details

property	value
status	complete
benchmark	2.27.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n187.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	1.13737 seconds
cpu usage	5.71239
user time	4.48933
system time	1.22306
max virtual memory	1938472.0
max residence set size	85224.0

stage attributes

key	value
starexec-result	YES

output

YES Problem: fib(0()) -> 0() fib(s(0())) -> s(0()) fib(s(s(0()))) -> s(0()) fib(s(s(x))) -> sp(g(x)) g(0()) -> pair(s(0()),0()) g(s(0())) -> pair(s(0()),s(0())) g(s(x)) -> np(g(x)) sp(pair(x,y)) -> +(x,y) np(pair(x,y)) -> pair(+(x,y),x) +(x,0()) -> x +(x,s(y)) -> s(+(x,y)) Proof: Matrix Interpretation Processor: dim=3 interpretation: [1 1 0] [sp](x0) = [0 1 1]x0 [1 0 0] , [1 0 0] [1] [fib](x0) = [0 0 1]x0 + [0] [1 0 0] [1], [1 0 0] [1] [g](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 1 1] [1 0 0] [pair](x0, x1) = [1 0 0]x0 + [1 0 0]x1 [1 1 0] [1 0 0] , [0] [0] = [1] [1], [1 0 0] [1 0 0] [+](x0, x1) = [0 1 0]x0 + [1 0 0]x1 [1 1 1] [1 0 0] , [1 1 1] [np](x0) = [0 1 1]x0 [0 1 1] , [1 0 0] [s](x0) = [0 0 0]x0 [0 1 0] orientation: [1] [0] fib(0()) = [1] >= [1] = 0() [1] [1] [1] [0] fib(s(0())) = [1] >= [0] = s(0()) [1] [1] [1] [0] fib(s(s(0()))) = [0] >= [0] = s(0()) [1] [1] [1 0 0] [1] [1 0 0] [1] fib(s(s(x))) = [0 0 0]x + [0] >= [0 0 0]x + [0] = sp(g(x)) [1 0 0] [1] [1 0 0] [1] [1] [1] g(0()) = [0] >= [0] = pair(s(0()),0()) [0] [0] [1] [1] g(s(0())) = [0] >= [0] = pair(s(0()),s(0())) [0] [0] [1 0 0] [1] [1 0 0] [1] g(s(x)) = [0 0 0]x + [0] >= [0 0 0]x + [0] = np(g(x)) [0 0 0] [0] [0 0 0] [0] [2 1 1] [2 0 0] [1 0 0] [1 0 0] sp(pair(x,y)) = [2 1 0]x + [2 0 0]y >= [0 1 0]x + [1 0 0]y = +(x,y) [1 1 1] [1 0 0] [1 1 1] [1 0 0] [3 2 1] [3 0 0] [3 2 1] [3 0 0] np(pair(x,y)) = [2 1 0]x + [2 0 0]y >= [2 0 0]x + [1 0 0]y = pair(+(x,y),x) [2 1 0] [2 0 0] [2 1 0] [2 0 0] [1 0 0] +(x,0()) = [0 1 0]x >= x = x [1 1 1] [1 0 0] [1 0 0] [1 0 0] [1 0 0] +(x,s(y)) = [0 1 0]x + [1 0 0]y >= [0 0 0]x + [0 0 0]y = s(+(x,y)) [1 1 1] [1 0 0] [0 1 0] [1 0 0] problem: fib(s(s(x))) -> sp(g(x)) g(0()) -> pair(s(0()),0()) g(s(0())) -> pair(s(0()),s(0())) g(s(x)) -> np(g(x)) sp(pair(x,y)) -> +(x,y) popout

output may be truncated. 'popout' for the full output.

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all output return to TRS Standard