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TRS Standard pair #487068302
details
property
value
status
complete
benchmark
t002.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n186.star.cs.uiowa.edu
space
HirokawaMiddeldorp_04
run statistics
property
value
solver
ttt2-1.20
configuration
ttt2
runtime (wallclock)
76.2823 seconds
cpu usage
299.05
user time
296.24
system time
2.81
max virtual memory
5391444.0
max residence set size
274280.0
stage attributes
key
value
starexec-result
YES
output
YES Problem: leq(0(),y) -> true() leq(s(x),0()) -> false() leq(s(x),s(y)) -> leq(x,y) if(true(),x,y) -> x if(false(),x,y) -> y -(x,0()) -> x -(s(x),s(y)) -> -(x,y) mod(0(),y) -> 0() mod(s(x),0()) -> 0() mod(s(x),s(y)) -> if(leq(y,x),mod(-(s(x),s(y)),s(y)),s(x)) Proof: DP Processor: DPs: leq#(s(x),s(y)) -> leq#(x,y) -#(s(x),s(y)) -> -#(x,y) mod#(s(x),s(y)) -> -#(s(x),s(y)) mod#(s(x),s(y)) -> mod#(-(s(x),s(y)),s(y)) mod#(s(x),s(y)) -> leq#(y,x) mod#(s(x),s(y)) -> if#(leq(y,x),mod(-(s(x),s(y)),s(y)),s(x)) TRS: leq(0(),y) -> true() leq(s(x),0()) -> false() leq(s(x),s(y)) -> leq(x,y) if(true(),x,y) -> x if(false(),x,y) -> y -(x,0()) -> x -(s(x),s(y)) -> -(x,y) mod(0(),y) -> 0() mod(s(x),0()) -> 0() mod(s(x),s(y)) -> if(leq(y,x),mod(-(s(x),s(y)),s(y)),s(x)) TDG Processor: DPs: leq#(s(x),s(y)) -> leq#(x,y) -#(s(x),s(y)) -> -#(x,y) mod#(s(x),s(y)) -> -#(s(x),s(y)) mod#(s(x),s(y)) -> mod#(-(s(x),s(y)),s(y)) mod#(s(x),s(y)) -> leq#(y,x) mod#(s(x),s(y)) -> if#(leq(y,x),mod(-(s(x),s(y)),s(y)),s(x)) TRS: leq(0(),y) -> true() leq(s(x),0()) -> false() leq(s(x),s(y)) -> leq(x,y) if(true(),x,y) -> x if(false(),x,y) -> y -(x,0()) -> x -(s(x),s(y)) -> -(x,y) mod(0(),y) -> 0() mod(s(x),0()) -> 0() mod(s(x),s(y)) -> if(leq(y,x),mod(-(s(x),s(y)),s(y)),s(x)) graph: mod#(s(x),s(y)) -> mod#(-(s(x),s(y)),s(y)) -> mod#(s(x),s(y)) -> if#(leq(y,x),mod(-(s(x),s(y)),s(y)),s(x)) mod#(s(x),s(y)) -> mod#(-(s(x),s(y)),s(y)) -> mod#(s(x),s(y)) -> leq#(y,x) mod#(s(x),s(y)) -> mod#(-(s(x),s(y)),s(y)) -> mod#(s(x),s(y)) -> mod#(-(s(x),s(y)),s(y)) mod#(s(x),s(y)) -> mod#(-(s(x),s(y)),s(y)) -> mod#(s(x),s(y)) -> -#(s(x),s(y)) mod#(s(x),s(y)) -> -#(s(x),s(y)) -> -#(s(x),s(y)) -> -#(x,y) mod#(s(x),s(y)) -> leq#(y,x) -> leq#(s(x),s(y)) -> leq#(x,y) -#(s(x),s(y)) -> -#(x,y) -> -#(s(x),s(y)) -> -#(x,y) leq#(s(x),s(y)) -> leq#(x,y) -> leq#(s(x),s(y)) -> leq#(x,y) SCC Processor: #sccs: 3 #rules: 3 #arcs: 8/36 DPs: mod#(s(x),s(y)) -> mod#(-(s(x),s(y)),s(y)) TRS: leq(0(),y) -> true() leq(s(x),0()) -> false() leq(s(x),s(y)) -> leq(x,y) if(true(),x,y) -> x if(false(),x,y) -> y -(x,0()) -> x -(s(x),s(y)) -> -(x,y) mod(0(),y) -> 0() mod(s(x),0()) -> 0() mod(s(x),s(y)) -> if(leq(y,x),mod(-(s(x),s(y)),s(y)),s(x)) Extended Uncurrying Processor: application symbol: leq symbol table: mod# ==> mod{0,#}/2 mod ==> mod0/2 - ==> -0/2 if ==> if0/3 false ==> false0/0 s ==> s0/1 s1/2 true ==> true0/0 0 ==> 00/0 01/1 uncurry-rules: leq(00(),x8) -> 01(x8) leq(s0(x11),x12) -> s1(x11,x12) eta-rules:
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