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TRS Standard pair #516967841
details
property
value
status
complete
benchmark
append-hard.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n072.star.cs.uiowa.edu
space
CiME_04
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.183835029602 seconds
cpu usage
0.076501912
max memory
3579904.0
stage attributes
key
value
output-size
4001
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 l1:S l2:S x:S) (RULES append(l1:S,l2:S) -> ifappend(l1:S,l2:S,is_empty(l1:S)) hd(cons(x:S,l:S)) -> x:S ifappend(l1:S,l2:S,ffalse) -> cons(hd(l1:S),append(tl(l1:S),l2:S)) ifappend(l1:S,l2:S,ttrue) -> l2:S is_empty(cons(x:S,l:S)) -> ffalse is_empty(nil) -> ttrue tl(cons(x:S,l:S)) -> l:S ) Problem 1: Innermost Equivalent Processor: -> Rules: append(l1:S,l2:S) -> ifappend(l1:S,l2:S,is_empty(l1:S)) hd(cons(x:S,l:S)) -> x:S ifappend(l1:S,l2:S,ffalse) -> cons(hd(l1:S),append(tl(l1:S),l2:S)) ifappend(l1:S,l2:S,ttrue) -> l2:S is_empty(cons(x:S,l:S)) -> ffalse is_empty(nil) -> ttrue tl(cons(x:S,l:S)) -> l:S -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: APPEND(l1:S,l2:S) -> IFAPPEND(l1:S,l2:S,is_empty(l1:S)) APPEND(l1:S,l2:S) -> IS_EMPTY(l1:S) IFAPPEND(l1:S,l2:S,ffalse) -> APPEND(tl(l1:S),l2:S) IFAPPEND(l1:S,l2:S,ffalse) -> HD(l1:S) IFAPPEND(l1:S,l2:S,ffalse) -> TL(l1:S) -> Rules: append(l1:S,l2:S) -> ifappend(l1:S,l2:S,is_empty(l1:S)) hd(cons(x:S,l:S)) -> x:S ifappend(l1:S,l2:S,ffalse) -> cons(hd(l1:S),append(tl(l1:S),l2:S)) ifappend(l1:S,l2:S,ttrue) -> l2:S is_empty(cons(x:S,l:S)) -> ffalse is_empty(nil) -> ttrue tl(cons(x:S,l:S)) -> l:S Problem 1: SCC Processor: -> Pairs: APPEND(l1:S,l2:S) -> IFAPPEND(l1:S,l2:S,is_empty(l1:S)) APPEND(l1:S,l2:S) -> IS_EMPTY(l1:S) IFAPPEND(l1:S,l2:S,ffalse) -> APPEND(tl(l1:S),l2:S) IFAPPEND(l1:S,l2:S,ffalse) -> HD(l1:S) IFAPPEND(l1:S,l2:S,ffalse) -> TL(l1:S) -> Rules: append(l1:S,l2:S) -> ifappend(l1:S,l2:S,is_empty(l1:S)) hd(cons(x:S,l:S)) -> x:S ifappend(l1:S,l2:S,ffalse) -> cons(hd(l1:S),append(tl(l1:S),l2:S)) ifappend(l1:S,l2:S,ttrue) -> l2:S is_empty(cons(x:S,l:S)) -> ffalse is_empty(nil) -> ttrue tl(cons(x:S,l:S)) -> l:S ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: APPEND(l1:S,l2:S) -> IFAPPEND(l1:S,l2:S,is_empty(l1:S)) IFAPPEND(l1:S,l2:S,ffalse) -> APPEND(tl(l1:S),l2:S) ->->-> Rules: append(l1:S,l2:S) -> ifappend(l1:S,l2:S,is_empty(l1:S)) hd(cons(x:S,l:S)) -> x:S ifappend(l1:S,l2:S,ffalse) -> cons(hd(l1:S),append(tl(l1:S),l2:S)) ifappend(l1:S,l2:S,ttrue) -> l2:S is_empty(cons(x:S,l:S)) -> ffalse is_empty(nil) -> ttrue tl(cons(x:S,l:S)) -> l:S Problem 1: Reduction Pairs Processor: -> Pairs: APPEND(l1:S,l2:S) -> IFAPPEND(l1:S,l2:S,is_empty(l1:S)) IFAPPEND(l1:S,l2:S,ffalse) -> APPEND(tl(l1:S),l2:S) -> Rules: append(l1:S,l2:S) -> ifappend(l1:S,l2:S,is_empty(l1:S)) hd(cons(x:S,l:S)) -> x:S ifappend(l1:S,l2:S,ffalse) -> cons(hd(l1:S),append(tl(l1:S),l2:S)) ifappend(l1:S,l2:S,ttrue) -> l2:S is_empty(cons(x:S,l:S)) -> ffalse is_empty(nil) -> ttrue tl(cons(x:S,l:S)) -> l:S -> Usable rules: is_empty(cons(x:S,l:S)) -> ffalse
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