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TRS Standard pair #516967319
details
property
value
status
complete
benchmark
TypeEx1.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n078.star.cs.uiowa.edu
space
Applicative_05
run statistics
property
value
solver
ttt2-1.20
configuration
ttt2
runtime (wallclock)
1.40160703659 seconds
cpu usage
4.256594859
max memory
7.15833344E8
stage attributes
key
value
output-size
5687
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem: ap(ap(ff(),x),x) -> ap(ap(x,ap(ff(),x)),ap(ap(cons(),x),nil())) Proof: Extended Uncurrying Processor: application symbol: ap symbol table: nil ==> nil0/0 cons ==> cons0/0 cons1/1 cons2/2 ff ==> ff0/0 ff1/1 ff2/2 uncurry-rules: ap(ff1(x1),x2) -> ff2(x1,x2) ap(ff0(),x1) -> ff1(x1) ap(cons1(x4),x5) -> cons2(x4,x5) ap(cons0(),x4) -> cons1(x4) eta-rules: problem: ff2(x,x) -> ap(ap(x,ff1(x)),cons2(x,nil0())) ap(ff1(x1),x2) -> ff2(x1,x2) ap(ff0(),x1) -> ff1(x1) ap(cons1(x4),x5) -> cons2(x4,x5) ap(cons0(),x4) -> cons1(x4) DP Processor: DPs: ff{2,#}(x,x) -> ap#(x,ff1(x)) ff{2,#}(x,x) -> ap#(ap(x,ff1(x)),cons2(x,nil0())) ap#(ff1(x1),x2) -> ff{2,#}(x1,x2) TRS: ff2(x,x) -> ap(ap(x,ff1(x)),cons2(x,nil0())) ap(ff1(x1),x2) -> ff2(x1,x2) ap(ff0(),x1) -> ff1(x1) ap(cons1(x4),x5) -> cons2(x4,x5) ap(cons0(),x4) -> cons1(x4) TDG Processor: DPs: ff{2,#}(x,x) -> ap#(x,ff1(x)) ff{2,#}(x,x) -> ap#(ap(x,ff1(x)),cons2(x,nil0())) ap#(ff1(x1),x2) -> ff{2,#}(x1,x2) TRS: ff2(x,x) -> ap(ap(x,ff1(x)),cons2(x,nil0())) ap(ff1(x1),x2) -> ff2(x1,x2) ap(ff0(),x1) -> ff1(x1) ap(cons1(x4),x5) -> cons2(x4,x5) ap(cons0(),x4) -> cons1(x4) graph: ap#(ff1(x1),x2) -> ff{2,#}(x1,x2) -> ff{2,#}(x,x) -> ap#(ap(x,ff1(x)),cons2(x,nil0())) ap#(ff1(x1),x2) -> ff{2,#}(x1,x2) -> ff{2,#}(x,x) -> ap#(x,ff1(x)) ff{2,#}(x,x) -> ap#(ap(x,ff1(x)),cons2(x,nil0())) -> ap#(ff1(x1),x2) -> ff{2,#}(x1,x2) ff{2,#}(x,x) -> ap#(x,ff1(x)) -> ap#(ff1(x1),x2) -> ff{2,#}(x1,x2) Matrix Interpretation Processor: dim=3 usable rules: ff2(x,x) -> ap(ap(x,ff1(x)),cons2(x,nil0())) ap(ff1(x1),x2) -> ff2(x1,x2) ap(ff0(),x1) -> ff1(x1) ap(cons1(x4),x5) -> cons2(x4,x5) ap(cons0(),x4) -> cons1(x4) interpretation: [0] [ff0] = [0] [1], [0 0 0] [0] [cons1](x0) = [0 0 1]x0 + [1] [0 0 0] [0], [0 1 1] [1 1 0] [1] [ap](x0, x1) = [0 0 1]x0 + [0 0 1]x1 + [0] [0 0 0] [0 0 0] [0], [1 1 0] [0] [ff1](x0) = [0 0 1]x0 + [1] [0 0 0] [0], [0] [nil0] = [0] [0], [0] [cons0] = [0] [1], [ap#](x0, x1) = [0 1 0]x0 + [0 1 1]x1, [ff{2,#}](x0, x1) = [0 1 1]x1 + [1], [1 0 0]
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