> ACK_IN(m:S,s(0)) ACK_IN(s(m:S),0) -> U11(ack_in(m:S,s(0))) ACK_IN(s(m:S),s(n:S)) -> ACK_IN(s(m:S),n:S) ACK_IN(s(m:S),s(n:S)) -> U21(ack_in(s(m:S),n:S),m:S) U21(ack_out(n:S),m:S) -> ACK_IN(m:S,n:S) U21(ack_out(n:S),m:S) -> U22(ack_in(m:S,n:S)) -> Rules: ack_in(0,n:S) -> ack_out(s(n:S)) ack_in(s(m:S),0) -> u11(ack_in(m:S,s(0))) ack_in(s(m:S),s(n:S)) -> u21(ack_in(s(m:S),n:S),m:S) u11(ack_out(n:S)) -> ack_out(n:S) u21(ack_out(n:S),m:S) -> u22(ack_in(m:S,n:S)) u22(ack_out(n:S)) -> ack_out(n:S) Problem 1: SCC Processor: -> Pairs: ACK_IN(s(m:S),0) -> ACK_IN(m:S,s(0)) ACK_IN(s(m:S),0) -> U11(ack_in(m:S,s(0))) ACK_IN(s(m:S),s(n:S)) -> ACK_IN(s(m:S),n:S) ACK_IN(s(m:S),s(n:S)) -> U21(ack_in(s(m:S),n:S),m:S) U21(ack_out(n:S),m:S) -> ACK_IN(m:S,n:S) U21(ack_out(n:S),m:S) -> U22(ack_in(m:S,n:S)) -> Rules: ack_in(0,n:S) -> ack_out(s(n:S)) ack_in(s(m:S),0) -> u11(ack_in(m:S,s(0))) ack_in(s(m:S),s(n:S)) -> u21(ack_in(s(m:S),n:S),m:S) u11(ack_out(n:S)) -> ack_out(n:S) u21(ack_out(n:S),m:S) -> u22(ack_in(m:S,n:S)) u22(ack_out(n:S)) -> ack_out(n:S) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACK_IN(s(m:S),0) -> ACK_IN(m:S,s(0)) ACK_IN(s(m:S),s(n:S)) -> ACK_IN(s(m:S),n:S) ACK_IN(s(m:S),s(n:S)) -> U21(ack_in(s(m:S),n:S),m:S) U21(ack_out(n:S),m:S) -> ACK_IN(m:S,n:S) ->->-> Rules: ack_in(0,n:S) -> ack_out(s(n:S)) ack_in(s(m:S),0) -> u11(ack_in(m:S,s(0))) ack_in(s(m:S),s(n:S)) -> u21(ack_in(s(m:S),n:S),m:S) u11(ack_out(n:S)) -> ack_out(n:S) u21(ack_out(n:S),m:S) -> u22(ack_in(m:S,n:S)) u22(ack_out(n:S)) -> ack_out(n:S) Problem 1: Subterm Processor: -> Pairs: ACK_IN(s(m:S),0) -> ACK_IN(m:S,s(0)) ACK_IN(s(m:S),s(n:S)) -> ACK_IN(s(m:S),n:S) ACK_IN(s(m:S),s(n:S)) -> U21(ack_in(s(m:S),n:S),m:S) U21(ack_out(n:S),m:S) -> ACK_IN(m:S,n:S) -> Rules: ack_in(0,n:S) -> ack_out(s(n:S)) ack_in(s(m:S),0) -> u11(ack_in(m:S,s(0))) ack_in(s(m:S),s(n:S)) -> u21(ack_in(s(m:S),n:S),m:S) u11(ack_out(n:S)) -> ack_out(n:S) u21(ack_out(n:S),m:S) -> u22(ack_in(m:S,n:S)) u22(ack_out(n:S)) -> ack_out(n:S) ->Projection: pi(ACK_IN) = 1
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