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TRS Stand 20472 pair #381713255
details
property
value
status
complete
benchmark
#4.29.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n089.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
muterm 5.18
configuration
default
runtime (wallclock)
0.120075941086 seconds
cpu usage
0.110381519
max memory
4161536.0
stage attributes
key
value
output-size
10578
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 x y) (RULES even(0) -> true even(s(0)) -> false even(s(s(x))) -> even(x) half(0) -> 0 half(s(s(x))) -> s(half(x)) if_times(false,s(x),y) -> plus(y,times(x,y)) if_times(true,s(x),y) -> plus(times(half(s(x)),y),times(half(s(x)),y)) plus(0,y) -> y plus(s(x),y) -> s(plus(x,y)) times(0,y) -> 0 times(s(x),y) -> if_times(even(s(x)),s(x),y) ) Problem 1: Innermost Equivalent Processor: -> Rules: even(0) -> true even(s(0)) -> false even(s(s(x))) -> even(x) half(0) -> 0 half(s(s(x))) -> s(half(x)) if_times(false,s(x),y) -> plus(y,times(x,y)) if_times(true,s(x),y) -> plus(times(half(s(x)),y),times(half(s(x)),y)) plus(0,y) -> y plus(s(x),y) -> s(plus(x,y)) times(0,y) -> 0 times(s(x),y) -> if_times(even(s(x)),s(x),y) -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: EVEN(s(s(x))) -> EVEN(x) HALF(s(s(x))) -> HALF(x) IF_TIMES(false,s(x),y) -> PLUS(y,times(x,y)) IF_TIMES(false,s(x),y) -> TIMES(x,y) IF_TIMES(true,s(x),y) -> HALF(s(x)) IF_TIMES(true,s(x),y) -> PLUS(times(half(s(x)),y),times(half(s(x)),y)) IF_TIMES(true,s(x),y) -> TIMES(half(s(x)),y) PLUS(s(x),y) -> PLUS(x,y) TIMES(s(x),y) -> EVEN(s(x)) TIMES(s(x),y) -> IF_TIMES(even(s(x)),s(x),y) -> Rules: even(0) -> true even(s(0)) -> false even(s(s(x))) -> even(x) half(0) -> 0 half(s(s(x))) -> s(half(x)) if_times(false,s(x),y) -> plus(y,times(x,y)) if_times(true,s(x),y) -> plus(times(half(s(x)),y),times(half(s(x)),y)) plus(0,y) -> y plus(s(x),y) -> s(plus(x,y)) times(0,y) -> 0 times(s(x),y) -> if_times(even(s(x)),s(x),y) Problem 1: SCC Processor: -> Pairs: EVEN(s(s(x))) -> EVEN(x) HALF(s(s(x))) -> HALF(x) IF_TIMES(false,s(x),y) -> PLUS(y,times(x,y)) IF_TIMES(false,s(x),y) -> TIMES(x,y) IF_TIMES(true,s(x),y) -> HALF(s(x)) IF_TIMES(true,s(x),y) -> PLUS(times(half(s(x)),y),times(half(s(x)),y)) IF_TIMES(true,s(x),y) -> TIMES(half(s(x)),y) PLUS(s(x),y) -> PLUS(x,y) TIMES(s(x),y) -> EVEN(s(x)) TIMES(s(x),y) -> IF_TIMES(even(s(x)),s(x),y) -> Rules: even(0) -> true even(s(0)) -> false even(s(s(x))) -> even(x) half(0) -> 0 half(s(s(x))) -> s(half(x)) if_times(false,s(x),y) -> plus(y,times(x,y)) if_times(true,s(x),y) -> plus(times(half(s(x)),y),times(half(s(x)),y)) plus(0,y) -> y plus(s(x),y) -> s(plus(x,y)) times(0,y) -> 0 times(s(x),y) -> if_times(even(s(x)),s(x),y) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: PLUS(s(x),y) -> PLUS(x,y)
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