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TRS Innermost pair #487092934
details
property
value
status
complete
benchmark
#4.28.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n147.star.cs.uiowa.edu
space
AG01_innermost
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0591971 seconds
cpu usage
0.052731
user time
0.02656
system time
0.026171
max virtual memory
113188.0
max residence set size
5284.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S x:S) (RULES bits(0) -> 0 bits(s(x:S)) -> s(bits(half(s(x:S)))) half(0) -> 0 half(s(0)) -> 0 half(s(s(x:S))) -> s(half(x:S)) ) (STRATEGY INNERMOST) Problem 1: Dependency Pairs Processor: -> Pairs: BITS(s(x:S)) -> BITS(half(s(x:S))) BITS(s(x:S)) -> HALF(s(x:S)) HALF(s(s(x:S))) -> HALF(x:S) -> Rules: bits(0) -> 0 bits(s(x:S)) -> s(bits(half(s(x:S)))) half(0) -> 0 half(s(0)) -> 0 half(s(s(x:S))) -> s(half(x:S)) Problem 1: SCC Processor: -> Pairs: BITS(s(x:S)) -> BITS(half(s(x:S))) BITS(s(x:S)) -> HALF(s(x:S)) HALF(s(s(x:S))) -> HALF(x:S) -> Rules: bits(0) -> 0 bits(s(x:S)) -> s(bits(half(s(x:S)))) half(0) -> 0 half(s(0)) -> 0 half(s(s(x:S))) -> s(half(x:S)) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: HALF(s(s(x:S))) -> HALF(x:S) ->->-> Rules: bits(0) -> 0 bits(s(x:S)) -> s(bits(half(s(x:S)))) half(0) -> 0 half(s(0)) -> 0 half(s(s(x:S))) -> s(half(x:S)) ->->Cycle: ->->-> Pairs: BITS(s(x:S)) -> BITS(half(s(x:S))) ->->-> Rules: bits(0) -> 0 bits(s(x:S)) -> s(bits(half(s(x:S)))) half(0) -> 0 half(s(0)) -> 0 half(s(s(x:S))) -> s(half(x:S)) The problem is decomposed in 2 subproblems. Problem 1.1: Subterm Processor: -> Pairs: HALF(s(s(x:S))) -> HALF(x:S) -> Rules: bits(0) -> 0 bits(s(x:S)) -> s(bits(half(s(x:S)))) half(0) -> 0 half(s(0)) -> 0 half(s(s(x:S))) -> s(half(x:S)) ->Projection: pi(HALF) = 1 Problem 1.1: SCC Processor: -> Pairs: Empty -> Rules: bits(0) -> 0 bits(s(x:S)) -> s(bits(half(s(x:S)))) half(0) -> 0 half(s(0)) -> 0 half(s(s(x:S))) -> s(half(x:S)) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.2: Reduction Pairs Processor: -> Pairs: BITS(s(x:S)) -> BITS(half(s(x:S))) -> Rules:
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