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TRS Innermost pair #487523974
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
n139.star.cs.uiowa.edu
space
AG01_innermost
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.135829210281 seconds
cpu usage
0.056938348
max memory
3502080.0
stage attributes
key
value
output-size
2704
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- 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.
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