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	n187.star.cs.uiowa.edu
space	Strategy_removed_AG01

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.080365 seconds
cpu usage	0.056793
user time	0.020893
system time	0.0359
max virtual memory	113188.0
max residence set size	5432.0

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)) ) Problem 1: Innermost Equivalent Processor: -> 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 term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. 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)) popout

output may be truncated. 'popout' for the full output.

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all output return to TRS Standard