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TRS Standard pair #516967646
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
n076.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.185606956482 seconds
cpu usage
0.130143717
max memory
4308992.0
stage attributes
key
value
output-size
12303
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 x:S y:S) (RULES even(0) -> ttrue even(s(0)) -> ffalse even(s(s(x:S))) -> even(x:S) half(0) -> 0 half(s(s(x:S))) -> s(half(x:S)) if_times(ffalse,s(x:S),y:S) -> plus(y:S,times(x:S,y:S)) if_times(ttrue,s(x:S),y:S) -> plus(times(half(s(x:S)),y:S),times(half(s(x:S)),y:S)) plus(0,y:S) -> y:S plus(s(x:S),y:S) -> s(plus(x:S,y:S)) times(0,y:S) -> 0 times(s(x:S),y:S) -> if_times(even(s(x:S)),s(x:S),y:S) ) Problem 1: Innermost Equivalent Processor: -> Rules: even(0) -> ttrue even(s(0)) -> ffalse even(s(s(x:S))) -> even(x:S) half(0) -> 0 half(s(s(x:S))) -> s(half(x:S)) if_times(ffalse,s(x:S),y:S) -> plus(y:S,times(x:S,y:S)) if_times(ttrue,s(x:S),y:S) -> plus(times(half(s(x:S)),y:S),times(half(s(x:S)),y:S)) plus(0,y:S) -> y:S plus(s(x:S),y:S) -> s(plus(x:S,y:S)) times(0,y:S) -> 0 times(s(x:S),y:S) -> if_times(even(s(x:S)),s(x:S),y:S) -> 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:S))) -> EVEN(x:S) HALF(s(s(x:S))) -> HALF(x:S) IF_TIMES(ffalse,s(x:S),y:S) -> PLUS(y:S,times(x:S,y:S)) IF_TIMES(ffalse,s(x:S),y:S) -> TIMES(x:S,y:S) IF_TIMES(ttrue,s(x:S),y:S) -> HALF(s(x:S)) IF_TIMES(ttrue,s(x:S),y:S) -> PLUS(times(half(s(x:S)),y:S),times(half(s(x:S)),y:S)) IF_TIMES(ttrue,s(x:S),y:S) -> TIMES(half(s(x:S)),y:S) PLUS(s(x:S),y:S) -> PLUS(x:S,y:S) TIMES(s(x:S),y:S) -> EVEN(s(x:S)) TIMES(s(x:S),y:S) -> IF_TIMES(even(s(x:S)),s(x:S),y:S) -> Rules: even(0) -> ttrue even(s(0)) -> ffalse even(s(s(x:S))) -> even(x:S) half(0) -> 0 half(s(s(x:S))) -> s(half(x:S)) if_times(ffalse,s(x:S),y:S) -> plus(y:S,times(x:S,y:S)) if_times(ttrue,s(x:S),y:S) -> plus(times(half(s(x:S)),y:S),times(half(s(x:S)),y:S)) plus(0,y:S) -> y:S plus(s(x:S),y:S) -> s(plus(x:S,y:S)) times(0,y:S) -> 0 times(s(x:S),y:S) -> if_times(even(s(x:S)),s(x:S),y:S) Problem 1: SCC Processor: -> Pairs: EVEN(s(s(x:S))) -> EVEN(x:S) HALF(s(s(x:S))) -> HALF(x:S) IF_TIMES(ffalse,s(x:S),y:S) -> PLUS(y:S,times(x:S,y:S)) IF_TIMES(ffalse,s(x:S),y:S) -> TIMES(x:S,y:S) IF_TIMES(ttrue,s(x:S),y:S) -> HALF(s(x:S)) IF_TIMES(ttrue,s(x:S),y:S) -> PLUS(times(half(s(x:S)),y:S),times(half(s(x:S)),y:S)) IF_TIMES(ttrue,s(x:S),y:S) -> TIMES(half(s(x:S)),y:S) PLUS(s(x:S),y:S) -> PLUS(x:S,y:S) TIMES(s(x:S),y:S) -> EVEN(s(x:S)) TIMES(s(x:S),y:S) -> IF_TIMES(even(s(x:S)),s(x:S),y:S) -> Rules: even(0) -> ttrue even(s(0)) -> ffalse even(s(s(x:S))) -> even(x:S) half(0) -> 0 half(s(s(x:S))) -> s(half(x:S)) if_times(ffalse,s(x:S),y:S) -> plus(y:S,times(x:S,y:S)) if_times(ttrue,s(x:S),y:S) -> plus(times(half(s(x:S)),y:S),times(half(s(x:S)),y:S)) plus(0,y:S) -> y:S plus(s(x:S),y:S) -> s(plus(x:S,y:S)) times(0,y:S) -> 0 times(s(x:S),y:S) -> if_times(even(s(x:S)),s(x:S),y:S) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: PLUS(s(x:S),y:S) -> PLUS(x:S,y:S)
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