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TRS Standard pair #516960871
details
property
value
status
complete
benchmark
thiemann10.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n071.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.24356007576 seconds
cpu usage
0.10101896
max memory
4829184.0
stage attributes
key
value
output-size
7841
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 l:S x:S) (RULES conv(x:S) -> conviter(x:S,cons(0,nil)) conviter(x:S,l:S) -> if(zero(x:S),x:S,l:S) half(0) -> 0 half(s(0)) -> 0 half(s(s(x:S))) -> s(half(x:S)) if(ffalse,x:S,l:S) -> conviter(half(x:S),cons(lastbit(x:S),l:S)) if(ttrue,x:S,l:S) -> l:S lastbit(0) -> 0 lastbit(s(0)) -> s(0) lastbit(s(s(x:S))) -> lastbit(x:S) zero(0) -> ttrue zero(s(x:S)) -> ffalse ) Problem 1: Innermost Equivalent Processor: -> Rules: conv(x:S) -> conviter(x:S,cons(0,nil)) conviter(x:S,l:S) -> if(zero(x:S),x:S,l:S) half(0) -> 0 half(s(0)) -> 0 half(s(s(x:S))) -> s(half(x:S)) if(ffalse,x:S,l:S) -> conviter(half(x:S),cons(lastbit(x:S),l:S)) if(ttrue,x:S,l:S) -> l:S lastbit(0) -> 0 lastbit(s(0)) -> s(0) lastbit(s(s(x:S))) -> lastbit(x:S) zero(0) -> ttrue zero(s(x:S)) -> ffalse -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: CONV(x:S) -> CONVITER(x:S,cons(0,nil)) CONVITER(x:S,l:S) -> IF(zero(x:S),x:S,l:S) CONVITER(x:S,l:S) -> ZERO(x:S) HALF(s(s(x:S))) -> HALF(x:S) IF(ffalse,x:S,l:S) -> CONVITER(half(x:S),cons(lastbit(x:S),l:S)) IF(ffalse,x:S,l:S) -> HALF(x:S) IF(ffalse,x:S,l:S) -> LASTBIT(x:S) LASTBIT(s(s(x:S))) -> LASTBIT(x:S) -> Rules: conv(x:S) -> conviter(x:S,cons(0,nil)) conviter(x:S,l:S) -> if(zero(x:S),x:S,l:S) half(0) -> 0 half(s(0)) -> 0 half(s(s(x:S))) -> s(half(x:S)) if(ffalse,x:S,l:S) -> conviter(half(x:S),cons(lastbit(x:S),l:S)) if(ttrue,x:S,l:S) -> l:S lastbit(0) -> 0 lastbit(s(0)) -> s(0) lastbit(s(s(x:S))) -> lastbit(x:S) zero(0) -> ttrue zero(s(x:S)) -> ffalse Problem 1: SCC Processor: -> Pairs: CONV(x:S) -> CONVITER(x:S,cons(0,nil)) CONVITER(x:S,l:S) -> IF(zero(x:S),x:S,l:S) CONVITER(x:S,l:S) -> ZERO(x:S) HALF(s(s(x:S))) -> HALF(x:S) IF(ffalse,x:S,l:S) -> CONVITER(half(x:S),cons(lastbit(x:S),l:S)) IF(ffalse,x:S,l:S) -> HALF(x:S) IF(ffalse,x:S,l:S) -> LASTBIT(x:S) LASTBIT(s(s(x:S))) -> LASTBIT(x:S) -> Rules: conv(x:S) -> conviter(x:S,cons(0,nil)) conviter(x:S,l:S) -> if(zero(x:S),x:S,l:S) half(0) -> 0 half(s(0)) -> 0 half(s(s(x:S))) -> s(half(x:S)) if(ffalse,x:S,l:S) -> conviter(half(x:S),cons(lastbit(x:S),l:S)) if(ttrue,x:S,l:S) -> l:S lastbit(0) -> 0 lastbit(s(0)) -> s(0) lastbit(s(s(x:S))) -> lastbit(x:S) zero(0) -> ttrue zero(s(x:S)) -> ffalse ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: LASTBIT(s(s(x:S))) -> LASTBIT(x:S)
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